ABT ASSOCIATES INC

5S WHEEl-ER STREET. CAMBRIDGE MASSACHUSETTS 02138

TELEPHONE AREA e17·492·7100

Subm~tted to:

Off~ce of polley Development and Research

u.s. Department of HouSlng and Urban Development

Washlngton l D.C.

THE DEMAND FOR RENTAL HOUSING:

EVIDENCE FROM A

PERCENT OF RENT HOUSING ALIDWANCE

Contract H-2040R

September 6, 1978

(Rev~sed June 1980)

Task 3.2.2

AAI #78-105

PrlnClpal Authors: Joseph Frledrnan

Daniel H. Weinberg

(jJ~Af 4Il.~""~QualltyControl Reviewer
,

,.

The research and stud1es form1ng the bas1s of th1S report

were conducted pursuant to a contract w1th the Department

of Hous~ng and Urban Development (HOO). The statements and

conclus10ns conta1ned here1n are those of the contractor and

do not necessar1ly reflect the V1ews of the u.s. government

~n general or HUD ~n part~cular. Neither the Un~ted states

nor HOD makes any warranty, expressed or ~p11ed, or assumes

respons1b1l1ty for the accuracy or completeness of the

1nforrnat10n conta1ned here1n.
ABSTRACT

This report analyzes the housing consumption of households partic~pating

in the Housing Allowance Demand Experiment that rece~ved Percent of Rent

housing allowances. Analyses of both hous~ng expend~tures and housing

serv~ces (a measure of real housing) are carried out us~ng a variety of

approaches. Also examJ.ned are household response over time and the

poss~~l~ty of b~as due to sample select~on.
ACKNOWLEDGEMENTS

We w~sh to thank four people who contr~buted cons~derably to th~s report:

Stephen Kennedy, Project D~rector, who prov~ded detailed comments throughout the analysis and was ~strumental in defining the model of selection

b~as presented in Section 6.2 and who was the author of Append~x XI; Stephen

Mayo, to whom we are ~ndebted for h~s analys~s of the f~rst year of data

from the percent of Rent experllnent, and who also contr~buted to several

sections of th~s report (Sect~ons 3.3, 4.1, and Appendices IV and VII);

Sally Merr~ll, who derived the hedonic ~ndex of housing serv~ces used ~n

Chapter 5 and contriliuted much of the analys~s Sect~on 5.2; and Kr~stina

Varena~s, who helped prepare Append~ces II, III, and part of X.

others provided valuable comments: James Wallace, Director of Des~gn and

Analys~s; walter Stellwagen, princ~pal qual~ty control rev~ewer for the

Demand Experunent; and Helen E. Bakeman, Deputy ProJect Director, who also

organ~zed and scheduled the myriad tasks necessary for completion of the

report.

We also w~sh to thank the data process~ng staff, ~n part~cular Fred Luhmann.

B~ll~e Renos, w~th the ass~stance of Phyll~s BrelllE!r, was respons1.ble for

produc~ng the report. Judy Alexander efuted the manuscript.

Joseph Fr~eaman

Dan~el H. We~nberg
TABLE OF CONTENTS

INTRODUCTION

REFERENCES

SUMMARY OF EXPENDITURE CHANGES

REFERENCES

EMPIRICAL ESTIMATES OF HOUSING EXPENDITURE

FUNCTIONS

. REFERENCES

THEORETICAL CONSIDERATIONS AND EMPIRICAL

ISSUES UNDERLYING THE ANALYSIS

59

~x

41

41

44

49

55

56

S-l

1

5

7

7

18

24

40

XV~~

Tabular overv~ew of Expend~ture Changes

Demand Functlon Est~ates

Appll.catJ.ons

3.3

3.1 consumer Demand Theory

The Funct~onal Form of Hous~ng Demand

Ev~dence From Recent Emp~rlcal

EstLmates of Hous~ng Demand

3.4 The Plan for the Rest of the Report

3.2

2.1

2.2

2.3

CHAPTER FOUR:-

CHAPTER TWO:

CHAPTER THREE:

ABSTRACT

ACKNOWLEDGEMENTS

LIST OF TABLES

LIST OF FIGURES

SUMMARY

CHAPTER ONE:

REFERENCES

REFERENCES

CHAPTER FIVE: THE DEMAND FOR HOUSING SERVICES

4.1

4.2

4.3

5.1

5.2

5.3

EmpJ.rJ.cal Specl.ficatlon of Housing

ExpendJ.tures Functlons

Elast~c~ty Est~mates

Demograph~c variables Affect~ng Demand

for HousJ.ng

Housing Qual~ty Changes

The Demand for Hous~ng serv~ces

Conclusl.ons

59

62

81

90

91

92

101

119

120

v
TABLE OF CONTENTS (continued)

ISSUES IN USING EXPERIMENTAL DATA

REFERENCES

DESIGN OF THE DEMAND EXPERIMENT

111.1 Data Sources

DESCRIPTION OF THE SAMPLES USED FOR ANALYSIS

REFERENCES

DATA SOURCES AND MAJOR VARIABLES USED IN THE

ANALYSIS

III.2 Key Varl.ables

REFERENCES

HOUSING PROGRAM EFFICIENCY

REFERENCES

THE ECONOMICS OF THE FOOD STAMP HOUSING

SUBSIDY

CHAPTER SIX:

APPENDIX I:

APPENDIX II:

APPENDIX III:

APPENDIX IV:

APPENDIX V:

6.1

6.2

6.3

Ll

L2

L3

L4

Dynam~c Spec~f~catl0n of Houslng Demand

Selectl0n Blas 1n Prlce Elastlclty

EstJ.Inates

program Understandlng

purpose of the Demand Exper~ent

Data Collect.l.on

Allowance plans Used .l.n the Demand

Exper.l.ment

Fl.nal sample

121

122

134

140

143

A-l

A-l

A-3

A-5

A-10

A-13

A-20

A-21

A-21

A-24

A-34

A-35

A-40

A-41

APPENDIX VI:

APPENDIX VII:

REFERENCES

AN ALTERNATIVE ESTIMATION OF EXPERIMENTAL

EFFECTS

VI.l Development of the Methodology

VI.2 Emp.l.r.l.cal Est.l.mat.l.on of Exper~ental

Effects

REFERENCES

A DISEQUILIBRIUM MODEL OF MOBILITY

VII.l Theoretl.cal Development of a Mobl.ll.ty

Model

VII.2 Empl.rl.cal Analysl.s of Mobl.ll.ty

VIL3 Summary

REFERENCES

Vl.

A-48

A-49

A-49

A-53

A-57

A-59

A-59

A-66

A-74

A-77
APPENDIX VIII:

APPENDIX IX:

APPENDIX X:

APPENDIX XI:

TABLE OF CONTENTS (contmued)

THE EFFECT OF DEHOGRAPHIC VARIABLES ON THE

HOUSING EXPENDITURES OF THE OVERALL SAHPLE

COHPARISON OF ELASTICITY ESTlHATES FROH

FIRST-YEAR DATA ANALYSIS AND THIS "REPORT

REFERENCES

DETAILED TABLES

EVALUATION OF SAHPLE SELECTION BIAS IN

ESTlHATED PRICE ELASTICITIES

XI.l The Sample Select~on problem

XI.2 Ser~al Correlat~on

XI.3 Emp~r1cal EV1dence

Append~x XI Note A

Append~x XI Note B

REFERENCES

VB

A-79

A-8S

A-89

A-91

A-l47

A-148

A-lSI

A-IS6

A-160

A-162

A-167
- --------------~----------------------,

LIST OF TABLES

Table 2-1

Table 2-2

Mean Monthly Housing Expend~tures at

Enrollment and at Two Years After Enrollment

Mean Monthly Hous~ng Expenditures at Enrollment

and at Two Years After Enrollment for UnConstrained Households

8

9

Table 2-3

Table 2-4

Table 2-5

Table 2-6

Table 2-7

Table 2-8

Table 2-9

Table 2-10

Proport~on of Allowance Payment Allocated

to Increased Rental Expend~tures 11

Changes in Rent Burden From Enrollment

to Two Years 13

Mean Monthly Hous~ng Expend~tures at Enrollment

and at Two Years After Enrollment 14

Proportion of Allowance Payment Allocated to

Increased Rental Expend~tures, by Mob~l~ty Status 17

Efficiency of Price and Income Subsidy 23

Predicted Effect of a Variable Percent of

Rent Formula 27

pred~cted Effect of Br~t~sh Rent Allowance Formula 29

Predicted Effect of a Rent-Condit~oned Housing

Gap Formula 30

Table 2-11

Table 4-1

Table 4-2

Table 4-3

Table 4-4

Table 4-5

Table 4-6

Income-Cond~t~onedPercentage Subsid~es Needed

to Reduce Rent Burden to 0.25 as a Funct~on of

In~tial Rent Burden

pr~ce and Income Elastic~ty Estimates for the

Overall Sample

pr~ce and Income Elast~c~ty Estimates for the

Movers Sample

Pr1ce and Income Elasticity Est~ates for the

Movers Sample (Pooled Sites)

Demand Elastic~t~es Using Samples Stratif~ed

by Median Monthly Income

Income Elasticities Using Spline Function

Est~tes of a Log-Linear Demand Equat~on With

Unconstrained Households

32

64

73

75

76

78

80
Table 4-7

Table 4-8

Table 4-9

Table 4-10

Table 5-1

Table 5-2

Table 5-3

Table 5-4

Table 5-5

Table 5-6

Table 5-7

Table 5-8

Table 6-1

Table 6-2

Table 6-3

Table 6-4

Table 6-5

LIST OF TABLES (continued)

Log-Linear Demand Functl.ons USl.ng Demograph1c

Varl.ables as Covarl.ates for the Mover Sample

Expenditure Elast~c~tl.es by Minonty Status

Expen~ture Elastl.citl.es by Household Compos~t~on

Price and Income Elastl.cl.ty Estimates for

Pooled 81.tes by Demographl.c Characterl.st1cs

Changes ~n Dwelhng Un~t Phys~cal and Occupancy

Standards

Changes in Hous~ng Adequacy from Enrollment to

Two Years for Control and Percent of Rent

Households

Changes ~n Hedon~c Housing Qual~ty

Comparl.son of Prl.ce and Income Elastl.cl.t.1.es

Es~mated Using Housing Expen~tures and an

Hedon~c Index of Hous~ng SerVJ.ces (Movers Sample)

Prl.ce and Income Elasticity Estl.mates for Bent

Components

Hous~ng Serv~ces Elast~cit~es by Household

Compos!.t1.0n

Housl.ng Services Elastl.cities by Ml.norl.ty Status

"Corrected" Prl.ce Elastl.cl.ties for Housing Servl.ces

Compared to Expen~ture Eshmates by Demographic

Characteristics

Parameter Estl.mates for a Dynanu.c Model of Housl.ng

Demand

Prl.ce Elasticl.tl.es of Demand for Dl.fferent Mover

Groups

Pr~ce Elast~c~ty Estimates by Pr~or Mobility

Comparison of Ohis and Thomas' Estimated Effects

of Experimental Income Transfers on Rental

Expenditures for Three- and F~ve-Year Guarantees

(Seattle/Denver)

Twa-Year Ser~al Correlations for Control Movers

x

84

86

87

89

95

97

99

102

108

112

113

115

128

130

13l

133

136
Table 6-6

Table 6-7

Table I-I

Table I-2

Table II-I

Table II-2

Table II-3

Table II-4

LIST OF TABLES (cont~nued)

Poss1ble Bias 1n Pnce ElashcJ.t1es

Part~c~pant Understand~ng of the Relationsh~p

Between Rent and Allowance Payment

Allowance Plans Tested

Sample Size After Two Years

OverVl.ew of SaIlIPles Used for Analys~s ~n

This Report

Percent of Rent Sample at ~o Years Used

for Analysis ~n Th~s Report

Selected Household Character~st~cs at Baseline

for the Ehgihle, Enrolled, and ~o-Year

Active Sample

Acceptance Rates of Percent of Rent and Control

Households Offered Enrollment

Page

139

142

A-9

A-12

A-14

A-IS

A-16

A-IS

Table II-5 Rates of

Rent and

Years

ContJ.nued Enrollment for Percent of

Control Households for the Full Two

A-19

Table III-l

Table III-2

Table III-3

Table III-4

Table IV-l

Table V-I

Table VI-I

Table VI-2

Data Sources Used to Derive Key Variables

COmponents Included ~n the Dehn~t~on of Net

Income for AnalysJ.s and Comparison with census

and Program El~g~b~lity Definit~ons

Income Ehgiliility L1mits at Enrollment for

Percent of Rent and Control Households

Components of M~n~mum Standards (Program

Dehnit~on)

Subs~dY Effic~ency of Percent of Rent Subs~fues

for D~fferent Subs~dy Rates and Price

Elast1CJ.ties

Comparison of Food Purchases and Food Stamp

Allotment

Expenmental Impact of Rent Rebates (Med~an

Percentage Increase in Rent Above Normal)

Pr~ce Elast~city Estimates From Normal

E~enfutures

n

A-22

A-26

A-27

A-31

A-36

A-47

A-54

A-55
Table VII-I

Table VII-2

Table VII-3

Table VII-4

Table VIII-I

Table VIII-2

Table VIII-3

Table VIII-4

Table IX-I

Table IX-2

Table X-I

Table X-2

Table X-3

Table X-4

Table X-5

Table X-6

Table X-7

LIST OF TABLES (continued)

Character~stics of Cost Measures Used in

Analysls of Mobillty

Characterl.stJ.cs of Benef1.t Measures Used 1.0

Analysls of Mobillty

Disequilibrium Legit Model of Two-Year Mobility

Predlctlve Power of Mobillty Equatlon

Log-Ll.near Demand Fl.ll1ctJ.ons Using Demographl.c

Vanables as Covariates for the Overall Sample

(Pittsburgh)

Log-L1.near Demand Functl.ons USJ.ng Demographl. C

Varlables as Covariates for the Overall Sample

(Phoenlx)

Strat1fl.ed Log-LJ.near Expen~ture Functl.ons

for the Overall Sample (Plttsburgh)

StratJ..fl.ed Log-Linear Expenditure Functions

for the Overall Sample (Phoenlx)

Comparl.son of Elasticity EstJ.mates: Fin<hngs

From First-Year Data Analysis vs. ThlS Report

(Overall Sample)

Comparison of Elastlcity Estimates: Flndlngs

From Flrst-Year Data Analysls vs. ThlS Report

(Movers Sample)

Changes 10 Rent From Enrollment to Two Years

After Enrollment

Changes ln Median Rent Burden From Enrollment

to Two Years

Change 1.n Mean Rent Burden From Enrollment to

'Iwo Years

Percentage Distr1.butJ.on of Rent Burden

O1anges in Rent From Enrollment to Two Years

After Enrollment for the Mover Sample

Changes 1.0 Rent From Enrollment to Two Years

After Enrollment for the Nonmover Sample

Change ln Rent Applying Selective Income

Eliglblllty Llmits to Control Households

xu

A-69

A-70

A-73

A-75

A-80

A-81

A-82

A-83

A-87

A-88

A-94

A-95

A-96

A-97

A-98

A-99

A-lOa
Table X-8

Table X-9

Table X-IO

Table X-ll

Table X-12

Table X-13

Table X-14

Table X-15

Table X-16

Table X-17

Table X-18

Table X-19

Table X-20

Table X-21

Table X-22

Table X-23

LIST OF TABLES (cont~nued)

Change in Rent Applying Selective Income

Eligibil~ty Limits to Control Households for

Mover Sample

Change in Rent Applying Selective Income

EI~gib~lity L~=ts to Control Households for

Nonmover Sample

Proportion of Allowance Payment Allocated to

Increased Rental Expen~tures

Enrollment Rent Burden by Income Class for

Combined sites

Overall Character~st~cs of Var~ables Used ~n

Regression Analys~s

Log-~near Expen~ture Funchons

Ll.near Expenditure Functions

Log-Linear I:emand Funct~on Allow~ng Variable

Price Elast~c~ty

Log-Linear Expenditure Functions - S~tes Pooled

Log-L~near I:emand Funct~ons for Movers Sample

Stratihed by Me~an Monthly Income

Log-Linear I:emand Funct~ons for Mover Sample

Est~mated Using Income Spline

Log-~near Expenditure Functions Us~ng DemographJ.c VarJ.ables as CovarJ.ates for the Mover

Sample

Mean Monthly Housing Expenditures at Enrollment

and at Two Years After Enrollment for the Mover

Sample by Race/Ethn~c~ty

Stratified Log-Linear Expend~ture Funct~ons for

the Movers Sample

Rent for Movers by Strat~fied Demograph~cs

Pooled Sites

Changes in Rates of Passing Lowest Hous~ng

Standards From Enrollment to Two Years for

Control and Percent of Rent Households

A-IOI

A-I02

A-I03

A-I04

A-lOS

A-I06

A-I07

A-I08

A-109

A-110

A-Ill

A-112

A-1l4

A-1l6

A-ll8

A-1l9
Table X-24

Table X-25

Table X-26

Table X-27

Table X-28

Table X-29

Table X-30

Table X-3l

Table X-32

Table X-33

Table X-34

LIST OF TABLES (contJ.nued)

Cllanges ~n Rates of Passing Program Housing

Standards From Enrollment to Two Years for

Control and Percent of Rent Households

O1anges ~n Rates of Pass~ng Program Occupancy

Standards From Enrollment to Two Years for

COntrol and Percent of Rent Households

Changes ~n Rates of Pass~ng Lowest Hous:Lllg

Standards From Enrollment to Two Years for

Control and Percent of Rent Households for

the Movers Sample

Changes ~n Rates of Passing Lowest Housing

Standards From Enrollment to Two Years for

COntrol and Percent of Rent Households for

the Nonmover Sample

Changes 1n Rates of Passing Program HousJ.ng

Standards From Enrollment to Two Years for

COntrol and Percent of Rent Households for

the Mover Sample

Changes 10 Rates of Passlng Program Housing

Standards From Enrollment to Two Years for

COntrol and Percent of Rent Households for

the Nonmover Sample

Changes 10 Rates of Passlng Program Occupancy

Standards From Enrollment to Two Years for

Control and Percent of Rent Households for

the Mover Sample

Changes J.n Rates of Passing Program Occupancy

Standards From Enrollment to Two Years for

Control and Percent of Rent Households for

the Nonmover Sample

Changes J.O HousJ.ng Adequacy From Enrollnent to

Two Years for Control and Percent of Rent

Households

Changes J.n HousJ.ng Adequacy From Enrollment

to Two Years for Control and Percent of Rent

Movers

Changes in HousJ.ng Adequacy From Enrollment

to Two Years for Control and Percent of Rent

Nonmovers

XJ.v

A-120

A-12l

A-122

A-123

A-124

A-125

A-126

A-127

A-128

A-129
Table X-35

Table X-36

Table X-37

Table X-38

Table X-39

Table X-40

Table X-41

Table X-42

Table X-43

Table X-44

Table X-45

Table XI-I

Table XI-2

Table XI-3

Table XI-4

Table XI-5

LIST OF TABIES (contJ.nued)

Change ~n Hedon~c Hous~ng Serv~ces Index From

Enrollment to Two Years for Control and Percent

of Rent Households

Changes ~n HedonJ.c HousJ.ng ServJ.ces Index From

Enrollment to Two Years for Control and Percent

of Rent Households for the Mover Sample

O1anges 1n Hedonlc Houslng Serv1ces Index From

Enrollment to Two Years for Control and Percent

of Rent Households for the Nomnover Sample

Search Effort for Last Move

Demand for Rent Components

Strat1fJ.ed Log-LJ.near Housl.ng Services FunctJ.ons

for the Overall Sample

StratJ.fied Log-L1.near Houslng Bervl-ces Functl.ons

for the Mover Sample

Mean Monthly HousJ.ng Services at Enrollrrent and

at Two Years After Enrollment for the Mover

Sample by RacejEthnicJ.ty

StratJ.fl.ed Log-L1.near Housl.ng ExpendJ.tures,

HousJ.ng SerV1ces, and Hedon1.c ResJ.duals

ElastJ..cl.tl.es for the Mover Sample

Log-Ll.near E~end1ture Functl.ons for Housing

ServJ.ces USJ.ng Full Sample and Submarket HedonJ.c

Indl.ces for Phoenix

Estimate of Log (Normal Rent) at Two Years After

Enrollment

Selection Effects for Expenfuture Price

Elastl.cib..es

Select~on Effects for Hous1ng SerV1ces Price

Elast1c1tl.es

EstJ.mation of the Selection Effect for

Expenditures

EstJ.mat~on of the SelectJ.on Effect for HousJ.ng

SerVJ..ces

CorrelatJ.on of ResJ.duals for Control Households

at Enrollment and Two Years After Enrollment

xv

A-131

A-132

A-133

A-134

A-135

A-137

A-139

A-141

A-143

A-144

A-145

A-157

A-159

A-163

A-164

A-166
F~gure 2-1

Figure 3-1

Figure 4-1

Figure 4-2

Figure 5-1

Figure IV-l

F~gure V-I

Figure V-2

F~gure VI-l

F~gure VII-l

F~gure VII-2

LIST OF FIGURES

Mean Percentage Change in Hous~ng ExpenChtures

Between Enrollment and Two Years After Enrollment

Optimal Hous~ng Consumption

Expenditure Functions: Rent vs. Pr1ce

Expendlture Functl0ns: Rent vs. Income

Mean Percentage Change In Housing Services Between

Enrollment and Two Years After Enrollment

Eff~c~ency as a Function of Percent of Rent Rebate

Retes and Price Elastic~ty

Food Stamp BUdget Constraints

Income -and Pr~ce Effects of Food Stal1!PS on Hous~ng

D~sposition of Exper~mental Households by Mobil~ty

Status

Compensating Income Variation

Initial and Induced Disequilibr~um for Percent of

Rent Households (No Moving Costs)

xvli

15

43

66

68

100

A-37

A-44

A-45

A-52

A-62

A-65
-~---~--------------------------------

SUMMARY

This report ~s one of a series of techn~cal reports on the final results of

housing programs tested ~n the Housing Allowance Demand Experiment. The

Demand Experiment, author~zed by Congress ~n the Housing Act of 1970, was

des1gned to test the concept of d~ect cash assistance to low-2ncome households enabling them to rent suitable housing. The experiment focused on

the ways low-income renter households use hous2ng allowances. It tested a

variety of allowance plans lnvolV2ng approX1rnately 1,200 lOw-lucorne Experlmental households and 500 Control low-income households at two sites:

Allegheny County, Pennsylvania (P~ttsburgh) and Maricopa County, Ar~zona

(Phoe=x), dunng 1973-1977. Each household enrolled ~n the experiment was

offered I10nthly allowance payments for three years. Analysis is based on

data from the first two years of payments.

The subJect of thlS report is Percent of Rent houslng allowances, one of the

maJor types of hous~ng allowance payment formulas tested in the Demand Experiment. The Percent of Rent plans offered eligible households rebates equal

to some fract~on of their gross monthly rent. Within the Demand Experiment,

households were dlvlded lUtO flve groups, receiving rebates of 20, 30, 40,

50, or 60 percent of their monthly rent. Thus, for example, a household

rece~v~ng a 50 percent rebate would be g~ven $50 if its rent were $100 and

$100 ~f ~ts rent were $200. Such a household could move into a unit twice as

expens~ve w~thout chang~ng its or~g~nal out-of-pocket hous~ng expenfutures.

Alternahvely, it could retain its orig~nal hous~ng at half the original cost.

A Percent of Rent rebate reduces the effectJ.ve prJ.ce of houslng for reclpJ..ents,

thereby creating a distinct l.ncentive for recJ.pients to iIqprove their housl.ng

by, J.n effect, makJ.ng housing a "bargain" relat~ve to other goods and serVJ.ces.

A household rece~v~ng a 50 percent rebate, for example, has ~ts rent cut ~n

half whether t stays where i t ~s or moveS to other housl.ng. Prl.ce cuts, l.n

the case of most goods, normally lead to ~ncreased purchases. When the prl.ce

cut is l.n the form of a rent rebate, demand and expenditures for hous~ng are

expeGted to ~ncrease--and hous~ng condit~ons to l.II!Prove commensurately.

-:£here are obvious potent~al advantages to this k~nd of housl.ng allowance payment. It automa~cally tl.es allowance payments to a household's own contrl.-

S-l
bution toward IlEet~ng ~ts housing needs and does so in an administratively

simple way. It allows each household a wide range of cho~ce by not requiring

households to choose housing of a particular type or in a part~cular location.

It automat~cally adJusts payIrents to take account of local hous~ng costs. On

the other hand, households mayor may not use their rebate to improve the~r

housing. Even ~f they do spend the rebate on hous~ng, they mayor may not

obtain decent housing that meets public policy object~ves unless spec~f~c

housing standards are irnposed and enforced. fue rebate may lead households

to shop less carefully for housing, result~ng ~n their payIrent of more than

they otherw~se would for the hous~ng they obtain. The effectiveness, efficiency, and equity of such rebate programs depend on exactly how households

respond to the rebates.

The percentage rebates offered ~n the experiment depended only on the exper~­

mental plan to wh~ch<they household was ass~gned. S~nce h~gher income households tend to have higher rental expenditures than do lower ~ncome households,

this means that they also tended to rece~ve larger allowance payments. An

actual program would probably vary the percentage rebate w~th ~ncorne or rent

so that higher ~ncome households would not tend to rece~ve higher payIrents.

The effects of such program variations can be estimated from the responses to

the exper~mental plans.

Income transfers through general ass~stance, soc~al secur~ty, or other

transfer programs, would provide an alternative to assistance spec~f~cally

t~ed to hous~ng. Such general transfers offer households a wider range of

cho~ce in spending the add~tional transfer J.ncome. Further, they may be

administrat~vely eas~er to operate and to coord1nate w~th other assistance

prograrnso The~r relative effect~veness, eff~ciency, and equ~ty in tenus

of housing aga~n depends on the way ~n wh~ch households change the~r hous~ng

in response to changes ~n household ~ncome. Thus the same questions arise

in evaluat~ng the housing impact of both rent rebate and income transfer

programs.

Estimates of hous~ng responses to income transfers are obta~ned from two

sources. First, s~nce income transfers essent~ally ~ncrease rec~p~en~

incomes, the~r impact on hous~ng can be estJ.mated by analyzing the way in

which low-~ncome households' hous~ng normally varies w~th household ~ncome.

Second, the Demand Experiment ~ncluded a small sample of households that

S-2
received an unconstrained lncome transfer. These households, called Unconstrained households, provide dl.rect observation of the effect of income

transfers on the housing of rec~p~ents.

The analysls described 10 thlS report fl.rst estimates an expenditure function

that shows how households change their housing expenditures in response to

the housing price reductions created by the Percent of Rent rebates and how

changes in nonexperlillental variables, particularly income, affect housing

expenditures. It then examines the extent to which changes 10 housing

expenditures due to rent rebates or other factors are likely to be translated ~nto improved housing. It thus provides the basic tools for des~gn­

~ng and evaluating alternate rent rebate and ~ncome transfer programs.

The following major conclusions emerged from the analys~s:

1. Relauve to Control households, experimental households rece~ving Percent

of Rent rebates increased their hous~ng expend~tures by a small but stat~stically s~gnif~cant percentage.

The overall increase in expendJ.tures for Percent of Rent households

at both s~tes was 26 percent, compared to 18 percent for Control

households. The expe=ence of Control households provides a benchmark estimate of normal behav~or--how Percent of Rent households

would have changed their housing expenditures in the absence of the

rent rebate. Thus, it appears that the net effect of the price

reduction was to induce only an 8 percentage point increase 10

housing expenditures above normal levels. This f~nding is confi:med

by an est~mated expenditure funct~on (which takes ~nto account nonexperimental ~fferences between Percent of Rent and Control households) .

2. As might be expected, households respond to Percent of Rent rebates only

when they move. Thus the full effect of a rent rebate will develop

gradually as recipients move.

Households that moved dur~ng the exper~ment had much larger normal

rent increases than those that ~d not. Control households that

moved increased their housing expenditures by 29 percent in Pittsburgh

and 30 percent in Phoenix as conpared with increases for nonmover

Control households of 13 percent and 7 percent respectively. Percent

8-3
of Rent households that moved ~ncreased the~r hous~ng expenmtures

16 percentage po~nts more than Control movers in P~ ttsburgh and 8

percentage po~nts more ~n Phoen~x. Percent of Rent households that

did not move increased their expenditures by only 2 percentage

points nore than Control nonmovers 10 P1ttsburgh and by the sane

percent as Control nOnrrK)vers 1.n Phoemx.

3.. The estJ.mated relat10n between the housing expenditures of low-income

households and changes 1D hous1ng prices and 1ncome is the same at both

sJ.tes.. These esb.mates 1ndicate only small changes 1.n housing expendJ.tures

in response to changes 10 price or incoIOO.. A 10 percent reductJ.on J.D the

prJ.ce of housing resulted in only a 2.2 percent l.DCrease in hous1ng expendl.tures; a 10 percent l.ncrease 10 household's average l.DCOme resulted in

only a 3.6 percent increase 1.D housing expendl.tures ..

Estimates for the two sl.tes gave almost identical results in terms

of the change ~n hous~ng expenditures with respect to changes =­

the price of housing or household J.Dcome. The est~ated response

to price changes are lower than estllUates from most prevJ.ous studies,

wh~ch are based on much less reliable price data than that prov~ded

by the Demand ExperJ.Inent. The estimated responses to ~ncome changes

are based on cross-sectJ.onal estllUates uSJ.ng three-year average

annual household ~ncome and are also somewhat lower than most prevJ.ous

stud~es. These estimates were conf~rmed by analys~s of the small

sample of Unconstra~ed households whJ.ch receJ.ved an J.ncome transfer

payment.

4. The estimated response of hous~ng expendJ.tures to changes in housing

prices are lower than most estimates based on nonexper~rrental data. '!he

estimated response to changes J.n income is also in the lower range of

estJ.mates based on nonexperimental data, though not markedly so.

Est~mates of the increase ~n gross housing expenditures to a 10 percent rent rebate based on nonexperimental data have ranged from l

percent to. 19 percent, with most studies giving values of around 7

percent. In contrast, the estunates in this report J.ndicate an increase in gross housing expenditures of 2.2 percent. NonexperJ.mental

estJ.mates are hampered by problems J.n estimating dafferences in housing prices whJ.ch may seriously b~as those results, however. On the

S-4
-- --------~------------- --

other hand, the experimental data are subject to several reservatlons;

they are limited to low-lncorne households, Whlch may have lower responses than h~gher ~ncome households; the duration of the experiment

may have l~ndted households' understand~ng or w~llingness to change

the~r hous~ng; and lt ~s possJ.ble to propose models under which longer

run responses would be larger than those observed at the end of two

years, even for households that move. No eVldence was found to support

any of these alternat~ves, though the tests ava~lable are not always

conclus~ve.

Est~mates of responses to a 10 percent increase In household income

based on nonexper~mental household data have generally ranged from a

1 percent to 6 percent increase ~n housing expenfutures.. The est~­

mate from the Demand Experiment ~s 3.6 percent, which ~s close to,

but somewhat lower than the :rru.d-point of the nonexper~mental estimates. Th~s ~s not unexpected, Slnce the Demand Experlment estlmate

is ~tself based on analysls of nonexperlmental var~at~ons ~n income,

though ~t ~s also conslstent w~th responses to the exper~mentally

lnduced changes In income provlded by the Unconstralned plan, as well

as estimated houslng expenfuture responses ~n the Seattle-I.:lenver Income

Ma1ntenance Experiments.

5. Most of the allowance payment under a rent rebate program will not be used

for lncreased houslng expendl.tures. Even less of an lncome transfer payment wlll be used to lncrease houslng expendl.tures. Glven the very hlgh

rent burdens of reclplents, some allocation of paynents to nonhousing expendl.tures may be deslrable even from a houslng perspective.

Mule the proportion of a rent rebate allowance payment used for

lncreased houslng expenditures tends to lncrease with the rebate

level, the est~ated responses to changes In houslng prlces indicate

that even a rebate of 90 percent of rent would result in increased

housing expend1tures arnount1ng to less than half the total payment.

A 40 percent rebate program would lead to 1ncreased hous1ng expenditures of about 27 percent of the allowance payments. The est:unated

effect of lncreased lncome transfers on housing expendltures is even

smaller. The lncorne transfer payment necessary to achleve the same

change in houslng expendltures as a rent rebate of 40 percent would be

from two to four tunes as large as the rent rebate payment.

5-5
At enrollment, half of the Percent of Rent households at each

site had rent burdens in excess of 32 percent of ~ncome and

almost a third had rent burdens greater than 40 percent of

income. After two years, the median rent burden for Percent of

Rent households net of the allowance payment was 21 percent of

income ~n pittsburgh and 24 percent of ~ncome 1n Phoenix. The

estimated expend~ture funct10ns suggest that reduct10n 1n rent burden

under a rent rebate w~ll be somewhat larger at h~gher rebate levels

and for households with higher pre-rebate rent burdens. Households

W1th a 40 percent of income rent burden would on average be expected

to reduce their rent burdens to 27 percent of income under a 40

percent rebate and to 20 percent of ~ncome under a 60 percent rebate.

6. Minority households (black ~n Pittsburgh but predo=nantly Span~sh 1\mer1can 1.n Phoemx) made smaller changes 10 housing expenditures 10 response

to changes 10 the prl.ce of housing or J.ncome than dl.d nOnrnJ.nority households. There is no consistent evidence of J.mportant differences J.O response among other demographic groups.

The percentage change ~n hous~ng expend~tures resu1t~ng from a

gl.ven percentage change in household J.ncorne 15 estimated to be about

half as large for minority households as for nonminority households.

The percentage change ~n response to rent rebates is estimated to be

about three-fourths that of nonminor~ty households. Although small

samples of movers preclude exact estl.matl.on for subpopulations of

ml.nority households, l.t appears that Spanl.sh American households ~n

Phoen~x may show even smaller responses than black households ~n

Phoen~x or P~ttsburgh. The lower response of minor~ty households

~s assoc~ated WJ.th a lower inJ.tial rent in PhoenJ.x, though not in

P~ttsburgh •

A var~ety of other demographic factors were tested, 1nclud1ng age,

sex, and educat10n of head of household, household size, and household composit~on. Of these only household compos~tion proved s~gnJ.ficant when the sites were analyzed separately, and even this

var~ab1e was not sign~ficant for est~ates based on the comb~ned s~tes.

7. The changes 1n real housing made in response to the rent rebates were

smaller than the expenfuture changes. It appears that from one-fifth to

S-6
one-half or more of the expenditure changes induced by the rent rebates

represented increasing spending w1thout~conco~tantincreases 10 houslng

services obta2ned.

Hedonic 1ndJ..ces, based on statistlcal relatlonshJ..ps between the housing characterJ.shcs of a UIll.t and its rent, were used to corrpare the

average market rent of units w~th the rents pa~d by Percent of Rent

households. Results fuffered among demographic groups and between

s~tes. Allow~ng for the fact that hedon~c ~ndices do not fUlly

reflect all real changes in hous~ng, it still appears that about onefifth of the ~ncreased hous~ng expend~ture by nOIll11J.nor~ty Percent of

Rent households ~n P~ttsburgh went for ~ncreased spend~ng above the

amounts usually needed to purchase the level of housing serv~ces

that they actually obtained. The comparable f~gure ~n Phoen~x ~s

one-half. Small sample sJ..zes make investJ.gatJ..on of mlnorJ..ty response

more tentative. It appears, however, that nunorJ.ties 1.n Phoenix, and

espec~ally 8pan~sh American households, may have had l~ttle or no

real change 10 their housing and little or no change in their housing

expendJ.tures. Once again, the smaller response for minorJ..ty households J.8 assocJ..ated wJ..th a much lower J..nJ..tl.al qualJ..ty in Phoenl.x.

8-7
SOURCES OF STATEMENTS

1. Tabulat10n of expenditure changes are g1ven in Table 2-1. Price elast1cities estimated based on all Percent of Rent households are given 1n Table

4-1.

2. Tabulation of expenditure changes are given in Table 2-5.

3. Cornpar1son of estimates for the two S1tes 1S based on households that

moved as shown 1n Tables 4-2 and 4-3. The results of prev10us stud1es

and the pr~ce data used ~n them are discussed 10 Sect10n 3.3. Est1mates

for Unconstra1ned households are shown 1n Table 4-6.

4. A summary of recent eVJ.dence on household response to changes J..n pr1ce

and 1ncome 15 presented 1n Sect10n 3.3. The possib111ty that higher

1nccme households have h1gher responses 15 exarruned in the d1.scuss10n of

Tables 4-4 and 4-5. The li=ted durat10n of the expenrnent 1S d1scussed

1.n SectJ.on 6.1.

5. Allocat10n of the Percent of Rent rebates and J.ncome transfers to 1ncreased

honsl-og expend1tures 15 d1scussed 1n Sect1.on 2.2. Rent burden f1gures

at enrollment and two y.ears are g1ven 1n Append1x Table X-4.

6. Est1mated expend1ture funct1.ons for d1f£erent demograph1.c groups are

d1scussed 10 SectJ.on 4.3. The comparison of minority and nonminor1ty

households 1S based on Table 4-10.

7. The compar1son of expend1ture changes and real changes in housing is

d1scussed throughout Chapter 5. See espec1ally Table 5-7 and the

d1scussion in the text.

S-8
CHAPTER 1

INTRODUcrION

'!ius ~s one of a ser~es of f1.nal technical reports on the Housing Allowance

De:mand Exper1.ment. The Demand Exper1ment was des1.gned to provlde lnformat1.0n on how low-1.ncome households use hous1.ng allowance payments. The

exper~ment offered monthly allowance payments to approoamately 1,200 lowl.ncome households selected at random l.n each of two 51-tes: P1.ttsburgh

(Allegheny County), Pennsylvan~a and Phoen~x (Mar~copa County), Ar~zona.

Several fufferent allowance plans were tested ~nvol=ng fufferent payment

formulas and hollS l.ng requ1.rements. In add1.tion I a control group of approx­

~rnately 500 low-~ncome households was enrolled at each site. Households

remal-ned l.n the exper1ment and received payments for three years after they

enrolled. The calendar perl-cd covered by the experJ.ment was roughly from

late 1973 to early 1977. Evaluat~on ~s based on household responses in the

fJ.rst two years after enrollment.

There were four baS1C treatment plans under WhlCh households were enrolled:

1 Houslng Gap, UnconstraJ.ned, Percent of Rent, and Control. Households ~n

Hous~ng Gap plans were offered payments des~gned to br~dge the gap between

the cost of modest, ex~st~ng standard hous~ng and a reasonable fract~on of

household lncome. The Houslng Gap allowance payment was llnked to part1c1­

pantsI houslng by houS1ng requlrernents--households rece1ved an allowance only

2 1f they occupled a un1t meet1ng the program's hous1ng standards. The Unconstra1ned plan offered households a payment based on the same formula as 1n

the Hous~ng Gap plan but w~thout a hous~ng requ~rement. Th~s plan resembled

general lncorne support programs, except that the payment amount was determlned

by need for hous~ng rather than for all household expenses.

Percent of Rent plans offered households a rent rebate 1n the form of a cash

payment equal to a f~xed fract~on of the~r monthly rent. Households ~n

Percent of Rent plans had no housl.ng requ1rements to meet. Thelr payment

was t~ed d~rectly to the amount spent for hous~ng. F~nally, the group of

1

See Appenfux I for a deta~led fuscuss~on of the des~gn.

2The housing response of these households is discussed in Fr1edman and

Weinberg (1979).

1
Control households did not receive any housing allowance payment beyond a $10

monthly cooperat~on payment for provlding the same lnformation as Experlmental

households. They provlded a comparlson group agalnst WhlCh to estlmate the

effect of d1fferent allowance plans.

ThlS report focuses malnly on the housing consumption of households 1D the

Percent of Rent houslng allowance plans. The Percent of Rent plans reduce

the prlce of houslng to particlpants because the government shares 10 the

cost of whatever hous1ng the part1c1pant selects. A household w1th a 50

percent rebate, for example, only has to spend $75 of ltS own money to rent

a $150 uDlt; ltS prlce of houslng has been halved. Thus analyzlng responses

to the Percent of Rent rebates 18 10 effect analyzing the way 1D which households respond to changes 1n the pr1ce of housing.

Previous analyses of household responses to varlatlons 1D the prlce of houslUg have been based on compar~sons of hous~ng expend~tures across c~ties or

years w~th dJ.fferent est~mated overall housing costs. The Percent of Rent

plans tested ~n the Demand Experiment provide the f~rst direct observations

of household responses to a well-defined change in the price of hous1ng relat1ve to other goods and serV1ces. Sinularly, t1ie Unconstrained plan and the

naturally occurr~ng varJ.anon ~n household income and rent can be used to

analyze households t housing response to changes J.n income.

1 The Percent of Rent plans 1n part1cular are not 1ntended as prototype programs.

Rather, they, together w~th Unconstra~ned and Control households, are ~ntended

to allow estimatJ.on of a general relation between housing consl.lIIY?tion and the

pr~ce of hous~ng, household J.ncome, and other demograph~c characteristics.

Th~s general relation--called a demand function--can then be used to estimate

the effects on hous~ng of a var~ety of housing assistance and incone maJ.nten2

ance programs.

lIn order to facilJ.tate analysis, the rent rebates tested in the Demand

Exper1ment offered a constant percentage rebate to e11g1ble households, regardless of the household's actual rent or ~ncome. A real~st~c program probably

would offer smaller rebates to hJ.gher J.ncome households and restrJ.ct the range

of hous1ng expenditures to wh1ch the rebate applied.

2In addJ.tJ.on, economic theory IJ.nk.s the demand function to a w.1.de var1ety of household behaV1or. Although these theoret1cal 11nks apply only to

J.nd1.vidual households, the average behav~or represented by an estimated demand

function can provJ.de J.mportant ~nsights ~nto the overall behaVl.or of e11gJ.ble

households •

2
Houslng demand functions are estImated In thls report both in terms of houslng expendltures and ln terms of an estImated hedonlc lndex of houslng servlees. The analysls of expendltures as a functlon of the prlce of housing

and household ~ncome prov~des est~ates of the extent to wh~ch payments

under a Percent of Rent hOUSlng allowance or an lnCOme ma1ntenance program

wl11 be translated lnto lncreased spendlng for houslng. This 15 of 1nterest

1n 1tself and because differences in hous1ng expendJ..tures are expected to

reflect real dlfferences in reclp1ent hous1ng as well.

However t changes in hous1ng expend1tures may not always lead to real changes

1n houslng. Most ObVl0uslYt general 1nflat10n implles hlgher dollar expend1­

tures wlthout any change 1n the houS1ng serv1ces prov1ded by a dweillng unlt.

The changes 2n expendl.ture est1mated here account for 1nflat10n, so that

thlS poses no problem. Even apart from inflatl0n t changes 1n expendlture

may st~ll not be reflected ~n real changes ~n part~c~pant hous~ng. If allowance rec1p1ents are unable to act effectlvely 1n the pr1vate market or 1f

they shop less carefully, then they m~ght end up spend~ng more for the same

housing than they otherwise would. Hedonic ~ndices address this problem by

prov1ding est1nlates of the normal market value of a unit 1n terms of l.ts

phys~cal characterishcs. COmparison of the hedonic value of a un~t w~th the

actual rent charged can be used to sort out the extent to which households are

paying above- or below-average rents and thus provides estimates of the real

ch . h' I ange 1n partl.Clpant OUSl.ng.

The mechan~sm that households use in chang~ng the~r hous~ng consumption is

also of ~nterest. As would be expected, renter households usually make large

changes ~n the~r hous~ng only when they move. Accordingly, the full ~mpact

of changes ~n the price of hous~ng may only be real~zed gradually, as households move. AIternatively, households may, even when they move, only adjust

the~r housing ~n stages. The analys~s below invest~gates the dYnamics of

hous~ng demand and examines the possiliility of gradual adJustment to changed

circumstances. Dynamic models also suggest that the li=ted duration of the

exper~ment (three years) may playa role in affect~ng the adJustment process,

and this possiliility ~s examined as well.

I Changes 1n other neasures, such as physl.cal housing standards, are

presented as well.

3
Chapters 2 through 4 of th~s report focus on expench ture changes ~n response

to rent rebates. Chapter 2 presents a basic tabular analysis of changes ~n

expendJ..tures and rent burden (the proportJ.on of J.ncome devoted to rent) I

111ustratJ.ng the J.mportant role resJ.dent1al mobJ.11ty plays 10 those changes.

It then provides a brief summary of the results of estl.matl.ng demand functl.ons and appll.es the demand functJ.on parameters to the estl.matl.on of impact

of eXl.sting and potentl.al government programs.

Chapter 3 develops the theoretl.cal issues l.nvolved 1ll estl.matl.ng housl.ng

demand functl.ons, presents the two functl.onal forms employed 1.n this report,

and dl.scusses the results of other recent attempts to estl.mate housing demand

functl.ons. O1apter 4 then presents the estl.rnated demand functl.ons 1.0 terms

of hous~ng expend~tures based on data from the Demand Exper~mant and taking

l.nto account both the prl.ce d1.s count offered to Percent of Rent households

and the ~ncorne transfer offered to UnconstraJ.ned households. The estimates

are contrasted wJ.th those from preVJ.Ous studJ.es of housJ.ng demand. Movers

are sele cted for prJ.mary analysJ.s and the l.nfluence of varJ.ous demograph1c

characteristics (J.n partJ.cular nu.norJ.ty status and household composJ.tJ.on) on

housJ.ng expendJ.tures 1.5 examined for thJ.s group.

Chapter 5 sh~fts the focus from hous~ng expenditures to housing servJ.ces and

eXamJ.nes household response to the housing allowance payment J.U terms of both

changes J.n the specif1.c phy5J.cal characterJ.stJ.cs of the dwellJ.ng unit and in

the est1.mated average market value of the unit (the hedoru.c J.ndex of hous1.ng

servJ.ces). The chapter compares household response as measured alternatJ.vely

by expendJ.tures and housing serVJ.ces. ThJ.s compar1.son enables deternunation

of the extent to wh~ch households overpay for the~r unit relahve to the

market average prJ.ce ..

Fl.nally, Chapter 6 fuscusses several technJ.cal problems J.nvolved J.n using

experJ.mental data to specJ.fy and estJ.mate response funct1.ons. The first

problem exanuned is the role of hous1.ng market dynanu.cs and 1.ts J.nteractJ.on

w~th the l~=ted durahon of the exper~ment ~n affect~ng household adjustment

to the rent rebate. Second 1.5 the problem of 5electJ.on bias on the elastiCJ.ty

estJ.mates (due to dJ.fferentJ.al accept~ce, attrJ.tJ.on, or mob1.l1.ty). The f1.nal

problem examined is the extent to wh~ch households chd not understand the

program and hence did not respond to the Percent of Rent rebates.

4
REFERENCES 

Friedman, Joseph and Daniel H. We~nberg, Hous~ng Constnnpt~on Under a Constrained Income Transfer: Evidence from a Housing Gap Hous~ng

Allowance, Carnbr~dge, Mass., Abt Assoc~ates Inc., April 1979 (revised 

June 1980). 

5 
alAPTER 2

SUMMARY OF EXPENDITURES alANGES

Tlas chapter prov~des a brief sunnnary of the effects of Percent of Rent allowances on housing expenditures. The chapter starts with a tabular overv~ew of

changes in hous~ng expenditures and rent burden for Percent of Rent households.

These are compared with changes for Control households. S~milar compar~sons

are presented for Unconstrained households, whJ.ch rece1.ved a dJ.rect inconeconfutioned payment, unconnected with their hous1.ng expenChtures.

Tabular analysis, however, does not control sufficJ.ently for other J.nfluences

on household behavior. Section 2.2 therefore presents the est~mated demand

function for hous~ng as developed ~n Chapters 3 and 4. This function, based

on the responses of Percent of Rent and Control households, relates housing

expenditures to household income and the pr~ce of hous~ng. It can be used to

est1.mate hous1.ng expenditure responses to

J.ncome-transfer programs, as J.ndicated in.

a wide variety

1 Section 2.3.

of rent rebate and

2.1 TABULAR OVERVIEW OF EXPENDITURE mANGES

Rent rebates provide an incentJ.ve to increase rental expenditures by reduc1.ng

the effective pr~ce of hous~ng to recip~ents. A household w~th a 50 percent

rebate, for example, would have to spend only $75 out-of-pocket to get hous­

~ng that rents in the manet for $150. From the point of v~ew of the tenant,

th~s rebate is eqmvalent to a hal=ng of the pnce of hous~ng. In general,

for a household W1.th a percentage rebate of "au, the price per unit of hous­

~ng drops from PH to (I-a) PH. Thus, recip~ent households are expected to increase hous~ng expenfutures relative to Control households during the exper~­

rnent. As shown in Table 2-1, the average increase in rental expenditures for

rec~pients was higher than that for Control households at both sites. Percent

of Rent households increased their hous~ng expenfutures by an average of 26

percent 1.0 each sJ.te, while Control households had a smaller increase--

2 18 percent.

lAppendix VII presents a further application of the demand funct~on results to a =croeconomic theory of residential mobihty.

2

More det~led tabulat~ons of rent changes are presented for each percentage rebate plan in Appendix Table X-I. The ~ncrease ~n rent ~s generally

larger for households with larger percentage rebates. The percentage changes

reported in the text are the mean of the ratio of the change in rent to the

rent at enrollment. The appenfux tables also report the rat~o of the mean

change ~n rent to the mean rent at enrollment.

7
Table 2-1

MEAN MONTHLY HOUSING EXPENDITURES AT ENROLLMENT

AND AT TWO YEARS AFTER ENROLLMENT

MEAN HOUSING MEAN CHANGE IN

EXPENDITURES HOUSING EXPENDITURES

At At Two SAMPLE

Enrollment percentagea TREATMENT GROUP Years Amount SIZE

PITTSBURGH

Percent of Rent

households $114 $139 $25 26% (385)

Control households 115 133 18 18 (289)

PHOENIX

Percent of Rent

households

Control households

132

128

162

145

30

17

26

18

(280)

(252)

SAMPLE: Percent of Rent and Control households act~ve at two years

after enrollment, excludlng those wlth enrollment lncornes over the e11g1­

bl11ty lkmltS and those I1vlng In thelr own homes or In SUbsldlzed housing.

DATA SOURCES: In~t~al and monthly Household Report Forms.

a. percentage change 18 deflned as the mean of the ratlo of the

change In rent to the rent at enrollment.

8
'lbese f~gures suggest that the rent rebate did ~ndeed ~nduce Percent of Rent

households to ~ncrease the~r housing expenditures and that households were

sensJ.tJ.ve to the prJ.ce of housJ.ng. A straightforward, but crude way of

measurJ.ng the expendJ.ture response J.nduced by the allowances J.5 the amount

by whJ.ch recJ.pJ.ent households' rent J.ncreases exceed that of control households. Table 2-1 ind~cates that the exper~mentally induced change ~n housing expendJ.ture, net of the "nonnalll J.ncreases represented by Control

households, averaged 8 percentage pOl-uts J.n each 5J.te. The average prJ.ce

reduct~on attr~butable to the rent rebate was approx~ately 40 percent.

Consequently, a rough estimate of the prJ.ce elastJ.cJ.ty of housJ.ng expendJ.­

tures (the percentage change ~n expend~tures for a 1 percent change ~n

pr~ce) ~s the rat~o of these two numbers or -0.20 (that ~s, for every 10

percent decrease J.n prJ.ce, housJ.ng expendJ.tures J.ncreased by about 2 percent).

Table 2-2 presents s~~lar hgures for Unconstramed households. For the

two 5J.tes combJ.ned, the mean percentage change J.n housJ.ng expendJ.tures for

UnconstraJ.ned households was almost the same as for percent of Rent households--27 percent (22 percent ~n P~ttsburgh and 35 percent ~n phoen~x). Thus,

the net increase ~n expend~tures above normal was about 9 percentage po~nts.

The payment averaged about 30 percent of ~ncome, ~ply~ng an ~ncome elast~cTable 2-2

MEAN MONTHLY HOUSING EXPENDITURES AT ENROLLMENT

AND AT TWO YEARS AFTER ENROLLMENT FOR UNCONSTRAINED HOUSEHOLDS

MEAN HOUSING MEAN CHANGE IN

EXPENDITURES HOUSING EXPENDITURES

At At Two SAMPLE

SITE Enrollment Amount Percentagea Years SIZE

P~ttsburgh $107 $128 $21 22% (59)

Phoen~x 135 165 30 35 (37)

SAMPLE: Unconstra~ned households act~ve at two years after enrollment, exclud~ng those w1th enrollment 1ncomes over the elig1b11~ty l~~ts

and those l1v~ng ~n the1r own homes or ~n SUbs1d~zed hous~ng.

DATA SOURCES: In~t~al and monthly Household Report Forms.

a. Percentage change 15 def1ned as the mean of the rat~o of the

change ~n rent to the rent at enrollment.

9
ity (the percentage change ~n expenChtu:res due to a 1 percent change ~n

mcome) of approXJ.mately 0.30.

The overall allocat~on of the Percent of Rent allowance payments between

~ncreased houslng expendltures and lncreased spendlng for other goods and

servlces can be est1ffiated roughly by dlvldlng the average net lncrease for

Percent of Rent households (the d~fference between expend~ture changes for

Percent of Rent and Control households, as shown ~n Table 2-l) by the

average allowance payment. Overall, only a small fractl0n of the total

1

allowance payments went to lncreased rent (see Table 2-3).

These flgures may be compared wlth changes for Unconstralned households.

ECOnOInlC theory asserts that the "prl.ce lncentlve" for 1ncreased spendlng

on hous~ng that ~s created-by.the rent rebates w~ll be larger than the

"lucerne J..ncentl.vell created by an equal cash grant unrelated to housing

expendltures. The former 1.5, 10 effect, a "matchlng grant" which rewards a

household lncreasl.ngly for ltS own expenditures, whereas the latter 1.S, 1n

effect, a "lump sumll transfer w~thout part~cular ~ncentl.ves for l.ncreased

housl.ng expendl.tures. Thus, households are expected to spend more on hous­

~ng of each dollar of a rent rebate than they would each dollar of a d~rect,

unrestr~cted cash grant. Th~s ~s confirmed by Table 2-3. Though the percentage ~ncreases ~n expenditures for Unconstra1.ned households in the Sl.tes

combl.ned was almost the same as for percent of Rent households, the average

allowance payment for Unconstral.ned households was much larger, so that the

l.ncrease as a percentage of the payment was smaller. Thl.s suggests that,

as expected, rent rebates are more effectl.ve than unconstralned l.ncome

transfers ln channel1.ng money lutO hous1.ng.

The pa~t of the payment not spent on lncreased houslng expendl.ture was

available for nonhous1.ng goods and serVl.ces. One measure of th1.s dl.version

~s the change ~n "rent burden," the proportl.on of lncome spent on housing.

Low-~ncome households that spend more than 25 percent of thel.r l.ncome on

2 hous~ng are often cons~dered to be depr~ved. These households are thought

to have too 11.ttle residual l.ucome aval.lable to spend on nonhouslug goods

and serVl.ces 1.n order to achl.eve a modest standard of ll.vlng. Absent the

recel.pt of a hous1.ng allowance, rent burden 1.S slmply the ratl.O R/Y, where

1The f~gures ~n the table are adJusted for normal changes ~n rent

as measured by the mean change for Control households.

2

Lane (1977) has d1.scussed the orl.g1.n and essential arbl.trarl.ness

of th1.S 25 percent "rule of thumb" for deprlvatl.On.

10
Table 2-3

PROPORTION OF ALLOWANCE PAYMENT

ALLOCATED TO INCREASED RENTAL EXPENDITURES

TREATMENT GROUP

MEAN CHANGE

IN RENT

ABOVE NORMALa

MEAN

PAYMENT

PROPORTION USED

FOR INCREASED

EXPENDITURESb

SAMPLE

SIZE

Percent of Rent

households

Unconstra~ned

households

Percent of Rent

households

Unconstra~ned

households

$7

3

13

13

PITTSBURGH

$49

55

PHOENIX

59

108

14%

5

22

12

(385)

(59)

(289)

(37)

SM1PLE: Percent of Rent and UnconstraIned households active at two

years after enrollment, exclud~ng those w~th enrollment incomes over the

el~g~b~l~ty l~m~ts and those l~v~ng ~n the~r own homes or ~n subsid~zed

hous~ng.

DATA SOURCES: In~t~al and monthly Household Report Forms, and

payments f~le.

a. Th~s ~s computed as the mean change for Exper=ental households

m~nus the mean change for Control households.

b. Th~s ~s computed as the mean change above normal d~v~ded by the

mean payment. It ~s ~ntended to represent a program average rather than a

household average.

11
1 R ~s monthly hous~ng expend~tures and Y ~s monthly ~ncome. With the rent

rebate, the out-of-pocket rent payments of rec~p~ents are reduced by the

amount of the rebate. The rent burden ~s then defined as (l-a)R/Y, where

nail 15 the percentage rebate.

Most households 1n the Demand Exper~ent had rent burdens well above what

has often been cons~dered the normat~ve target (25 percent).

the medlan rent burden for Percent of Rent households was 32

At enrollment,

2 percent.

ReClplents of the rent rebates reduced thelr rent burden slgnlflcantly over

the two years of the experlment. As shown 1n Table 2-4, the medlan rent

burden for percent of Rent households fell from 0.32 at enrollment for both

3 s~tes to 0.21 ~n P~ttsburgh and 0.24 ~n Phoen~x at two years. Reduct~on of

hlgh rent burdens to free household resources for other expendltures may be

an lmportant polley goal 1n ltself. However, reductl0n of rent burden 15

not pecull.ar to Percent of Rent. The net-of-payment rent burden for

Unconstra~ned households at the end of two years was 0.20 ~n P~ttsburgh and

4 0.13 1n phoenl.x.

Increased expendl.tures on houslng often accompany rnovlng to a new unlt wlth

h~gher rent. In both p~ttsburgh and Phoen~x, households that moved exper~­

enced an 1ncrease In rental expend1tures at least tW1ce as high as that of

5

nonmover households (see Table 2-5). A str~k~ng feature ~s the larger

1ncrease ln rent apparent for movers w1th larger percentage rebates as shown

~n F~gure 2_1. 6 On the other hand, Percent of Rent and Control households

lRent burden stat1st1cs are h1ghly senSlt1ve to def1n1tlons of the

1ncorne varlable used 1n the denom1nator~ Statlstlcs reported 1n the text

are rnedlan f1gures based on net d1sposable 1ncome. (For a further d1scuss~on of th~s ~ssue, see Append~x III and Budd~ng, 1978.)

2If rent burden 1S further broken down by 1ncorne, h1gher-income

households have lower rent burden than do low-lncorne households S1nce hous1ng expend1ture does not lncrease in proport1on wlth 1ncorne.

3Appendlx Tables X-2 and X-3 present medlan and mean rent burden,

respectlvely, by percentage rebate level.

4See Append~x Table X-4 for add~t~onal deta~l on the d~str~but~on

of rent burden.

5

Breakdowns of these figures by rebate level are pro~ded in Appenmx Tables X-5 and X-6.

6

Most of the v1sual 1ffipreSS10n of larger exper1mental effects for

hlgher rebates 1S the result of very hlgh responses of movers under the 60

percent plan. In fact, households asslgned to thls plan were generally

(cont~nued)

12
Table 2-4

CHANGES IN RENT BURDEN

FROM ENROLLMENT TO TWO YEARS

MEDIAN RENT BURDEN

At At Two MEDIAN CHANGE SAMPLE

TREATMENT GROUP Enrollment years IN RENT BURDEN SIZE

PITTBURGH

percent of Rent households 0.32 0.21 -0.11 (388)

Control households 0.29 0.26 -0.04 (290)

Unconstra1ned households 0.35 0.20 -0.17 (59)

PHOENIX

percent of Rent households 0.32 0.24 -0.09 ( 282)

control households 0.32 0.30 -0.02 (256)

Unconstra1ned households 0.33 0.13 -0.23 (38)

SAMPLE: percent of Rent, Unconstra1ned, and Control households

act1ve at two years after enrollment, exclud1ng those w1th enrollment

1ncomes over the e11g1b111ty 1~1ts and those I1v1ng 10 the1r own homes

or 10 SUbS1dized hous1ng.

DATA SOURCES: Init1al and monthly Household Report Forms.

NOTE: Rent burden 1S def1ned as the rat10 of net rent to disposable

1ncome (see Append1x III for definit10ns of these var1ables).

13
Table 2-5

MEAN MONTHLY HOUSING EXPENDITURES AT ENROLLMENT

AND AT TWO YEARS AFTER ENROLLMENT

MEAN HOUSING

EXPENDITURES

CHANGE IN HOUSING

EXPENDITURES

HOUSEHOLD

GROUP

At

Enrollment

At Two

Years Amount a Percentage

SAMPLE

SIZE

PITTSBURGH

Movers

Percent of Rent

Control

Unconstra~ned

$114

120

109

$156

147

145

$41

26

36

45%

29

39

(142)

(94)

(22)

Nonmovers

Percent of Rent

Control

Unconstra~ned

114

112

106

130

127

119

16

14

13

15

13

12

(243)

(195)

(37)

PHOENIX

Movers

Percent of Rent

Control

unconstra~ned

135

132

128

179

160

175

44

28

48

38

30

55

(169)

(123)

(21)

Nonmovers

Percent of Rent

Control

Unconstralned

127

125

145

134

132

151

8

7

7

7

7

8

(111)

(129)

(16)

Report Forms.

of the rat~o of the

In~tial and monthly Household

change J.5 defJ.ned as the mean

rent at enrollment.

SAMPLE: Percent of Rent, UnconstraJ.ned, and Control households actJ.ve

at two years after enrollment, excludJ.ug those wJ.th enrollment lucornes over

the elJ.glbJ.lJ.ty IJ.mlts and those IJ.vJ.ug in theJ.r own homes or 10 SubSldJ.zed

hous~ng.

DATA SOURCES:

a.. Percentage

change 10 rent to the

14
Figure 2-1

MEAN PERCENTAGE CHANGE IN HOUSING EXPENDITURES BETWEEN

ENROLLMENT AND TWO YEARS AFTER ENROLLMENT

Phoenix

Nonmovers

Pittsburgh

Nonmovers

Phoenix

Movers

[74J Pittsburgh

Movers

- -

- - 57 -------

.

- 49

I

I

44 1

43 I

1

I

- 1-------- 1

37 37 1 40 I 1

r------- _______ I 1

1 I I

1 I I

I 1 32 I

1 1-------1 --______ 30 1

29 I 27

- 17 16 15 I

13 13 12 I

- ,-------1 [9J

7 1 10 1 1--------

f-------j 5 I 1 6 1

I 5 ------- _______J --______1

I I I I o ,

20

50

10

70

60

0%

(Controls)

20% 30% 40%

Percentage Rebate

50% 60%

SAMP LE' Percent of Rent and Control households active at two years after enrollment,

excluding those with enrollment Incomes over the eligibility limits and those living In their

own homes or in subsidized housing. .

DATA SOURCES: Initial and monthly Household Report Forms.

NOTE. Brackets indicate entries based on 15 or fewer observations.

apercentage change in rent IS defined as the mean of the ratio of the change In rent to the

rent at enrollment.

15
that d~d not move exper~enced about the same change ~n rental expend~tures.

Th~s suggests that any exper~ental effect will man~fest ~tself through

mob~lity.

Elast~c~t~es for movers can be computed from the data ~n Table 2-5. Percent

of Rent movers had a net effect averaged between the s~tes of about 12 percentage po~nts w~th an average rebate of about 40 percent, g~v~ng a pr~ce

e1ast~c~ty of about -0.30. Unconstra~ned households had an average net

~ncrease of about 17 percentage po~nts with payments equal on average to

about 30 percent of the~r ~ncome, xmply~ng an ~ncome elast~clty of about 0.57.

Both est~mates for movers are larger than for the overall sample.

Movers also allocated a much larger proport10n of the rebate to 1ncreased

rental expend1ture than d1d nonmovers, due to the~r larger ~ncrease ~n rent

1 (see Table 2-6). Further, the percentage of the allowance payment allocated

to 1ncreased hous~ng expend1tures by Unconstra1ned movers was 12 percentage

po~nts less than that for percent of Rent movers ~n P~ttsburgh and 5 po~nts

less 1n phoen1x, conf~rmlng the relat~ve effectlveness of rent rebates to

lnceme transfers.

In sum, Percent of Rent households d~d respond to the rent rebate offered

to them by lncreaslng thelr heuSlng expendltures more than they otherWlse

would have. As IDlght be expected, responses were closely tled to movlng.

Percent of Rent and Unconstralned households that dld not move changed the1r

expendltures by approx1.IDately the same amount as Control households. Even

among movers, however, much of the allowance payment went to expendlture on

nonhouslng goods. Percent of Rent payments were, however, more efflc1ent In

channellng money ~nto houslng than were the unconstralned lncome transfers.

lower-lncome households than households enrolled ln the other Percent of Rent

or Control plans. Comparlson of the mean percentage change for these households wlth s~llar Control households, however, shows that there 18 stlll a

marked d~fference between Percent of Rent and Control movers ~n Plttsburgh,

but the dlfference 18 much smaller 1n phoenlx (and more llke other rebate

levels). Households asslgned to the 20 percent plan were hlgher-lncome

households. These households show, ln p1ttsburgh, a very low or nll net

response. Comparlson wlth Control households of the same lncome does not

change th~s f1nd~ng. (See Append= Tables X-7 through X-g.)

1

The net changes by mobll1ty status were computed us~ng Control movers

or nonmovers as approprlate. The flgures In Table 2-6 show that the mean

proportl0n for both percent of Rent movers and nonmovers exceeded the mean

proport~on for s~~lar Unconstrained households. See Append~x Table X-IO for

the proportlons for households receiv~ng each percentage rebate.

16
Table 2-6

PROPORTION OF ALLOWANCE PAYMENT ALLOCATED TO

INCREASED RENTAL EXPENDITURES, BY MOBILITY STATUS

MEAN CHANGE PROPORTION USED

~O:~ORMALa MEAN FOR INCREASED SAMPLE

TREATMENT GROUP PAYMENT EXPENDITURESb SIZE

PITTSBURGH

percent of Rent

households

Movers $15 $56 27% (143)

Nonmovers 2 46 4 (248)

Unconstra~ned

households

Movers 10 64 15 (22)

Nonmovers -1 49 -2 (37)

PHOENIX

percent of Rent

households

Movers 16 68 24 (171)

Nonmovers 1 46 2 (114)

unconstraJ.ned

households

Movers 20 104 19 ( 21)

Norunovers 0 114 0 (16)

SAMPLE: Percent of Rent and Unconstral.ned households actJ.ve at two

years after enrollment, excludJ.ng those wJ.th enrollment lucornes over the

elJ.gJ.bJ.lJ.ty l:unJ.ts and those IJ.vl.ng J.O theJ.r own homes or 1.0 subsJ.dl.zed

housJ.ng.

DATA SOURCES: In~t~al and monthly Household Report Forms, and

payments f~le.

a. Th~s is computed as the mean change for Experimental households

m~nus the mean change for the appropr~ate Control households.

b. Th~s ~s computed as the mean change above normal d~v~ded by the

mean payment. It 18 intended to represent a program average rather than a

household average.

17
The next section presents the main results of the analysis of the Percent of

Rent housing allowance.

2.2 DEMAND FUNcrION ESTIMATES

As discussed in Section 2.1, the rebates offered to Percent of Rent households

can be cans1dered as reductions in the effectl.ve price of housl.ng. Exanunl.ng

response to the experuEntally arranged rebate J.S thus equivalent to eXamJ.nJ.ng

housl.ng response to prl.ce changes. The posswl.ll.ty of obtaining evidence on

the effect of housl.ng prl.ce changes on the housl.ng consumptl.on of indiVl.dual

households was l.ndeed one of the major reasons for l.ncluding Percent of Rent

plans J.n the Demand Experiment. l The eVJ.dence presented J.n SectJ.on 2.1 was

inadequate for thJ.s determJ.natJ.on as tabulatJ.ons do not control for addJ.tional

factors that may have affected housing expendJ.tures.

'Ihe problem of relatl.ng consumptl.on response to prices and l.ncome is not new.

Econonusts have developed a xl.gorous fra.I09.work for analyzing such responses-­

consumer demand theory. The behavioral relatJ.onshJ.p between housJ.ng consumptl.on on the one hand and prl.ces and l.ncome on the other is termed the demand

functJ.on for housl.ng. The demand function 18 one way to obtain a smoothed

response surface. Along with experJ.mental variatJ.ons J.o prl.ce and l.ncome,

nonexperl.rrental varl.ations l.n household J.ncome among the Exper1rrental and Control households enable es tJ.mat~on of such a housJ.ng demand function. 2 AnalyS1S of these data in terms of demand functions is useful l.n two ways. First,

the theory of demand both provides some empJ.r~cal hypotheses about the expected sJ.gn of estimated coefficients and allows readY apphcation of the est~mated demand functions to the estJ.matJ.on of responses to a variety of possJ.ble

programs. Second, previous estimates of demand funct~ons both help to J.ndJ.­

cate the probable magn~tude of effects and provide a better understanding

about possJ.ble estJ.mation dJ.ffJ.culties and the confJ.dence WJ.th which the

results may be used.

1

Sect1.on 3.3 d1.scusses some of the prev1.ous research on th~ effects

of prl.ce (and l.ncome) changes on housing consumptl.on.

2EXper1.mental var1.ation l.n income was prov1.ded by the Unconstrained

allowance plan. Households l.n thl.s plan recel.ved an l.ncome-based payment,

available s~ply as addl.tJ.on to income wl.th no constral.nts placed on its

expend1.ture. The sample Sl.ze for th1.s plan 1S small, however, so that est1­

mates l.n th1S report are based pr~arl.ly on nonexperimental differences J.n

income.

18
The demand funct~on ~tself can be used to prov~de ~nformat~on to model a

w~de range of possl-ble alternative houslng pollcles. Any demand functl0n

permlts est~atl0n of changes 1n houslng consurnptlon resultlng from glven

changes 10 houslng prlces or in lucame. For example, knowJ..ng how houslng

demand responds to pr~ce changes would be valuable for evaluat~ng alternatlve rent-condl.tioned houslng allowance payment formulas.. SllTlJ.larly, knowledge of how houslng demand responds to lucame changes would be valuable 1n

evaluatlng the houslng response to any lucame-conditioned transfer program.

Whlle econornJ..c theory provldes guldance on the varlables expected to lnfluence hous~ng demand, as well as on the~r expected d~rection of ~nfluence,

only general constralnts are placed on the functlonal form of the relatlonShlp. Chooslng a functl0nal form 1.8 sJ.mply one way of smooth1.ng the response

funct~on presented ~n Figure 2-1. Two forms are exam~ned ~n Chapters 3 and 4

of th~s report--a linear form (a l~near expeniliture funct~on) and a loga,.

r~thmic form (called log-linear). Neither ~s superJ.or 1n all respects,

each has attractive features I and both yield sJ.nu.lar results. For conven­

~ence, the log-linear form estimated for households that moved during the

exper~ment ~s focused on for the rest of th~s chapter. Parallehng the

tabulatJ.ons of the previous section, thJ.s form can be used to demonstrate

the effect of the percentage rebate on rental expenilitures, on the proportl.on of the payIlEnt devoted to increased rent, and on the change in rent

burden.

One way of characterJ.zJ.ng demand functJ.ons 18 by the elastJ.cJ.tJ.es of demand

--the percentage change 1n expendJ.tures resultJ.ng from a gJ.ven percentage

change 1n prJ.ces or 1U lucame. For the log-lJ.near form, these elastJ.cJ.tJ.es

are constant:

(1)

where

In (R) a + Sl In(Y) + S2 In(l-a)

R the gross rental expend~tures

Y = average monthly lucame

a = the percentage rebate offered

a = the estLmated constant term, and

Sl and S2 = the 1ncome and price elast1cit1es of demand,

respect1vely.

19
The average elast~c~t~es for the low-~ncome renters ~n the Demand Exper1ment

populat1on, estLmated for households that moved dur1ng the experLment, are

approxLmately -0.22 for pr1ce and 0.36 for 1ncome--fal11ng between the crude

est1ffiates presented ~n Sectl0n 2.1 for the samples of all households and

1 movers. Thus, for households that move, a 10 percent decrease ~n prlce

w~ll lead to, on average, a 2.2 percent lncrease 10 houslng expendlture

wh11e a 10 percent ~ncrease 1n ~ncame would lead to, on average, a 3.6

percent 1ncrease ~n expend1tures. The average rebate of 40 percent would

therefore lead to an lncrease of 9 percent above normal, controillng for

lncome changes.

Interestlngly, the average est1mated pr1ce and 1ncome elastic1ties for all

households ~n the two sites are almost 1dent~cal to those estJ.rnated for households that moved. (They are somewhat lower 1n P1ttsburgh and h1gher 1n Phoen1x

wJ.th almost no dlfference 1n the two-site average.) '!'hlS 15 true despite the

fact that Percent of Rent recipients that fud not move showed little or no

lncrease in expenditures beyond that found for nonmoVl.ng Control households.

It appears that the Percent of Rent rebates 1nduced some households to move

to more expensive uruts sooner than they otberwlse would have. Th1S effect

would be expected to m=n1sh over hme as normal mobi11ty rates catch up to

the experlmentally generated increase 1n mob1lity. At the sane ture, as

m::>re households move, more would be expected to J.ncrease tbeJ.r expenditures

in response to the rebate. Thus, although 1nmvidual households adjust to

the rebates gradually, as they move, the total aggregate effect of the rebate

on the demand for housJ.ng may not J.ncrease substantJ.ally over tJ.me, at least

not after two years.

The log-hnear form can be used to show the effect of the rebate on the

proport10n of the payment devoted to rent as a function of the percentage

1

These est~ates are from a log-llnear demand functl0n for movers,

pool~ng the two s1tes wlth a slte-specJ.flc lntercept, uSlng average J.ncome.

Chapter 4 d1scusses the lmpllcatlons of demographJ.c and lncome differences

for the elastlc1tles. The elastlclt1es appear to vary wJ.th these SOC10­

economlC characterlstlcs. Furthermore, they are estlmated wlth stochastlc

error. See Chapter 4 for confldence lntervals and Chapter 6 for a dlSCUS810n of posslble sources of blas.

20
1 rebate:

(2) LlRS=

112 (I-a) -1

a(1_a)1l2

Equat~on (2) ~nd~cates that, g~ven the est~ated price elast~c~ty of -0.22

and the average rebate of 40 percent, 27 percent of the allowance payment

w~ll be devoted to ~ncreased rent (cf. Table 2-6). The proportion of the

payment devoted to ~ncreased rent ~n Equation (2) ~ncreases w~th the rebate,

though gradually. Using the same pr~ce elasticity of -0.22, 24 pe~cent of

the payment w~ll be allocated to increased expenmtures under a 20 percent

rebate and 30 percent under a 60 percent rebate.

of the Percent of

2 be expressed as

The same form can be used to demonstrate the effect

plans on rent burden. The change ~n rent burden can

Rent

(3)

1

From Equat10n (1), lnltial expendlture 18

R = e"'yill. o

The rebate changes des~red rent to

(n)

S~nce the payment S ~s a fract~on of Rl (S = aRl) ,

as a fract~on of S ~f the household were to adJust

level ~pl~ed by the demand funct~on ~s thus

R R (1_a)1l2R -R 1- 0 0 0

-S- = ---;;Il"--'::­

a(l-a) 2RO

wh~ch ~s Equat~on (2).

2 From Equat~on (1):

the change In rent, lI.R,

~ts expend~ture to the

(n)

R

O = e"'ylll and

R = e"'ylll(1_a)1l2, 1

as In footnote 2 on the prevJ.ous page. From (~) and (~~),

(~~~)

(I-a) R

l RO [(I-a) e"'ylll (I-a) Ilz _ e"'ylll], y - y= y

whwh reduces to EquatJ.on (3) .

21
For the mean ~ncome of approx~ately $420 per month and for the average

rebate of 40 percent, th~s ~pl~es a change ~n mean rent burden of 11 percentage po~nts, from 35 percent to 24 percent. As the percentage rebate ~ncreases,

the ~mplied decrease ~n rent burden w~ll be larger as well.

F~nally, the relatlve Lmpact on rental expendltures of unrestricted lucame

transfers and rent rebates of equlvalent magnltude may be compared uSlng the

est~ated numbers. A stralghtforward comparlS0n 18 posslble because unrestrlcted lucerne transfers operate through lucarne elasticltles of demand, and

rent rebates operate through prlce elastlcltles of demand.

A prlce SubSldy should always produce a greater lncrease 1n houslng expendltures than an equlvalent lucerne SubSldy. Wlth an equlvalent lucame SubSldy,

the household can purchase the same amounts of houSlng and other goods as It

purchases under the prJ..ce subsJ..dy. However, under the J..ncorne subsJ..dy lt

stlll faces the orlglnal, hlgher prJ..ce for houslng and so may be expected to

buy less houslng than under the prlce SUbSldy, which offers the lncentJ..ve of

1 lower houslng prlces.

The extent of the d~fference ~n hous~ng expend~tures under the two types

of subsidy depends on the income and pr~ce elast~c~t~es and the ~n~tial

rent-J..ncorne ratJ..o. The relatJ..ve efflclency of prlce subsldles (E, the

ratlo of the SubSldy needed under a price SUbSldy, S , to that needed

p

under an lncorne subsJ..dy, S ) 10 translatlng an allowance payment lnto a

y 2

glven addltl0nal expendlture on housing 1S:

(4) E = :~ = a (:0) [l_a)-S2(1-S~)_(1_a)-S2J-l

The efflclency 1S generally larger (for a glven lnltlal rent-income rat10),

as the price elastlclty lS larger ln absolute value, and 1S larger as the

lncorne elastlc1ty 1S smaller.

Table 2-7 presents the efflclency of a price SubSldy relatlve to an lncorne

subSldy for various rent-lucorne ratl0S and price dlSCQUnts based on a 10gIThe household will be able to purchase more nonhous~ng goods for

each u=t of housing g~ven up under the h~gher housing pnces preva~ling

under the income subsidY than undsr the rent subs~dY, imply~ng that the

quantity of hous~ng consumed will be less.

2see Appendix IV for derivation of th~s formula.

22
l~near demand funct~on with a prlce elastlclty of -0.22 and an lncame elastlClty of 0.36, assumlng households are lnltlally consurnlng an amount of

housing determlned by the demand functl0n using lnltlal prices. For an

~n~t~al (med~an) rent-~ncome rat~o of 0.30, the payment needed under a

pr~ce d~scount plan would range from less than one-half (w~th a 20 percent

rebate) to less than one-th~rd (w~th a 60 percent rebate) that needed under

an unrestrlcted lucame transfer to induce the same houslng change. For

example, for a household with ~ncome of $500, spend~ng 30 percent of ~ts

~ncome on rent ($148), a pr~ce subsidy of 40 percent would lead to an

~ncrease ~n rent to $166 and result in a subs~dy payment of $66. To ~nduce

the same change 1.n eqUl.llbrl.UIn rent, an l.ucame subsl.dy would have to be

$183. 1

Table 2-7

EFFICIENCY OF PRICE AND INCOME SUBSIDya

PRICE DISCOUNT INITIAL RENT-INCOME RATIO

(percentage Rebate) 0.20 0.30 0.40

20 percent 0.29 0.43 0.57

40 percent 0.24 0.37 0.49

60 percent 0.20 0.29 0.39

NOTES: Assumpt~ons: log-l~near demand funct~on

pr~ce elast~c~ty = -0.22

income elast~city = 0.36

a. Eff~c~ency ~s defined as the rat~o of s~ze of pr~ce subs~dy

needed to Sl.ze of l.ucarne sUbsl.dy needed for a gl.ven change 10 rental

expend~ture. See Append~x IV for der~vat~on of the eff~c~ency formula.

1 . Thl.s effl.cl.ency 1.n convertl.ng subsl.dy payments l.nte housing changes

~s obta~ned at the cost of a reduced value of the payment to the rec~p~ent.

JUst as rent rebates are always theoretl.cally more effl.cl.ent than direct

l.ucerne transfers 1D achl.evl.ng a gl.ven change 1.0 rent, an 1ncome transfer

1S theoret1cally more eff1c1ent than rent rebates at mak1ng people

"better off" (1n the1r own tenns). Part of the rent rebate 18 spent 1nduc~ng households to buy extra hous~ng.

23
It is worth noting that there ~s evidence (reported ~n Chapter 5) that a pr~ce

d~scount (such as that prov~ded by a Percent of Rent subsidy) may lead to

shopping ~neffic~ency on the part of the household. In other words, 51.nCe

households are not pay~ng the market price for additional amounts of hous~ng

serV1.ces obtained, they may well be w1.111ng to accept less than the market

average of hous1.ng services per dollar of l.ncreased gross expenditure. Thl.S

reduces 1 but does not entl.rely ell.Inl..nate the relatively greater effl.cacy of

prl.ce dJ.scaunts over l.ncame supplements l.n promoting changes J.n recl.pient

housing.

2.3 APPLICATIONS

The lack of any housl.ng requJ.rement or l.ucame conditJ.on l.n the s1ffiple rent

rebate plans tested J.n the Demand ExperLment make them unlJ.kely candl-dates

for an ongolng program. Though very slmple to adrnl.nl.ster and analyze, they

suffer from l.nequJ.ty because hl.gher-J.ncome households would typl.cally have

hl.gher rents and therefore larger payments. This drawback could be overcome

by a more complex des1gn, such as allow1ng the percentage rebate to depend

on 1ncome. Est~ates about household response to the s~ple form of rent

rebates tested 1n the Demand Exper1ment can prov1de a bas1s for est~at1ng

response to alternatlve forms of rent rebates. They can also be used to

evaluate hous1ng response to proposed (or ex1st1ng) lncome malntenance

schemes, as well as eXlstlng asslstance programs W1th rent SubS1dy features.

The rest of th~s sect~on ~llustrates the way ~n wh~ch the est~ated demand

funct~on can be appl~ed to these problems.

Income-condlt10ned Percent of Rent plans

A houslng aSS15tance plan based on percentage rent rebates would probably

have a percentage rebate which 15 related to 1ncome 1n order to reduce 1nequlty. An "lncome-cond1t10ned percent of rent" plan lS one such prototype.

In such a plan, 1nequlty 18 reduced by decreaslng the percentage of rent

Subsldlzed Wlth lncome. The SubS1dy formula would be

24
(5) s a(Y) oR

where

s the subs~dy payment

aCyl the percentage of rent Subs1dized, a

funct10n of 1ncome Y, and

R = rent.

Var10Us forms of the funct10n a(Y) can be cons1dered, rang1ng from an

adm1n1strat1vely sLmple schedule, such as that used 1n the federal personal

1nCorne tax system:

(6) aCyl

a for Y < Y < Y

n n-1 - n

o forY <Y

n

to an analyt~cally s=ple formula, such as Carlton and Ferre~ra (1977),

termed var1able percent of rent,

(7) s {

[l - :£ ] R Y*

o

for Y < Y*

for Y > yo.

Analys~s of the potent~al hous~g expend~ture ~mpact of an income-cond~tioned

percent of rent plan w111 depend on numerous factors 1nclud1ng the formula's

1ncorne levels, household 1ncome, and rent. For 1l1ustrat10n, the effects of

The focus of the discuss10n 1S on the effect of each program

2

on households' rent burdens and expendJ.tures 0

several alternat1ve plans are d1scussed below for hypothet1cal four-person

1 households 0

Var~able percent of rent. For ~llustrat~on, the parameter y* in Equation (7)

--the income level at wh~ch the subs~dy falls to zero--is set to $600 per

month, approx~mately the income el~gibility ll=t for fa=l~es of s~ze 3 or 4

1

The effects of possible different~al partic~pat~on rates ~n these

plans is ignored.

2

In add1t1on to expend1ture changes, when payments depend on J.ncorne,

households may be ~nduced to change the~r incomes, if possilile. This implication 1S 19nored here.

25
1 enrolled ~n Percent of Rent plans. Table 2-8

for households of th~s s~ze for varl0US ~ncome

shows the effects on hous~ng

2 levels.

Brltlsh rent allowance. Alternatlvely, lucame may be used to adjust the payment level rather than the rebate as ~n the case of a formula actually in use

. 3 1n Great Brltaln :

forY>Y*

for Y < y*

The Brltlsh allowance for:mula

.25 (y*-y)

{

.6R +

.6R +

S

.17 (y*-y)

4

subJect to S Smax'

where y* 15 called the "needsll allowance. 5

(8)

prov~des both a price and an ~ncome subs~dy (see Ricketts, 1976). Pr~ce

decl~nes by 60 percent. Us~ng an est~mate of -0.22 for pr~ce elast~c~ty,

6 thlS decllne leads to a 22.3 percent lncrease 1n expendltures. The addltl0n to Lncome depends on lncame level. For example, for a household wlth

lncerne of $200 a month and a needs allowance of $250 , the percentage l.ncrease

7 J.n housing expendJ.tures due to the lncame effect J.5 2.2 percent.. In contrast, for a household w~th ~ncome of $300 a month and the same needs

1

The actual enrollment lucerne IJ.nuts were $6,750 per year 10 PJ.ttsburgh and $8,650 per year in Phoenix for a household of s~ze 3 or 4.

2

WJ.de varJ.atJ.on J.n outcomes are possli>le because ~n~hal household

s~tuat~ons d~ffer. The mean 1.n~t1.al rent and rent burden are used to provide

a benchma:rk. Use of the estimated demand equations to prov~de ~mhal rent

does not change the results.

3

See R~cketts (1976) or Trutko, Hetzel, and Yates (1978).

4

The roaX1.murn payment, Smax' 1.S ~8 per week l.n London and (6.50 per

week elsewhere (R~cketts, 1976, p. 237). These can be adJusted for ~nflation. This max1.~um effect1.vely l~m1.ts the range of rents subs1.d1.zed.

5

The needs allowance schedule ~s:

s1.ngle person ~17. 75 per week

marr1.ed couple .(24.25 per week

each dependent

ch~ld .! 3.55 per week

(see R~cketts, 1976, p. 244).

6The Percentage change ~n rent = [(l-a)S2_1] = [(0.4)-0.22_1 ] = 0.223.

7

The subs~dy leads to an ~ncrease ~n ~ncome of 0.25 x ($250=200) =

$12.50 or 6.3 percent. Us~ng the est~ated ~ncome elast~c~ty of demand of

0.36, [(1 + lIy!y)Sl-lJ = [(1.063) '36_1] = 0.022.

26
--------------~-- - ~- -

,

Table 2-8

PREDICTED EFFECT OF A

VARIABLE PERCENT OF RENT FORMULAa

HOUSEHOLD

INCOME

INITIAL RENT

BURDENb

INITIAL

RENTc

SUBSIDY

RATE

INITIAL

PAYMENT

CHANGE IN RENT

percentaged Amount

FINAL

PAYMENT

FINAL RENT

BURDENe

$200

300

400

500

600

0.50

0.38

0.32

0.28

0.25

$100

114

128

140

150

0.667

0.500

0.333

0.167

0.000

$67

57

43

23

o

27.3%

16.5

9.3

4.1

0.0

$27

19

12

6

o

$85

67

47

24

o

0.21

0.22

0.23 ,

0.24

0.25

a.

b.

payment =

From Append~x

Incomel

y* j

Table X-ll.

x rent, where Y* ~s set equal to $600 per month for a fam~ly of four.

c. Income times In~t~a1 Rent Burden.

d. Percentage change ~n rent = [(1-a)~2-1l where ~2 ~s the price e1ast~city (-0,.22) and "a" ~s the subs~dy

rate.

e. F~na1 rent burden ~s def~ned as init~a1 rent plus the change ~n rent m~nus the f~na1 payment d~v~ded by

J.ncome.
1 allowance, the ~ncorne effect ~s negat~ve, -1.0 percent. The ~ncome effect

w~ll counteract the pr~ce effect for any household w~th 1ncome above the

needs allowance. F1nally, the max1mum SubSldy limlts the range of rents

Subsldlzed. Thus for rents above a certalo level, the formula reduces to

2

a slffiple lucame transfer.

Table 2-9 ~llustrates the effect of the Br~t~sh rent allowance on var~ous

prototyp~cal households.

Rent-condltloned Houslng Gap. Another posslble houslng aSslstance plan that

lncludes elements of prlce dlSCOuntS 15 a "rent-condltJ..oned Housl-og Gap" form,

10 WhlCh [' ",-"" for R < C* and Y < C*/b C*

(9) s = C*-bY for R > C* and Y < C*/b

0 for Y> C*/b

where C* and b are parameters of the program (see Carlton and Ferrelra, 1977).

For rents above C* I th15 form behaves as a Houslng Gap formula or unrestrlcted

cash grant, whl.le for rents below C*, it behaves l~ke a Percent of Rent formula.

Table 2-10 ~llustrates the pred~cted effects of a program with C* set at $130

and the contr~but~on rate set at 0.25. Households w~th ~ncomes $400 or below

are rece~v~ng Percent of Rent subs~dies at a rate (C*_by)/c*.3 The household w~th ~ncome of $400, however, ~s spend~ng $128 on rent already, therefore, ~t w~ll rece~ve a Percent of Rent subs~dy only for ~ts next $2 of

expend~ture on hous~ng. After that ~t w~11 rece~ve only a Hous~ng Gap type

of subsl.dy, w~th the amount unaffected by l.ts rent.. Households w~th ~ncomes

up to $520 (=C*/b) w~ll also rece~ve Hous~ng Gap subs~d~es, ~ncreas~ng the~r

rent 10 response to thlS change ~n ~ncome..

Income-cond1t10ned Percent of Rent. Alternat~vely, the demand funct~on parameters can be used to deslgn a rent allowance program of the type presented

1n Equatlon (6). As an lllustrat10n, assume that the government's pollCy

d~zed.

$8.50

1

The subs~dy leads to a decrease ~n8~ncome of 0.17 x ($300-250) =

or 2.8 percent of ~ncome, [(1 + ~Y/Y) 1-1] = [0.972).36_1 ] = -0.010.

2

In thlS case the budget 11.ne 1S klnked at the rnax~rnum rent subsl.-

3

For each addlt~onal dollar spent on rent, R, the 1.ncrease 10 payment

(dS/dR) ~s (C*-bY)/C*.

28
a.

Table 2-9

pREDICTED EFFECT OF

BRITISH RENT ALLOWANCE FORMULAa

HOUSEHOLD INITIAL RENT INITIAL INITIALd CHANGE IN RENTd FINAL FINAL RENT

INCOME BURDENb RENTc pAYMENT percentagee Amount PAYMENTd BURDENd,f

$200 0.50 $100 $60 9.9% $10 $60 0.25

(73) (25.0) (25) (88) (0.19)

300 0.38 114 60 6.8 8 60 0.21

(60) (21.1) (24) (74) (0.21)

400 0.32 128 51 11.3 15 60 0.21

(51) (19.5) (25) (66) (0.22)

'" 500 0.28 140 42 18.5 26 57 0.22 <!>

600 0.25 150 31 17.8 27 47 0.22

t {

0.6 Rent + 0.25 (Y* - Income) for Income yo, or

paymen = 0.6 Rent + 0.17 (Y* - Income) for Income> yo,

where yo, the "needs allowance" for a fam~ly of four, ~s set equal to $250 per month. The payment ~s

subject to a maximum of $60.

b. From Append~x Table X-II.

c.

d.

e.

f.

Income t~mes In~t~al Rent Burden.

F~gures ~n parentheses show the effect ~f th~re were no restr1ction on the maximum payment.

S2 6.Y Sj Percentage change ~n rent = (0.4) (1 + j() where S2 ~s the price elast~city (-0.22), Sj is the

~ncome elastic~ty (0.36), 0.4 ~s one m~nus the subs~dy rate of 0.6, and 6.Y ~s the ~ncome term in

the payment formula (e.g., 0.25 (Y* - ~ncome) or 0.17 (y* - ~ncome». The actual increase ~s l~m~ted

by the max~mum payment.

F~nal rent burden ~s def~ned as ~nit~al rent plus the change ~n rent m~nus the f~nal payment d~v~ded by

1ncome.
Table 2-10

PREDICTED EFFECT OF A

RENT-CONDITIONED HOUSING GAP FORMULAa

HOUSEHOLD

INCOME

INITIAL RENT

BURDENb

INITIAL

RENTc

SUBSIDY

RATEd

INITIAL

PAYMENT

CHANGE IN RENT

percentagee Amount

FINAL

PAYMENT

FINAL RENT

BURDENf

$200

300

400

500

600

0.50

0.38

0.32

0.28

0.25

$100

114

128

140

150

0.62

0.42

0.23

0.00

0.00

$62

48

30

5

o

23.7%

12.7

2.6

0.4

0.0

$24

15

3

1

o

$77

54

30

5

o

0.24

0.25

0.25

0.27

0.25

Y < C*/b,

Y < C*/b, or

a.

{

R~~t (C* - b. Income) for R 2. C* and

Payment C

o

* - b.Income for R > C* and

for Y 2:. C*/b,

where C*, the cost of standard hous~ng, ~s set equal to $130 for ~llustrat~on, and b, the contribut~on

rate, ~s set equal to 0.25.

b. From Appendix Table X-ll.

c. Income t1mes Initial Rent Burden.

d. Rate at wh~ch payment ~ncreases for each add~t~onal dollar spent on rent, up to C* ($130).

e. If the change ~n rent ~s less than C* minus the ~nitial rent, this ~s a pure pr~ce effect. If not, there

~s also (or ~nstead) an ~ncome effect.

f. Final rent burden ~s def~ned as ~n~t~al rent plus the change in rent m~nus the final payment d~v~ded by

income.
--------------------------

target ~s a household rent burden of 25 percent. A sJ.IDple payment formula

Wh1Ch var1.es by 1ncome, a(Y) 1 can be der1ved from the formula for rent

burden:

(10)

where

Flnal rent burden

R = in~t~al rent o

LlR change in rent ~nduced by the payment

S payment, and

Y = l.ucerne.

The payment, S, rece~ved by the household ~s

(11) S = a (y) • [RO + LlR].

The l.nduced change 1.0 rent can be computed from

(12)

where S2 ~s the pr~ce elast~c~ty.

Us~ng Equat~ons (10) Uhrough (12),

(13) Fl.nal rent burden = (I-a) (S2+!)Ro

Y

Gl.ven the pol~cy target, the schedule aryl can be solved ~n terms of the

elast~c~ty (S2) and the ~n~t~al burden (Ro/Y) :

1 prl.ce rent

(14) aryl [ J

l/(S2+l)

= 1 _ .25Y

RO

lAlternatively aryl could be solved ~n terms of Y by us~ng the

estimated demand funct~on to express RO as a funct~on of the pr~ce of

housl.ng and l.ucerne.

31
------------------------------ - - - -

Table 2-11 presents the Solutlons to thlS equatlon for varlOUS income

classes. The SubSldy rate declines to zero as lucame rises because the

rent burden decllnes to the policy target, 0.25. It 18 also worth notlng

that the derlved rate 15 not very dlfferent for varl0US values of the prlce

elastlclty, as computed at the extremes of the 95 percent confldence luterval

for the estimated elast~c~ty.

Table 2-11

INCOME-CONDITIONED PERCENTAGE SUBSIDIES

NEEDED TO REDUCE RENT BURDEN TO 0.25

AS A FUNCTION OF INITIAL RENT BURDEN

MONTHLY

INCOME

$83.3 - 150

151 - 250

251 - 350

351 - 450

451 - 550

551 - 650

651 +

INITIAL PERCENTAGE 0E

RENT BURDENa RENT SUBSIDY

0.69 0.73

0.50 0.59

0.38 0.42

0.32 0.27

0.28 0.14

0.25 0.00

<0.25 none

"CONFIDENCE

INTERVAL" C

(0.69, 0.77)

(0.55, 0.63)

(0.38, 0.45)

(0.25, 0.30)

(0.12, 0.15)

a. From Append~x Table X-II.

b. Computed us~ng Equat~on (14) ~n the text, us~ng a pr~ce e1ast~c~ty of -0.22.

c. Computed USlng bounds of the 95 percent confidence ~nterva1 for

the est~mated pr~ce e1ast~c~ty: (-0.13, -0.30).

The Food Stamp Program

Appllcatlons of the est1ffiated demand parameters are not l~lted to analyses

of houslng allowance strategles, as

Most federal lucame-tested programs

the followlng example demonstrates.

1

mandate speclflc deductlons from 1ncome.

These deductJ.ons can be classJ.fJ.ed as e1ther work-related expenses or as

expenses for "merJ.t goodsII (goods or serv1.ces Wh1Ch those providJ.ng support

1

See Hausman (1977).

32
deem worth prov1d1ng to the rec1p1ent). The former category 1ncludes deduct~ons for ltems such as Chl1d care, commutlng costs, and UOlon dues wh21e

the latter 2ncludes deductl0ns for educatl0nal expenses, medlcal care, and

houslng. Exclusl0n of houslng expenses from lucame 18 similar to a rent

rebate 1n that the amount of the transfer 1S related to actual hous1ng

expend1tures. Th1s p01nt 1S 111ustrated here by reference to the Food

1

stamp program.

Until October 1978, the Food Stamp program based benefits on lucerne net of

numerous deductlons. After subtractlng from lucame itemlzed deductlons for

Chl1d and adult care, work-related expenses lncludlng taxes, medlcal care,

dlsaster and casualty losses, and educatlonal expenses, any shelter expendltures 10 excess of 30 percent of the remainl.ng net lucame are also deducted

2 3 from l.ncome.' The resultl.ng net lucerne deterrnl.nes the IIpurchase requl.rement" for food stamps and thus the amount of the subsidy to be rece1ved by

a household.

The effect of such a program feature ~s to subs~d~ze ~ncreases ~n housing

expend~tures at a rate detenn~ned by the "benef~t reduct~on ratio" (the

rate at wh1ch benef1ts fall per dollar of 1ncreased household 1ncome)

lffipl~c~t ~n the Food stamp program. The benef~t reduct~on ratlo ~s approx~-

4 mately 30 percent. Thus for every $1 of hous1ng expense 1n excess of 30

percent of net lncame, adJusted ~ncome lS reduced by $1, and Food stamp

beneflts are lncreased by $0.30. A fract~on of increased shelter expendltures ~s In effect g~ven as a rent rebate to partlclpat~ng households,

thereby creatlng an lncent~ve to consume more houSlng.

1other government programs excludlng part of rent from ~ncome are

A1d to Fam111es w1th Dependent Ch11dren (exclus1on var1es by sta~e) and the

Nat10nal School Lunch and Other Ch11d Nutr1tion Programs (see Hausman, 1977).

A further example might be the Federal Income Tax, wh1ch prov1des deduct10ns

for mortgage ~nterest and property taxes.

2

Note also that Slnce expenses are deducted from gross lncome before

shelter expenses, the threshold at WhlCh net lncome lS further reduced due

to shelter expendltures 1S 11kely to be a much smaller proportlon of gross

lncome than 30 percent. If, for example, other deductlons average 20 percent of gross lncame, the rent-to-gross ~ncome "threshold" would be 24 percent of gross lllcorne.

3

The Food Stamp Act of 1977 reVlses thlS procedure somewhat, as

dlscussed later In thlS sectl0n.

4

The benef1t reduct10n rat10 1S approX1mately 20 percent for s1ngleperson households. Est1mated effects do not take th1S fufference 1nto account.

33
Th~s program feature ~s l~kely to have a maJor impact on hous~ng expend~­

tures, g~ven that a s~gn~f~cant fract~on of the populat~on below the poverty

l~ne rece~ves Food stamps and have rent-to-lncome rat10s 10 excess of 30

percent. Over t~e, lncreases 10 cost of houslng would tend to be partlally

and automatically subs~dized by increased Food stamp benef~ts. On the other

hand, elllUlnation of the deductlons for "excesslvell houslng expenditures

would theoretlcally reduce the demand for houslng, lncrease households' rent

burden, and ellmlnate what amounts at present to an automatlc adJustment to

1 houslng cost changes.

Th~s hous~ng subs~dy component ~n the Food Stamp program ~s substant~al.

According to the Food and Nutr~t~on Serv~ce of the U.S. Department of

2 Agr~culture (USDA), ~n September 1976, 5.03 m~ll~on households were Food

Stamp rec~pients. A large fract~on of the Food Stamp households (74.3 percent) recelved a shelter deductl0n; the average shelter deductlon c!almed

was $73 a month (g~v~ng an average over all households ~n the program of

$54). Sluce the beneflt reductJ..on rat1.0 was approxJ..Inately 0.3, the add1.­

tlonal governmental expend1.ture due to the shelter deduct1.on can be computed:

(5.03 m~ll~on) x ($54) x (0.3) $81.5 m~ll~on per month or

$977.8 m~ll~on per year.

In compar1.son, current Department of Hous~ng and Urban Development (HUD)

total annual contr~but~on comm~tments are less than tw~ce th~s f~gure ($1.85

billlOn).3

1

It 1.S 1.nterest~ng to note that the IIhous~ng subs~dy" that occurs

through Food Stamps ~s l~kely to benef~t nonpart~c~pants ~n federally subs1.d1.zed hous1.ng more than part~c1.pants, S1-nce tenant contribut1.ons 1.n federal

programs outs~de of Sect~on 236 (w~thout rent supplements) almost always

result 1n rent to l.ncome ratlos less than 30 percent--the p01.nt at wh1.ch the

Food stamp lIhouS1.ng subsJ.dyll begJ.ns. Thus wh1-le publJ.c hous1ng partJ.cJ.pants

get more hous~ng sUbs~dy, otherw~se comparable poor households w~ll tend to

get greater Food Stamp benef~ts.

2

The data are from U.S. Department of Agr~culture (1977).

3

U.S. Department of Hous~ng and Urban Development (1977) as of

September 30, 1976. Sect~on 23 housing assistance comm~tments are $23

m1ll10n, SectJ.on 8 commJ.tments are $488.5 mJ.llJ.on, and leased housJ.ng commJ.tments are $269.5 mJ.llJ.on. The remainder are contr1-butl..ons to publ.1.c hous1ng

projects. Of course, HDO has other commJ.tments to hous1ng programs 1n terms

of loans and loan guarantees ($5.28 b~ll~on).

34
Estimat~ng the xmpact of the Food stamp program on hous~ng ~s, ~n theory,

a fa~rly complex problem that would require information on the mean demand

function for food, the cross-pr~ce elast~c~ty of hous~ng and food, and the

d1str1butlon of food and hous1ng consumpt1on patterns, as well as the estl.-

1 mated mean demand funct~on for hous~ng. In fact, the xmpact of Food Stamps

on hous~ng can be fairly well approx~rnated us~ng the estimated demand funct10n for hous1ng alone.

As ~nd~cated above, the Food Stamp program allows rec~p~ents to purchase a

certa~n amount of food--the coupon allotment (determined by household s~ze)-­

at a reduced pr~ce--the purchase requ~rement (determ~ned by net ~ncome).

The maXl.mmn Food Stamp bonus, B , 18 gl.ven by m

(15)

where

B

m

A - cr [y - S]

A the coupon allotment (a funct~on of household sae)

cr = the benef~t reduct~on rate (approximately

0.3)

Y = net 1ncome before the shelter deduct1on, and

S the shelter deduct~on.

The shelter deduct~on ~s the amount spent on hous~ng above 30 percent of net

1ncome:

(16)

where

S = {: - 0.3Y

R = rent.

for R > .3Y

forR<.3Y

Thus Equat~on (15) can be written

(17)

B = {A - cr (1. 3Y-R)

m A _ crY

for R > .3Y

for R < .3Y.

1

See Append1X V for a more deta~led d~scuss~on.

35
Not~ce that the max~mum bonus value does not depend on the amount of food

purchased. If the household purchases more food than ~ts coupon allotment,

the ~pact on hous~ng can be est~ated ~n terms of the effect of the additl0nal lucame from the Food Stamp bonus and the reduced prlce of houslng

~pl~ed by the shelter deduct~on.

B

where

(18)

Households that want to purchase less food than thelr coupon allotment obtaln

PFF they purchase some fractlon, , A

(Y-S). Thus, the~r benef~t is:

a propo~tl0nal reductlon 1n cost--that 15,

of thelr allotment, A, at the cost/(P~F) a

(P()Bm

B the Food Stamp bonus

F the amount of food purchased, and

PF the pr~ce of food.

For these households, the prlce of food 15 essentlally reduced by the factor

(B /A). In th~s case, then, the ~mpact of the Food Stamp program on hous~ng m

depends on the response of houslng consumptl0n to changes 10 lucame and the

pr~ces of both hous~ng and food.

The rest of thlS seetlon conslders the ~pact of the Food stamp program on

the hous~ng of rec~p~ents that spend at least their full coupon allotment

percent of

1

category.

for food. Fortunately, as d~scussed in Append~x V, at least 61

Food Stamp rec~p1ents, and qu~te poss~bly more, fall ~nto this

The analys~s, carr~ed out on the bas~s of est1mated demand for hous1ng alone,

would appear to cover a maJor part of the Food Stamp program.

The ~pact of the Food Stamp program on hous~ng can be decomposed ~nto the

~ncome effect of the subs~dy and the add~t~onal hous~ng pr~ce effect of the

shelter deduct~on. Data publ~shed by the Department of Agriculture for

September 1976 g~ve an average bonus value of $71 and an average shelter

deduct~on of $54. Thus, $16 (30 percent of $54) of the $71 may be cons~dered a hous~ng pr~ce dlscount. The rema1n1ng amount, $55, is the lncome

transfer component of the Food Stamp SubSldy. The average household's net

~ncome was $224, 1mplYlng a percentage ~ncrease 1n income due to the lncome

transfer component of about 24 percent (55/224).

1

See Appen~x Table V-I. MacDonald (1977, p. 54) estimates that

roughly two-tmrds of all recip~ent households are effect~vely unconstr~ned

by the program.

36
8.1 percent.

Us~ng the est~mated ~ncome elast~c~ty of 0.36, the percentage change in

expend~tures for households that adJust the~r hous~ng due to the ~ncome

effect can be approx1mated by

(19) [hRRln:om{l + r~l = (1.24)~:

The pr~ce effect can be computed ~n a slltlJ.lar way. For households el~gl.ble

for a shelter deduct~on the pr~ce of hous~ng ~s reduced by 30 percent (a).

Us~ng the est~mated pr~ce elast~c~ty of demand of -0.22, the percentage

change ~n expend~tures due to the pr~ce effect for those households that

adJust to the change ~n relat~ve prJ.ces 1S

(20) [~lr:ce(l + ,:t-l = (7 F1

22

= 8.2 percent.

For an ~n~t~al rent of $120, the percentage change expenditures due to

the Food Stamp ~ncome transfer component ~s about $10 and that due to the

hous~ng pr~ce subs~dy (for those el~g~ble) another $10. S~nce only 74

percent of Food Stamp households rece~ved the pr~ce subs~dy, the overall

1ncrease J.n hous~ng expendJ.tures due to both the 1ncome and pr~ce effects

would be about 14.2

For an inJ.tJ.al rent

percent (8.1 percent plus 74 percent of 8.2 percent).

1 of $113, the overall ~ncrease would be about $16,

d~v~ded ~nto $9 of ~ncome effect and $7 of average pr~ce effect.

The Food Stamp program thus clearly prov~des an 1mportant form of housing

ass~stance to part~c~pat~ng households w~th h~gh rent burdens. How much

thJ.s ass~stance changes hous1ng expend~tures J.s, however, diff~cult to

determJ.ne exactly. As dJ.scussed, the Food stamp program 1ncreases recJ.pient

real J.ncome, whJ.ch should ~ncrease theJ.r hous~ng expendJ.tures. In add1t~on,

J.t provJ.des a 30 percent rent rebate for expendJ.tures above 30 percent of

net ~ncorne, whJ.ch, J.f households actually understand the connectJ.on between

theJ.r housJ.ng expendJ.tures and Food Stamp costs, should lead to ~ncreased

hous~ng expendJ.tures ln much the same way as the percent of Rent rebates do.

1

The average shelter cost of Food Stamp households was $128.50,

which of course ~ncludes any ~ncome and price effect ($128.50/1.142 = $112.50).

37
The net effect w~ll d~ffer for different households. S~nce each household

~s likely to have d~fferent preferences, ~t ~s 1ncorrect to attrlbute the

average effect est1ffiated here to all households. In particular, as d~scussed above, the Food stamp reClplents for whom the program also changes

the pr~ce of food may behave qu~te d~fferently. F~nally, households can be

expected to adJust the~r hous~ng only occas~onally, for example, when they

move. The effect would then be 11ffi~ted only to households that move while

~n the Food Stamp program.

The Food Stamp Act of 1977 changed the rules for ~ncome deduct~ons. After

a standard deductl0n of 20 percent from gross income, addltl0nal deductl0ns

of up to a total of $80 are allowed for dependent Care and for shelter

expenses 10 excess of 50 percent of net lncame (l.e., 40 percent of gross

income). Th~s change w~ll reduce the 1ffipact of Food Stamps on hous~ng

expendlture.

No statlstlcs are aval1able to estimate the xmpact preclsely, but educated

guesses can be made about the effects of the change. F~rst, the average

shelter deductl0n wl11 decrease. Sluce an addJ.tional 20 percent of net

lucerne 15 now no longer deductJ.ble as a shelter deductJ.on, the average

shelter deduct~on (~gnor~ng ~nflation) should decrease by about $45 (20

percent of average net ~ncome, $224), from $73 to $28.

No dlrect J.nformatJ.on on the percentage of households Wlth rent burdens 1n

excess of 40 percent of gross lucerne is avaJ.lable. Annual Hous~ng Survey

(AHS) data for 1975 (U.S. Bureau of the Census, 1978) show that 49 percent

of households w~th annual ~ncomes of less than $10,000 had rent burdens ~n

excess of 35 percent of gross lncome. Thus, 49 percent would seem to be an

1

upper bound. No lower bound ~s ava~lable, but one m~ght be arb~trar~ly set

at one-th~rd. USlng these bounds, the addlt~onal government expendlture due

1

The tabulated data on rent burden are not broken down above 35 percent. Except for th~s problem, the Census probably prov~des a fa~rly good

est~mate. If the current deduct~on used ~n the Food Stamp program (before

the shelter deductlon) averages 20 percent, then the shelter deductlon of

rents above 30 percent of net lncome 1S equ1valent to a deductlon for rents

above 24 percent of gross 1ncome. Seventy-four percent of Food Stamp households had these shelter deduct~ons (USDA, 1977)1 likew~se, the AHS data

shOW 74 percent of households w~th annual ~ncanes of less than $10,000 had

rent burdens 10 excess of 25 percent of gross lncome.

38
to the shelter deduct~on under the new regulat~ons (~n 1976 dollars) w~ll

1 be reduced from $81.5 m~ll~on per month to between $20.7 m~ll~on per month

2 and $14.1 m~ll~on per month --a reduct~on of between 75 and 83 percent.

Sim~larly, the effect on the average household w~ll be reduced as well. The

average bonus value will be reduced. If the part of the subs~dy not due to

the shelter deduction rema~ns unchanged, the income effect w~ll also be unaffected. Fewer households will, however, be affected by the price d~scount.

The overall ~ncrease ~n hous~ng expend~ture w~ll average between 10.8 and

12.1 percent (an unchanged 8.1 percentage points of ~ncome effect and e~ther

49 percent or one-th~rd of the 8.2 percent pr~ce effect), instead of an

average 14.2 percent.

1(5.03 m~ll~on households) x (.49) x ($28) x (0.3).

2(5.03 m~llion households) x (.33) x ($28) x (0.3).

39
REFERENCES

BuddJ.ng, DaVl.d W., Housl.ng Deprl.vatl.on Among Enrollees in the Housing

AIICMance temand Experl.lnent, Cambrl.dge, Mass .. , Abt Associates Inc.,

November 1978 (reV1.sed June 1980).

Carlton, Dennis W. and Joseph Ferrel-ra, Jr., "Se l ectl.ng Strategl.es for

Housing Allowance Programs," Journal of Urban Economics I vol. 4,

no. 3, July 1977, pp~ 221-247.

Fnedman, Joseph and Daniel H. Wel.nberg, Housl.ng Consumptl.on Under a Constrained Incom:!: Transfer: Evidence from a Housing Gap Housl.ng

Allowance, Cambridge, Mass., Abt AssoCl.ates Inc., Apr~l 1979 (reV1.sed

June 1980).

Hausman, Leonard, Characteristl.cs of Selected Income-Tested Programs,

Cambridge, Mass .. I Abt Assocl.ates Inc., 1977.

Lane, Terry S., Orl.gl.n and Uses of the ConventJ.onal Rules of ThuniJ, Cambridge,

Mass .. , Abt Assocl.ates Inc., 1977.

MacDonald, Maun.ce, Food Stamps and Income Maintenance, New York, Acadenu.c

Press, 1977.

RJ.cketts, Mart~n, "The Economics of the Rent Allowance," Scottish Journal

of Po1~t~ca1 Econ0m?' vol. 23, no. 3, November 1976, pp. 235-260.

Trutko, John, Otto J. Hetzel and A. Dav~d Yates, A Compar~son of the

Exper~rrental Hous~ng Allowance Program and Great Britain's Rent

Allowance Program, Wash~ngton, D.C., Urban Inst~tute, 1978.

U.S. Bureau of the Census and U.S. Department of Housing and Urban Development, Annual Hous~ng Survey: 19715, Part c: Financ~al Characterist~cs of the Hous~ng Inventory, Wash~ngton, D.C., U.S. Government

Print~ng Off~ce, 1978.

U.s. Department of Agriculture, Food and Nutr~t~on Serv~ce, Characteristics

of Food Stamp Households, September 1976, Report FNS-168, September

1977.

U.S. Department of Hous~ng and Urban Development, 1976 Stat~st~ca1 Yeamook,

Report HUD-338-5-UD, December 1977.

40
CHAPTER 3

THEORETICAL CONSIDERATIONS AND

EMPIRICAL ISSUES UNDERLYING THE ANALYSIS

Th~s chapter presents the analyt~cal framework used ~n the analys~s of the

effect of rent rebates on hous1ng expend1tures. sect10n 3.1 uses standard

m1croeconom1C theory to describe the rat10nale underlying analys1s of hous1ng response to a rent rebate. The key concept used 1S a demand funct10n

for hous1ng. Sect10n 3.2 d1scusses two alternate spec1f1cat10ns, l1near

and log-11near demand funct10ns,.and the1r 1mp11cat10ns for the analys1s of

hous1ng response. Sect10n 3.3 br1efly d1scusses the eV1dence from recent

stud~es on the demand for hous~ng. F~nally, Sect~on 3.4 presents the plan

for the rest of the report.

3.1 CONSUHER DEHAND THEORY

The effect of a rent rebate on hous1ng expend1tures can be analyzed 1n a

standard rnlcroeconom1C framework, the theory of consumer behav10r. In most

emp1rlcal studles of houslng consumpt10n, houslng expendltures depend on the

pr1ce of houSlng relatlve to the pr1ce of other consumer goods, on household

lncome, and on other household characterlst1cs. Such a relatl0nshlp lS known

as a demand functl0n for hous1ng. Sluce rent rebates effectlvely change the

relat1ve prlce of hous1ng, the1r effects can be analyzed uS1ng a houslng

demand functlon.

Households 1n percent of Rent plans reCe1ve a payment, P, equal

percentage, "a,1I of the1r gross hous1ng expend1tures (1nclud1ng

to a hxed

1 ut~l~t~es),

1

There were two mlnor l~ltatlons 1mposed. If average monthly dlSposable lncome was greater than 4.8 t~es the estlmated cost of modest

eXlstlng standard hous1ng, C* (varled by household Slze and slte), the percentage rent rebated was reduced on a slld1ng scale. ThlS lImltat10n was

rarely encountered. At the end of two years, only 6 percent of the Percent

of Rent households ~n P~ttsburgh (23 out of 407) and 3 percent ~n Phoen~x

(9 out of 298) had reduced rebate rates. The analyses ~n th~s report do not

take account of these reductlons 1n the rebate rate. However, estlmates of

elast~c~ties us~ng the actual rebate rate slmply exclud~ng households w~th

reduced rebates changed the estlffiated elast~c~t~es by less than 0.01.

A second I1mltatl0n, that the rebate was not appl1ed to houslng expendltures

1n excess of C*/a, applled to only two households 1n Plttsburgh and one In

Pho~nlx. ThlS, too, has been 19nored 1n the analysls.

41
(1) P = aR.

The household's net hous~ng expendlture, R , thus conslsts of the dlfference

n

between thelr gross expendlture and the allowance payment,

(2) R = R - P = (l-a)R. n

(3)

Gross expenditures may be thought of as a quantlty of houslng servlces t~es

1 the pn.ce per un~t: R = PHH. For the same quant~ty of housing, the net

outlay for Percent of Rent households ~s

R = (l-a)R = (l-a)p H.

n H

Thus, the rent rebate can be vlewed as changlng the effectlve relatlve prlce

of hous~ng from PH to (l-a)PH·

Household response to such a change 1n prlces may be analyzed 1n terms of

conventl0nal economlC theory. Assume that households value houslng and

other goods accordlng to a utl11ty functlon

(4)

where

U = U(H,Z)

H the amount of houslng serVlces consumed, and

Z a composlte commodlty of all nonhollsing goods,

and that households max~~ze the~r ut~l~ty subJect to a budget constra~nt

(BO)' determ~ned by the level of ava~lable ~ncome,

(5) y = PHH + PZZ

where

household 2

y lucame

PH = the prlce of housJ.ng, and

Pz the prJ.ce of nonhouslng goods.

1

The term houslng serV1ces 1S used because renters do not actually

bUy a unit but only rent 1tS use for a g1ven per1od. Thus, what they bUy

~s the hous~ng serv~ces prov~ded by the un~t durillg the rental per~od. The

hous1ng consumpt10n of homeowners can theoret1cally be analyzed on a bas1s

comparable to renters by conceptually separat1ng their purchase of an asset

(the1r house) and the1r consumpt10n of hous1ng serv1ces wh1le living 1n the

house (see Ka~n and Qu~gley, 1972).

2

Household 1ncome J..5 often defJ..ned as "pennanent" or "normal" lllcome

rather than current measured income. The household 1S viewed as makJ..ng J..ts

budget plans based on expected normal 1ncome. Dev1atJ..ons of actual J..ncome

from normal 1ncome are absorbed by changes 1n sav1ngs or d1scretionary

purchases.

42
F~gure 3-1 represents th~s s~tuat~on, where Uo ~s the max~um level of

ut~l~ty obta~nable, w~th the household choosing what ~s termed the "opt~mal"

1

amounts of hous~ng and nonhous~ng goods, HO and Zo' respect~vely. The

slope of the budget l~ne BO is s~ply the negat~ve of the relat~ve pr~ce of

housing, that ~s, -P~PZ'

Figure 3-1

OPTIMAL HOUSING CONSUMPTION

HOUSING (H)

UtIlity = U 0 Utility = U,

g

o

t:l

t:l

Z

o

:r:

z

o

z

z, _ 2 0 -------------I

I

I

1

I

I

1

I

1

The l~nes U = Uo and U = U

l ' called ~nd~fference curves, show the

comb~natl0ns of houslng and nonhouS2ng goods needed to malntaln a given

level of ut~l~ty. A key assumption ~s that indifference curves are concave

fram above--as housing consumptl0n 15 reduced, It takes an lncreasing amount

of nonhous~ng goods to leave the household as well off. See, for example,

Henderson and Quandt (1971), for further d~scuss~on.

43
Introduct1on of rent rebates reduces the relat1ve pr1ce of hous1ng to the

household, s~nce ~t pays only (l-a)PH rather than PH for each un~t of houslng services. In Figure 3-1, bUdget 11ne B1 represents the comb1natl0n of

houslng and nonhouslng goods obtalnable by a household wlth a Percent of

Rent hous~ng allowance, the slope of Bl ~s -(l-a)PH/PZ and ~s thus less

steep than BO. If the household were then to maX1mlZe 1tS utl11ty, lt

would consume HI houslng and Zl nonhouslng goods, glv1ng lt a utl11ty VI =

The funct10nal relatlonshlp between the optlmal amount of each good chosen

and household lncome and prlces lS termed a demand functlon. The demand

functl0n for hous1ng serVlces can be expressed as

(6)

predlctl0ns about thlS functl0n; ~n

(

3H 1f demand for houslng 1ncreases as lncome lncreases ay >

wlll decllne as pr1ces rlse (~H < 0). PH

to lncome and prlces, other varlables may also affect houslng

then demand

Consumer demand theory provldes some

partlcular,

In addltlon

demand. D~fferent demograph~c groups may have d~fferent relat~ve preferences for hous1ng versus other goods and serV1ces. Furthermore, pollcy

lnterest lS often focused on certaln demographlc groups, 1n partlcular

m~nor~ty and elderly households. The emp~r~cal work described ~n Chapter 4

examlnes several dlfferent types of characterlstlcs: age of head of the

household, household Slze, household type, and race of head. For s~pliclty,

the exposltl0n of funct10nal forms In Sect10n 3.2 below deals only Wlth prlce

and lncome, omlttlng any expllc1t dlScusslon of other demographlc varlables.

3.2 THE FUNCTIONAL FORM OF HOUSING DEMAND

The exact 1mpact of a rent rebate depends on the shape of the demand functl0n

for hous1ng. The theory of consumer demand does not suggest a partlcular

form for demand functlon, and the cholce of the functional form lS usually

based on emplrlcal conslderatlons. Two dlfferent speclflcatlons are used In

thlS report 1n order to galn some lnSlghts lnto the sensltlvlty of the estlmates to the exact speclflcatl0n. Both relate the quantity of houslng

demanded (H) to a consumer's lncome (Y), houslng prlces (PH)' and nonhous1ng

pr~ces (pz ). The f~rst ~s the log-l~near demand funct~on, wh~ch has been

44
wldely used In emplrlcal studles of houslng demand. The second ls.a demand

functl0n that 15 11near 10 lts parameters, where the parameters can be

interpreted 1n terms of a Stone-Geary utlilty function.

Log-llnear Demand FunctJ.on

Sluce the rent rebate offered Percent of Rent households 10 effect reduces

the prlce of houslng, ltS 1mpact may be expressed terms of the prlce

elastlclty of demand for houslng. The prlce elastlclty of demand lS deflned

as the ratlo of the percentage change In quantlty demanded to the percentage

change 10 houslng prlce. ThlS can be expressed mathematically as

(7)

If

be

(8)

the prlce and

I log-llnear.

lucame elastlcltles are constant, the demand functlon wlll

Z ThlS log-llnear demand functlon 18 wrltten as

where So 18 a constant and the coef£lClents Sl and S2 are, respectlvely, the

lncome and prlce elastlclty of demand for houslng.

Equatlon (8) can be wrltten In terms of rental expendltures rather than the

abstract "quantJ.ty of houslng servl.ces" by recognl.zl.ng that rental expendJ.-

3 tures are equal to the product of prlce and quantlty. In the log-llnear

form of the demand equatlon, thls lS done by addlng the logarlthm of prlce

to both sldes of the equatlon:

(9) In(R) = In(PJI)

I

The lncome elastlclty of demand lS deflned analogously to the prlce

elastlclty: n = aln(H)/aln(Y).

z y

In thJ.s equatJ.on, Pz ~s normalJ.zed to equal one. The log-lJ.near

demand functJ.on could be wrJ.tten )

In (H) = So + Slln (:z) + Szln ( ::

[so - (Sl + SZ) In (pz)] + Slln (y) + SZln (PH) •

If Pz J.s unobservable and dJ.ffers across sJ.tes, then the est~ated constant

term wlII dlffer as well.

3

The POSSlblllty that the Percent of Rent offers altered the normal

relatlonshlp between rent and the quantlty and quallty of houslng obtalned

lS explored In Chapter 5.

45
Eguat~on (9) expresses the logar~thm of hous~ng expend~tures, In(R) , as a

11near functlon of the logarlthms of lnCome and of the relatlve prlce of

housing. Note that the prlce elastlclty of houslng expenditures 15 equal

to one plus the prlce elastlclty of houslng servlces.

The advantages of the log-llnear form are several: It 15 skffiple to est~ate

uSlng Ord1nary Least Squares (OLS); It 18 wldely used; ltS parameters are

easl1y lnterpreted as (constant) prlce and lucame elastlcltlesi and only

the constant term 15 affected by changes 1n the unltS of measurement. Thus,

lnflatl0n 15

So' to change

over tlme and

easl.ly accommodated 1n estl.matl.on by permlttlng the lntercept,

1

over tlffie. Thl.s attr~ute greatly faCl11tates comparlsons

across cltles. On the other hand, restrl.cting the prl.ce and

lncome elastlcltles to be constant may not be desirable I and the function

itself cannot be der~ved from a known ut~l~ty function. 2

Llnear Expendlture Functl0n

As an alternatlve to the log-llnear functl0n l a llnear expendlture functlon

3 takes the form:

IThis 15 a well-known feature of the logar1thm1c speclflcatlon. To

see thlS 1 let denote the rate of general 1nflation ln both houslng and nonhouslng goods. Then I 10 terms of enrollment dollarS I the relatlonshlps

between rent and lncome at enrollment and at two years can be wrltten as

(u)

In (RO) = So + Slln(Yo )

In(Rl!(l + w» = So + Slln(Yl!(l + w»

where the subscr~pts ~nd~cate enrollment (t = 0) and two years after enrollment (t = 1).

Equation (11) can be rewrltten as

(~~~) In(Rl ) = [So + (1 - Sl)ln(l + w)] + Slln(yl ).

The express~on, [So + (1 - Sl) In(l + W)], ~s the new constant for the equat~on for the t~me t = 1-

2

Indeedl the 10g-11near demand functlon is not compat1ble wlth any

utillty function over ltS entlre range (except for the case of unltary elastic­

~ties).

3

The demand flll1ct.l.on for h01.lS1ng correspondJ.ng to this I1near expend1 ture functl0n .l.S

H = C + B (:J + A ~:) •

The expenmture funct~on (10) ~s obtained by mult~plying both s~des of the

demand function by PH' us~ng the normaliz~ng assumption Pz = 1.

46
(10) R = A + BY + CPH.

Just as the log-11near form expressed the logar1thm of rent as a 11near functlon of the logarlthms of lncarne and price, the linear form expresses rent

as a I1near functl0n of lucame and prlce. It can also be est~ated uSlng

Ordinary Least Squares.

but vary W1th both pr1ce and 1ncome.

For the IJ.near

1 constant,

expendlture functlon, income and prlce elastlcltles are not

2 The pr1ce elasticity 1S

(11) -(A + BY) 11 = -=---'----'''"''-'-­

P A + BY + CpH

and the lucame elastlclty 15

(12) BY

A + BY + CPH •

In contrast to the log-11near demand function, the 11near expenditure functlon can be derived from a utl1ity functl0n. ThlS utl11ty functlon, known

as the Stone-Geary utlilty functlon, 18 written as

(13)

3 where b, 81 , and 82 are parameters, 0 < b < 1, H > 8

1 , and Z 820

1

They w111 be constant only 1n the spec1al case of un1tary elastic1ties.

2

These formulas are derlved from

where

and Y

H

H = + C,

=

--,,(A~+:--=:B=-Y),- d 2 1 an

PH

3

Th1s funct10n is more general than the Cobb-Douglas form, 1n wh1ch

8

1 82 = o.

47
When th~s ut111ty funct10n 18 max1ffi1zed subJect to the budget constra1nt

[Equation (5)] and 1S norma11zed by sett1ng the

good, Z, equal to one (pz = I), the equ111br1um

pr1ce of the compos1te

1 demand funct10n 1S:

(14) H

In terms of rental expend1tures, Equat10n (14) becomes

(15)

1n form 1dent1ca1 to Equat10n (10), where A = -b8Z' B = b, and C = (1-b)81 •

Moreover, 1n contrast to the log-11near form, S1nce th1s funct10n 18 der1ved

d1rectly from a ut111ty funct10n, 1t 8at1sf1es the theoretical constra1nts

1The demand fQ~ct10n 1S der1ved by tak1ng the log of the uti11ty

funct10n [Equat1on (13)J and def1n1ng the Lagrang1an

L = b1n(H-81 ) + (1-b)ln(Z-8z) + A(Y - PHH - PZZ).

The f1rst order cond1t10ns are:

(1) dL b

APH

0 dH = (H-81 )

(11) dL (l-b) - AP = 0 dZ = (Z-8Z) Z

(111) dL = Y-pH-pZ = 0 dA H Z

b

or

(l-b)

Th1s can be rewrltten as

P H - P 8 - b(p H - P 8 ) H H 1 H H 1

H =

F1na11y, uS1ng (111):

b 81 + --(y - PH81 - PZ8Z) , PH

wh1ch Y1e1ds Equat10n (14) when Pz 1S set equal to one. Thus, equ111br1um

rent (PHH) can be 1nterpreted as some m1n1mum (PH81 ) plus a constant fract10n

(b) of 1ncome above some m1n1mum amount (supernumerary 1ncome).

48
1

on demand funct~ons w~thin certa~n ranges (see Phl~ps, 1974).

The parameters 8

1 and 8

2 have been interpreted as m~n~um subslstence levels

of houslng and nonhous~g goods, Slnce the underlying utillty functlon 18

def~ned only for values of H greater than or equal to 8

1 and Z greater than

or equal to 82 - ThlS lnterpretation 15 untenable 1£ the as are negatlve, as

w~ll be true ~f the price elast~c~ty of demand ~s greater than one (in abso2 lute value). Alternately, the parameters 8

1 and 82 can be viewed merely as

parameters that affect the shape of the household demand function.

3.3 EVIDENCE FROM RECENT EMPIRICAL ESTIMATES OF HOUSING DEMAND3

ThlS seetlon presents some empirical eVldence based on recent studles of the

prlce and lncome elastlcltles of demand for rental houslng. For the most

part, houslng demand analyses have 19nored the role of houSlng prlce in 10­

fluenclng demand, chooslng lnstead to focus on the role of income. For each

analysls that estlmates the prlce elastlclty of demand there are several that

est1mate the lncome elastlclty. The maJor reason for th~s focus 1S the diff1­

culty of constructlng accurate and generally app11cable 1nd1ces of hous1ng

prlce and the lack of t1me-ser1es measurements of household hous1ng demand

under d1fferent hous1ng pr1ces.

The d1fflcultles of measur1ng the I1pr1ce" of hous1ng are more severe than

those of measur1ng the pr1ces of most consumer goods. There is no s1ngle

1The potent~al usefulness of the theoret~cal l~nk to ~nd~v~dual

ut111ty funct10ns 1S largely lost 1n est1matl0n. The constra1nts on the

coeff1c1ents are those for the ut1l1ty funct10n--that for every household,

o < b < I, H aI' and Z a2 . These restr1ct10ns may 1n theory be ma1nta1ued for every observat10n 1U e1ther of two ways. Flrst, 1f tastes are

assumed to be the same for all households (so that the stochast~c term

represents d1sequ111br1um hous1ng expendltures), then parameters can

be restrlcted so that no lucorne and prlce observatlon ylelds a predlcted

expend~ture level less than PH81' Alternat~vely, a (restr~cted) stochastlC dlstrlbutl0n of parameters could be spec~fled. Nelther of these

procedures lS attempted 1n thlS report.

2

Th~s can be seen by rewr~t~ng Equat~on (11) ~n terms of the StoneGeary parameters as

-1 + < -1

>

3

Th~s sect~on was adapted from an earl~er report by Stephen K. Mayo

(1977). See Mayo (forthcoming) for a more extens~ve rev~ew of recent stumes.

49
price of housing. The percentage difference in cost of an ~dentical onebedroom un~t between two cities may not be the same as the percentage difference in cost for an l.dentical four-bedroom unit in those two cities.

Most recent housl.ng demand analyses that attempted to estl.mate prl.ce elasticit~es have rel~ed on aggregate data from the C~ty Worker's F~ly Budgets

established by the Bureau of Labor Stahst~cs (BIS). However, s~nce the BIS

budget ~s est~mated only for a parhcular housing type, the ~ndex based on

1 it may be mislead1.ng concerning price differences across housl.ng in general.

In add~t~on, the type of household (as def~ned by household s~ze, compos~­

tl.on, or l.ncome, for example) that occupl.es the BLS prototYPl.cal unit may

differ from place to place or over tLme, due to, among other thl.ngs, dl.fferences 1n the prl.ce of hOUSl.ng. In thl.s case, measurement errors 1U the prl.ce

index may be systemat~cally related to household character~st~cs. Unless

such factors are expll.cl.tly accounted for 1n estLmated demand relatl.onshl.ps,

the est~mated pr~ce elast~city of hous~ng demand based on the BLS ~ndex w~ll

subsume the effects of

may produce misleadl.ng

such household

2 results.

characterl.stl.CS on housl.ng demand and

One further l~tatl.on of convent~onal hous~ng pr~ce lndlces 15 that they

typ~cally apply to ent~re metropol~tan areas, and consequently fa~l to

account for houslng prlce varlatlons withln those areas. There 1S grow1ng

eVldence that intra-clty prlce var~atlons may be conslderable, relatlve to

between-clty varlatlons, as a result of geographlcal or ethnlc submarkets,

rac~al pr1ce d~SCr1mlnatloo, and spat1al var1atlons 1n land prlces and

rental unlt operatlog expenses. Not only have such price varlatlons been

~dent~f~ed, but households have been found to adJust the~r hous~ng consumptlon patterns ratlonally to lntra-area prlce varlatlons (see partlcu1ar1y

Straszhe1m, 1975, and K10g, 1972). By ~gnorlng such var1atlons, convent10nal hous1ng pr1ce lndlces are subJect to what may be conslderable

1

The r1 rent shelter component of the (C1ty Worker's) Budget refers

to an unfurn1shed f1ve-room UOlt (house or apartment) 1n sound condlt10n

and w~th a complete bath, a fully equ~pped k~tchen, hot and cold runn~ng

water, electrlclty, central or other 1nsta1led heat1ng, access to pub11C

transportatlon, schools, grocery stores, play space for chlldren, and

locatlon 10 reSldentlal nelghborhoods free from nUlsances" (Gilllngham,

1975).

(1974),

2

For a more extended

espec~ally pp. 7-22.

discuss10n of th1S problem see Mayo and Fenton

See also Pol~nsky (1977).

50
measurement error, thereby ra~s~ng the poss~bil~ty that est~ates of pr~ce

elast~c~tles of houslng demand are blased.

The lnadequacles of conventlonal prlce lndices provlde an explanation for

the wlde varlation 10 prJ.ce elastlclty estImates aMong studles that have used

s~11ar or even ldentlcal data but dlfferent emplrJ.cal speciflcatlons of

hous~ng demand funct~ons or d~fferent sets of explanatory variables. For

example, three recent analyses have relled on data from the same panel

survey, the "Panel Study of Income Dynam~cs" (PSID), admin~stered by the

unlverslty of Mlchigan Survey Research Center, and have all used BLS "rent

shelter component" data as the basls for honsl-ug prJ.ces (Carllner, 1973;

Fenton, 1974; and Lee and Kong, 1977). The maJor differences among the

analyses are due to the d~fferent explanatory var~ables (other than hous~ng

price) ~ncluded ~n the est~ated demand funct~on. The analyses produced

str~k~ngly d~fferent results. Carl~ner found that in no alternat~ve demand

functlon speclflcatlon was the estimated prlce elastlclty for renters slgnif~cant at a h~gh level; est~ated magn~tudes ranged from -0.1 to +0.02,

dependJ.ng on the speclflcatlon. Fenton, on the other hand, observed unJ.­

formly s~gn~f~cant price elast~c~ty est~mates rang~ng from -0.7 to -1.9

dependlng on WhlCh of several SOCl0economlC groups was belng consldered,

and est~ated the pr~ce elast~c~ty for the ent~re renter populat~on at -1.27.

Further, Lee and Kong estlmated statlstlcally slgnlficant prlce elastlclties

of -0.6 for renters In two alternatlve speclflcatl0ns of housing and demand

funct~ons. From the results of these three analyses w~th nearly ident~cal

baslC data, the speclflcatl0n of the hOUSlng demand functl0n appears crltlcal

in lnfluenc1ng estlmated prlce elastlclties.1

several other stud~es have found elast~c~t~es of about -0.7. DeLeeuw (1971),

us~ng BLS pr~ce data and 1960 Census data on renters, estimated a pr~ce elastic~ty of about -0.7, but conceded that the true value could be as h~gh as

-1.5 as a result of sLmultaneous determlnatlon of houslng prlces, quantlties,

IThe estlmated income elastlcitles are generally qulte simllar among

the three analyses, desplte some dlfferences J.n speclflcatlon. carllner

estLmates lncome elasticltles from about 0.4 to about 0.5 for renters, dependlng on the fWlctlonal form and the deflnltlon of lucome. Fenton's lucome

elastlclty estimates also center on the 0.4 to 0.5 range for most SOCloeconomlC groups. Lee and Kong est~ate lncome elastlcltles ranglng from about 0.3

to 0.7 for renters (dependlng on the lncome deflnltl0n and estlmatlon method);

for the~r most carefully spec~f~ed model, they obta~n an est~ate of about 0.5.

51
and rents. Nelson (1975) reproduced deLeeuw's analys~s us~ng 1970 Census

1 data and found a pr~ce elast~c~ty for renters of about -0.7. One recent

rev~ew of empir~cal analyses of hous~ng demand (Pol~nsky, 1977) concludes

that although blases on prlce and lucame elastlcltles may be serious In most

extant analyses, by correctlng for such biases a prlce elastlclty of houslng

demand on the order of -0.75 18 obtalned. Desplte pollnsky's analysis, there

appears to be I1ttle consensus on an approprlate value for the price elastlc­

~ty of hous~g demand. The d~sparate results of the three analyses of the

PSID data (Carllner, Fenton, and Lee and Kong) lilustrate most dramatlcally

the range of uncertalnty that surrounds the subJect of prlce elastlclty,

partlcularly for renters.

Experlmentally created varlatlons In houslng prlces--the result of rent

rebates offered Percent of Rent households--have the potent~al to reduce

that uncerta~nty cons~derably for three ma~n reasons. F1rst, the percentage

pr~ce reduct~on appl~es to all hous~ng equally. Thus the pr~ce of every un~t

~s reduced by the same proport1on, so that the effect of a proport~onal change

1n pr~ces can be est~mated w1thout hav1ng to know the base pr1ce of housing.

Second, asslgnment of households to the Percent of Rent rebate groups lS

random, so that the "pr~ce" of hous1ng created by the rebate should not be

correlated w1th household characterlst1cs that lnfluence hous~ng consumption,

thereby allev~atlng one of

conventl0nal hous1ng pr1ce

the more ser10US problems assoc1ated w1th uS1ng

2 1nd1ces 1n demand stud1es. Th1rd, the range of

pr1ce var1at1ons result1ng from the SubS1dy lS large relat1ve to var1at~ons

1n such hous1ng pr1ce lnd1ces as the BLS lndexi thus hous1ng consumpt10n

responses may be estlmated over a broader range of prices than has been typ1­

cal of nonexper~ental analyses.

ExperlIrental data present their own problems, however. The lulU.ted duration

of the I::emand Experlment may have affected household response to the allowance

1

Nelson found a prlce elast1clty for homeowners of about -0.3. Other

analyses of hous1ng prlce elast1c1tles for homeowners have estlmated values

of -0.3 (Carl~ner, 1973), -0.8 to -0.9 (Ma~sel, Burnham, and Aust~n, 1971),

and -0.7 to -0.8 (Muth, 1971). The last two analyses were based on Federal

Houslng Adm1nlstratl0n (FHA) data on lndlv1dual homeowners, and the f1rst on

the PSID.

2

As noted above, because measurement errors ln convent10nal prlce

llldlCeS are llkely to be systemat1cally related to household characteristics,

the1r use 1n est~at1ng demand functlons can result in biased prlce elastlc1ty estJ.Itlates.

52
paynent. In addit~on, attr~t~on from the sample may create problems of bias 

due to possJ..ble self-select1on, resultl.ng 1.n a potentially noncmrparable control group. Finally, households may =sunderstand the rebate, and thus not 

respond cOIT!Pletely. Such l.ssues are exarru.ned 1.ll more detail in Chapter 6. 

Wh11e the eV1.dence presented is not conclusl.ve, it suggests that these potential problems were not in fact important. 

The relationshl.p between l.ncome and housing consUIt!Ption has recel.ved consl.derable attentl.on 1ll recent empl.rical analyses of housing demand. An important reVl.ew article (deLeeuw, 1971) cl.ted several analyses that estl.mated 

l.ncome elastl.cl.tl.es greater than one (indl.catl.ng that housl.ng consumptl.on 

1.5 hl.ghly sensl.tJ.ve to l.ncome changes), and only one analysis that fOillld 

an income elastl.city less than one (Lee, 1968). Since deleeuw's reVl.ew, 

however, many analyses have lndlcated lncome elastlcltles less than one; and 

no recent analysls has lndlcated an lucome elastlclty for renters even 

approachlng one. Some analyses, ln fact, have lndlcated lncome e1asticltles 

as low as 0.1 and 0.3 (Ka~n and QUlgley, 1975; L~, 1973; and Nelson, 1975). 

Several others have lndlcated elastlcltles from 0.4 to 0.6 (Carllner, 1973; 

Fenton, 1974; Lee and Kong, 1977; Mayo, 1973; and Straszhe~, 1976). 

The maJor source of the dlscrepancles between the results of the analyses 

rev~ewed by deLeeuw and of subsequent analyses ~s the level of aggregat~on

of the data. Nearly all of the analyses c~ted by deLeeuw used data aggregated to at least the Census tract level, and most were based on Standard 

Metropol~tan Statlstlcal Area (SMSA) averages. The subsequent analyses have 

been based on lndlvldual household data. 

Three recent analyses have lndlcated that blases In estlmated lncome elastlcltles may be severe as a result of uSlng aggregate data. In one (Malsel, 

Burnham, and Austln, 1971), demand functl0ns were estimated for homeowners 

uSlng FHA data--flrst for lndlvldual households, and then for SMSA averages 

of the same households. The dlsaggregated data produced an ~ncome elastlc~ty

est~mate of about 0.45, whereas the SMSA-average data produced an elastlcity 

of about 0.9. Pol~nsky (1977) argues that aggregat~on of the data and mlSspeclflcatlon of demand relatl0nshlps camblne to account for the differences 

between lncome elastlclty est1mates uSlng household data and those using 

aggregated data. He suggests that an appropr~ate value for the ~ncome elast~c~ty ~s about 0.75, although the flgure could be h~gher for homeowners and 

53 
lower for renters. Nelson (1975), uS1ng data on 1nd1v1dual households, est1­

mated 1ncome elast1cit1es (for renters) of about 0.28. When 1nd1vidual data

were grouped randomly, 1ncome elastlclty estimates were about 0.35. When

they were grouped accordlng to Census tracts, lucarne elastlcitles were

O.76--an lncrease of about 170 percent over estlffiates using indlvldual

about

1 data.

EstLmated income elastlcltles may also be biased by errors 10 measurlng

household lucerne. In partlcular, 1f households make deC1S10ns about houslUg expendltures on the basls of expectatl0ns concernlng lucame to be

recelved over a long perlod of tLffie rather than on the basls of current

lucame, then some measure of "pennanentU or "normal" lucame wlll be more

approprlate than current lucerne to use 10 est1ffiatJ.ng demand functlons (see

Fr1edman, 1957). If households expect to rent a un1t for an apprec1able

length of tLffie, then they are l~kely to base the~r consumpt~on dec~s~on on

a more stable measure of ~ncome than current ~ncome, such as some permanent

lncOme measure. Use of a short-term lncome measure would then be l~kely to

underestimate the ~ncame response, In that changes 1n short-run lncome would

lead to hous~ng changes only as they are reflected ~n changes ~n long-run

(permanent) 1ncome.

In general, analyses that have used household data to est1ffiate demand funct~ons have attempted to estLffiate ~ncome elastlc~t~es w1th respect to permanent

lncame rather than (or ~n addltlon to) elast1cltles wlth respect to current

1ncome. The methods used have var1ed greatly and have generally tended to

be somewhat ad hoc. Two alternate income measures are examlned 10 th1S

report--current lncome and lncome

chosen to approxJ.Inate "permanent"

averaged

2 mcome.

over three years, the latter

1There may be blases 10 estlffiates from household data as well.

Po11nsky (1977), for example, argues on theoret1cal grounds that many such

estLmates of income elastlcltles are based as a result of ~proper speclflcatlon of housing prlce, that lS, by uSlng a metropol1tan areawlde 1ndex

lnstead of an observatlon-based one. Slnce the Demand Experl.Illent uses

observatlon-based prlce var1atlons, this lS not a concern. Furthermore,

empu1cal work by P011nsky and Ellwood (1977) suggests that desp1te the

theoretlcal argument of Pol1nsky, the estJ.Inate of lncome elast1clty 18

vlrtually unaffected by lncluslon or exclu810n of a prlce term.

2

An addlt10nal measure of permanent lncome--one based on lllcome

pred1cted from an lnstrumental varlable regresslon uSlng SOCloeconomlC

characterlstlcs--was tested but gave results sJ.Inllar to the average lncome

measure. See Mayo (1977) for results uS1ng 1nstrumental variables to est1­

mate permanent lnCome.

54
3.4 THE PLAN FOR THE REST OF THE REPORT

The maJor empir~cal results from the analysis of housing response to rent

rebates are conta1ned 1n the following two chapters. Chapter 4 shows how

pr1ce and 1ncome elast1c1ties can be est1mated uS1ng the exper1ffiental percentage rebate as a pr~ce term and two measures of lncome--current and

average lucerne. It then presents the results for the houslng expendJ.ture

equations, for both the log-11near and the linear (Stone-Geary) formulat10ns.

In addJ.tJ.on, the effect of demographJ.c varlables 18 dJ.scussed 1n detalI.

Chapter 5 focuses on responses 10 terms of housJ.ng servJ.ces and normat2ve

physJ.cal standards. Houslng servlces are measured by an hedonic lndex--a

we1.ghted sum of numerous hOUSJ.l1g and nelghborhood attributes. A discusslon

and analysls of problems and lssues speclflc to experLmental data are presented 1n Chapter 6.

55
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deLeeuw, Frank, "The Demand for Hous1ng - A ReV1ew of the Cross-Sect1.on

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February 1971, pp. 1-10.

Fenton, Chester, liThe Permanent Income Hypothesls, Source of Income and the

Demand for Rental Housl.ng," Analysl.s of selected Census and welfare

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1974.

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Desl.gn of a Houslng Allowance program," Analysl.s of Selected Census

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Assl.stance Program, Cambrl.dge, Mass., JOl.nt Center for Urban Studl.es,

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no. 4, November 1971, pp. 410-413.

56
Mayo, Stephen K., HousJ.ng Allowance Demand Experiment: Housing ExpendJ.tures

and Quality Part 1: HousJ.ng Expenditures Under a Percent of Rent

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____-:::-__.,-' "Theory and Estimation ln the Economics of Housing Demand,u

Journal of Urban Economlcs, forthcoming.

--------c---' "Welfare and Houslng,lI AnalysJ.s of Selected Census Data to

DetermJ.ne Relatl0n of Household Characterlstlcs, HousJ.ng Market

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StudJ.es, 1973.

Mayo, stephen K., and Chester Fenton,

the Cost of Standard Houslng,

December 1974.

Alternatlve Mechanlsms for Determlning

Cambrldge, Mass., Abt Assoclates Inc.,

Muth, RJ.chard F., liThe Derlved Demand for Urban Resldentlal Land, II Urban

StudJ.es, vol. 8, no. 3, October 1971, pp. 243-54.

Nelson, Davld, "Income ElastJ.clty of Houslng Demand," unpubllshed Ph.D.

dlssertatlon, Department of Economlcs, Unlverslty of Oregon, 1975.

phllPS, LOU1S, Applled Consumptlon Analysls, New York, Amerlcan Elsevler,

1974.

pollnsky, A. Mltchell, liThe Demand for Hous1ng: A study In Speclfl.catlon

and Group1ng,II Econometrlca, vol. 45, no. 2 1 March 1977, pp. 447-461.

Poll.nsky, A. Mltchell and Davld J. Ellwood, "An Ernplrlca1 Reconcl11atlon of

Mlcro and Grouped Estl.mates of the Demand for Housl.ng, II Harvard

Instltute of EconomlC Research D1SCUSS1on Paper l Number 567, August

1977.

Straszhelm, Mahlon, An Econometrlc Analysls of the Urban Housl.ng Market,

New York, Natlona1 Bureau of EconomlC Research, 1975.

57
CHAPTER 4

EMPIRICAL ESTIMATES OF

HOUSING EXPENDITURE FUNCTIONS

Chapter 3 presented consumer demand theory and appll.ed l.ts hypotheses to

houslng. ThlS chapter analyzes responses to rent rebates wlthln that

framework, using the sample of Percent of Rent and control households, and

presents estlmates of elastlcltles of demand. Section 4.1 presents the

emplrlcal speclflcatlons of the houSlng demand functl0ns descrlbed In

Chapter 3. sectl.on 4.2 descrJ.bes the estl.mated model of housl.ng demand,

focusl.ng on households that moved durl.ng the fl.rst two years of the Demand

Experlment. The effect of demographlc varlables on houslng expendltures 18

dl.scussed l.n Sectl.on 4.3.

4.1 EMPIRICAL SPECIFICATION OF HOUSING EXPENDITURES FUNCTIONS

ThlS sectlon provldes the emplrlcal speclflcatlon for the log-llnear and the

11near houslng expendltures functlons. The log-llnear houslng expendltures

functl0n 18 wrltten as

(1)

where

R = hOUSLng expendltures

PH = prl.Ce of housl.ng

H quantl.ty of houslng, and

y = household lucerne.

experimental var1ation 1n pr1ces due to the Percent

Wh1Ch 1S not observable on

The coeffl.cl.ents 8 are interpreted, respectlvely, as lucame and price 1 and 8

2

elastlclties of demand for

1mportant var1able,

However, because of

housl.ng. Equatl.on (1), however, lncludes one

1 the household level.

of Rent rebates, 1t 1S not necessary to observe PH.

1

As dlscussed 1n Sect10n 3.3, several researchers have c1rcumvented

thl.s problem by uSl.ng the Bureau of Labor Statl.stics housl.ng budget index

computed on a metropol1tan basls as a proxy for housing prlce. However,

Poll.nsky (1977) has shown that such a proxy l.S theoretically ll.kely to lead

to b1ased est1mates of both lnCome and price elastlcltles.

59
As shown 1n Chapter 3, the pr1ce of hous1ng faced by Percent of Rent rec1p1ents changes from PH to (I-a) PH' Subst1tut1ng (l-a)PH for PH 1n Equat10n

(1) glves

Equat10n (2) can be rearranged as

(3) [So + (1+S2)ln(PH)] + Slln(Y)

+ (1+S2)ln(1-a).

Equat10n (3) lS 1n terms of net rent. An alternat1ve 1S to transform the

equat10n to be 1n terms of gross rent. Subtract1ng In(l-a) from both sldes

of Equat10n (3) y1elds

(4 )

Here, the dependent var1able 1S the logar1thm of the actual (gross) rent.

The only d1fference 1n parameters between Equat10ns (3) and (4) lS the

coeff1c1ent of In(l-a). In Equat10n (~), the coeff1c1ent of In(l-a) lS

equal to the pr1ce elast1c1ty of hous1ng demand, whereas 1n Equat10n (3) 1t

1S equal to one plus th1S pr1ce elastlc1ty.

Equat10n (4) conta1ns the unobservable var1able, PH' the pr1ce of hous1ng

serV1ces. In order to be est1mated, the equat10n must be rewr1tten 1n

term~ of observable var1ables as

(5)

1 where

8 a stochast1c error term.

As long as Y and (I-a) are 1ndependent of the unobserved var1able PH' the

parameters of Equat10n (5) may be est1mated uS1ng an Ord1nary Least Squares

(OLS) regress1on. Exper1mental households were ass1gned to rent rebate

categor1es at random, assur1ng that the "a" level 1S stochastJ..cally

1

If the relat1ve prlce of housJ..ng d1ffers across s1tes, the estlmated

constant term w1l1 d1ffer S1nce 1t 1S a funct10n of that unobserved var1able.

If PH d1ffers wlth1n S1tes as suggested 1n Chapter 3, varlations around the

mean are lncluded 1n the stochastJ..c term, e.

60
1 ~ndependent of the unobserved prlce PH- Llkewlse, there 15 no reason to

belleve that lucerne 15 slgnlflcantly correlated wlth the overall unlt price

2

of houslng serVlces.

The I1near houslng expendltures functlon 18 wrltten as:

(6)

where the coefflClents can be lnterpreted 1n terms of the parameters b, 8

1 ,

and 82 of a Stone-Geary utlilty functlon (presented In Chapter 3, Equatlon

(13»:

b = B,

8

1

C = , and I-B

82

-A

B

Rent rebates can be lntroduced 1n a way ldentlcal to the log-llnear case.

Replaclng PH wlth (l-a)PHH In Equatlon (6) ylelds,

(7)

An equatlon 1n terms of gross rental expendltures 15 obtalned by dlvidlng

3 both sldes of Equatlon (7) by (I-a):

(8) .R = P H = A (~) + B (2-) + c' + E. H I-a I-a

1

The Percent of Rent plan wlth a 60 percent rebate was only offered

to households In the lower thlrd of the lncorne dlstrlbutlon of the ellglble

populatlon, whlle the 20 percent plan was only offered to households In the

upper two-thlrds. Sluce lucerne 15 lncluded as a varlable 1.n the demand equation, thlS wlll not blas the results (assumlng that the form of Equation (5)

lS correctly speclfled). 2 . Some models of resldentl.al locatl.on have l.mpll.ed that PH and Yare

negatl.vely correlated (that lS, hlgher ~ncome households pay less per un~t

of houslng than lower lUCorne households). In that case, Sl would be rnlSest1ffiated. Th~s partlcular object~on ~s not appl~cable here, Slnce those

locatlon models separate 10catl0nal attr~butes from housing serVlces. In the

analys~s presented above, the conunod~ty "houslngll lncludes location and

accesS~ll~ty. If minorltles pay more for a g~ven housing unlt than do nonmlnorltles, then lncome and PH may be correlated because lucome and race

are usually correlated. Merr~ll (1977), however, found no ev~dence of any

large prlce dlfferences ~n the Demand Exper~ent sites.

3Note that C' = CPH = PH81 (l-b). The term PH81 can be lnterpreted

as the dollar value of 81 . Slnce H, the lIquant~ty of hous~ng serv~ces,II is

an abstract measure, ~ts un~ts can be deflned so that PH = 1.

61
In Equation (8), the term l/(l-a) enables estDnat~on of the parameters of

the stone-Geary utility funct~on (b, 61 , and 62), us~ng ind~vidual household data.

Introductl0n of the rent rebates also modlfles the formulas for the prlce

and ~ncome elast~c~t~es of demand (Equat~ons (11) and (12) of Chapter 3).

The prlce elastlclty becomes

(9) - (A + BY) = A + BY + C'(l-a)

and the lncame elastlclty becomes

(10) n

y

BY

A + BY + C'(l-a)

4.2 ELASTICITY ESTIMATES

ThlS sectl0n presents estlmated prlce and lucame elastlclties based on Percent

of Rent and Control households. Both the log-llnear and I1near speclflcatl0ns

descrlbed 1n Sectl0n 4.1 are used. The sectl0n beglns wlth estlmates based on

all Percent of Rent and Control households st~ll enrolled ~n the experDnent at

1 the end of two years. The dlScusSlon focuses on the slml1arlty of the estlmated log-llnear and 11near forms. The slffil1arlty of est~ates for the two

sltes and dlfferences from est1ffiates 1n other analyses are also noted.

The sectlon then turns to est1mates based on households that moved dur1ng the

exper1mental per10d. Agaln, the two speclflcatl0ns glve very s1ID11ar results,

and the est1mated elastlcltles for the two sltes are almost ldentlcal. A

pooled slte equatl0n 1S then estlmated and further alternatlve speclflcatlons

examlned. Flnally the estlmated income elastlcltles based on the nonexperlmental van.ations In household lncame are compared with estimates obtained

uslng the sample of Unconstralned households, wh1ch received an experimental

lncorne supplement.

Two income varl.ables were used in est3.matlon--a current lncome measure and

a permanent lncorne measure (three-year average lncome). 5J.nee the theoretical argurrents rev1ewed in Sectlon "3.3 suggest that response to the average

lnCome measure lS more interestlng as lt reflects longer-term adJustments,

~otential blas from attrl.tJ.on is examined In SectJ.on 6.2.

62
1

average ~ncome w~ll be dlscussed 1U the text. Table 4-1 presents the estlmated pr2ce and lucame elastlcltles 1n the overall percent of Rent and Control

2 sample, for both the log-linear and the l~near models. The log-l~near spec~-

flcatlon constralns each elastlclty estlmate to a 51ngle value for all ranges

3 of lucame and prlces. By contrast, under the I1near speclflcatlon the elas4

tlcltles vary wlth prlce and lucame.

The two numbers presented for comparlson represent derlved I1near prlce and

lucerne elastlcltles. They are computed from the est~ated parameters of the

linear demand functl0n uSlng the mean monthly lucame and mean relatlve

price, (I-a), for the sample, and also the mean of the elastlcltles computed

5 for ~nd~v~dual households. Even though the l~near elastic~t~es r~se (~n

absolute value) w~th ~ncome, the mean l~near elast~c~ty ~s close to the log11near est~ate. That the 11near and log-11near estLmates are so close for

the low-~ncome Demand Exper~ent populat~on suggests that ~f a single elast1C1ty est~ate 1S needed, the log-11near demand funct10n prov1des a

reasonable approXJ.mation for the mean of the sample. Accordingly, ~t will

be focused on for much of the rest of the report. For some. applJ..cat10ns,

one should nevertheless realJ.ze that the log-lJ.near prl.ce elast1c1ty estimate may be affected by the level and fustrlbut~on of income in the sample.

IThe current income estimates are presented in Appendix X. If households respond less to a temporary change in income than to a permanent change,

the est~mated current ~ncome elasticities will be smaller than the permanent

elasb..cJ.tJ..es. The est1mated current elasticit1es are indeed somewhat less

than those est1mated for average 1ncome.

2Appenfux Tables X-13 and X-l4 present the demand function estimates

for the log-l~near and linear IlOdels, respectively. Neither the l~near nor

the log-bnear form f~t the data better in both sites (us~ng actual rent).

3

A log-l~near equat~on was also est~ated us~ng In(~ncome) and f~ve

dummy var~ables (for the f~ve d~fferent percentage rebate levels) ~nstead

of the term In(l-a). In both s~tes, the F-tests suggest that the spec~f~­

cat~on w~th the f~ve dummy var~ables ~s not preferable to the one w~th the

term In(l-a); the F-stat~st~cs were less than 1.0 (see Append~x Table X-IS).

A d1fferent method for comput1ng response based on normal behavior is

presented ~n AppendlX VI.

4Except for the spec~al case of un~tary elastic~t~es. 5

S1nce the l1near e1astl.C1t1es are computed from rat10s of the parameters obta1ned from the est1mated demand equatl.on, the1r variance does not

eX1st 1f the error term, and hence the est1mates, are normally d1str1buted.

An approx~ate asymptotl.C var1ance can be computed, however, based on the

asymptot1c distr1bution of the est~ators (see, for example, Kmenta, 1971,

pp. 444-445). The standard error of the mean of the elastic~t~es ~s reported

also.

63
Table 4-1

PRICE AND INCOME ELASTICITY ESTIMATES

FOR THE OVERALL SAMPLE

PITTSBURGH PHOENIX

ELASTICITIES ELASTICITY ESTIMATE ELASTICITY ESTIMATE

Pr~ce Elastlclty

Log-llnear -0.178** -0.234**

(0.038) (0.049)

Llnear

At mean l.ucame -0.164** -0.213**

and prl.cea (0.042) (0.051)

Mean of lndlvl.dual -0.172 -0.211

estJ.Inates (0.005)° (0.007)°

b Income Elastl.cl.ty

Log-llnear 0.333** 0.435**

(0.028) (0.032)

Llnear

At mean lUCame 0.291** 0.377*

and prl.ce (0.021) (0.024) . Mean of lndlvldual 0.323 0.404

estunates (0.006)° (0.008)°

SAMPLE SIZE (674) (532)

SAMPLE: Percent of Rent and Control households actJ.ve at two years

after enrollment, excludlng those wlth enrollment lucornes over the elJ.gJ.­

bJ.ll.ty IJ.MJ.ts and those livlng in thelr own homes or 1n subsJ.dized houslng.

DATA SOURCES: Inltlal and monthly Household Report Forms, payments

flle, Appendlx Tables X-13 and X-14.

NOTE: Standard error 1n parentheses.

a. Mean monthly household lnoome = $417 for plttsburgh and $434 for

Phoenlx. Mean prlce - 0.75 for Plttsburgh and 0.77 for Phoenlx.

b. Three-year average lucarne 15 used here as a measure of permanent

lucame.

c.

**

Standard error of the mean.

t-statlstlc Slgnlflcant at the 0.01 level.

64
It ~s diff~cult to d~st~ngu~sh the two forms. F~gure 4-1 shows predicted

rent ~n each s~te as a funct~on of pr~ce, uSlng the estlmated log-llnear and

1 I1near expendlture functl0ns. Only for very hlgh and for very low 1ncames

do the curves dlverge, and then only for low rebate levels (the mean

monthly average ~ncome was $417 ~n P~ttsburgh and $434 ~n Phoen~x). Figure

4-2 compares predlctl0ns as a functlon of lucarne, controlling for the prlce

level. Agaln, predlcted values are generally close, beglnnlng to dlverge

only for hlgh lucornes.

The 11near speclflcatl0n, allowlng lnterpretatl0n of the parameters as

Stone-Geary parameters, 15 theoretlcally appeallng as the demand functl0n

can be der~ved from a known ut~l~ty funct~on (see Chapter 3). Plaus~ble

est1mates do result when lndlvldualohousehold data are used for estlmatlon.

However, the estlmates were not constralned to satisfy (and for a good part

2

of the sample do not sat~sfy) the ut~l~ty funct~on constraint, R ~PH81.

The pr~ce elast~c~ty po~nt est~ates for the total sample are about -0.18

1n P1ttsburgh and about -0.23 1n Phoenlxi the lncome elastlcity estlmates

are about 0.33 ~n P~ttsburgh and 0.44 ~n Phoen~x. Both the pr~ce and ~ncome

elastlc1ty est~ates are In the lower range of est1mates reported In the

economlC I1terature (see Sect10n 3.3). The 1ncome elast1c1ty est.1.mates,

1

The pred~cted rent for the l~near form ~s s~mply [from Equat~on (8)]

, ,( 1 ) R = A -- + I-a

(n)

For the log-l~near form, pred~cted rent ~s [from Equat~on (5)]

...... , ,

InR = B' + B In(Y) + B2 In(l-a) o 1

and

,I"'.. 1 '2 R = exp[ln(R) + - cr ] 2 E:

where &2 lS the est1mated var1ance of the log-llnear error term. ThlS

E: pred~ctor follows from the fact that ~f Z ~s lognormally d~str~buted, the

expected value of Z .1.S

E(Z) = exp[]l +

where and cr2 are the mean and var1ance, respectlvely, of In(Z). (see

Hast~ngs and Peacock, 1975, pp. 84-89.)

2

The est~ates of PH81 were $134 ~n P~ttsburgh and $148 ~n Phoen~x

while the mean rent for Control households at two years was $134 in P~ttsburgh and $144 ~n Phoenix. The est~mated demand funct~on represents a relat10nshlP descn.blng a "representative" household's taste for hous1ng. If

tastes differ across households, then It J.s not surprlsJ.ng that the constra1nt

~s not sat~sf~ed for all households.

65
Figure 4-1

EXPENDITURE FUNCTIONS: RENT VS. PRICE

(Pittsburgh)

1.00

0.95

0.90

085

Income =

$250

•

•

•

•

•

•

•

•

Income =

$400

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

Income =

$550

•

•

•

•

•

•

•

•

•

·.

•

•

•

•

•

•

0.80

.!;;" 075 ...

i

;; 0.70

ct:

065

0.60

0.55

0.50

, .

•

·

•

•

•

•

•

Linear

Log-linear

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

90 95 100105110115120 125 130135 140145 150155 160165 170 175 180 185 190195200205

Rent ($)

SAMPLE. Pittsburgh Percent of Rent and Control households active at two years after

enrollment, excluding those with enrollment Incomes over the ellglbhty limits and those

living In their own homes or in subSidized housing

DATA SOURCES. Initial and monthly Household Report Forms, and payments file.

66
FIgure 4-1 (continued)

EXPENDITURE FUNCTIONS: RENT VS. PRICE

(Phoenix)

•

1.00

0.95

0.90

0.85

0.80

.!! 0.75

et

..,

.; 0 70

a:

0.65

060

0.55

0.50

••••••••••

Income =

$250

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

•

Lmear

Log·lmear

•

•

•

Income =

$400

•

•

•

•

•

•

•

•

Income =

$550

•

•

•

•

•

•

•

•

90 95 100105110115120125130135 140145150155160165170175180185190195200205

Rent ($)

SAMPLE: Phoenix Percent of Rent and Control households active at two years after

enrollment, excluding those with enrollment incomes over the eligibility limits and those

living In their own homes or In subsidized hOUSing

DATA SOURCES Initial and monthly Household Report Forms, and payments file.

67
Figure 4-2

EXPENDITURE FUNCTIONS: RENT VS. INCOME

(Pittsburgh)

700

650

600

550

500

350

300

250

200

•••••••••

Lmear

Log·llnear

.

.

.• .• .

Price = 1 0 Price =0 75 Price =0 5

90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240

Rent ($)

SAMPLE. Pittsburgh Percent of Rent and Control households active at two years after

enrollment, excluding those With enrollment Incomes over the ellglbllty limits and those

liVing In their own homes or In subsidized housmg.

DATA SOURCES Initial and monthly Household Report Forms, and payments file.

68
Figure 4-2 (continued)

EXPENDITURE FUNCTIONS: RENT VS. INCOME

(Phoenix)

Pnce =1 0 Pnce =0 75 Pnce = 0.5

. ,

,

,

,•

. ,•

• • • •,

•

•,

•

•

•

,•

,

,

•,• ,

,

.• ,

,•

,• ,•

,•

• ,•

• ,• .,

,

.•

•

•

•

.' ,•

"

"

Linear

Log·lmear

,

,

,

,

,

•,

,

,

,• ,

,

•

• .'

300 ..........

550

200

700

500

650

250

600

~400

c

o

:iii

350

90 100 110 120 130 140 I

150

I

160 170 180 190 2~0 2~0 240

Rent ($)

SAMPLE: Phoenix Percent of Rent and Control households active at two years after

enrollment, excluding those With enrollment Incomes over the eligibility limits and those

liVing In their own homes or In subSidized housing

DATA SOURCES. Initial and monthly Household Report Forms, and payments file.

69
though low, are more closely comparable to estimates ~n the literature than

are the price elast~c~ty estimates. 1 Indeed, among the studJ.es c~ted ~n

Chapter 3 based on ~nd~v~dual household data, three found lower J.11come elastic~t~es (~n the 0.1 to 0.3 range) and f~ve found h~gher ones (~n the 0.4 to

0.6 range). In contrast, estimated price elastic~ties have ranged from -0.1

to -1.9, with most stud~es giv~ng values of -0.7 or lower. As noted in

Chapter 3, none.xper~menta1 est~mates of pr~ce elast~c~t~es are hampered by

problems ~nvolved ~n est~mat~ng price dJ.fferences across c~t~es or over time.

Thus the est~mates prov~ded by the Demand Exper~ment would appear to be more

rel~able. Chapter 6 dJ.scusses some reasons why the est~mated price elast~c~­

ty might be b~ased downward from the true elast1c~ty, though no e=dence of

b~as can be found.

The s~m~lar~ty ~n est~mates between the s~tes ~n both lucome and prlce elas2 t~c~ty ~s somewhat ~n contrast to the f~nd~ngs reported by Mayo (1977) us~ng

prelJ.nunary, fJ.rst-year data from the Demand Experiment. He found a somewhat

3 lower prJ.ce elastlclty 10 Plttsburgh.

Select~on of Movers

The entlre sample of renters may not be the best sample to use to estimate

the demand functJ.ons. The hous1ng demand and expendlture functlons dlscussed

~n Sectlons 3.1 and 3.2 were 1n theory based on the household's cho~ce of

1

The 11near specJ.flcatlon suggests that elastJ.cltles w~ll be lower

for lower-J.ncome populat1.ons. However, the estJ.mated coeff1.c1.ents for the

lJ.near expend1.ture funct~on lndlcate only small dlfferences ln elast1.c~t1.es

over a conslderable range of lncame. The med~an lncome for the u.s. renter

populat~on ~n 1975 was $7,900 (Annual Hous~ng Survey, 1975), wh~le the med~an

lncome of households ~n the Demand Exper1ffient was $4,578 In PJ.ttsburgh and

$5,199 ~n Phoen~x (us~ng the Census def~n~t~on of ~ncome). The ~mpl~ed

elastlcltJ.es from the 11near form at the U.S. medJ.an incorre (W1.th no rent

rebate) are only:

Prlce ..........•........

Income .

P~ttsburgh

-0.23

0.32

PhoeuJ.X

-0.29

0.40

the hypotheses

Table X-15).

coeffJ.clents,

(see Append~x

2

DespJ.te the s~J.larJ.ty of est1.mated

of homogeneJ.ty for the two sltes is reJected

3

Mayo·s est~ates (based on two-year average lncame) were -0.109

~n P~ttsburgh and -0.234 in Phoen~x for the pr~ce elastic~ty, and 0.338 ~n

p~ttsburgh and 0.400 ~n Phoen~ for the ~ncome elast~c~ty (p. 81). The

somewhat larger pr~ce elast~c~ty shown ~n Table 4-1 largely reflects further

changes 1.n expendltures durJ.ng the second year of the experLment. For

deta~ls, see Append~x IX.

70
opt~mal, ut~lity-maxl.InJ.z~ng, amounts of hous1.ng under the ~mp~c~t assumpt1.on

that the search and IlIOVl.ng costs of adJusting hous~ng consumpt~on to changed

household circumstances are negl1.gible. However, these costs may be sJ..gnif1.­

cant. Households may not adjust ~mmediately to correct ini::>alances ~n the~r

consumption of hous~ng and nonhousing goods. Thus, llllless they have moved

1 recently, they may not be consmn~ng their des~red amollllt of hous~ng. Such

dev~at~ons may involve both over- and llllderspending for hous~ng and might

tend to cancel out 1n general. However, the price changes creat~d by the

rent rebates were 1n one direco.on. Thus estJ.rnates of price elasticittes

based on all households may llllderest~mate the true elast~c~ty. .Th~s suggests

that .1.t 18 desJ.rable to estJ.mate a separate demand function solely for movers.

If renters generally adjust the~r hous~ng by IlIOv~ng, then households that did

not move would be expected to shcm httle change in housing expenfutures ~n

2

response to the Percent of Rent rebates. As these households move, they may

3 resporid more lJ.ke the households that moved dunng the experuental per~od.

Thus, estimates for movers may provide a better estJ.mate of the underlyJ..ng

demand functJ.on and the eventual response to a rent rebate than would estJ..­

mates based on the entl.re sample.

The ~dea that the psychological and f~nanc~al costs of moving may lead some

households to consume nonoptimal amollllts of housing for long per~ods of time

(see, for example, Muth, 1974) raises several other issues relevant to the

est~mat~on of demand fllllct~Ons.4 Thus, for example, households may attempt

to base theJ.r current housing purchases on their best notion of what the~r

income and pr~ces are likely to be over some period of tJ..Re. In part~cular,

they =ght e~ther adjust slowly to the price changes offered by the Percent

of Rent rebates or they =ght fuscount these rebates because the exper~IOOnt

lasted for only three years. These factors would suggest that even the

1

Some adJustments may be made by repairs or alterat~ons to the household's current unit, wJ..thout movJ..ng. These entail thelr own dJ..fficultJ..es and

in any case are IJ..kely, for renters at least, to be conf~ned to relat~vely

nu..nor i terns .

2Nonmovers' rental eJq?enditures may change due to inflatJ..on or as a

result of landlord ~mprovements to the dwelling llll~t.

3

Ev~dence developed by MacM1.11an (1978) suggests that most low-~ncome

renter households will move wJ..thin a perJ..od of f1ve years.

4

Appenfux VII explores the ~lI\Pl~cations of housing diseqmhbr~um

and mov~ng costs for mobihty.

71
responses of movers observed during the experJ.ment might be lower than the

eventual respens e to a permanent program.

On the other hand", households that move may have the greatest long-run response to the rent rebate offer and hence the greatest 2ncent1ve to adJust

the1r hous1.ng. Th1S would mean that the responses of movers would tend to

overest1mate the eventual response to a long-term program. Chapter 6 d1.scusses these and other 1SSueS 1n the analysis, and develops eV1dence that

they do not 1n fact pose ser1.OUS problems 1n using households that moved to

est1mate household responses to changes in pr1ce and 1ncome.

Table 4~2 presents the elastJ.cJ.tJ.es estJ.mated for the sample of households

mov1ng between enrollment and two years after enrollment. The estLffiated

pol-nt elast1c1t1.es for pr1ce are -0.21 1n P1ttsburgh and -0.22 1n Phoen1x,

wh1.1e for 1ncame, they are l.dent1.cal: 0.36 1n both S1.tes. The S1.te

slm1.1ar1ty ~s strlking, especlally Slnce Mayo's (1977) results for movers

1 us~ng flrst-year data showed a markedly lower prlce elastlclty In Plttsburgh.

Indeed, the close s~llarlty suggests that one demand equatl0n can be estlmated for the ent~re mover sample (pooled across the sltes).

When a slte-speclflc ~ntercept lS allowed, the hypothesls that prlce and

2 lncorne elastlcltles are the same In the two Sltes lS not reJected. (The

1

Mayo's estJl11ates for flrst-year movers of the prlce and lncorne

elastlcltles of demand based on two-year average lncorne are (p. 82)

Prlce elastlclty

Income elastlclty

pJ.ttsburgh

-.045

.365

phoenlX

-.354

.348

due to the

(see Sectl0n

J.s largely

exper1m.ent

The dlfference In the prlce elastlclty estlmates

behavlor of movers durlng the second year of the

6.1). For further detaJ.ls, see AppendJ.x IX.

2

A slte-speclflc lntercept allows houslng and nonhouslng prlces to

vary between the sltes. ThlS can be seen by rewrltlng Equatl0n (1) for

:::" ",C. "~.<"'.:::~::"":: ~:,P::(':~)O~::'~ ~~) (p,"

+ In(p~GH) (PITTSBURGH)

and

(J.J.) So + Sl In (:~HX) + S2

+ In (p~HX) (PHOENIX)

(footnote contlnued)

72
Table 4-2

PRICE AND INCO~m ELASTICITY ESTIMATES

FOR THE MOVERS SAMPLE

PITTSBURGH PHOENIX

ELASTICITIES ELASTICITY ESTIMATE ELASTICITY ESTIMATE

Prlce Elastlclty

Log-llnear -0.211** -0.219**

(0.063) (0.059)

Llnear

At mean lncame -0.222** -0.198**

and prlcea (0.069) (0.061)

Mean of lndlvldual -0.227 -0.216

estlIDates (0.008)c (0.008)c

b Income Elast~c~ty

Log-llnear 0.363** 0.364**

(0.052) (0.042)

Llnear

At mean 1.ncorne 0.375** 0.330**

and prlce (0.038) (0.029)

Mean of lndl.vl.dual 0.403 0.380

estunates (0.011) c (O.OlO)c

SAMPLE SIZE (236) (292)

SAMPLE: Percent of Rent and Control movers actlve at two years

after enrollment, excludlng those wl.th enrollment l.UCOrnes over the e11.g1­

blilty ll.rnl.ts and those 11.Vlng 1D thel.r own hames or 1n subsl.dized housl.ng.

DATA SOURCES: In~t~al and monthly Household Report Forms, payments

f~le, Append~x Tables X-13 and X-14.

NOTE: Standard error 10 parentheses.

a. Mean monthly household ~ncome·= $416 for p~ttsburgh and $430

for phoen~x. Mean pr~ce = 0.75 for P~ttsburgh and 0.80 for Phoen~x.

b. Three-year average lucerne 18 used here as a measure of

permanent l.ucerne.

c. Standard error of the mean.

** t-statl.stlc sl.gnl.fl.cant at the 0.01 level.

73
hypothes~s of homogene~ty of all regress~on coeff~c1ents ~n the two 51te5

(1nclud1ng the 1ntercept) was reJected.) The pr1ce elast1c1ty est1ffiated by

th1s pooled log-11near regress10n with different site 1ntercepts 1S -0.22,

and the 1ncome elast1c1ty 1S 0.36, both s1gn1f1cantly d1fferent from zero at

the 0.01 level (see Table 4-3).

The linear form of the expendJ.tures equation reqm.res that pr1ce and income

elasticities increase as income rises (except for the case of unltaxy elastlcit1es). As a further test for nonconstant elasb.cltles, the sample was

SpIlt 1n half accordJ.ng to average income and a log-11near expenditures

equat10n est1mated for each half. The results for the elast1C1t1es are

summarized 1n Table 4-4. The estimates for each half are close (all households are of course relatlvely low-lncome). The pr1ce elast1cit1es for

both s1tes are slightly h1gher for the upper half of the 1ncome distr1bution.

The J..ncome elast1cities are larger for the h1gher l.ncome group 1n Phoenix

(footnote cont1nued)

Rewr1t1ng Equat10n (1.1) 1n terms of P1.ttsburgh pr1.ces and rearrang1ng terms

(111) In (RpHX) = ilO + ill In (y)

+ (l+il2) In(p:GH) _ (ill+il2) In(p~GH)

r) r) + (1+il2 ) In - lill +il2) In-- PGH PGH

PH Pz

Subtract1ng (1) from (111), the d1fference between the logar1thm rent 1n

Phoemx and 1n Pittsburgh for the same household is

(1V)

Th1s should equal the coeff1c1ent of the dummy var1able 1ncluded to represent

phoen1.x pr1.ces. The approxlrnate rat1.0S of hous1ng and nonhouslng pr1.ces are

ava1lable from the BLS C1ty Worker 1ntermed1ate budgets for 1975 for P1ttsburgh

and from Ins1de Phoen1x 1977 for Phoen1x. (The latter only reports total

hous1ng bUdget rather than the more des1rable total rental budget.) These

rat1.os are 1.028 and 0.955 for hous1.ng and nonhous1ng pr1ces, respect1vely,

1ffiply1ng a s1te-spec1f1c 1ntercept 0.029 h1gher 1n Phoen1x. The actual est1­

mate was 0.098 w1th a standard error of 0.026, a good deal larger. If the BLS

data for total houslng underest~ate the rat10 of rental pr1.ces and the true

rat10 1S 1n the range 1.05 - 1.10 (as computat1ons by Merr1ll, 1977, p. 114,

suggest), then the 1mp11ed coeff1c1ent would be between 0.045 and 0.082, closer

to the est1.mated coeff1.c1.ent.

74
Table 4-3

PRICE AND INCOME ELASTICITY ESTIMATES

FOR THE MOVERS SAMPLE

(Pooled SJ.tes)

ELASTICITY ESTIMATE

Price elastJ.cJ.ty (log-lJ.near)

95 percent confldence interval

a Income elastJ.cJ.ty (log-lJ.near)

95 percent conf~dence ~nterval

SAMPLE SIZE

-0.216**

(0.043)

[-0.301, -0.131]

0.364**

(0.033)

[0.299, 0.429]

(528)

SAMPLE: Percent of Rent and control movers actlve at two years

after enrollment, excludlng those wlth enrollment lucornes over the

elJ.gJ.blJ.ty lJ.mJ.ts and those lJ.vJ.ng J.n theJ.r own homes or in subsJ.dJ.zed

housJ.ng.

DATA SOURCES: InJ.tJ.al and monthly Household Report Forms, payments

fJ.le, Appendix Table x-16.

NOTE: Standard error J.n parentheses.

a.. Three-year average income 15 used here as a measure of pennanent

J.ncome.

** t-statJ.stic sJ.gnJ.fJ.cant at the 0.01 level.

75
Table 4-4

DEMAND ELASTICITIES USING SAMPLES STRATIFIED

BY MEDIAN MONTHLY INCOME

PITTSBURGH PHOENIX

LOWER HALF UPPER HALF LOWER HALF UPPER HALF

OF INCOME OF INCOME OF INCOME OF INCOME

ELASTICITIES DISTRIBUTION DISTRIBUTION DISTRIBUTION DISTRIBUTION

Pr1ce elast1c1ty -0.167* -0.26S** -0.21S** -0.222**

(0.OS2) (0.010) (O.OSl) (0.OS7)

Income elast~c~ty 0.439** '0.427** 0.357** 0.415**

(0.121) (0.123) (0.096) (0.129)

SAMPLE SIZE (lIS) (lIS) (136) (156)

SAMPLE: Percent of Rent and Control movers act~ve at two years after enrollment, exclud~ng those

w~th enrollment ~ncomes over the el~g~b~l~ty l~m~ts and those l~ving in their own homes or ~n subs~d~zed

housing.

DATA SOURCES: In~t~al and monthly Household Report Forms, payments f~le, and Appendix Table X-17.

NOTES: Standard errors ~n parentheses. Med~an income was $37S per month in Pittsburgh and $415 per

month 1n Phoen1x.

* t-stat~st~c s~gnif~cant at the 0.05 level.

** t-stat~st~c s~gnif1cant at the 0.01 level.
and smaller ~n Pittsburgh. None of the mfferences is larger than the error

of estimate. A log-l~near spline funct~on that allowed the est~mated income

coeffic~ent to differ for each half of the ~ncome mstribution was also est~-

1 mated. The results showed no s~gn~f~cant mfference in elasttc~ties at mfferent income levels, at least w~thin the ~ncone range of exper~mental households (see Table 4-5). Further investigation of a s~le show~ng wider ~ncome

variab~lity would be useful.

Unconstra~ned Households

Payments to households the Unconstra~ned plan were des~gned to equal the

d~fference between the est~ated

for the~r household s~ze, and 25

cost of modest, eXlst~ng standard houslng

2 percent of thelr lncome~ ReClpients were

where D

free to spend the payments, Whlch were unrelated to theJ.r actual houslng,

as they w~shed. Thus, the payment's effect on housing expend~tures

provldes dlrect eVldence on the wayan uncanstralned lncame transfer payment

~s l~kely to be allocated to hous~ng. Because of the d~rect funct~onal relatlonshlp between household lucame and the unconstraJ.ned allowance payment, a

hous~ng expend~ture funct~on should not be used to est~ate d~rectly the

3 expendJ.ture elastlclty of an lucame transfer payment.

lA spl~ne functton pe=ts the estimated elastic~ty to vary slIr:>othly

from one regression regime to another Wl.thout a discontlnm.ty. The spllne

functl.on estl.mated was

1 In(R) = So + Sl In(Y) + Sl D[ln(Y) - In(Y)] + Szln(l - a)

< A

{

o ~f Y - Y,

1 ~f Y > Y, and

Y mefuan l.ucame.

Fur a further explanat~on of spl~ne funct~ons, see Su~ts, et al (1978).

2

The payment formula was

S = C* - 0.25Y

where

S monthly payment

c* est~ated cost of modest, ex~st~ng

standard hous~ng, var~ed by household s~ze, and

Y = monthly household ~ncome.

3

For example, ~n the l~near expend~ture funct~on R = n + SY + yS,

S and Y are def~n~tionally related through the payment formula.

77
Table 4-5

INCOME ELASTICITIES USING SPLINE FUNCTION

PITTSBURGH PHOENIX

HOUSEHOLD GROUP INCOME ELASTICITY INCOME ELASTICITY

Lower half of 0.375** 0.342**

~ncorne d~str1bution (0.103) (0.077)

Upper half of 0.351* 0.395*

lucame dlstrlbutl0na (0.158) (0.145)

SAMPLE SIZE (236) (292)

SAMPLE: percent of Rent and Control movers actlve at two years

after enrollment, excludlng those wlth enrollment lucornes over the eligibl11ty 11mlts and those 11vlng 1n their own homes or 1n Subsldlzed housing.

DATA SOURCES, In~tial and monthly Household Report Forms, payments

f~le, and Appendix Table X-lB.

NOTES: Standard errors ~n parentheses. Med~an ~ncome was $378 per

month ~n P~ttsburgh and $415 per month in Phoen~x.

a. The difference 1n elastlclty 15 not slgnlflcant.

* t-stat~st~c s~gn~f~cant at the 0.05 level.

** t-stat~st~c s~gn~ficant at the 0.01 level.

78
Several tests were carr~ed out to see whether the Unconstra~ned households

treated the payment as ~ncome and, ~f so, whether their response to income

changes was the same as the J..ncorne response estimated for percent of Rent

and control households. Flrst, rent for UnconstraJ..ned movers at two years

was pred1cted uS1ng the log-11near demand equations estimated for percent

of Rent and Control movers treatJ..ng the allowance payment as J.ncome--the

I f1t was as good or better than for Percent of Rent and Control households.

Next, two log-lJ..near demand equatlons were estJ..roated for Unconstralned and

Control movers, f1rst to test whether a dummy var1able for UnconstraJ..ned

households ind1cated a further exper1mental effect when the allowance payment 15 J..ncluded J..n the J..ncome varJ..able, and second, to test whether the

J..ncome elastJ..cJ..ty d1ffered between UnconstraJ..ned and Control movers. The

results are presented ~n Table 4-6. The est~mated ~ncome elast~cities

(us1ng average income) are 0.29 1n P1ttsburgh and 0.34 1n phoen1x, not

s1gn1f1cantly d1fferent from the est1ffiates obta1ned for Percent of Rent and

Control movers. Furthermore, the separate var~ables allow~ng for d~fferences

~n the level and ~ncome elast~c~ty of hous~ng expend~tures between Unconstrained and Control households were not s1gn1f1cant. Th1s suggests that

the responses of Unconstra~ned households are adequately characterized 1n

terms of add1t~ons to ~ncome that are treated like any other ~ncome.

F1nally, a model used by Hyrnans and Shap1ro (1974) to 1nvestigate the elast1c~ty of food expend~tures w~th respect to transfer ~ncome, was est~ated.

In that model, the compos~t1on of ~ncome ~s assumed to affect the elast~c~ty.

The expend~ture equat~on, adapted to the present case, ~s

(Il)

where Y is average ~ncome, and S ~s the allowance payment, and

(12)

where n1 ~s the elast~c~ty w~th respect to average ~ncome, and n2 measures

the extent to wh1ch the 1ncome elast1c1ty changes w1th changes 1n the composition of ~ncome.

~or Unconstra1ned movers, the R2 equaled 0.22 1n P1ttsburgh and 0.41

1n Phoen1x compared to 0.18 and 0.23, respectively, for the cornb1ned Percent

of Rent and Control household sample.

79
Table 4-6

ESTIMATES OF A LOG-LINEAR DEMAND EQUATION

WITH UNCONSTRAINED HOUSEHOLDS

PITTSBURGH PHOENIX

DUMMY DUMMY

VARIABLE INTERACTION VARIABLE INTERACTION

INDEPENDENT VARIABLE MODEL MODEL MODEL MODEL

Constant 3.172** 3.176** 2.960** 2.961**

(0.475) (0.474) (0.407) (0.408)

In (lncomea + payment) 0.292** 0.292** 0.340** 0.340**

(0.078) (0.078) (0.067) (0.067)

Unconstralned household 0.029 -- 0.067 --

(0.067) (0.074)

Unconstralned household

x 1n(1ncome + payment) -- 0.005 -- 0.010

(0.011) (0.012)

AdJusted R2 0.110 0.110 0.169 0.168

Sample SHe (116) (116) (144) (144)

SAMPLE: Unconstralned and Control movers actlve at two years after

enrollment, excludlng those Wlth enrollment lucornes over the eliglblilty

lLmlts and those Ilvlng 10 thelr own homes or 1n SubSldized houslng.

DATA SOURCES: In1t1a1 and monthly Household Report Forms, and

payments f11e.

NOTE: standard error 1n parentheses~

a. Income measured as average J..ncome.

** t-statlstlc slgnlflcant at the 0.01 level.

80
If households respond to the allowance paynent as they would to income, TJ 2

should equal zero. When est~mated, the null hypothesis, H

O:TJ2 = 0, could not

be rejected in elther slte, confl.rming the earller f1.ndJ.ng that households

1 respond to the payment as they would to ~ncome from other sources. The

est~ates of the ~ncome elast~c~ty were 0.28 ~n P~ttsburgh and 0.35 ~n

Phoenlx, once aga1n not 51gnlflcantly dl.fferent from the estlmates for

Percent of Rent and Control movers.

In sUIn, l.t appears that low-1.ncome households do respond to both rent rebates

and 1ncome subs1d1es by 1nCreaS1.ng their hous1ng expendltures. In response

to a 10 percent decrease 1.0 pr1ces, these households, when they move, wl11

lncrease thelr expendltures on average by approximately 2a2 percent. In

response to a 10 percent lncrease In lncome, these households, when they

move, wl11 lllcrease thelr expendltures on average by approximately 3.6

percent.

4.3 DEMOGRAPHIC VARIABLES AFFECTING DEMAND FOR HOUSING

The precedlng two sectlonS dlscussed prlce and lncome elasticltles based on

houslng expendlture functl0ns that lncluded only prlce and lncome as lndependent varlables. Other varlables may also affect houslng demand, Slnce

dlfferent demographlc groups may have dlfferent relatlve preferences for

houslng versus other goods and servlcesa Furthermore, pOI1Cy lnterest 1S

often focused on certaln demographlc groups, 1n partlcular, mlnorlty or

elderly households.

The data collected dur~ng the Demand Exper~ent enable deta~led characterlzat10n of each household In terms of demographlc attrlbutes. A comblnatl0n

of statlstlcal tests, conslderatl0n of sample slzes, and Judgment was used

to reduce the relevant demographlc characterlstlcs to two statistlcally

slgnlflcant and pollcy-relevant varlables: mlnorlty status and household

2 compos~t~on. M~nor~ty status ~nd~cates whether the head of the household

1

The est1mates of nl and n2 uSlng Unconstralned and Control movers

were: p~ttsburgh

0.285

(0.082)

-0.007

(0.073)

phoenl.x

0.352

(0.066)

0.062

(0.051) 2

Age, sex, and educat~onal atta~nment of the head of household, as

well as household s~Ze (w~thout compos~t~on) were also tested. These had

no s~gn~f1cant effect on the est1rnated parameters of the demand funct10n

or on the overall f1t when 1ncluded as CQVar1ates 10 the same equatlon as

mlnorlty status and household composltlon.

81
is a member of a IlIJ.nority g=up (black in P~ttsburgh, black or Spanish

Anerican in Phoemx). Household composition indicates whether the household

consists only of a s~ngle person (restr~cted by p=gram rules almost exclusively to elderly persons); is a s~ngle head of household (w~th ch~ldren or

other family members present); ~s a couple (w~ th or without children). I

These three types of household are denoted s~ngle-person, single-headed w~ th

others present, and couple, respectively.

Two alternat~ve methods for determin~ng the ~mportance of demographic charactenstl.cs in the housl.ng demand functl.ons were used: (1) the characterl.stics were J.ncluded as vanables (covariates) in the expenditure function,

thus perIllJ.tt~ng the intercept to vary, or (2) the sample was strahf~ed to

pernu.t the elastl.cl.tl.es to vary as well. The results of thl.S l.nvestl.gatl.on

2

are fuscussed below for the sample of movers. Because the results for the

log-ll.near and the ll.near equatl.ons are very sl.nu.lar, only the former are

discussed. In adchtion, the l.ncome measure used, as in Sectl.on 4.2, 1.5

average l.ncome ..

Despite the nearly ident1.cal estl.mates obtal.ned for movers l.n each 81.te l.n

Sectl.on 4 .. 2, the dJ.scussion starts with separate analysl.s for each site. This

is done partly for comparability with the analys~s of Chapter 5 and partly

because it seemed plaus~ble that demograph~c differences ~n response may exist

between the s~tes. In fact, fufferent patterns of demograph~c effects do

emerge l.n the two sl.tes.. In the end, however I it appears that, from a stat!.stical viewpoint, the s~ tes can still be pooled. The only cons~stently important dernograph~c fufference in ~ncome and price elasticit!.es is between nu.nor­

~t2es and non~nor~t!.es.

I

S~nce there ~s a partl.cular pol~cy interest ~n elderly householas,

var~anee rat~o tests were carr~ed out to exanune whether the elderly and

nonelderly s~ngle-person households compr~se a homogeneous group, that J.s,

whether the~r housing demand funct~ons are the same. Tins hypothesis could

not be reJected, ma~nly because there were so few nonelderly s1ngle-person

households in the sample. There were too few elderly couples to analyze

separately. Secondly, S1nee 1n Phoenix the nu.nor1ty group consJ.sts of both

black and Spanish American households, variance rano tests were used to

test whether there is a difference in behavior between these two minority

g=ups. Again, the hypothesis of homogene~ty could not be reJected, probably

because the sample of black households in Phoenix is small. Accorfungly, all

s~ngle-person and all IlIJ.nor~ty households are examined, rather than separating

the groups.

2 . 4 . b . SectJ.on .2 dJ.scussed the reason for choosJ.ng th1S sample as e1ng

more suitable for the est~mat~on of demand funct~ons. The results for the

overall sample are nevertheless presented and fuscussed in Appenfux VIII.

82
DemographJ.c Variables as CovarJ.ates

Under this approach, demographJ.c variables were included as dUlllll\Y variables

in the demand equation. As a consequence, only the intercepts can differ

among groups. The variables J.ncluded were those infucatJ.ng minorJ.t:y status

and household compositJ.on. Models that J.ncluded just a minorJ.t:y variable,

Just household composJ.tJ.on varJ.ables, and combinatJ.ons of the two were estiI mated; these are presented J.n Appenfux Table X-19.

Different demographJ.c vanables are important at the two sites. In PJ.ttsburgh, no demographic covariate has an effect on the housJ.ng expel1ditures

of movers. The household composition varJ.ables J.ncrease the adjusted value

of R2 slightly (this IOOdel is presented in Table 4-7), but once these varJ.ables are included J.n the specification, there J.S no further gain by addJ.ng

the minorJ.ty status varJ.ables.

In Phoenix, the household compOSl.tl.on varl.ables are not sl.gnificant by themselves but minority status 1.8. Interaction between the two variables is

2 infucated; the complete J.nteraction model has the highest adJusted R ThJ.s

model (also presented in Table 4-7) infucates that there J.S not much difference among nonmJ.nority IOOver households J.n Phoenix by household composJ.tion

and that (with the possible exceptJ.on of minorJ.ty single-person households)

mJ.nority households spend less on housJ.ng.

Complete StratifJ.cation

The covarJ.ate analysJ.s showed that the delOOgraphic groups should have separate

l.ntercepts. The specifl.cation discussed J.n the covarl.ate analysis implicJ.tly

assumes that all the groups have the same prl.ce and income elasticihas.

Stratification allows these to vary among groups. Each equation was estJ.mated

for nonmJ.nority and mJ.nority households, for sJ.ngle-person households, households headed by a couple, and for households headed by a sJ.ngle person with

others present. In addition, each equatJ.on was estJ.mated for the subsamples

created by combl.ning the minority and the household compositl.on criteria.

These equations (presented in Appendix Table X-19) were used to test whether

elasticJ.ties differed a=ng the groups.

I

The excluded classes (represented by the constant term) are nonnu.norities for regressions with a minority variable, couples (with and wJ.thout children) for regressl.ons WI.th household compositl.on varl.ables, and nonminorJ.ty couples (wJ.th and wJ.thout children) for regressJ.ons wJ.th combined

minorit:y/household composition variables.

83
Table 4-7

LOG-LINEAR DEMAND FUNCTIONS USING DEMOGRAPHIC VARIABLES

AS COVARIATES FOR THE MOVER SAMPLE

INDEPENDENT

VARIABLE

Constant

Income elast1c1ty

Prlce elast1c1ty

S~ngle-person households

S~ngle head of household

W1th others present

Nonminority s2ngle-person households

Nonnunority s~ngle head of household

w~th others present

M1nor1ty s1ngle-person households

M~nor~ty s~ngle head of household

w1th others present

M~nor~ty households headed by

a couple

Sample S~ze

PITTSBURGH

2.540**

(0.401)

0.391**

(0.064)

-0.219**

(0.064)

0.031

(0.067)

0.075t

(0.043)

0.188

(234)

PHOENIX

2.915**

(0.299)

0.365**

(0.048)

-0.226**

(0.58)

-0.080

(0.071)

-0.064

(0.049)

-0.065

(0.139)

-0.105t

(0.058)

-0.289**

(0.054)

0.285

(285)

SAMPLE: Percent of Rent and Control movers act1ve at two years after

enrollment, exclud1ng those w1th enrollment lucornes over the e11gib111ty

1~1ts and those 11v1ng 10 the1r own homes or 10 SubSld1zed houS1ng.

DATA SOURCES: In~t~al and monthly Household Report Forms, payments

f~le, Append~x Table X-l~.

NOTE: standard error 10 parentheses.

t t-stat~st~c sign~f~cant at the 0.10 level.

** t-stat1stlc s1gn1f1cant at the 0.01 level.

84
Analys~s of nu.non ty status. In P~ttsburgh, minodty (black) and nonminority

households have approximately the same eqUJ.I~briurn demand for hous~ng. Tlus

1 ~s ~nd1.cated by an ~ns~gru.f~cant coeffJ.cJ.ent on the Inl.norJ.ty dummy varJ.able,

as well as by an .l.nsJ.gru.f.l.cant variance-ratio test statJ.stJ..c on the chf£erence

~n elastic~t~es (see Table 4-S). Moreover, minor~ty and nonnu.nority households

spent app=ximately the same amount on rent at enrollment (see Appenfux Table

X-20) •

In Phoenix, where rru.norJ.ty households are predominately Sparush AnerJ.can,

nu.nor~ty and nonnu.nonty households appear to have different eqUJ.libr~urn demand

functions. A variance-ratio test for homogeneity of the estimated elastJ.cJ.ties,

g~ven different ~ntercepts for nu.nority and nonnu.nority households, rejects that

hypothesis. MinorJ.ty households in PhoenJ.x have much lower price and income

elastic~hes than do nonminonty households (see Table 4-S). 2 Further, nu.nority

households there start out ~n less expens~ve housing. The lower elashcit~es

found for nu.nonty households in Phoen~x appear to reflect lower elastic~hes

for SpanJ.sh 1merican households in partJ..uclar, but sample SJ.zes are too small

to allow conclus~ve results. While the estimated elasticities for Spanish

American households are lower than for any other g=up and are not s~gnificantly

dl.fferent from zero, the errors of estJ.mate are too large for a conclusive fJ.nd­

~ng of fufference. The est=ates for Span~sh Amer~can households are also not

s~gn~ficantly fufferent f=m the overall est~mates (which are significantly

different from zero) .3

Analys~s of household compos~t~on. In P~ttsburgh, the equation w~th household

compos~tion dummy var~ables (Appenfux Table x-19) ~ndicated that ~ntercepts

may va:ty among the three household types. Table 4-9 presents the results of

strat~fy~ng the sample by household type. A var~ance rat~o test of homogeneity

of the elast1c~t~es, given fufferent ~ntercepts, rejects the homogene~ty hypo1

See Appenfux Table X-19.

2Note J.n particular that the overall est.l.mated income elasticity in

Phoenix (0.37) does not fall ~n the 95 percent conf~dence ~nterval of the

minor~ty estimate ~n that s~te (0. IS) •

3

Mayo (1977) found that nu.nor~ty households were at least as responsive

as nomru.nor~ty households, and perhaps more responsJ.ve. H1S results depend on

the particular model used ~n that report--a part~al adJustment model for all

households. Since MacMillan (197S) found a s~gnif~cant rac~al effect on mobil­

~ty, ~t ~s l~kely that Mayo's results to some extent reflect fufferences in

mob~hty.

S5
Table 4-8

EXPENDITURE ELASTICITIES BY MINORITY STATUS

PITTSBURGH PHOENIX

PRICE INCOME SAMPLE PRICE INCOME SAMPLE

HOUSEHOLD GROUP ELASTICITY ELASTICITY SIZE ELASTICITY ELASTICITY SIZE

All households -0.213** 0.359** (234) -0.219** 0.370** (285)

(0.064) (0.053) (0.060) (0.043)

Nonm~nority households -0.210** 0.386** (196) -0.287** 0.431** (185)

(0.069) (0.057) (0.068) (0.047)

Minor~ty householdsa -0.204 0.212 (38) -0.179t 0.177* (100)

(0.179) (0.148) (0.105) (0.083)

Black households b b -0.255 0.224 (28) 00

'" (0.217) (0.168)

Spanish American households c -0.137 0.133 (72)

(0.122) (0.101)

SAMPLE: percent of Rent and Control movers act~ve at two years after enrollment, exclud~ng those w~th

enrollment incomes over the el~gib~l~ty lim~ts and those l~ving ~n the~r own homes or ~n subsid~zed hous~ng.

DATA SOURCES: In~t~al and monthly Household Report Forms, payments f~le, and Append~x Table X-21.

NOTE: Standard error ~n parentheses.

a. A var~ance-ratio test could not reJect the hypothes~s of homogeneity between nonm~nority and

~nority households ~n Pittsburgh (F(2,227) = 0.50) but could in Phoen~x (F(2,279) = 4.42), (cr~t~cal value

= 3.00 at the 0.05 level).

b. ~nonty households ~n P~ttsburgh are all black.

c. A var~ance-ratio test could not reject the hypothesis of homogeneity between Span~sh Amencan and

black households in Phoen~x (F (2,94) = 0.49), critical value = 3.11 at the 0.05 level).

t t-stat~st~c s~gn~ficant at the 0.10 level.

* t-stat~st~c s~gnif~cant at the 0.05 level.

** t-statist~c signif~cant at the 0.01 level.
Table 4-9

EXPENDITURE ELASTICITIES BY HOUSEHOLD COMPOSITION

PITTSBURGH PHOENIX

PRICE INCOME SAMPLE PRICE INCOME SAMPLE

HOUSEHOLD GROUP ELASTICITY ELASTICITY SIZE ELASTICITY ELASTICITY SIZE

All households -0.213** 0.359** (234) -0.219** 0.370** (285)

(0.064) (0.053) (0.060) (0.043)

S~ng1e-person households -0.077 0.274 (33) -0.245t 0.480** (32)

(0.189) (0.184) (0.138) (0.080)

S~ng1e-headed households -0.156t 0.165 (98) -0.128 0.342** (121)

w~th others present (0.092) (0.102) (0.087) (0.072)

Households headed by -0.364** 0.613** (103) -0.327** 0.383** (132)

a couple (0.096) (0.090) (0.100) (0.083)

0:>

-.J

SAMPLE: Percent of Rent and Control movers active at two years after enrollment, excluding those with

enrollment incomes over the e1~g~bi1~ty limits and those living ~n the~r own homes or in subsidized hous~ng.

DATA SOURCES: Initial and monthly Household Report Forms, payments f~le, and Append~x Table X-21.

NOTES: Standard error in parentheses. A variance-rat~o test could reject the hypothes~s of homogene~ty

among household types in Pittsburgh (F(4,225) = 3.20) but could not in Phoenix (F(4,277) = 1.62), (crit~ca1

value = 2.37 at the 0.05 level).

t t-statist~c significant at the 0.10 level.

** t-stat~st~c s~gn~ficant at the 0.01 level.
thesis. Exanu.nat~on of the estllnates (presented in Table 4-9) shows large

apparent fufferences among elashc~ties by fanu.ly type. Households headed by

1

a couple have the largest elast~C1t~es with respect to ~ncome (0.61) and

w~th respect to pr~ce (-0.36) (see Table 4-9). The other two groups have

lower elastl.cl.ties. However, the estimated coeffl.cients have large standard

errors, and the equat~ons have low R

2 (see Appendix Table X-21). 2 P~rw~se

compar~sons of the elast~C1t~es among the three deIOOgraph~c groups showed

only one sl.gnificant difference (between the l.ncone elastl.CJ.ties for sJ.ngleheaded households and couples ~n P~ttsburgh).

In contrast, though, ~n Phoen~x, the hypothes~s of homogene~ty of the dsmand

elasticit~es by household type cannot be reJected once the different intercepts noted earll-er are taken into account.

PooIJ.ng the 51-tas was reasonable for the complete mover saIl'Y?le (see Section

4.2). Although the infuvidual exam~nation of the two sites above idsnt~f~ed

sorrewhat dl.fferent demographl.c patterns l.n each 51-te , varl.ance ratio tests

cannot reJect the hypotheses that the two s~tes can be pooled when stratif~ed by either race or by household composition (allow~ng for site-spec~fic

~ntercepts). Table 4-10 presents these est~mated elast~c~ties. Further,

once the 51-tes are pooled, homogeneity across demographJ.c groups is rejected

for race/ethn~city, but not for household types (desp~te the w~de var~at~on

~n coeff~c~ents among the different groups).

In concluslon, the statist1cal eVl.dence J.ndJ.cates that due to the fairly

large variances of some of the elasticity estimates, the two sites can stJ.ll

be pooled when estimates are obtained strat~bed by demograph~c groups. It

appears that nunar1-tJ.es have smaller responses to price and income than

nonrninor~tJ.es. This effect ~s especially marked in Phoenix. In add~t~on,

while there is eV1.dence of dl.fferences 1.n elast~cl. ties across household

types in P~ttsburgh, these are not statistically sig=f~cant for the pooleds1te estimates or for Phoenix alone.

1

The overall est~mated ~ncome elast~c~ty ~n P~ttsburgh (0.36) does not

fall ~n the 95 percent confidence ~nterval of the couple est~mate ~n that s~ te

(0 .61) • 2

A further test of homogene~ty w~th respect to household compos~t~on

~s poss~ble w~th~n the nonminor~ty subsample. (Such a test is not meaningful

for the minonty subs amp Ie because of small sample s~zes.) As with the overall

sample of movers, the hypothesis of homogeneity of the elasticities for non­

=nor~ty households ~n Pittsburgh among household types can be reJected. ('!he

test statistic is F(4,187) = 3.44, with a cr~tical value of 2.37 at the 0.05

level.)

88
Table 4-10

PRICE AND INCOME ELASTICITY ESTIMATES

FOR POOLED SITES BY DEMOGRAPHIC CHARACTERISTICS

HOUSEHOLD PRICE INCOME VARIANCE-RATIO SAMPLE

GROUP ELASTICITY ELASTICITY F-STATISTICa SIZE

All movers -0.217** 0.366** 0.017 (519)

(0.044) (0.033)

wh~te households -0.249** 0.413** 0.437 (381)

(0.048) (0.036)

M~nor~ty households -0.183* 0.184** 0.023 (138)

(0.089) (0.071)

SJ.ngle-person -0.175 0.426** 0.723 (65)

households (0.116) (0.083)

S~ngle head of house- -0.137* 0.294** 0.999 (219)

hold w~th others (0.063) (0.058)

Households headed -0.327** 0.468** 1.665 (235)

by a couple (0.070) (0.061)

SAMPLE: percent of Rent and Control movers actJ.ve at two years after

enrollment, excludlng those wJ.th enrollment lncornes over the elJ.gibJ.lJ.ty l~J.ts

and those livJ.ng J.n theJ.r own homes or J.n subsJ.dJ.zed housJ.ng.

DATA SOURCES: In~t~al and monthly Household Report Forms, payments

hIe, Appenfux Table X-22.

NOTE: Standard error l.n parentheses. Varl.ance-ratio tests ind1.cate

that once pooling across sltes is performed, pooling across household types

is possible (F(6,507) = 1.90, cnt~cal value = 2.10 at the 0.05 level) but

pool~ng across races is not (F(3,5ll) = 9.17, cntical value = 2.60 at the

0.05 level).

a. Testing 81te hOIOOgeneJ.ty allowing slte-specifJ.c J.ntercepts.

* t-staustic s~gnificant at the 0.05 level.

** t-statist~c sign~f~cant at the 0.01 level.

89
REFERENCES

HastLngs, N.A.J. and J.B. Peacock, stat~st~cal Dlstrlbutlons, New York,

John W11ey and Sons, 1975, pp. 42-43.

Hymans, Saul and Harold Shaplro, liThe Allocatl0n of Household Income for

Food Consurnptl.on,lI loll James N. Morgan (ed.) Fl.ve Thousand American

Farnl.lJ.es--Patterns of Economl.C Progress, Vol. II, Ann Arbor,

Un1vers1ty of M1chigan Survey Research Center, 1974.

Kmenta, Jan, Elements of Econometrl.cs, New York, The MacMl11an Company,

1971.

MacMillan, Jean, Mobihty in the Housing Allowance Demand Experiment,

Cani:>ridge, Mass., 1\bt Associates Inc., June 1978 (revised June 1980).

Mayo, Stephen K. I Housing Allowance Demand Experl.rnent: Housl.ng ExpendJ.tures

and Quahty Part 1: Housing Expenfutures Under a Percent of Rent

Housl.ng Allowance, Cambndge, Mass .. , Abt Associates Inc., 1977.

Merr111, Sally R., Hedoll1c Infuces as a Measure of Hous1ng Quality, Cambndge,

Mass., 1\bt Assoc1ates Inc., December 1977 (revised June 1980).

Muth, Richard F. I "MoVJ.ng Costs and Housl.ng Expendl.ture," Journal of Uman

EconoID1cs, vol. 1, 1974, pp. 108-125.

Po11nsky, A. Mitchell, "The Demand for Hous1ng: A StudY in Spec1fication

and Group1ng," Econorretnca, vol. 45, no. 2, March 1977, pp. 447-461.

SUJ.ts, Daniel B., Andrew Mason, and Loul.s Chan, IISpline Functions F~tted by

Standard Regression Methods," Rev~ew of Econonucs and StatJ.st~cs,

vol. 60, no. 1, February 1978, pp. 132-139.

U.S. Bureau of the Census and U.S. Departrrent of Housing and Urban Development,

Annual Housing Survey 1975, Part C, Wash1ngton, D.C., U.S. Government

Printing Off1ce, 1977.

90
QlAPTER 5

THE DEMAND FOR HOUSING SERVICES

Olapter 4 demonstrated that households responded to the Percent of Rent

:rent rebates by J.ncreasing their housing expenditures. However, increased

expenditures may not always lead to real changes in housJ.ng. If allowance

recipients are unable to act effectively in the private market or if they

shop less carefully, then they might end up spending more for the same housing

than they otherwise would. There is no reason to expect differences in

effect1veness between Percent

may, however, affect shoppJ.ng

of Rent and

1 behavJ.or.

Control households. The rent rebate

A person looking for a rental housing unit in a partJ.cular neighborhood J.S

lJ.kely to find that similar units rent for varyJ.ng amounts of money. In

other words, different households end up paying different amounts of rent

for the same level of housJ.ng services. This sJ.tuation may be expressed

mathematJ.cally as:

(1)

where R rent

PH = the average prJ.ce of housJ.ng services

H amount of housJ.ng serv1ces, and

E = a stochastic term, wJ.th zerO mean and varJ.ance cr2 • 8

A unit W1th £.<0 w.l.ll normally be consJ.dered a "good deal" or a "bargal.n,"

whJ.le a unit with 8>0 will normally be consJ.dered a "bad deal." competitive

market forces wJ.ll tend to reduce the variance of 8, but wJ.ll probably not

reduce the var1.ance to zero.

In this context, shopping for rental housing may be viewed as looking for

unJ.ts wJ.th negatJ.ve 8 (bargaJ.ns).

alreadY paying less out-of-pocket

However, Percent of Rent households were

than market rent since their net rent payments were reduced by 20 to 60 percent, dependJ.ng on the rent rebate plan

lGeneral inflatJ.on also J.mplies hJ.gher dollar expenditures WJ.thout any

change in the housing servJ.ces provided by a dwelling unit. SJ.nee J.nflatJ.onary changes apply to all households, the J.mpaet on expendJ.tures estimated J.n

Olapter 4 accounted for inflatJ.on by inelufung Control households in the sample, so that this posed no problem there.

91
they were enrolled 1n. For a household w1th a 50 percent rebate, for example,

findlng a unlt that rents for $10 more or less than another only makes a

dlfference of $5 ln the out-of-pocket cost to the household. Thus, Percent

of Rent households mlght be expected to have shopped for new houslng less

vlgorously than Control households. This can be tested by estimating the

effects of the rent rebates on housing services and comparing these effects

wlth the effects already estimated for houslng expendltures.

In contrast to expenditures, housing services are not easy to measure. Housing

serv1ces are, at least in-part, Sub]ect1ve. Two kinds of housing qua11ty

measures are used in th1s chapter--normat1ve measures and hedon1c 1ndices.

The normative measures used involve physlcal housing standards developed for

the Demand Experlment. These standards were based on the Amerlcan PubllC

Health Assoclation/Publlc Health Servlce model housing code and are simllar

1n type to standards used in existing hous1ng programs such as Sect10n 8.

HedoIllc 1ndices, on the other hand, do not attempt to rate units 1n the sense

of determining the1r adequacy. Rather they pronde est1mates of the average

market rent of a un1t 1n terms of 1tS physJ..cal character1stics and locat10n.

Compar1son of the hedonic valoo of a unit W1th the actual rent charged can

be used to sort out the extent to Whlch households are paying ebove average

rents and thus prov1de est1mates of the real change in participant hous1ng.

SectJ..on 5.1 discusses these measures and exam1nes the tabular eV1dence of

household response to the Percent of Rent rebates as measured by the change

in proportlon of households meetlng houslng standards and the percentage change

III the hedonlc lndex of hOUSlllg services. Section 5.2 then uses the demand

theory developed ln Chapters 3 and 4 to estlmate a demand function for hous1ng serv1ces. D1fferences in household response between expendJ..tures and

quallty (as measured by the hedonlc index) emerge and several alternate

explanatlons for the divergence are tested. Section 5.3 concludes the chapter

wlth a brief sUlllIIlary of fllldlngs.

5.1 HOUSING QUALITY CHANGES

There 1S no generally agreed-upon way of measuxJ..ng housJ..ng qua11ty. Measures

range from the s1mple Census measure of substandardness to more complex measures

of d11apJ..dat10n and deter10rat10n. 1 These measures stnve to achieve an objec1

See Buddlng (1978) for a detal1ed dlscusslon of various extant hous10g quality neasures.

92
tive measure that policy-makers can agree measures the presence or absence

of adequate housing. As such, they become normatl.ve measures. '!he nonnab.ve

measures used here to measure housl.ng quality include two physical standards

--lIlow" housl.ng standards and "programH housl.ng standards--and one occupancy

standard based on the MJ.n~mum Standards requ~rements and for certa~n parts of

the Demand Exper~ment, as well as two physical standards based on analysis of

hous~ng adequacy by Budding (1978).1 Percent of Rent households were not reqUl.red to meet these standards and were probably not aware of their eXl.stence.

fureover, the standards may not be cons~stent w~th what the households themselves :rru.ght consider IIbetter quality, II because the standards include only a

l~mited number of dwelling unit components and did not include any neighborhood component. Therefore, the Percent of Rent rebates may have enabled recl.­

pient households to improve the~r hous~ng ~n ways that are not measured by

these normat~ve standards (parucularly ~f these included various quality or

ne~ghborhood components not included ~n the standard).

The hedon~c index offers a d~fferent method for est~ting the impact of

Percent of Rent rebates on hous~ng serv~ces. The hedonic ~ndex, developed

for the Demand Exper~ent s~tes by Merrill (1977), g~ves a dollar value for

the amount of housing servl.ces provl.ded by a unl.t. The measure can be interpreted as the expected or average market rent of unl.ts with given locatl.on,

s~ze, and other phys~cal characterist~cs. In terms of Equation (1), the

hedonl.c l.ndex gl.ves the expected rent of a unit if l.t 1.S nel.ther a good nor

2

a bad deal (£=0).

lThe physical qual~ty of the =ts was evaluated at least annually

COl.nCl.dent with enrollment and the Second and Thl.rd Periodic Interviews. The

housl.ng evaluations measured nmnerous quall.ty l.tems including such items as

surface and structure characteristics, ll.ght and ventilation, etc.

"Program" standards reflect the phys~cal hous~ng requirements that households

in another part of the exper~ment--the Hous~ng Gap Minimum Standards plans-­

had to meet ~n order to receive payments (see Appenfux I for a descnpt~on of

the Housing Gap plan). The occupancy standard ~s def~ned as no more than two

people per "adequate" bedroom, Wl.th IIadequate II defined l.n accordance Wl.th the

physl.cal standards. The "low" housl.ng standards were less strl.ngent than

those apphed for "program" ehgibility for Hous~ng Gap MJ.n~mum Standards

households. A more detal.led descrl.ption of the "low" and the uprogram" hous­

~ng standards is found ~n Append~x III. The measure of overall adequacy

developed by Budfung (1978) is descnbed further below.

2For a detailed chscussl.on of the use of hedonl.c l.nd1.ces to measure

housing qual~ty, see Merr~ll (1977) and KennedY and Merrill (1979).

93
The hedonic ~ndex takes ~nto account a w~de variety of phys~cal and locat~onal

character~stics, wh~ch account for from two-thirds to four-f~fths of the

observed var1ation 1n rents. Furthermore, as discussed in Section 5.2 below

and 1n Merr111 (1977) and Merr111 and Kennedy (forthcom1ng), tests of 1tS

validity support the contention that 1t measures housing services w1th a high

degree of accuracy. Nevertheless, it would be unreasonable to clallD. that

the hedonic index captures all of the variation 1n housing serv~ces across

units. As a consequence, changes ~n hedon~c 1nd~ces of hous1ng will generally

be smaller than changes 1n expenditures. Given the support~ng ev~dence on

the accuracy of the measure, the d1fferences should not be large, however.

In add1tion, 1t 1S possible to test whether d1fferences between changes in

hedonic 1ndices and assoc1ated changes in expend1tures due to the Percent

of Rent offers follow the normal pattern of rent-hedon1c 1ndex differences.

If they do, then 1t can be concluded that the expend1ture changes 1nduced by

the Percent of Rent offers led to concornm~tant real changes in hous~ng services.

If they do not (~f, for example, the changes 1n hedon1c 1ndlces for Percent of

Rent households are much smaller than those that would normally accompany the

expend1ture changes for these households), then 1t would appear that Percent

of Rent households did not obta1n the real improvements in the1r hous1ng

that would normally have accompanied the1r increased expenditures.

Tabulat10ns of the normat1ve standards for Percent of Rent and Control

households are presented in Table 5-1. There seems to be no clear evidence

that the Percent of Rent program either encouraged or made 1t poss1ble for

households to lmprove thelr dweillng un~ts above the level eXlst~g at enrollment as measured by the normatlve standards. Moreover, there 1S no eVldence

that d1fferences ~n the percentage rebate were assoc~ated w~th the lnc~dence

of units passing the standards. 1 Nor, when moving and nonmov~ng households

were analyzed separately, did movers lncrease tbe1.r hous1.ng qual~ty as

measured by these three measures slgnif~cantly more than did nonmovers. 2,3

1

See Append1x Table X-23 through X-25.

2

See Append1x Tables X-26 through X-31.

3As noted ear11er, Percent of Rent households may have obta1ned improvements in the~r housing not reflected in the normatlve standards. While

rrore expens1.ve un1.ts do tend to neet the MJ..mmum Standards hous1.ng reqUJ.re­

:rrents more often, the relationsh~p ~s not strong. Thus l.t seems quite reasonable that changes 1.n specif~c dwelling un~t attributes to meet a normat~ve

standard cannot be induced without explicitly requiring them of households

(see Mernll et al., 1975, pp. 161ff).

94
Table 5-1

CHANGES IN DWELLING UNIT

PHYSICAL AND OCCUPANCY STANDARDS

Low Standard

Percent of Rent

households

Control households

Program Standard

Percent of Rent

households

Control households

Occupancy Standard

Percent of Rent

households

Control households

Low Standard

Percent of Rent

households

Control households

Program Standard

Percent of Rent

households

Control households

Occupancy Standard

Percent of Rent

households

Control households

PERCENT PASSING

ENROLLMENT

81%

81

37

33

49

46

72%

66

33

28

43

38

PERCENT PASSING

TWO YEARS

PITTSBURGH

84%

80

34

29

47

41

PHOENIX

75%

74

41

36

55

53

CHANGE

+3

-1

-3

-4

-2

-5

+3

+8

+8

+8

+12

+15

SMlPLE

SIZE

(391)

(299)

( 391)

(299)

(390)

(299)

(279)

(258)

(279)

(258)

(279)

(258)

SAMPLE: Percent of Rent and Control households active at two years

after enrOllment, exclud1ng those w1th enrollment 1ncomes over the e11g1b111ty

I1m1ts and those I1v1ng 1n the1r own homes or 1n Subs1d1zed hous1ng.

DATA SOURCES: Inltlal and monthly Household Report Form and Houslng

Evaluat10n Forms.

NOTE: See Appendlx III for a full descrlptlon of the measures used

here.

95
BuddJ.ng (1978) created a neasure of hous~ng adequacy, derived from the indiVJ.dual hous~ng evaluat~ons perfonned for each dwel1~ng unit. Th~s measure

class~fJ.es units 10to one of three cateqorJ.es:

If there was clear eVJ.dence' that a dw'elling unJ.t contaJ.ned

one or more serious housing defJ.cJ.enc1es, the UIUt J.5 classJ.­

fJ.ed as clearly J.nadequate.

If the unl.t passed every one of the J.nmcators l.ntended to

measure serious housJ.ng defl.cl.encl.es and recel.ved an overall

evaluator ratl.ng consistent Wl.th such a classJ.fl.catl.on, the

uru.t 15 classifl.ed as at least miol-mally adequate.

Otherwl.se, the unit 15 classl.fl.ed as ambl.guous.

The neasure w~ll tend to understate to some unknown degree both the number of

persons J.O clearly

=mmally adequate

l.nadequate

1 housl.ng..

housl.ng and the nunber of persons 1.0 at least

This measure 15 closely related to the ~nl.mum

Standarde neasure ~n that the adequacy measure ~ncludes all but one (bathroom

w~ndow adequacy) of the Min~mum Standards ~ndJ.cators and only two additional

J.ndJ.cators (presence of rate and w~ndow cond~t1on).. The key dJ.fference ~s

the presence of the arri::l~guous category' wh~ch allows a finer dJ.st~nction to be

made between adequate and ~nadequate hous~ng than that pe=tted by the MJ.n~­

mum Standards measure.

The use of th1S rreasure does not, however, change the basic conclus1.ons reached

w~th the other measures. Table 5-2 ~ndicates that Percent of Rent households

dJ.d not obta~n more adequate hous~ng than did Control households, measured as

change 10 either percentage of households 10 lTU.ru.mally adequate units or the

2 3 percentage of househOlds in clearly 1nadequate un1.ts..' These results do not

change when households are strat~f~ed by mobility status, w~th the exception

1

The category' "clearly 1.nadequate" enconpasses a range of hous~og, 1.neluding both dwell~ng un~ts that are completely dJ.lap~dated w~th multiple def1.c1.encies and un1.ts W1.th a s1.ngle maJor defect. The category "at least m1nimally adequate" is subject to the l1.lTU.tat1.ons of the data base, and it seems

ll.kely that of these some of these UIutS have ser1.OUS housing problems that

went 1.lIlIreasured 1.n the Demand Exper1.ment. F1nally, the amb~guous category

undoubtedly cont=ns both un~ts that are properly class~f~ed as clearly inadequate and un~ts that are properly cons~dered at least =n~mally adequate. The

ambiguous category eXl.sts because there was not suffic1ent 1nformation to make

either class1f1.cat1.on.

2

Append~x Table X-32 presents these results for each percentage rebate

level.

3

Changes from =mmally adequate to amb~guous approXJ.mately balance

those in the reverse chrect1.on.

96
Table 5-2

QIANGES IN HOUSING ADEQUACY

FROM ENROLLMENT TO TWO YEARS FOR

CONTROL AND PERCENT OF RENT HOUSEHOLDS

PERCENTAGE IN

MINIMALLY ADEQUATE HOUSING

PERCENTAGE IN

CLEARLY INADEQUATE !lOUSING

TREATMENT GROUP

At

Enrollment

At 'lWo

Years a Change

At

Enrollment

At 'lWo

Years a Change

SAMPLE

SIZE

PITTSBURGH

Percent of Rent

households 31% 28% -3 41% 35% -6

"'

..., Control households 29 25 -4 38 35 -3

PHOENIX

Percent of Rent

households 36 39 +3 44 39 -5

Control households 35 37 +2 45 41 -4

( 391)

(301)

(284)

(256)

SAMPLE: Percent of Rent and Control households act1ve at two years after enrollment, excluding

those wlth enrollment lucornes over the ellgiblilty I1mits and those livlng In thelr own homes or In sUb51dlzed houslng.

DATA SOURCES· Hous1ng Evaluat10ns Forms.

a. Percentage pOlnts.
of Percent of Rent JIK)vers in Pittsburgh, which show a larger lncrease ln percentage =n~mally adequate than do Control movers but only a slightly larger

decrease in percentage clearly inadequate (see Appendix Tables X-33 and X-34) .1

Changes ln the mean value of the hedonic index for Percent of Rent and Control

households are presented ~n Table 5-3. Wlule the ~ndex ~ncreased for Percent

of Rent households at both sites, ne~ther the overall level of change for nor

the difference ~n change between Percent of Rent and Control households is as

2 large as for expend1tures.

At least three factors contr~bute to the lower overall change ~n the index

between enrollment and two years after enrollment. First, s~nce households

wlth long tenure ln a unlt recelve a rent dlSCOunt (see Merrlll, 1977), movers

must by necesslty lncrease expend~tures more

lces obtalned merely to overcome the loss of

than the increase ln housing

:3

the dlSCOunt. Second, rent

servapproximately 2 to 4 percentage points of the

expendltures and changes in houslng servlce. 4 F~nally, rent changes ~nclude

inflat~onary adjustments whereas the hedonic index does not.

changes lnclude an adJustment for lncreased utl1lty costs over the two-year

perlod, wh~le the hedonlc index does not. ThlS latter factor accounts for

d~fference between changes in

However, none of these factors explain why the net change ~n the ~ndex for

Percent of Rent households ~n compar~son to Control households was smaller

than for expend~tures. The qual~ty of hous~ng, as evaluated by the hedonic

~ndices, rose ~n P~ttsburgh by an average of 9 percent for the Percent of

Rent households, and 6 percent for the Control households. In Phoen~x, the

average increase was 16 percent for the Percent of Rent and 17 for the

Control households (see Table 5-3). There thus appears to be only a small

net experimental effect ~n P~ttsburgh and no net effect at all in Phoemx.

F~gure 5-1 illustrates that, as =ght be expected, movers at both s~tes

increased the hedonlc values of thelr resldences much more than dJ.d nonmover

~onmove~ tend to shCM a decrease 10 houslng adequacy.

2

Sample s~zes for hedonlc lndex computatlons compared to earller chapters are typ~cally smaller due to the ~ncreased data reqmrements. Appenfux

Table X-35 presents the changes for each rebate level.

3

That ~S, a household mOV1ng lnto a unlt generally pays more than the

preVJ..ous tenants would have had to pay merely because they are "newll tenants.

4

AdJustments vary accord.1.ng to the unlt Slze and the util~ties purchased.

98
Table 5-3

CHANGES IN HEDONIC HOUSING QUALITY

TREATMENT GROUP

Percent of Rent

households

Control households

MEAN HEDONIC INDEX MEAN CHANGE

At At Two SAMPLE

Enrollment Years Amount Percentage SIZE

PITTSBURGH

$114 $121 $ 7 9% (353)

114 120 5 6 (273)

PHOENIX

percent of Rent

households

Control households

132

128

149

144

17

16

16

17

(241)

(231)

SAMPLE: percent of Rent and Control households active at two years

after enrollment, exclud~ng those with enrollment ~ncornes over the eligib~l~ty

l~lts and those 11vlng in thelr own homes or In subsidlzed housing.

DATA SOURCES: In~t~al and monthly Household Report Forms, Housing

Evaluatl0n Forms, 1970 Census of Population, and Basellue and Perlodlc

IntervJ.ews.

99
Figure 5-1

MEAN PERCENTAGE CHANGE IN HOUSING SERVICES BETWEEN

ENROLLMENT AND TWO YEARS AFTER ENROLLMENT

Phoenix

Nonmovers

[12]

[49] 1-------- Phoenix

I Movers

I

1

I

~I---,[~4~OJ,---_ Pittsburgh

Movers

18

18

13

32

-------: 29

--------,I

I

I

I

I

I , 20 ,

~--:..[1:.,:7,,-J_~: .1:,.7. 1 19

r 15

991

,-------

r------, -------~ I , I L __2 J

'---~----r 7 __J 3 3 3 Pittsburgh

L __]2==~ ,::==1=~I~ Nonmovers

I I -. I I I o

50 _

20 -

10 _

"

"'co i :340 - .J::u (,);

"," "

"en.. c c :: 0;;" " :1:30

" -

" c " .- :;

0%

(Controls)

20% 30% 40%

Percentage Rebate

50% 60%

SAMP LE. Percent of Rent and Control households active at two years after enrollment,

excluding those with enrollment Incomes over the eligibility limits and those living In their

own homes or In subsidized housing

DATA SOURCES Imtlal and monthly Household Report Forms, HOUSing Evaluation

Forms, 1970 Census of Population, and Baseline and PeriodiC Interviews.

NOTE. Brackets indicate entries based on 15 or fewer observations.

apercentage change In hOUSing services IS defined as the mean of the ratio of the change In

hOUSing services to hOUSing services at enrollment.

100
1 households. There is still" hwoever, no clear difference in the increase

for Percent of Rent households as compared to Control households. In P~ttsburgh, Percent of Rent households that moved had an overall 19 percent

increase in the hedonic 1ndex over txme while the nonmover Percent of Rent

households only ~ncreased the~r hedon~c value by 3 percent. Increases for

Control households were sl~ghtly lower for both groups--13 percent if they

moved and only 2 percent when they did not. In Phoen~x, Percent of Rent

movers had an ~crease of 22 percent ~n the hedonic value of the~r hous~ng

while nonmovers showed a 7 percent 1ncrease. For Control households in

Phoenix, the increase was 32 percent ~f they moved and only 5 percent ~f they

d~d not (that is, Phoe~x control movers had a larger mean ~ncrease than

d~d Percent of Rent movers) .

In all, the results ~ndlcate that an lncrease 10 houslng expendltures for

a household does not always 1ffiply an lncreaSe 10 houslng servlces. Movers

do lmprove thelr houslng 10 terms of the hedonic 2ndlces relatlvely more

than do norunovers. Yet there seem to be only small dlfferences between

the hedon~c values for the Control and percent of Rent households, ~nd~­

cat~g that rent subsldles may not be very effectlve 10 helplng percent

of Rent households ~ncrease the qual~ty of their housing units (at least as

measured by the Minimum Standards housing requirements or by the hedon~c

index of housing services). In order to control for fufferences ~n income

(and other character~st~cs) between Experimental and Control households, Section 5.2 analyzes the hous~ng services response of Percent of Rent households

~n the context of a demand funct~on.

5.2 THE DEMAND FOR HOUSING SERVICES

The hedon~c index, described in Sect~on 5.1, ~s used as the dependent variable

in a demand equatl0n 1n order to est1IDate the responsiveness of a household's

consumptJ.on of housJ.ng serVJ.ces to changes .l.n J.ncome and price. The logl~near form of the demand function is used, estimated for the sample of

movers. As J.n Chapter 4, average J.ncome J.5 used as the measure of permanent

l.ncorne. The estimates of price and

and the hedonl.c index are presented

income elastl.citl.es for both expenditures

2 ~n Table 5-4. In Phoen~x, the ~ncome

lAppenfux Tables X-36 and X-37 present the data for this figure.

2

The sample ~s somewhat smaller than that used in O1apter 4 due to

the extra data requirerrents of the hedonic .l.ndex. The expend1ture estJ.mates

are consequently sl~ghtly fufferent.

101
ELASTICITIES

Pr~ce Elastic~ty

Table 5-4

COMPARISON OF PRICE AND INCOME ELASTICITIES

ESTIMATED USING HOUSING EXPENDITURES

AND AN HEDONIC INDEX OF HOUSING SERVICES

(Movers Sample)

PITTSBURGH PHOENIX

Expenditures est~ate

Hedon~c est~ate

Income Elastlc1ty

Expend1tures estkffiate

Hedon1C est~ate

SAMPLE SIZEa

-0.230**

(0.065)

-0.113*

(0.057)

0.338**

(0.054)

0.226**

(0.047)

(214)

-0.215**

(0.064)

-0.045

(0.060)

0.353**

(0.046)

0.375**

(0.043)

(257)

SAMPLE: Percent of Rent and Control movers act:J..ve at two years

after enrollment, exclud1ng those w1th enrollment :Lucornes over the e11gib111ty I1m1ts and those liv1ng 10 the1r own homes or in Subs1d1zed hous1ng.

DATA SOURCES: In~tial and monthly Household Report Forms, Hous~ng

Evaluatl0n Forms, 1970 Census of populatl0n, and Base!lne and perl0dlc

IntervJ.ews.

NOTE: Standard error 10 parentheses.

a. Sample s~ze d~ffers from the expend~ture estimates ~n Chapter 4

due to the extra data requirements of the hedon~c ~ndex.

* t-stat~st~c sign~f~cant at the 0.05 level.

** t-stat~st~c s~gn~f~cant at the 0.01 level.

102
elasticity estimates are the same for expenditures and housing serv~ceSi

in P~ttsburgh, the incane elastic~ty of housing services is lower than that

for expenditures but is st~ll reasonably large. Rather str~king differences

are evident in the price elasticity estimates, however. The estimated pr1.ce

elasticity for housing serv~ces in Phoenix is not s~gnificant. In pittsburgh the est=ated pr~ce elasticity of housing services is only one-half of

the estimated pr~ce elasticity of expenditures. These results confirm the

f1.ndings of Sect1.on 5.1--1.0 response to a decrease 1.0 the price of heusl-ng,

households increased their housing serV1.ces by less than thelr expend1.tures.

Moreover, in Phoenix the change in hansl-ug serV1.ces for Percent of Rent households was no larger than that for Control households.

Several explanations are poss~le for these results. A rent rebate program

such as a Percent of Rent allowance that provides no direct l.ncentive for

households to increase the~r housing quality may lead to inefficiency in

shopp~ng behav~orr households would no longer be pay~ng full market price

for each additional un~t of hous~ng services and would poss~bly be willing

to accept less hous~ng serv~ces per dollar than the market provides on the

average. If households do ~n fact act this way, the rent subsidy may permit households to reduce search costs.

On the other hand, the hedonic ~ndex may be subJect to several types of

spec~ficat~on bias. For example, ~f important attributes of the hous~ng

bundle were om~tted from the est~t~ng equation, the index would not

adequately reflect the unit's housing services.l If =portant positivelyvalued attributes of dwelling unit or neighborhood quality are m~ss~ng from

the hedonic est=ates, the estimated pr~ce and income elastic~t~es for housing

services would be biased downward from the true elastic~ties.

Next, ~f the housing market in Pittsburgh or Phoenix ~s segmented, that is,

if different groups of households (central c~ty versus suburban or racial

differences, for example) face different housing prices, the same set of

relative attribute prices est=ated by an overall index may not be applicable

to all suhmarkets. Finally, the attribute weights est=ated dur~ng the baseline per~od may not be applicable after two years due to changing market

I

Om~tted variables increase the est~mated standard error of the

hedonic l.ndex.

103
condl.tions or, more likely, to decl.sions made by movers to rent units l.n

1

areas un1~ke those included in the or~gina1 sample.

These issues can be addressed in a formal framework. As descr~bed ~n

Sect~on 5.1, the hedonic housing services index was der~ved by regress~ng

rent on housing unit and neighborhood characterl.stics and on conditions of

tenure at enrollment,

(2)

where

In(R) = a + xS + Zy + P

R = rent

x = a vector of housing un~t and ne~ghborhood

character~st~cs, where (a+XS) is the hedon~c ~ndex

of housl.ng services

Z a vector of tenure characteristl.cs such as

length of the household's residence ~n the

un~t and whether the landlord lives ~n the

bui1d~ng, and

= a stochastic error.

When rent at two years ~s predicted using the est~ated coefficients, the

estimated resl.dual, ~, may represent omitted quall.ty variables, omitted

tenure var~ab1es, experimentally induced shopp=g ~neffic~ency, and luck or

other random effects.

Several hypotheses can be tested to determ1ne the correct lonterpretat10n of

the estllnated res1dual,~. If the res1dual lonvolves some oml.tted qua11ty,

then ~t should be pos~t~ve1y correlated w~th household income and poss~b1y

w~th household sat~sfact~on. If the res~dua1 reflects changes ~n shopp~ng

behavloor, then the search behavloor of Percent of Rent households should show

some dlofferences from Control households. These speciflocatloon loSsues have

been assessed in detail by Merrill (1977) (~n the development of the hedomc

index), and Kennedy and Merrill (1979) (~n analys~s of the ~ndex's behav~or

over the experimental per10d).. The remalonder of th1s section summarJ.zes

some of these analyses and proVJ.des some hypotheses concernlong the reasons

1

The hous~ng un~ts of all enrolled households were used to est~ate

the hedonw ~ndex. The sample is not a random sample of all dwel1~ng units

s~nce those households all have low or moderate =comes. See Merr~ll (1977).

Further, Census tracts wJ.th low concentrations of rental unlots (~5 percent

of hous~ng un~ts) were excluded from the sampling frame. These tracts m~ght

possili1y have rental units with h~gher average quality.

104
for the differences ~n the elastic~ty estimates for expenditures and housing

services.

Analys~s of the Hedonic Residual

If the hedonic residual ()1) cont~ns only o=tted quahty ~tems, then analysis of housing quality should examine the sum of the hedon~c index and the

res~dual (n + XS + )1) rather than Just the ~ndex alone. On the other hand,

~f the residual ~s not only 0=tted quality, then analys~s of the pr~ce response should take account of possible shopping inefficienc~es.

If the hedonic res~dual includes some o=tted quality (Le., quality unneasured by the hedonic ~ndex), then to the extent that sausfaction ~s pos~­

t~vely related to the level of housing qUal~ty the res~dual should be pos~­

t~vely related to the household's satisfaction with its dwelling unit. If,

on the other hand, the hedon~c res~dual is due largely to price effects rather

than onu.tted qual~tyI the assoc1at1on 1;171 th satJ.sfaction 1.5 expected to be negative--that 15, that satl.sfactJ.on increases as the amount of quality rel.atl.ve

to expenchtu:res increases. To test these assurqptions, the change l.n hedomc

quahty and the change in the hedon~c res~dual over the two years of the experl.rnent were each regressed on the change l.n dW"ellJ.ng UIll.t sahsfactJ..on, for

1 Control households. The results showed that the change ~n quality and sausfaction have a signl.ficant and positl.ve relationsh.l.p J.n both Sl.tes. Further,

in both sites the change in satisfaction and the change in the

ual have the expected signl.fl.cant and negatl.ve relationship.2

that the hedonic res~dual is not solely due to om~tted qual~ty

hedonic residThus ~t seems

. 3 .1.tems.

~t ~s often unclear what a quest~on about household satisfaction

actually neasures because households q=te possibly have mfferent reference

pol.nts. Change in dwellJ.ng unit satisfaction is a measure internally consJ..stent Wl.thl.n a household. Further, while demographic characteristl.cs may

affect household satisfaction, they are unlikely to affect the change in

sat~sfact~on (except insofar as they affect housing change).

2For movers, all relationships were 1n the sane direct10n as those

for all households and were s~gnif~cant (except for the residual and un~t

satisfact~on in Phoen~x). The same lOCldel was also tested for ne~ghborhood

satisfact10n. In Phoen1x, an increase 1n hedonic qua11ty results in an increase ~n neighborllood sahsfaction for both movers and all households. None

of the other relationsh1ps were s1gnificant.

3

I.ocat~onal attriliutes are apparently accounted for adequately by

the hedonic index; no mscernilile pattern to the res~duals by location

energed (Merr~ll, 1977) •.

105
Sim1lar hypotheses were tested concerning the relat~onship of search effort

to quality and price effects. If the hedon~c residual reflects pr~ce heterogeneity, then a d~l~gent search will result ~n a better deal (more qual~ty

per dollar) than would a haphazard search. If true, the hedon~c residual

will be negatively associated w~th search effort. Unfortunately, there is

some evidence that some households that do not search obtain good deals by

luck--be~ng referred to a unit by friends or relatives (vidal, 1978). Tests

were conducted accountJ..ng for thJ..s "windfall search" as well as more actJ..ve

1 search. One measure of the search effort is the number of days spent searching for housing. Increased search tJ.Ine does 10 fact result 10 getting a

better deal, that is, more qual~ty per dollar of expenditures in both

Pittsburgh and Phoenix. Search time is also associated with a larger change

in the quality index ~n Pittsburgh. 2

Part of the smaller J..ncrease 10 housing servJ..ces relatJ..ve to expendJ..tures

for Percent of Rent households ~n both Phoen~x and Pittsburgh may be due to

a conscJ..ous decJ..sJ..on on thelr part to use less effort 10 search1ng for a

new un1ta S1nce there 15 a s1gn1f1cant aSSoc1at10n between 1ncreased search

time and obtaining more housing servwes per dollar of expenditures, ~f

Percent of Rent households search less than Control households, then the

pr~ce discount w~ll have a smaller effect on their housing services than on

their expenditures.

There 15 some weak evidence that decrease 10 search effort occurred--

Percent of Rent movers spent fewer days looking for a un~t than did Control

movers, though not signif~cantly so (97 versus 119 days in Pittsburgh, 34

versus 46 days in Phoen~x).3

Another approach to analyz1ng the resldual 15 dlrect est~at10n of demand

for the res~dual and for the qual~ty and tenure components. Dur~ng the

development of the hedon1C J..ndex, extenS1ve analys1s of the res1dual was

carr~ed out us~ng the ent~re enrolled sample (see Merr~ll, 1977). The

hedonlc res1duals and the percent dev~at~on of pred~cted and actual rent were

regressed on household ~ncome, race, household s~ze, and age and educat~on

of head of the household. The maJor hypothesis tested was the following:

1

See Kennedy and Mer=ll (1979) for adfut~onal det~l.

2

Th . . ere ~s no relat~onsh~p between qual~ty and other measures of

search effort (the number of units looked at or the number of un~ts called).

3

See Appenfux Table X-38.

106
if important qualJ.ty attributes were 0=tted, the:re would be a signJ.fJ.cant

positive relatJ.onship between the resJ.dual and J.ncome and perhaps educatJ.on.

The income coeffJ.cients were in fact significant but were extremely small in

both Pittsburgh and Phoenix.

A series of sJ.mJ.lar models have been estJ.mated for households remaJ.ning

active in the experJ.ment for two years. In logarithmic form, Equation (2)

becomes

(3)

where

In(R) In(Q) + In(T) + In(s)

In(Q) = (a + XS), the hedonic J.ndex of housJ.ng servJ.ces

abstract~ng from tenure character1stlcs

In(T) Zy, the value of tenure characteristics, and

In(s) = ~, the stochastJ.c error.

If each component of EquatJ.on (3) (In(R), In(Q), In(T), and In(s)) J.S

regressed on the logarlthms of price and lucame, It wl11 be true that

EquatJ.on (3) J.mplJ.es the sum of the prJ.ce (or J.ncome) elastJ.cJ.ties for Q,

1 T, and s wJ.ll equal the prJ.ce (J.ncome) elastJ.cJ.ty of R:

(4)

These elasticities may be estJ.mated uSJ.ng 10g-1J.near regressions of the

resJ.dual, the quality index, tenure adjustments, and rent adJustments on

price and J.ncome; they are summarized J.n Table 5_5. 2 In Pittsburgh, both

the price and J.ncome elasticJ.tJ.es of housing services fall relative to those

for expenditures. The dJ.fference J.S accounted for almost entJ.rely by the

hedonic residual and not the tenure characterJ.stJ.cs. SJ.nce there J.S a

significant positJ.ve income elastJ.cJ.ty for the resJ.dual in Pittsburgh, it

1

From Equation (3),

aln(R) = aln(Q) aln(T) aln(s)

aln(P) - aln(P) + aln(P) + aln(P)

and these elasticJ.ties are the estimated coeffJ.cJ.ents of log-linear demand

functions for R, Q, T, and 8.

Actually, since the rent definition used for the hedonJ.c analysJ.s and the

rent defJ.nJ.tion used for the housing consumption analysis are slightly

dJ.fferent, there J.S another term representing this adjustment. The

adJustment has no impact on any of the fJ.ndJ.ngs reported here.

2Additional equations, estimated J.ncludJ.ng demographJ.c covariates,

did not change the results. (See Kennedy and Mernll, 1979.)

107
Table 5-5

PRICE AND INCOME ELASTICITY ESTIMATES

FOR RENT COMPONENTS

PITTSBURGH PHOENIX

PRICE INCOME PRICE INCOME

DEPENDENT VARIABLE ELASTICITY ELASTICITY ELASTICITY ELASTICITY

Rent (expendl.tures -0.230** 0.338** -0.215** 0.353**

def~n~t~on) (0.065) (0.054) (0.064) (0.046)

HedonJ.c J.ndex -0.113* 0.226** -0.045 0.375**

(0.057) (0.047) (0.060) (0.043)

.

Hedonlc resldual -0.159** 0.089* -0.193** --0.021

(0.047) (0.039) (0.048) (0.034)

Tenure characterlstJ.cs 0.027* 0.019t 0.017 0.001

(0.013) (0.010) (0.011) (0.008)

DeflnJ.tlonal dlfferencea 0.016 0.004 0.005 -0.002

(0.013) (0.010) (0.007) (0.005)

SAMPLE SIZE (214) (257)

SAMPLE: Percent of Rent and Control movers active at two years after

enrollment, excludlng those wlth enrollment lucornes over the ellglblilty

lLmlts and those IJ.vlng In thelr own homes or 1ll SUbs1dlzed hons1ug.

DATA SOURCES: In~t~a1 and monthly Household Report Forms, Hous~ng

Evaluatlon Forms, 1970 Census of Populatlon, Basellne and perlodlc Intervlews,

and Append~x Table X-39.

NOTE: Standard error In parentheses.

a. Dlfference between the analytlc rent varJ..able used for the

expendlture analysls and that used In the derJ.vatlon of the hedonlc lndex.

t t-stat~st~c s~gn~f~cant at the 0.10 level.

* t-stat~st~c s~gn~f~cant at the 0.05 level.

** t-statlstlc slgnlflcant at the 0.01 level.

108
becomes plausible to assume that the res~dual ~n that site at least partially

represents omitted quality var~ables. The presence of a s~gnif~cant pr~ce

elast~city for the residual ~n both sites suggests that pr~ce factors are

also present ~n the res~dual.

The ratio of the elastic~ties can also provide some information on the relat~ve importance of om~tted qual~ty and price effects. The signif~cant income

elastic~ty in Pittsburgh suggests that, ~n that site at least, the hedonic

residual does ~nclude some omitted quality. In th~s case, the estimated pr~ce

and income elast1c1t1es based on the hedonic 1ndex would underestxmate the

true elast1c1ties of housing serv1ces; at least part of the change 1n the

hedonic residual would represent real changes ~n hous~ng in addition to the

changes reflected by the index.

One way to correct this problem may be to use the ~ncome elasticity of the

hedonic residual. If the ~ncome elast~Nty of the hedonic res~dual represents

increased expenchture for housing ser,,'"1..ceS not included J..n the hedon1C index,

then households allocate increased expenditures between ~ncluded and om~tted

~tems in the proport~on (n;/n;) , where n; and n; are the income elastic~t~es

of the hedonic resJ..dual and hedonl.c index, respectJ..vely. Sl.nce the rent rebates

offered by Percent of Rent apply to both ~ncluded and omitted qual~ty, it

seems reasonable to suppose that the allocation of increased expenditures

between the items included in the hedonic ~ndex and those included in the

hedonic res~dual would be the same as that for increases ar~sing from higher

incomes. l One can then write the followJ.ng:

'08 8

- 'Y

(5) n

Q n

Q

p y

where

'08

n the (unknown) pr~ce elast~c~ty of om~tted ~tems p =

n

Q the pr~ce elasticity of housing servJ..ces l.ncluded

p in the hedonic ~ndex

8 the ~ncome elast~c~ty of the hedon~c residual, and 'Y =

lsee KennedY and Merrill (1979) for a detailed d~scuss~on of the

conmhon under wh~ch th~s w~ll be true.

109
the income elasticity of housing services ~cluded

~n the hedonic index.

In words, the ratio of the price elastic~ties for omitted ~tems to that for

housing services is assumed to be the same as the ratio of the income elasticities, where the income elastic~ty for omitted qual~ty is approximated by

the ~ncome elasticity for the hedon~c residual. Equation (5) can be solved

to give the estimated price elastic~ty of omitted ~tems as a funct~on of the

estimated hedon~c ~ndex price and income elastic~t~es and the estimated

hedonic residual income elasticity:

(6)

Put another way, Equations (5) and (6) essentially accept the income elast~city

of expenditures as a benchmark for the normal relation between changes in

expen<htures and changes in the hedonic J.ndex (ignoring tenure characteristics

and defin~tional differences, which have only a small effect). The adJusted

pr~ce elast~city (~8) ~ncorporates th~s normal relat~on. The d~fference p

between the expend~ture price elasticity and the adjusted price elast~c~ty

thus 'measures the extent to whJ.ch the rent rebates altered the normal relatl.onsh~p between housJ..ng expenchtures and housJ.ng se~ces. It is worth emphasizing

the arbl.trary nature of tlll.S procedure. Other methods of correctJ.on are possible.

Table 5-5 ~pl~es a

price elast~city of

1 "'8 . h va ue for n ~n P~ttsburg of -0.045. S~nce the total

p

hous~ng services ~s the sum'of the hedon~c elastic~ty

and the elast~c~ty of omitted ~tems, this ~plies an overall price elast~c~ty

in P~ttsburgh of -0.158. Since the expend~tures pr~ce elastic~ty ~s -0.230,

this implies a shopping effect of -0.072--that is, only about two-th~rds

of the expend~ture increase induced by the Percent of Rent plans goes to

increased housl.ng servl.ces. 1

In conclusl.on, the evidence 1.0 Phoenix seems most consistent with viewing

the hedonic residual solely as a pr~ce effect, representing changes in shopping

behavl.or, and not as om~tted qual~ty. The 2ncome elastic2ty estJ.mates are

the same for the quality ~ndex and rent, and zero for the residual. Almost

1

In Phoen~x, the 2ncome elast~c~ty ~s small, negat~ve, and not

s~gn~f~cantly d~fferent from zero. Furthermore, the model beh~nd Equation

(6) only considers the poss~bil~ty of a pos~t~ve ~ncome elast~c~ty for the

res~dual (reflect~ng om~tted quality). Therefore, no adJustment ~n the

phoenix housing serv~ces elast~c~ty ~s 2nd~cated.

110
all of the d~fference ~n pr~ce elasticity estimates ~s found in the residual.

On the other hand, the res~dual in P~ttsburgh represents both some om~tted

quallty and some prlce behavl0r changes.

Demographic Strat~fication

As was seen in Section 4.3, expenditure elasticihes differ among certain

demographic groups. In particular, the est~mated minority price and ~ncome

elastl.cl.ties were lower than those for nonminorities. Stratl.f.l.cation by

household composit~on was ~ndicated ~n pittsburgh, and stratification by race

was indJ.cated in Phoeru.x. 5l.nee expenCh tuxes elastl.cJ.tl.es were not un.l.fonn

across demographic groups, hous~ng service elasticities probably will not be

either. Appenfux Table X-44 presents hedon~c estimates cross-classif~edby

these demographic character.l.stl.cs for movers. 1 Varl.ance ratio tests inChcate

that, as for expenditures, pr~ce and incone elast~c~ties differ by household

compos~t~on ~n P~ttsburgh but not ~n Phoe=x (see Table 5-6). The overall

estimated housing services pr~ce elastic~ty for Pittsburgh movers is -0.11

(s~g=f~cantly different from zero only at the 0.10 level). The est~mates

for the different types of households vary a great deal. The pr~ce elast~city

of housing servJ.ces was insignifl.cant for sl.ngle-person and sl.ngle-headed

households. In contrast, the pnce elastic~ty ~s -0.25 for households headed

by a couple (still smaller than the expenfutures eshmate of -0.36, though

w~thin that est~mates 95 percent conf~dence ~nterval). The hous~ng services

income elasticl.hes are much closer to each other. The largest estJ.mate is

that for households headed by a couple: 0.49 (again w~th~n the 95 percent

conf~dence interval of the expend~tures est~mate of 0.61). Indeed all the

est~mated hous~ng services elastic~hes by household type fall within the 95

percent confidence J.ntervals of the correspondJ.ng expenditure estl.mates

(compare Tab les 5-6 and 4-9).

In contrast to housing expendJ.tures where racl.al stratl.fication was l.Iqportant

only in Phoen~x, th~s strat~f~cat~on y~elds sign~f~cant fufferences at both

s~tes for housing se~ces (see Table 5-7). Minor~ty households have an

insignif~cant and posihve estimated pr~ce elast~c~ty ~n both sites, wh~le

non=nor~ty households, even ~n Phoemx (which has an ~nsignif~cant overall

elast~city), have a negative and sign~f1cant pr~ce elastic~ty. On the other

hand, nu.norl.ty households have zero or very low pr~ce and ~ncome elast~cities

(though the estimated housing sernce incone elast~c~ty for Phoenix =nority

~e estimated equations for all households are presented in Appenfux

Table X-40.

III
Table 5-6

HOUSING SERVICES ELASTICITIES

BY HOUSEHOLD COMPOSITION

PITTSBURGH PHOENIX

PRICE INCOME SAMPLE PRICE INCOME SAMPLE

HOUSEHOLD GROUP ELASTICITY ELASTICITY SIZE ELASTICITY ELASTICITY SIZE

All households -0.1l3t 0.226** (214) -0.045 0.375** (257)

(0.057) (0.047) (0.060) (0.043)

SJ.ngle-person -0.118 0.241 ( 32) -0.366t 0.464** (29)

households (0.168) (0.163) (0.197) (0.101)

SJ.ngle-headed -0.038 0.181t (87) 0.045 0.416** (111)

household with (0.085) (0.095) (0.081) (0.067)

I-' others present

I-'

IV

Households headed -0.246** 0.489** (95) -0.121 0.365** (117)

by a couple (0.080) (0.076) (0.098) (0.082)

SAMPLE: Percent of Rent and Control movers active at two years after enrollment, exclud~ng those

with enrollment lucornes over the el1gibl11ty I1mlts and those 11vlng In thelr own homes or In Subsldized

housing.

DATA SOURCES: InitJ.al and monthly Household Report Forms, HousJ.ng Evaluation Forms, 1970 Census of

Population, Baseline and Periodic Interviews, and lIppendix Table X-41.

NOTE: Standard error J.n parentheses. A variance-ratJ.o test could reject the hypothesis of homogeneJ.ty among household types J.n Pittsburgh (F(4,205) = 6.27), but could not in PhoenJ.x (F(4,248) = 1.69),

(critJ.cal value = 2.37 at the 0.05 level).

t t-statJ.stJ.C signJ.fJ.cant at the 0.10 level.

** t-statJ.stic signifJ.cant at the 0.01 level.
Table 5-7

HOUSING SERVICES ELASTICITIES

BY MINORITY STATUS

PITTSBURGH PHOENIX

PRICE INCOME SAMPLE PRICE INCOME SAMPLE

HOUSEHOLD GROUP ELASTICITY ELASTICITY SIZE ELASTICITY ELASTICITY SIZE

All households -0.113t 0.226** (214) -0.045 0.375** (257)

(0.057) (0.047) (0.060) (0.043)

Nonm~nor~ty households -0.143* 0.269 (180) -0.129* 0.440** (168)

(0.057) (0.048) (0.065) (0.045)

Minor~ty householdsa 0.067 -0.012 (34) 0.023 0.154t (89)

..... (0.201) (0.151) (0.106) (0.085) .....

w b b Black households --- -0.138 0.159 ( 27)

(0.218) (0.165)

Span1sh Amer1can 0.116 0.100 (62)

householdsc (0.121) (0.102)

SAMPLE: Percent of Rent and Control movers act~ve at two years after enrollment, excluding those

w~th enrollment ~ncomes over the elig~bil~ty l~mits and those l~v~ng ~n their own homes or ~n subs~dized

hous~ng.

DATA SOURCES: In~t~al and monthly Household Report Forms, Hous~ng Evaluat~on Forms, 1970 Census of

Populat~on, Basel~ne and Periodic Interv~ews, and Appenfux Table X-41.

NOTE: Standard error ~n parentheses.

a. A var~ance-ratio test reJected the hypothes~s of homogene~ty between non~nor~ty and ~nor~ty

households ~n both P~ttsburgh (F(3,208) = 3.48) and in Phoenix (F(3,251) = 16.96), (crit~cal value = 2.60

at the 0.05 level).

b. Minor~ty households ~n P~ttsburgh are all black.

c. A var~anoe-rat~o test did not reJect the hypothesis of homogene~ty between Spanish Amer~can

and black households in Phoenix (F(3,83) = 1.07), (critical value = 3.30 at the 0.05 level).

t t-statistic s~gn~ficant at the 0.10 level.

* t-stat~st~c s~gn~f~cant at the 0.05 level.

** t-statistic s~gn~ficant at the 0.01 level.
movers is very close to the expenfutures estimate and is s~gm.f~cant at the

1 0.10 level).

As noted from Table 5-5, the hedoIllc residual has a sign~bcant income elast~c~ty in P~ttsburgh but an insign~f~cant (and negattve) ~ncome elast~c~ty

~n Phoenix. One possible explanat~on for th~s is that the ~ndex ~s less

accurate in Pittsburgh than in Phoenix. It was prev~ously suggested that

measurement error in housing services elasticities may be adJusted for by

computing

{ n

Q e: n + n y y y

(7) e:

n

Q n

Q ny np

+

p p n

Q

y

where

the "true"~ncome elast~c~ty of hous~ng serv~ces,

and

the "true" pr~ce elast~c1ty of hous1ng serv~ces..

The f~rst express~on in Equat~on (7) ~s s~ply the income elasticity of

expenditures (except for minor effects due to tenure characteristics and

rent defin~t~on)--that ~s, all d~fferences in expenditures assoc~ated

w1th ~fferences 1ncome are assumed to reflect real changes 1n hous1ng

serv~ces. The second expreSS10n g~ves an adJusted estimate of the pr1ce

elast1city. Table 5-8 g1ves IIcorrected" price elastic1t1es for the two

sites strat~fied by household type and by m~nority status.

The results for the two sites are qU1te d~fferent. In Phoen~x, the 1ncome

elasticities of the hedonic res1dual are un1formly small and 1ns1gn~f~cant

for all demograph~c groups (see Append~x Table X~43). As a result, the

adjusted hous1ng services pr~ce elasticit~es in Phoen1x are close to the

unadjusted values, ~nd~cat~ng that the Percent of Rent offers d~d ~ndeed

have a substant1al effect on the shopp~ng behavior of rec1p1ents.

In pittsburgh, on the other hand, there are several large hedonic res1dual

1ncome elasticit~es. AdJusted price elas~cit1es are all closer to the

expenditure elast1c~t1es than are the unadJusted ones. Th1S conf~rms the

IFurther, =nonty households ~n Phoenix (but not ~n Pittsburgh)

start out w~th lower levels of hous~ng ser=ces (see Appendix Table X-42).

114
Table 5-8

"CORRECTED" PRICE ELASTICITIES FOR HOUSING SERVICES

COMPARED TO EXPENDITURE ESTIMATES BY DEMOGRAPHIC CHARACTERISTICS

PITTSBURGH PHOENIX

CORRECTED CORRECTED

HOUSING HOUSING

SERVICES EXPENDITURE SERVICES EXPENDITURE

HOUSEHOLD PRICE PRICE SAMPLE PRICE PRICE SAMPLE

GROUP ELASTICITya ELASTICITY DIFFERENCE SIZE ELASTICITY ELASTICITY DIFFERENCE SIZE

All households -0.158 -0.230 -0.072 (214) _0.045° -0.215 -0.170 (257)

S~ngle-person -0.188 -0.055 +0.133 (32) -0.375 -0.404 -0.029 (29)

households

S~ngle-headed house- _0.038° -0.216 -0.178 (87) 0.045° -0.073 -0.028 (Ill)

holds Wlth others

.....

..... Households headed -0.289 -0.349 -0.060 (95) -0.123 -0.356 -0.233 (117) lJ1 by a couple

Nonnunority hoUfEho1ds -0.181 -0.233 -0.052 (180) _0.129° -0.290 -0.161 (168)

Mlnorlty households _0.207° -0.207 0 (34) 0.027 -0.154 -0.181 (89)

Black households b b --- -0.141 -0.277 -0.136 (27)

Spanlsh Amerlcan 0.183 -0.081 -0.264 (62)

households

SAMPLE: Percent of Rent and Control movers actlve at two years after enrollment, excluding those wlth

enrollment lncornes over the ellgibl11ty limits and those I1vlng 1n thelr own homes or in Subsldlzed houslng.

DATA SOURCES: Inltlal and monthly Household Report Forms, Housing Evaluation Forms, 1970 Census of

pOpulatl0n, Base!lne and Perlodic Intervlews, and Appendix Table X-43.

a. See Equatlon (7) for the method of correctlon.

b. M1nor1ty households 1n P1ttsburgh are all blaok.

c. The corrected pr~ce elast~c1t1es are computed as 1nd1cated 10 Equat10n (7) w1th the following except10ns

F1rst, the correct1on only applies in theory when the 1ncame elastic1ty of the res1dual 15 pos1tive (when the

hedon1c income elasticity 18 less than the expend1ture income elastic1ty). Cases other than this are assumed to

represent stochast1c error, w1th a true value of n£ of zero (so that the hedon1c pr1ce elast1c1ty is not changed).

In add1t10n, m1nority households 1n pittsburgh pre~ent a special case. In th1S instance the hedon1c 1ucame elast1C1ty 15 near zero. Th1S suggests that the 1ndex captures I1ttle or no quality change for minor1ty households 1n

P1ttsburgh and the expenditure pr~ce elasticity was accepted as the corrected housing serv~ces elast~c~ty.
earl~er f~ndings that the Percent of Rent offers ~n P~ttsburgh had only a

small effect on the shopp~ng behav~or of rec~pients.

Substant~al shopping effects are indicated in Phoenix for all the demographic

strata (except for single-person and s~ngle-headed households). Minorities

and single-headed households in particular seem to'have almost no pr~ce

response ~n tenns of housing services. These groups also have lower expenditure response, however, so that the d~fference between expenditure and hedonic

price elast~c~ties 15 similar for mlnorities and nOnm2norities In Phoenix.

When minority households ~n Phoen~x are further divided into black and Spanish

American groups, It 15 clear that It is the Spanish Amer1can households that

did not increase thelr expenditures In response to these changes either (compare Table 5-7 and 4-8). Further, the f~t for both expend~tures and hous~ng

services is very poor (R2 = 0.02 and R2 = 0.03, respectively).

Apparently, then, the estimated equations do not describe the behavior of Span1sh Amerlcan households 1n partlcular very well. The pr1ce and lnceme elastlcl.ty estl.mates for Inl.norl.ty households J.n Phoem.x, partl.cularly for Spanlsh

Arner~can households, strongly suggest that these households d~d not respond

to the Percent of Rent rebates by ~ncreas~ng their consUll\Ption of housing

serVl.ces or thel.r housl.ng expendJ.tures. One possJ.ble explanat~on for th~s ~s

that =nor~ty households face market barr~ers that prevent them from purchas­

~ng an average amount of hou.s~ng services per dollar of additional expend~ture

or that prevent them from entering l.nto areas w~th higher rent and h~gher

quahty un~ts. If =nority households face a fufferent structure of hous~ng

attrJ.bute pr~ces due to market segrnentat10n or only haVe access to a l~m1ted

range of hou.s~ng cho~ces (perhaps due to racial or ethnl.c dJ..scr~minat~on) then

use of an hedon~c ~ndex wl.th l.mpl~c1.t attr~bute pr1.ces based on the full Sal11Ple

would misest~mate the actual hous1.ng serVl.ces consumed by ~nor~t~es.

A serl.es of tests to assess market segmentat~on (d~fferent relat1.ve attr~bute

welghts) were made durlng the development of the hedonic ~ndex (Merr~ll,

1977). In phoen~xl separate equat~ons were est~ated for wh1.te households

and Span~sh Amerl.can households and compar~son of these regress1.ons dl.d not

. 1 h l.nd~cate the ex~stence of market segmentatl.on. T e F-test for the ex~stence

of a submarket was not sl.gn1.f1.cant for the sem1.log form of the hedon1.c 1.ndex

used ~n th1.S report. Furthermore I the standard errors of the full sample and

1

There were too few black households 1.n phoen1.x to est1.mate a separate

submarket 1.ndex for them.

116
submarket equations differ by less than 1

operationally unimportant (Merrill, 1977,

percent, an amount that is

1

p. 130). Even though overall

differences are minor, however, several ~portant pr1ces, part1cularly

for space, do differ.

As an additional assessment of submarket effects, therefore, a separate

hedonic ~ndex, based on estimated attribute prices for Spanish American

households, has been computed. Separate estimates of price and income

elast~c~ties have been made us~ng this subsample index. Est~tion based

on the span~sh American subsample ~ndex does not change the results for

any group (see Appendix Table X-44). This may be interpreted as an

~ndication that specification b~as due to m~sestimated attribute prices

for Spanish Amer~can households ~s apparently not responsible for the

1nsign1ficant hous1ng serv1ces price and income elastic1ties.

Two ad~tional potent~al explanations for the difference between Spanish

Amer~can and white households deserve attent~on. F~rst, quality var~ables

may be om~tted from the hedon~c ~ndex wh~ch are systemat~cally assoc~ated

w~th the purchases of Spanish Amer~can households but not wh~te households.

Secondly, m~nor~ty Experimental households may have searched less than

m~nority Control households.

It ~s not at all clear wh~ch var~ables, ~f any, m~ght be systemat~cally

assoc1ated with m1nority or Span1sh Amer1can hous1ng consumption. In order

to determine if om~ssion of data on build~ng type, private yard, and the~r

interact10n was important for minor1ty households, the hedon1c res1duals

were regressed on these variables (Merr~ll and Kennedy, forthcoming).2

IMerr~ll (1977) found no ev~dence of price d~scr~minat~on against

Spanish Amer1can or black households in Phoen1x; that 1S, m1nor1ties do not

pay more than whites for the same hous~ng.

2

EXanl1nat10n of the data reveal that Spanish Americans are much

more l~kely than wh~te households to l~ve ~n single family un~ts and less

likely to l~ve ~n larger mult~fam~ly un~ts. Further, ~t has also been

suggested that the Spanish Amer~can households in Phoenix have a strong

preference for yard space. The full sample hedonic equation does include

a dummy var~able for multifamily buildings with f~ve or more un~ts but no

other variables indicating building type or presence of a yard were

s~gnificant.

117
None of these variables appear to be related to qual~ty for wh~te households.

Spanish Amencan households appear to prefer pr~vate yards, espec~ally ~f

associated w~th a small mulbf~ly un~t. It is not l~kely, however, that

g~ven the small coeffic~ent for the yard variable, the omiss10n would b1as

the pr1ce elastic1ty est1mate suff1c1ently to make 3..t zero. Further I 5l.nee

J..ncorne is not signifl.cantly related to the hedonl.c residual 10 Phoe~x for

Spanish Arrerl.can movers, even at two years after enrollment, the evidence of

systematl.c bl.as due to omitted varJ.ables seems rather slim..

The last l.nvestigation concerns the effect of search effort on obta1ning

an amount of hous~ng serv~ces per dollar of expenditure. As suggested above,

part of a smaller l.ncrease in housing servl.ces relatl.ve to expend1tures

for Exper=ental households ~n both Phoen~x and P~ttsburgh may be due to a

conscious decisJ.on on their part to use less effort in searching for a new

unit. Spanl.sh Amerl.can movers receiv1ng a Percent of Rent rebate did spend

sign~f~cantly fewer days search~ng (28 days) than d~d Control households

(76 days) (see Append~x Table X-29).

Atkinson et al. (1979) noted that Spanish Amencan Percent of Rent movers

were less l~kely to leave their ~ru t~al neighborhood than were Control Span­

~sh American movers. They suggest that th~s may result from a chance group­

~ng ~n the Percent of Rent category of households that were strongly interested ~n remaJ..n~ng ~n the~r in1.tJ.al neJ.ghborllood. If the initJ.al neighborhood has a li=ted range of un~ts ava~lable, these households may be prevented

from obtaJ.nJ.ng J.mproved housl.ng by supply constra1.nts There 1.5 not strong

eVl.dence for thJ.s constraJ.nt, however, as the varJ.ance J.n the hedon1.c value

of u=ts occup~ed by Span~sh Amer~can households at enrollment and at two

years ~s almost ~dent~cal to that of non=nor~ty households.

In sum, there is a general pattern of reduced shopping effectJ.veness J.n

Phoe~x. The extent of th~s shopping effect ~s s~lar for all demograph~c

groups (w~th the except~on of single-person and s~ngle-headed households).

There ~s also some eV1.dence of reduced effectJ.veness 1.n PJ.ttsburgh, but J.t

is not widespread.

MJ.nor1.ties ~n PhoenJ.x, and espec~ally Span1.sh AmerJ.can households, showed

IJ.ttle or no real change J.n hous~ng or rent 1.n response to the percent of Rent

offers. No clear reason for thJ.s lower response--wJ.th the poss1.ble except1.on

of reduced search effort--has been found. Indeed, the error of estJ.mate

for this group 1.8 large enough that the very low response estJ.mates could

118
s~mply reflect stochast~c error.

Furthermore, in contrast to houslng expendJ.ture functl.ons, varJ.ance ratio tests

reJect the possl.bil~ty of pooling the sites, even when the combined hous~ng

services function l.ncludes a 5J.te-specific 1.ntercept. The hypothesis of homogeneity across sites of the demand for hous~ng se~ces was rejected for all

mover households and for the mover subsamples stratif~ed by race (see Table

5-7). The different results w~th respect to pooling the sites between expendl.tures and housl.ng services 1.5 due to the dJ.fferent shopping behavior 1.0 the

two 51tes.. Part of the l.ncrease 1.n expenfutures 1.n Phoenl.x was due to l.nefficient shopping, whl.le no eVl.dence of inef£J.cl.ency waS present in Pl.ttsburgh.

5.3 CONCLUSIONS

The hous~ng serv~ces response of Percent of Rent households to the pr~ce mscount offered to them was smaller than the expenmtures response. Th~s is

ture not only for all movers, but for most demographic groups as well. Increased expendl.tures on housl.ng combl.ne two changes: l.ncreases in the amount

of housl.ng serVJ..ces that the household consumes and/or l.ncreases 1.0 the prl.ce

per = t of housing services that the household pays. The hedo=c index was

desl.gned to measure the increase in housing services.. The consistent difference between changes 1.0 housl.ng services and the larger cHanges l.n expenditures

across all groups l.nvest1.gated prompted further l.nvest1.gat1.on 1nto the nature

of the hedonic index. It seems Llkely that some quality components were omitted from the P~ttsburgh hedonic index. Nevertheless, adJust~ng for o=tted

items still results ~n a significant est~mated effect on the pr~ces paid by

non=nor~ty households. 1

In Phoenix, there was little ev~dence of o=tted quality, imply~ng that Percent

of Rent households have shopped ~neff~ciently and received less hous~ng services

per dollar than Control households. This shopp~ng effect was much the same for

all demograph~c groups except s~ngle-person and s~ngle-headed households. In

addition, ~t appears that s~ngle-headed households and =nori~es had l~ttle

real change in housing l.n response to the Percent of Rent offers 6 Th1.S was

espec~ally marlced for Spanish American households. 2 They also appear to have

had little or no change J.n eJq;)enditures 6 These low response levels may, however, reflect stochastJ.c error rather than a genmne difference l.n behavior.

1

See Kennedy and Merrill, 1979, Table 4-2.

2The sample of black movers was too small to examine individually.

119
REFERENC&S

Atkinson, Reilly, W~lliam Hanu.1ton, and Dowell Myers, EconoIlll.c and Rac~a1/

Ethnic ConcentratJ.on J.n the Housing Allowance Demand ExperJ.ment,

Cambrl.dge, Mass., Abt Assocl.ates Inc., Janua:r::y 1979 (r09VJ.sed June

1980) •

Budfung, David W. , Housing DeprJ.vatl.on Among Enrollees 1.n the Housl.ng Allowance Demand Experiment, Cambridge, Mass., Abt Associates Inc.,

November 1978 (revised June 1980).

Mernll, Sally R., Hedonic Infuces as a Measure of Hous~ng Qua1~ty, cambndge, Mass., 1\bt Assoc~ates Inc., December 1977 (revised June 1980).

Kennedy, Stephen D. and Sally R. Mern11, "The Use of Hedonic Infuces to

D~stingmsh Changes ~n Hous~ng and Hous~ng Expenditures: E=dence

From the Housing Allowance Demand Experiment, II Paper presented at

the Research Conference on the HOUSJ.ng ChoJ.ces of Low-Income Fanul­

~es, Wash~ngton, D.C., March 1979.

Martill, Sally R. , Stephen K. Mayo, Margaret Dewar, Lucina Vernazza, "Housl.ng

Consumption," Chapter 4 1.0 Working Paper on Early F1.ndl.ngs: Experimental Housl.ng AIIOW'ance Program, Demand Experiment, Cambrl.dge, Mass.,

1\bt Associates Inc., 1975, pp. 75-186.

V~dal, AV~s, The Search Beha=or of Black Households in the Hous~ng Allowance

Demand Exper~ment, Cambndge, Mess., 1\bt Assoc~ates Inc., July 1978

(re=sed June 1980).

120
CHAPTER 6

ISSUES IN USING EXPERIMENTAL DATA

Th~s chapter d~scusses three lssues lnvolved 1n est1rnatlng demand equatlons

us~ng the data from the Demand Experiment: (1) the dynamws of behav~or

over time, (2) pos51ble blas in estlmatl0n due to sample selectl0n, and (3)

the extent to wh~ch households understood the Percent of Rent offers.

HouSlng dynamlcs are 1ffiportant because est~ated responses to changes in

the prl.ce of housl.ng presented 10 thl.S report are based on the responses of

households dur~ng the hrst two years of the Demand Exper=ent. Econom~c

theory suggests that under certal.n cl.rcumstances thl.s could underestl.mate

the eventual response to a permanent prl.ce reductl.on. Sectl.on 6.1 examl.nes

the pattern of expendl.tures over the two years of the experJ.Inent for eVl.dence

of any systematl.c trend that would l.ndl.cate a larger eventual response.

Sample selectl.on can also bl.as est~ates based on experimental data. Not all

households offered enrollment ~n the Percent of Rent plans accepted the offer.

Nor d~d all enrolled households rema~n ~n the exper=ent for the full two

years. Agaln, economlC theory suggests that Percent of Rent households that

dld enroll and remaln ln the experlment may have tended to spend more for houslng

than other households. If thlS were the case, the est1mated responses for

these households would overest=ate the response of the populat~on as a

whole. In add~t~on, much of the analys~s ~s based on households that moved

dur~ng the exper~ment. Theory suggests that some of these households may be

ones wlth espec1ally large expend1ture changes so that later movers would not

change the1r hous1ng expend1tures to the same extent. Sectlon 6.2 compares

the hous~ng of the samples used ~n analys~s w~th that of households offered

enrollment to determ1ne whether there 18 any eV1dence of such select10n

effects.

Program understand1ng may also have affected the estxmat10n. If some households d~d not understand the Percent of Rent offer, the~r responses m~ght

mlsestimate the eventual response to a well-understood price reduct10n or

rent rebate program. Sectlon 6.3 examlnes eV1dence from 1nterview data

about program understand1ng and lts effect on household responses.

121
6.1 DYNAMIC SPECIFICATION OF HOUSING DEMAND

Chapter 4 presented est1ffiates of an equ~l~brium model of housing demand

based on the assumpt~on that movers adJust completely to the percent of Rent

rebates. Once a household moved, ~t was assumed to allocate its ~ncame between hous~ng and other goods accord~ng to ~ts equ~l~r~um demand for housing.

No further change was expected until the household's c~rcumstances changed

aga~n.

Another approach to demand analys~s ~s based on the ~dea that consumpt~on

(of any good) lDvolves aspects of hahlt formatl0n, lnertla, 19norance, uncerta~nty, and costs of change, wh~ch lead households to respond only gradually

to changes lD prlces and lucame. The two best known such models are the

1 partial AdJustment and the Adapt~ve Expectat~ons Models. While these models

vary ~n some deta~l, they both lead to the same reduced form equat~on (though

wlth dlfferent error structures). ThlS can be seen as follows.

Under the Part~al AdJustment Model, actual rent ~s adJusted by some fract~on

of the dlfference between deslred rent and the prevlous perlod's actual rent.

Th~s

tioD

(la)

(lb)

occurs as

2

pattern.

where

the household gradually feels ~ts way to ~ts opt~mal consumpThus, under th~s model(~gnor~ng for the moment changes in price),

R*

t

the household's desired expenditure on

houslng lD perlod t

lucame (current or pennanent)

actual houslng expendlture In perlod t

lsee Johnston (1972), pp. 300-320, or Intr~ligator (1978), pp. 235­

248 for deta~led descr~pt~on of these models.

2Mayo (1977) showed that the Part~al AdJustment Model w~ll also ar~se

~f households fully adJust the~r consumpt~on, but do not all adJust ~ed~ately. Thus ~f households adJust fully when they move, but do not all move

Lmmedlately, an est~ated demand funct10n for the entlre populatlon wlll have

the form of Equat~on (lb). Th~s poss~b~l~ty ~s dealt w~th ~n th~s report by

separate estlffiat10n of the responses of movers.

122
y = the Itcoe f£l.cl.ent of adJustment,1I and

V

t = a stochastic error term.

Comb~n~ng Equat~ons (la) and (lb) and rearrang~ng terms, the Part~al AdJustment Model can be wrl.tten

(2)

under the Adapt~ve Expectat~ons Model, expectations about permanent ~ncome

are

the

adjusted by some fractl.on of the dl.fference between current l.ncome and

1 prev1.ous perl-od's permanent l.ncorne. Thl.s arl.Ses because households

are uncertal.n about thel.r future l.ncame. Expectations about permanent l.ncame

and the hous~ng expend~tures based on ~t are only developed gradually. Thus,

under thl.S model,

(3a)

(3b)

where

In(Y*) - In(Y* ) t t-l

y* = measures of permanent or normal l.ncome t expected to preva~l as of period t

o the "coeffl.c~ent of expectatl.ons," and

~t = a stochastl.c error term.

Combining Equat~ons (3a) and (3b) and rearrang~ng terms, the Adapt~ve Expectat~ons Model can be wr~tten

(4 )

Equat~ons (2) and (4) are ~dent~cal except for the error terms.

The d~fference between Equat~on (2) or (4) and the Complete AdJustment Model

dl.scussed in Chapter 4 for movers 15 the presence of the lagged rent term,

R

t

_l , and the resulting interpretation of the coefficients. Under the models

of Equat~ons (2) and (4), households would in~t~ally adjust to a change ~n

income, 1I1nY, by the amount ~y(1I1nY) or ~o(1I1nY), respect~vely. The term ~y (or

~o) is the ~ediate or short-run ~ncome elast~c~ty. If the change ~n income

1

Thl.s process can be extended to other varl.ables as well.

123
~s ma~nta~ned over t~e, however, households w~ll eventually change the~r

income by S(d1ny), where S 1S the long-run income e1astic1ty. Th1s suggests

that long-run responses might be estimated more accurately by Equat10n (2)

or (4) than by the model used 1n Chapter 4. Unfortunately, 1t is almost

1mposs1b1e empirically to d1stinguish these gradual adjustment models from

qu~te d~fferent models based on serial correlation.

Ser~al correlat~on between the error terms of two consecut~ve years ~s

almost inev~table. There may be several reasons for such ser1al correlat~on, the most conv~nc~ng of wh~ch ~s that some unobservable var1able

deter.mlnlng behavlor, such as taste for houslng, wll1 remaln more or less

constant over a span of years when households are observed over t~e. If

the true model 1S the Complete AdJustment Model of Chapter 4, ser1a1 correlatl0n ~plles that

where Et lS the error term In t~e t, nt lS random error, and p 1S the serlal

corre1at1on coeff1c1ent. Comb1n1ng Equat10ns (Sa) and (Sb) gives

It 1S d1ff1cu1t to d1st1ngu1sh Equat10n (6) from Equat10ns (2) or (4)

emplrlcally. Indeed~ lf ~ncame ~s measured as three-year average lucame, Y,

Equat10n (6) becomes

(7)

wh1ch 1S 1dent1ca1 to Equat10n (2).

Both the Demand Experlment data and a longer tlme serles of data from the

Panel study of Income Dynamlcs were 1nsufflclent to dist1ngulsh among the

three models. Therefore, 1n testlng for dynamlc response patterns, It was

assumed that the dynam1c model conta1n1ng 1n(Rt _

1 ) as an 1ndependent

varlable could also ~nvolve serlal correlatlon. The equatlon estlmated

1S then (1nc1ud1ng the pr1ce term)

(8)

where the e t are ser1ally correlated.

124
The problem 1n est1IDating Equation (8) 1S that in the presence of ser1al

correlat~on, R

t _ 1 , which includes et_I' will be correlated with e t - Thus the

est1mated coefficient of In(Rt

_

l ) may reflect the b1as due to serial correlation rather than any gradual adJustment process. Th1s problem can be

addressed by US1ng a two-stage procedure that subst1tutes a pred1cted value

1 of the log lagged rent, In (Rt

_

l ) for In(Rt

_

l

). The var1able In(Rt

_

l ) 1S

pred1cted from a regress10n In(R 1) on lagged values of exogenous variables tand 1S, by construct10n, uncorrelated with et and h1ghly correlated w1th

In(Rt _l ).2 This procedure y1elds consistent est1mators of the parameters.

The ~nstruments used to pred~ct enrollment rent were enrollment ~ncome, Y

t

-

1 ,

and length of res1dence at the enrollment dwel11ng un1t, L

t

_

l . Enrollment

1ncome 1S by 1tself too h1ghly correlated with subsequent 1ncome to serve as

an effectlve Lnstrument (t~, 1£ enrollment lucame alone 18 used as the

instrument, the values of In(Rt _

l ) are too correlated with In(Yt ) to d1stingu1sh

therr effects; the error of estimate of D 1n Equation (8) becomes very large).

Length of residence, L

t

_

l , provides enough independent var1at1on in In(Rt

_

l ) to

overcome thlS. Form an econometrlc vlewpolnt, Lt_1 18 a COnvenlQnt lnstrument;

it 1S correlated W1th Rt_

l but not w1th Rt (since all movers have zero length of

tenure in thelr new unit), and hence 18 lndependent of e

t -

It must be adrnltted, however, that length of residence 18 an lnapproprlate

lnstrument for the Adaptlve Expectatl0ns Model and may not be approprlate for

the Part1al AdJustment Model. Length of reS1dence apparently affects expend1­

tures because households with longer tenures enJoy exceptionally good deals,

3 pay1ng less for comparable un1tS than new tenants (Merr111,1977).

If the Part1al AdJustment Model is developed 1n terms of hous1ng serv1ces,

H, rather than hous~ng expend~tures, R, Equat~on (2) becomes

(2)'

Isee Gr1l1ches (1967), p. 41. Mayo (1977), 1n est1mating a Part1al

AdJustment Model for the prel1ffi1nary f1rst-year data, 19nored the poss1bi11ty

of s1multaneous equat10n b1as.

2 ............... The two-equat1on system 1S recurS1ve and In(R ) can be pred1cted t-l uS1ng Ordinary Least Squares.

3

Th~s may ar~se because landlords offer d~scounts to reta~n tenants

and avo~d the costs of turnover or because tenants w~th good deals tend to

hold onto the~r un~ts.

125
To wr~te Equation (2)~ ~n terms of expenditures~ the term In(Pt ) the log

of housing price, is added to both sides of the equation. However, if because

of the tenure discount, the hous~ng price at any period, Pt , varies w~th

length of tenure, then

(9)

where

Pt = the price of housing

0 the pr1ce of housing for new tenants~ and P

t =

Lt

the length of tenure.

Us~ng thlS specificat~on of pr~ce, Equation (2)1 becomes

(10)

Collect~ng pr~ce terms and substitut~ng Equat~on (9) ~nto Equation (10) g~ves

(11)

Since households that move all have L equal to zero, Equation (11) becomes

t

(12)

where

o (l-y)ln(pt _

l ) + ay].

1ncluded 1n the est1mated equat10n ~o beg1n wlth and

adJustor, but only helps to characterlze hous1ng

Thus, L

t _l should be

lS thus 1nsufflc1ent as an 1nstrument. However, ~f L

t

_

l acts

expendltures

not as a pr~ce

at enrollment~

1t may be used as an 1nstrument. Th~s could ar~se~ for example, 1£ the

relat~on between length of tenure and enrollment rent 1n part reflects the

fact that households w~th long tenure have not adJusted the~r hous~ng

expend~tures for some t1me. In th1S case, length of tenure would reflect

126
the extent of a household's d~sequlllbr~um (with an overall negatlve correlat~on with rent if household ~ncomes tend to dr~ft up over time) and be

an ~deal instrument for the partial Adjustment Model.

In the Adaptive Expectations Model, lagged rent ar~ses through substitution

of (In(I\_l) - Cl - llt_l) for

appropriate specification of

Bln(Y~_l)' us~ng Equation (3a).

Equation (3a) is

If the

(3a) ,

then Equat~on (4) becomes

(4) ,

Thus the lagged rent var~able should be net of the effects of tenure d~scount

for the Adapt~ve Expectat~ons Model.

The emp~r~cal results are summar~zed ~n Table 6-1. In both s~tes the

"adJustment coeff~c1ent" 1S h1gh, and 1n Plttsburgh 1t 1S not signlf1.cantly

d1.fferent from one. For th~s reason the estlmated long-run elastic1.t1es are

very slm1lar to the est1mated short-run elast1C1.t1.eS, and both are S1m1lar

to those presented ~n Chapter 4. The ev~dence therefore does not suggest

the superior~ty of e~ther the Part~al AdJustment or the Adapt~ve Expectat~ons

Models. The data are cons~stent w~th v~ew~ng the Complete AdJustment Model

1

as an adequate theoret1.cal descrlptJ.on of the behav1.or of 10w-1ncome renters.

The dynamics of response to pr1.ce changes need not be the same as those of

response to lncome changes. However, there may also be gradual adJustment

to the pr1ce change, so that prlce response would l.ncrease over t1me. In

th~s case, est1mated

would understate the

responses based on the f1rst two years of the exper1ment

2 eventual response. If such gradual adJustment takes

place, then one would expect (under an Adaptive Expectat~ons Model) that later

moverS would have larger responses than earlier movers or at least (under a

Part~al AdJustment Model) that repeat movers would respond more on the second

lThe h~gh correlation between Rt and Rt-l can be used to lIl\prove

premction of ~f Rt-l is known and thus ~mprove est~mates of p~ece elast~­

c~ues as discussed ~n Appenmx VI.

2In fact, the estimated price elast~cit~es presented ~n Chapter 4

are fairly low and are less than most of the estimates based on nonexper1.­

mental data discussed ~n Secuon 3.3.

127
Table 6-1

PARAMETER ESTIMATES FOR A

DYNAMIC MODEL OF HOUSING DEMAND

PITTSBURGH PHOENIX

ESTIMATES ESTIMATES

Short-run ~ncome elast~c~ty 0.302** 0.268**

(0.049) (0.040)

Short-run pr~ce elast~c~ty -0.201** -0.215**

(0.060) (0.052)

AdJustment coeff1c1ent 0.848a 0.693b

(0.166) (0.117)

Long-run income elastic1ty 0.368 0.387

-

Long-run pr~ce elast~c~ty -0.237 -0.310

SAMPLE SIZE (236) (291)

SAMPLE: Percent of Rent and Control movers actlve at two years

after enrollment, excl~dlng those wlth enrollment lucornes over the e11g1­

bl11ty l~ltS and those I1vlng In thelr own homes or lD SUbsldlzed houslng.

DATA SOURCES: In1t1al and monthly Household Report Forms, and

payments f11e.

NOTE: standard error estlrnated uSlng Two-Stage Least Squares. The

lnstruments used for lagged rent were enrollment lucame and length of reSldence at enrollment dweillng unlt. Current lucame was used for the lucerne

measures. Standard errors In parentheses. The estlmated elastlcltles from

a stat1c model (see Append1x Table X-12) were: 1n P1ttsburgh 0.324 for

1ncome and -0.195 for pr1ce; 1n phoen1x 0.325 for 1ncome and -0.219 for

prlce.

a.

b.

**

Not S1gn1f1cantly d1fferent from one at the 0.10 level.

S1gn1f1cantly d1fferent from one at the 0.01 level.

t-stat1st1c s1gn1f1cant at the 0.01 level.

128
rrove than on the f1rst.

Unfortunately, these patterns Inl.ght be offset by the effects of the lim~ted

durat.1.on of the exper1ment. If mov~ng costs are substantial, then households

may be reluctant to move to hous~ng so expens~ve as to requ1re that they

vacate 1t when the exper1ment ended. In th1s case, households would be less

11kely to respond toward the end of the exper~ment, when the period over

1 WhlCh payments would be rece~ved was smaller. Th1s would be espec~ally true

en Plttsburgh where households generally move less often (so that the prospect of hav1ng to move mlght pose a more ~mportant barr1er). If both of

these factors--gradual adJustment and exper~ental durat10n--were lmportant,

then they conce~vably offset each other in the second year. While the overall response would be lower, f1rst and second year responses would not be

very dlfferent.

Table 6-2 presents the est1ffiates of the prlce elastlc~tles for movers durlng

each of the three t1me per10ds and for comblnat10ns of the per~ods. The

results are arnb~guous--the largest response lS for the latest movers ~n

P~ttsburgh (those movlng only In the second year) and the earl~est In Phoen~x

(those mov~ng 1n the f~rst SlX months). Response 1ncreases for movers in

Plttsburgh (-0.16 for f~rst year only movers to -0.37 for second year only

movers) but decreases ~n Phoen~x (-0.29 to -0.10 for the same two groups).

One adfutlonal test for problems due to durat~on ~s based on expected mobil1ty.

There 1S a strong connect1on between prlor moblilty and subsequent mob1lity

(see MacMJ.llan, 1978). Thus, households that moved frequently ~n the years

before the experlment are more llkely to move 1n the next several years. But

1f a household ~s llkely to move in any case, 1 t should be less concerneq Wlth

the prospect of hav~ng to move at the end of the expenment. If exper~mental

durat10n 1S a factor, the responses of households w1th hlgh levels of pr10r

mob~hty should be larger than those of households w~th lower prior mobil1ty.

As ~s lllustrated ~n Table 6-3, th~s ~s true for households mov~ng only ~n the

flrst year, but not for households mOVJ.ng only In the second year or ln both.

years. Nor does controll1ng for prlor rnobil1ty make the pattern of response

for movers reflect e~ther of the patterns expected ~f e~ther the Partial

IFurther, 1£ households aid not expect to remain el1gible for the

allowance payment for long (as thelr incomes lncreased), then they may have

preferred to retaJ.n the allowance as savlngs rather than respond.

129
Table 6-2

PRICE ELASTICITIES OF DEMAND

FOR DIFFERENT MOVER GROUPS

PITTSBURGH PHOENIX

SAI-lPLE SAI-lPLE

MOVER GROUP ELASTICITY SIZE ELASTICITY SIZE

Moved dur~ng the two years -00211 (236) -00219 (292)

(0.063) (0.059)

Moved dur~ng the f~rst year -00132 (166) -0.273 (213)

(00074) (0.069)

Moved durl.ng the f~rst -00189 (99) _00364a (151)

51-X months (00111) (00083)

MOved dur~ng the second -00140 (88) -00264 (129)

SJ.X months (00108) (0.090)

Moved dur~ng the fust -00163 (127) -00291 (129)

year only (00085) (00110)

Moved dur~ng the second year -0.260 (109) -00201 (185)

(00095) (0.069)

Moved durl.ng the first 00035 (36) -0.285 (94)

year and the second year (0.142) (00089)

Moved durl.ng the second _00366a (69) -OolOOa (79)

year only (00122) (00115)

SAMPLE: percent of Rent and Control movers actl.ve at two years

after enrollment, excludl.ng those wl.th enrollment l.ncomes over the e11.g1.­

bl.ll.ty l~l.ts and those ll.vl.ng 1.0 thel.r own homes or 1.0 subsl.dl.zed housl.ng.

DATA SOURCES: In~t~al and monthly Household Report Forms, payments

f~leo

NOTE: Prl.ce elastl.cl.tl.es were estl.mated uSl.ng average l.ncome.

standard error in parentheses below the elastl.cl.tl.es.

a. The est~mate does not fall w~th~n the 95 percent conf~dence

interval of the est~ate for all households that moved during the two

years: (-0.334, -0.088) ~n P~ttsburgh and (-0.335, -0.103) ~n Phoen~x.

130
- ---------

Table 6-3

PRICE ELASTICITY ESTIMATES

BY PRIOR MOBILITY

PITTSBURGH PHOENIX

MOVER GROUP

Moved durlng the

flrst year only

Sample Slze

LOW PRIOR HIGH PRIgR LOW PRIOR HIGH PRIgR

MOBILITya MOBILITY MOBILITYa MOBILITY

-0.110 -0.352 -0.178 -0.448

(0.100) (0.155) (0.150) (0.166)

(80) (47) (49 ) (58)

Moved durlng the

second year only

Sample Slze

Moved durlng both

the flrst and

second years

Sample s~ze

-0.393

(0.153)

(43 )

-0.073

(0.240)

(18 )

-0.341

(0.230)

(26)

0.107

(0.198)

(22 )

-0.091

(0.176)

(41)

-0.357

(0.180)

(34 )

-0.120

(0.149)

(38 )

-0.238

(0.097)

(72 )

SAMPLE: Percent of Rent and Control movers actlve at two years

after enrollment, excludlng those wlth enrollment lucornes over the ellgJ.­

bll1ty limltS and those 11vlng in thelr own homes or ln SubSldlzed houslng.

DATA SOURCES: Inltlal and monthly Household Report Forms, payments

flIe, and Basellne Intervlew.

NOTE: Prlce elastlcltles est~ated uSlng average lucarne. Standard

error In parentheses below coefficlent.

a. One or fewer moves durlng the three years prlor to the Basellne

Intervlew.

b. ~vo or more moves durlng the three years prlor to the Basellne

IntervJ.ew.

,

131
dlfference ~n elast~clt~es reported

to a m2splaced decJ..mal pOJ..nt ~n tran­

~s one-tenth of that reported J..n

estlmates of J..ncome elast~c~ties among households

those reported here--O .420 ~n Denver and O. 331 ~n

Table II-6, p. 35).

1 AdJustment or the AdaptJ.ve Expectations Models were true.

More ch.rect eVl.dence on the effect of e~erimental durat~on 1.5 ava1.1able from

the Seattle/Danver Income Maintenance ExperlIl'le;nts. Those exper1.ments offered

a var1.ety of l.ncome-concht1.oned payments s1.milar in form to the Unconstra1.ned

payments tested in the Demand Exper~ment. In addition, unlike the Demand.

Experiment, the Seattle/Denver Income Maintenance Experirrents l.ncluded both

three- and five-year offers. If the -three-year durat~on of the Demand Experurent 1.n fact lum..ted the changes 1n hous1.ng undertaken 1.n response to the

Percent of Rent pr1.ce rebates 1 then one would expect to fJ.Ild lower responses

to the l.ncome transfers by Seattle and Denver households W1.th three-year

offers as compared to those w~th f~ve-year offers. In fact, analys~s by

Ohls and Thomas (1979) infucates almost no fufference between the two groups.

Ohis and Thomas est1.mate, among other thl-ngs, the effect of the exper1.roental

l.ncome transfers on rental expenfutures three years after enrollment, by

regress~ng monthly rental expendJ.tures on var~ables for race/ethn~c~ty ( household type, average (three-year) exper~mental payment, and average (three-year)

income from other sources.. As shown in Table 6-4 ( estJ..mates for households

w~th f~ve-year offers were almost ~dent~cal to estimates for the ent~re sample

of households (inclufung both households with three-year offers and those w~th

f~ ve-year offers).. L1.kewJ..se, dJ.rect est~mates of the dJ.fference ~n response

for the two groups (reported only for Denver) are small and insig=ficant. 2 ,3

These results suggest that the three-year durat~on of the Demand Expenrrent fud

not in itself matenally affect household responses to the rent rebates offered

by the Percent of Rent plans. Accorfungly, the fa~lure to find cons~stent patterns of ~ncreased hous~ng change over t~me seems less likely to reflect the

~nfluence of h=ted durat~on and more likely to infucate that the adaptive expectat~ons or part~al adJustment models do not apply to changes in rental housing.

1

Some addJ.tJ..onal ev~dence that durat~on ilid not matter ~s presented

~n Appenfux VII, wh~ch compares the effect on mob~hty of expenmentally

~nduced changes ~n des~red expend3.tures and pre-experlmental deviation between actual and desJ..red e~end1tures.

2

Th . e sJ..gn~fJ..cant( though small

~n Table C-8 of Ohls and Thomas ~s due

scr~pt~on (the actual esumated effect

Table C-8 for rental expend~tures).

3

Ohls and Thomas'

that moved~are s~TIU.lar to

Seattle (Ohls and Thomas,

132

-----------------
Table 6-4

COMPARISON OF OHIS AND THOMAS' ESTIMATED EFFECTS

OF EXPERIMENTAL INCOME TRANSFERS ON RENTAL EXPENDITURES

fOR THREE- AND FIVE-YEAR GUARANTEES

(SEATTLE/DENVER)

ESTIMATED COEFFICIENT fOR EXPERIMENTAL PAYMENTS

All renter households

Renter households w~th

five-year guarantees

All renter households,

w2th interact20n for

f~ve-year offers

[D~fference ~n

coeff.l.c.l.ent for

fJ.ve-year guarantees]

DENVER

COEFFICIENT

.007**

(.oOll

.007**

(.002)

.006**

( .002)

.0008

( .0015)

SAMPLE

SIZE

(824)

(486)

(824)

SEATTLE

COEfFICIENT

.008**

(.002)

.009**

( .002)

N/A

N/A

SAMPLE

SIZE

(401)

(231)

DATA SOURCES: Ohls and Thomas, 1979, Tables F-l, F-2, F-44.

NOTE: Standard errors .l.n parentheses.

** t-statist~c s~gn~f~cant at the 0.01 level.

133
In conclus~on, the most irqportant dynanuc factor in response may be the difference ~n response between movers and nonmovers discussed J.n Chapters 2 and

4. There ~s no evidence of other ~Il\Portant dynanu.c patterns. It must be

admitted, however, that the various dynannc models consJ.dered in this section

cannot be conclusively reJected w~th the available data.

6.2 SELECTION BIAS IN PRICE ELASTICITY ESTIMATES

The sample of households offered enrollment ~n Percent of Rent plans was

carefully desJ.gned to be a random sample of the low-J.ncome populat~on J.n

each slte. The equllJ.brlurn demand functJ.ons were est~mated on a dJ.fferent

sample of households--households that accepted the enrollment offer, were

verlfled to be wlthJ.n the lncome ellgibJ.l~ty llmlt, remalned ln the experJ.­

ment, and moved somet~e between enrollment and two years after enrollment.

Each of these selectlon crlterla may have introduced blas ln the estLmated

coeff~clents, so that they may dlffer from the populatlon coeff~clents, as

follows:

Acceptance b~as. Households offered higher payments may have

been more l~kely to accept the enrollment offer than households

offered lower payments. SJ.nce, for each rebate level, payment

increases wlth housing expendltures, households that accepted

the Percent of Rent offers may have tended to spend more for

houslng than Controls. In thlS case, cross-sectional comparJ.­

son of Percent of Rent and Control households mJ.ght overest:unate the effect of the rebate.

Attr~t~on b~as. L~kew~se, households may be mOre l~kely to

remaln ln the program 1£ they received hJ.gher payments. Agaln,

Percent of Rent households that tend to spend more on housJ.ng

regardless of the experlment may be more lJ.kely to remaln J.n

the exper1ment.

Mobl!J.ty blas. In theory, households move to change theJ.r

housJ.ng and hence should be, other thlngs equal, more llkely

to move the larger thelr desired changes. Households may move

J.n order to spend less or to spend more on houslng. The rent

rebates offered to Percent of Rent households would be expected

to encourage movJ.ng by households that would have moved to

lncrease thelr spendlng. Thus the sample of Percent of Rent

1

movers may not be comparable to the sample of Control movers.

lOne other possJ.ble bJ.as 1S not considered here. If the price elastlclty

is ~tself stochastic, then households that moved during the f~rst two years =ght

tend to J.nclude more IIhlgh response 11 households. Estimates based on these households would overest1mate the responses of later movers. As dlS cussed 1n Sect10n

6.1, there 1S no conslstent evidence of decl1nlng response over tlme.

134
The ~mainder of this sect~on evaluates the actual extent of such select~on

bias. A more cOI[!fllete discuss~on of the models involved is presented ~n

Appenfux XI.

The selection b~as problem may be formally character~zed ~n terms of the

stochast1c error term 1n the estlffiated demand functl0n. Speclfy, for

example, the log-llnear expendlture function 18

(13)

(14)

where

R

t hous~ng expend~tures at t~me t

Yt = household ~ncome at t~me t, and

a = the percentage rent rebate.

under Equat~on (13), ~f households had not had the Percent of Rent rebates,

the value of In (I-a) would have been zero (a=O) , and the~r rental expendftures would have been determ~ned by

N In (Rt ) = So + Slln(Yt ) + 8

t

N where R

t ~s the normal level of expend~tures that would have occurred ~n the

absence of the experlment.

The sample select~on b~ases descr~bed above all ~n effect suggest that at

N var~ous per~ods, Percent of Rent households w~th h~gher levels of In(Rt)--that

1S, wl.th hJ.gher values of 8

t

--were more 11kely to accept enrollment, stay 1.n

N the exper~ment, or move than households w~th lower levels of In(Rt ). Furthermore, th~s effect ~s l~kely to be larger at h~gher rebate levels. Thus

even 1.£ households were randomly assl.gned so that ~t was, for the entire

assigned populat~on, ~ndependent of In(l-a), among selected households

8 t and In (I-a) may be correlated. In th~s case, the Ord~nary Leas~ Squares

est~ate of S2 w~ll be biased.

The expenditure functions est~ated = th~s report are based on crosssect~onal observat~ons at the end of two years (t=2). Thus the concern

for estimation ~s sample selection that d~rectly or ~nd~rectly affects 8

2 •

The problem ~s that observations at two years after enrollment cannot d~st~nguish between genuine exper~ental effects and the art~facts of sample

selection. Some infurect way must be found to identify sample selection.

135
The basic method used ~n th~s report for test~ng for select~on bias ~s

serial correlation. To the extent that the stochastic term, £t' reflects

underlying differences in tastes or other slowly chang~ng factors, ~t ~s

reasonable to assume that the value of E

t for any ind1v1dual household w111

only change gradually over t~e. Thus 8

t

and 8t+l or 8t _l are expected to

be related. More exactly, the usual assumptlon is that Et and Et _ 1 have a

blvarlate normal dlstr2butlon wlth means Pt , Pt - 1 v~rlances, a~ and a~_l'

and correlatlon coefflCl.ent, p. But thlS means that 82 and EO (the values

of € at two years and at enrollment, respectlvely) are Ilnked by the reIatl0nshl.ps

(15)

where p ~s the correlat~on between 8

2 and 80 , and n2 and Yo are stochast~c

terms dl.strl.buted l.ndependently of EO and 82 , respectl.vely, wlth mean zero.

The est~ted two-year ser~al correlat~on, based on estimating Equation (15)

at enrollment and two years for Control households that move, are shown ~n

Table 6-5.

Table 6-5

TWO-YEAR SERIAL CORRELATIONS

FOR CONTROL MOVERS

Expenditures

Housing Services

sample Size

PITTSBURGH

0.478

0.415

(82)

PHOENIX

0.461

0.383

(98)

SAMPLE: Control movers active at two years after enrollment exclu~ng

those w~th enrollment ~ncomes over the elig~bil~ty limits and those l~v~ng in

the~r own homes or ~n Subs2dized hous~ng.

DATA SOURCES: In~t~al and monthly Household Report Forms, Hous~ng

Evaluation Forms, 1970 Census of Populat2on, and Base11ne and Per10d~c

Interviews.

136
---------------------------- --

NC''' assume that there ~s some selection, S, of households between to and t Z'

Observations are ava~lable at to for both selected and nonselected households

and at t z for selected households. G~ven the ser~al correlation of Equat~on

(15) ~f the select~on S does affect the d~str~but~on of 8

Z for the selected

sample, so that

(16)

S where 8

Z ~s 82 for the selected sample and E(A2)

related to (I-d), using Equat~on (15), by

S 0, then 8 0 w~ll also be

(17)

or,

(18)

S

8 = II + o 0

110 +

If 8

0 has some prior relat~on to In(l-a) g~ven by

(19)

where E(AO) = 0, the effect of the subsequent select~on, S, can be ~dentified

by

(zo) 6

l

ln(1-a) °0 °08

0 = 6

0 + + (poz "Olli + (p- "1) ,,In(l-a) + ~O °z

= 6

0

+ 6

l

ln (I-a) + ao" + a1,,In(l-a) + ~o

where

,,={l~f Oif

the household is subsequently selected,

the household is not sUbsequently selected,

If they

S

8 Z by the

of Un (I-a)

Equat~on (Z) can be used to test for the effects of select~on by test~ng

the hypothes~s that the coeff~c~ents of " and "In (I-a) are zero.

are slgnlficantly dlfferent from zero, the blas lntroduced lUtO

selectl0n can be lnferred by dlvldlng the est~ated coefflClent

137
It should be clear that the exact correct~on impl~ed by find~ng evidence of

a prior selection depends on when the selection took place. The model above

suggested the select~on processes: one occurr~ng before enrollment (t=O)

which ~ntroduced the prior relat~onsh~p between €o and In{l-a) shown in

Equation (19); the other occurring at two years after enrollment (t=2)

which introduced an additional relationship for €o of the selected sample

as shown in Equation (16). The prior selection will shift the expected

value of €2 (via ser~al correlat~on) by the amount (p °

0/°2) (60 + 611n~1-a».

The correction for €2 ~s obta~ned by mult~plying 60 or 61 by (p °

0/°2).

The subsequent select~on ~nduces a relationsh~p with €o of (p °

2

/°0)

laO + alln(l-a». The correct~on for €2 ~s obta~ned by divid~ng a

o

or al

{the effects on €o as shown in Equation (20» by (p °

2

/°0). Yet a th~rd

possib~l~ty ~s that a select~on process occurs between 8

0 and 8

2 - If so,

it may affect both errors (€o and €2) equally. In th~s case, the correct~on

for €2 is s~ply equal to the effect on eO.

The deta~ls of alternative models are d~scussed further ~n Appendix XI.

The ~mportant point to be made here ~s that the exact correct~on depends

crltically on prlor speciflcatlon of when the selectlon occurred. This

can be more complicated than it seems, as the time of the selection depends

on the t~e period on which the selectlon decislon was'based rather than the

moment at wh~ch the dec~s~on was actually made. {For example, ~f households

acceptance of the enrollment offer reflects thelr assessment of thelr future

1ThlS 15 slmply the usual components of varlance case 10 WhlCh serlal

correlat~on can be used to control for sampl~ng error or select~on effects

10 the lnltlal asslgnment to experlmental plans. As 18 well known, th15

provldes more exact estlmates of exper1mental effects. ThlS technlque was

not used In the main body of the report because of the lnterest ln estlffiatlng

both prlce and lucome elastlcltles. Controlilng for lnltlal posltlon would

clearly be appropr~ate ~n est~mat~ng the effects of the percent of Rent

rebates. It would Just as clearly g~ve spur~ously t~ght conf~dence ~ntervals for income elast1c1tles.

To take the extreme case, say that the three-year average lncame data

collected by the exper~ent ~s used for all est~ates (that ~s, the

same lnCarne varJ.able 1S used for estlffiatlng the pre-experJ.n1ental demand

function and lnltJ.al error term and in estJ.n1atlng the final cross sectlon).

In this case the estimated inJ.tial error, 80' 1S by constructlon orthogonal

to In{Y). Thus, its inclusion cannot possible affect the estimated income

elasticity. It would therefore be misleading to use it ~n the two-year crosssectional estimates to reduce the standard error and thus the estimated error

of estimate for the income elast~c~ty. See Append~x VI for estimated pr~ce

elasticities taking account of serial correlationo

138
expenditures, the select~on would not be on EO (the error at enrollment)

but on later values of E.} Desp~te these compl~cations, the most plaus~ble

model appears to be that select~ons subsequent to enrollment occurred on

average one year after enrollment and will thus affect both E and E

o 2

equally.

Actual est1mat1on of select10n effects was done uS1ng both the ent~re

Basel~ne sample (the sample of households that completed the Baseline Interview, admin~stered before hous~holds were told about the experiment) and

the sample of enrolled households. While several models of select~on ~nd~cate

no s~gnif~cant selection effects, the most plausible model of select~on

effects suggests that expend~ture and hous~g services elast~cities could

be biased by the amounts shown ~n Table 6-6.

Table 6-6

POSSIBLE BIAS IN PRICE ELASTICITIES

Expenditures

Housing serV.l.ces

SOURCE: Appendix XI.

PITTSBURGH

+0.059

+0.008

PHOENIX

-0.092

-0.052

The only stat~stically s~g=f~cant b~as found was for Phoenix expenditures.

Note also that while the est~mated d~rection of b~as is consistent w~th theory

.l.U Phoem.x (that .l.S, the b.l.as ~ncreases the absolute size of the estimated

pr~ce elastic~ty), there ~s an opposite effect ~n Pittsburgh. Th~s suggests

that the est.l.mates may reflect s~l.l.ng error more than systematic selectJ.on..

In any case, while correctl.ug elasticJ.ty est.l.mates for b.l.as would increase

the absolute value of the est~mated elastic~ty ~n P~ttsburgh and reduce ~t

l.U Phoenl.x, the two-Sl.te average .l.S essentially unchanged.. Thus it appears

that sample selectl.on processes .l.f they occurred were not severe enough to

materially alter the conclusions of Chapters 4 or 5.

139
6.3 PROGRAM UNDERSTANDING

Program understand~ng by part~c~pant households ~s a d~ff~cult ~ssue to

deal w~th. If households rece~v~ng a rent rebate d~d not properly understand the relatlonship between thelr rent payment and the rebate, then they

would not have responded ~n the theoret~cal1y expected way. If th~s problem

were wldespread, then the interpretatlon of the est1ffiated price elastlclty

is questl0nable~

Households enrolled ~n the percent of Rent plans were contacted up to f~ve

tlmes durlng the exper1ffient wlth both speclflc and general lnforrnatlon about

how a rent rebate worked, on both an lndlvldual and a group basls. The flrst

relevant contact was the Enrollment Intervlew Ln WhlCh the percentage rent

rebate was descrlbed 10 detall (10 Engllsh or Spanlsh, as approprlate), the

household's partlcular percentage rebate identlfled and explalned wlth an

1 example, and any questlons clarlfled.. ThlS lntervlew was followed up by a

booklet (~n English or Span~sh) expla;willg the Demand Exper=ent procedures

and the concept of a rent rebate payment. In add~t~on, there was a Hous~ng

Inforrnat~on program wh~ch, ~n the flrst seSS10n held ~n the f~rst weeks of

part1clpat10n, also gave a general descr~ptl0n of the rent rebate offer

2 (attendance, however, was voluntary). F1nally, detalled letters lnclud~ng

examples were sent to each household at 4 and aga~n at 12 months lUto the

3

program.

Two questl0ns were ~ncluded on each Perlodlc Intervlew to assess households'

program understand~ng: (1) "What do you th~nk would happen to your hous~ng

allowance payments ~f your landlord ~ncreased your rent by $10 a month...

would your payments go up, go down, or stay the same?" and (2) (~f the

respondent answered go up or down), "By how much would you expect your

4 monthly allowance to change?" As m~ght be expected, a larger percentage

of the populat~on got the f~rst quest~on correct than the second (see Table

1

The 1utervlew also collected lnformatl0n for flnal determlnat10n

of program el~g~~l~ty and allowance amount.

2

Only about one-quarter of all Exper=ental households attended

th~s sess~on (29 percent ~n P~ttsburgh, 25 percent ~n Phoen~x).

3

Further, households were free to query slte off~ces at any t~e

w~th quest~ons about the program.

4F~rst per~od~c Questions 13.2 and l3.2A, Second Per~od~c Quest~ons 4.2 and 4.2A, and Th~rd Per~od~c Quest~ons 5.2 and 5.2A.

140
6_7).1 The mean percentage rebate g~ven by respondents that answered the

flrst quest10n correctly appears to be lndependent of the actual percentage

rebate, however. Th1S 15 because of the large proportlon of households

respondlng "$5" or "$10" to the second questlon, lrrespectlve of treatment

group. Indeed, most of the correct responses for the whole sample can be

attrlbuted to responses of 11$5" for the 50 percent treatment group. Thus It

appears that the answers to the second questl0n are not valld and cannot be

2 used for further lnvestJ..gatlon.

Program understandlng has therefore been deflned on the basis of the flrst

questlon. The followlng deflnltlon of understandlng was used: a household

understood the program 1£ It gave the correct response on any PerlodlC Inter3 v~ew (74 percent d~d so ~n p~ttsburgh, 76 percent ~n Phoen~x). A log-l~near

demand funct~on was est~mated for all movers and also separately for those

def~ned as understandlng and those not understandlng (that 15, never understood the general d~rect~on on any Per~od~c Interv~ew). Var~ance rat10

tests for overall homogene1ty 1n the relat1onsh1ps could not reJect the

hypothes~s of no d~fference between the groups. An add~t~onal test allowed

the pr~ce elast~c~ty alone to d~ffer between the groups. Analys~s of covariance could not reJect the hypothes1s of nO d1fference.

In conclusion, ~t appears that though many households do not appear to have

understood the program (as understand1ng lS def1ned here), thelr response to

the allowance payment can be analyzed as ~f they understood. It appears

more l~kely that households d~d not understand the quest~on than that they

d~d not understand the program.

1

A correct response to the f1rst questlon would be "go up. 11 A correct

response to the second would be the actual dollar change, depenfung on their

treatment group, subsequent to a correct answer on the f1rst.

2It ~s true, however, that the proport~on of households responding

"$JO" tended to ~ncrea5e with the percentage rebate level, so that the mean

dollar estJ.mate 1ncreased as well.

3

A more restrict~ve de finl t1.on, understanmng on all perlOChc Inter-

~ews, resulted ~n a much smaller sample (25 percent understOod ~n P~ttsburgh,

and 29 percent ~n Phoen~x).

141
Table 6-7

PARTICIPANT UNDERSTANDING OF THE RELATIONSHIP

BETWEEN RENT AND ALLOWANCE PAYMENT

UNDERSTOOD DIRECTION UNDERSTOOD BOTH THE

OF THE RELATIONSHIP DIRECTION AND THE AMOUNT

TIME OF RESPONSE p~ttsburgh Phoen~x P~ttsburgh phoenix

S~X months after

enrollment 56% 61% 14% 12%

One year after

enrollment 56 54 19 18

Two years after

enrollment 45 49 20 25

SAMPLE SIZE (171) (142) (171) (142)

SAMPLE: Percent of Rent households act~ve at two years after

enrollment, excludlng those wlth enrollment lncornes over the ellg~111ty

l~ltS and those 11vlng in thelr own homes or 10 SUbSldlzed houslng.

DATA SOURCES: First, Second, and Th~rd Per~od~c Interv~ews.

142
REFERENCES

Gr~llches, ZVl., "DJ.strlbuted Lags: A Survey," Econometrlca, vol. 35, no. 1,

January 1967, pp. 16-49.

Intrlilgator, Mlchael D., Econometrlc Models, Technlques, and Appllcatlons,

Englewood Cliffs, N.J., Prentlce-Hall, 1978.

Johnston, J., EconometrJ.c Methods, 2nd edltlon, New York, McGraw-Hlll, 1972.

MacMillan, Jean, Mobility ln the Housing Allowance Demand Experlnent, Carobrldge, Mass., Abt Associates Inc., 1978 (revised June 1980).

Mayo, Stephen K., Houslng E"Penditures and Quality Part I: Housing Expenditures Under a Percent of Rent Houslng Allowance, Carribridge, Mass.,

Abt Associates Inc., 1977.

Marrlll, Sally R., Hedomc Indices as a Measure of Housing QualJ.ty, Carobrldge,

Mass., Abt Assoclates Inc., Decarober 1977 (revlsed June 1980).

Ohls, Janes C. and Cynthia Thomas, The Effects of the Seattle and Denver Incone

M~ntenance Experlments on Housing Consumption, OwnershJ.p, and Mobl.llty I

fi3;nver, Colorado, Mathematlca POlley Research, Inc., December 31, 1979.

143
APPENDIX I

DESIGN OF THE D&~ EXPERIMENT

This appen~x presents a br~ef overview of the Demand Experiment's purpose,

data collect~on procedures, experimental design, and sample allocat~on.

I.l PURPOSE OF mE DEMAND EXPERIMENT

The Demand Exper~ment ~s one of three exper~ments establ~shed by the U.S.

Department of HOUSUlg and Urban Development (HOD) as part of the Experi1 mental Hous~ng Allowance Program. The purpose of these exper~ments ~s

to test and ref~ne the concept of housing allowances.

Under a housUlg allowance program, money is g~ven mrectly to individual

low-income households to ass~st them in obt~ning adequate hous~ng. The

allowance may be l~nked to housUlg e~ther by making the amount of the

allowance depend on the amount of rent p~d or by reqmring that households meet certa~n housUlg reqmrements ~n order to rece~ve the allowance

payment. The ~n~t~ative ~n usUlg the al-lowance and the burden of meeting

housUlg "eqmrements are therefore placed upon households rather than upon

developers, landlords, or the government.

The housUlg allowance exper~ments are intended to assess the des~rab~l~ty,

feas~~lity, and appropr~ate structure of a housing allowance program.

Hous~ng allowances could be less expens~ve than SOme other kinds of hOUSUlg

programs. Allowances pe~t fuller utilizat~on of exist~ng sound housing

because they are not ~ed to new construct~on. Housing allowances may

also be more' eqmtable. The amount of the allowance can be adJusted to

changes ~n ~ncome w~thout forc~ng the household to change un~ts. Households may also, if they des~re, use the~r own resources (e~ther by pay~ng

h~gher rent or by searchUlg carefully) to obt~n better hous~ng than ~s

requ~red to qual~fy for the allowance. As long as program re~rements

are met, hous~ng allowances offer households considerable cho~ce ~n

select~ng hous~ng most appropr~ate to the~r needs--for example, where

they l~ve (opportun~ty to locate near schools, near work, near fr~ends

1

The other two exper~ments are the Hous~ng Allowance Supply

Exper~ent and the Adm~n~strat~ve Agency Exper~ent.

A-I
or relat~ves, or to break out of racial and soc~oecono~c segregat~on)

or the type of un~t they l~ve in (s~ngle-fam~ly or multifam~ly). F~nally,

hous~ng allowances may be less costly to adm~n~ster. Program req~rements

need not ~nvolve every deta~l of partic~pant housing. The burden of

obta=~ng hous=g that meets essent~al requ~rements ~s sh~fted from

program adm~nistrators to paruc~pants.

'lhese potenual advantages have not gone unquest~oned. Cr~t~cs of the

housing allowance concept have suggested that low-=come households may

lack the expe~se necessary to make effective use of allowances; that

the ~ncreased supply of housing needed for spec~al groups such as the

elderly w~ll not be prov~ded without mrect ~ntervenuon; and that an

increase ~n the demand for housing w~thout mrect support for the construction of new un~ts could lead to a substant~al inflation of hous~ng

costs. 1

If housing allowances prove des~rable, they could be ~mplemented through

a wide range of posswle allowance formulas, housing requirements, nonf~nanc~al support (such as counsel~ng), and adm=istrative practices.

The cho~ce of program structure could sUbstantially affect both the

program's costs and =pact.

'!he Demand Experiment addresses ~ssues of feasib~l~ty, des~rab~l~ty, and

appropr~ate structure by measur=g how ~ndividual households (as opposed

to the hous=g market or adm=istrat~ve agenc~es) react to var~ous allowance formulas and hous=g standards re~rements. The analys~s and

reports are des~gned to answer s~x policy quest~ons:

1. Part~cipation

Who part~c~pates ~n a hous~ng allowance program? How does

the form of the allowance affect the extent of partic~pation

for var~ous households?

2. Housing Inmrovernents

Do households that rece~ve housing allowances ~mprove the

quality of their hous=g? At what cost? How do households

1

The ~ssue of ~nflat~on ~s being addressed d~rectly as part of

the Hous=g Allowance Supply Experiment.

A-2
that receive a hous~g allowance seek to ~mprove their

housing--by moving, by rehabilitation? W~th what success?

3. Locat~onal Choice

For part~c~pants who move, how does the~r loca~onal cho~ce

compare w~th ex~s~ng res~dential patterns? Are there nonfinanc~al barr~ers to the effect~ve use of a hous~ng allowance?

4. A~~stra~ve Issues

What admin~strati"e issues and costs are involved ~n the ­

implementation of a housing allowance program?

5. Form of Allowance

How do the dJ.fferent forms of housing allowance compare ~n

terms of part~cipat~on, housing qual~ty ach~eved, locational

choice, costs (including a~n~strat~ve costs), and eq=ty?

6. Compar~son w~th Other Programs

How do hous~g allowances compa~e w~th other hous~ng programs

and w~th ~ncome ma~tenance ~n terms of part~cipa~on, hous~ng

qual~ty ach~eved, locat~onal cho~ce, costs (~ncluding admin~strat~ve costs), and equity?

The Demand E>cperiment tests alterna~ve housing allowance programs to

provide ~nformation on these policy ~ssues. Mule the exper~ment ~s

focused on household behavior, ~t also offers data on program a~n~strat~on

to supplement ~nformation g~ned through the Adm~n~stra~ve Agency Experiment.

Finally, the Demand Exper~ent gathers direct information on part~c~pants

and hous~g cond~t~ons for a sample of households in conventional HUDass~sted housing programs at the two exper~ental s~tes for compar~son

w~th allowance rec~pients.

I. 2 DATA COLLECTION

The Demand Exper~ent was conducted at two s~tes--Allegheny County,

Pennsylvan~a (P~ttaburgh), and Maricopa County, Ar~zona (Phoen~x).

HOD selected these two sites from among 31 Standard Metropol~tan

Stat~s~cal Areas (SMSAs) on the bas~s of the~r growth rates, rental

A-3
vacancy rates, degree of rac1al concentrat10n and hous1ng costs~

P~ttsburgh and Phoen~x were chosen to prov~de contrasts between an

older, more slowly grow~ng Eastern metropol~tan area and a newer,

relanvely rap~dly grow~ng Western metropol~tan area. In adfut~on,

P~ttsburgh has a substant~al black minority and Phoen~x a substannal

Span~sh American ~nor~ty populanon.

Most of the =formatJ.on on partic~pating households was collected from:

Basel=e Inte~ews, conducted by an independent survey operanon before households were offered enrollment;

In~t~al Household Report Forms and monthly Household Report

Forms, completed by part~c~pating households dur~ng and after

enrollment, wh~ch provided operat=g and analytic data on

household size and income and on hous=g expenditures.

Supplements to the Household Report Forms, completed annually

by part~c~pat~ng households after enrollment, which provide

data on assets, ~ncome from assets, actual taxes paid, 1ncome

from self-employment, and extraord~nary medical expenses;

Payments and status data on each household ma~ntained by

the s~te off~ces;

Hous=g Evaluat~on Forms, completed by site office evaluators

at least once each year for every dwelling un~t occup~ed

by partJ.cipants, wh~ch prov~de ~nformation on housing qUal~ty;

Per10dic Interv1ews, conducted appro:nmately 51X, twelve,

and twenty-four months after enrollment by an ~ndependent

survey operat10n; and

Ex~t Interviews, conduc,ted by an ~ndependent survey operation

for a sample of households that declined the enrollment offer

or dropped out of the program.

Surveys and hous~g evaluat~ons were also admin~stered to a sample of

partJ.c~pants ~n other housing programs: Public Hous~ng, Section 23/8

Leased Hous~g, and Sect~on 236 Interest Subs~dy Housing.

S~nce households were enrolled throughout the first ten months of

operat~ons, the operat~onal phase of the exper~ment extended over

nearly four years in total. Analys~s w~ll be based on data collected

from households dur~ng the~r first two years after enrollment ~n the

experiment. The exper~mental programs were contJ.nued for a th~rd year

A-4
~n order to avo~d confusion between part~c~pants' react~ons to the

exper1.mental offers and the1.r adJustment to the phaseout of the

exper1.ment. Dur1.ng the1.r last year 1.11. the exper:unent el1.g1.l>1e and

1.nterested households were a1.ded in enter1.ng other hous1.ng programs.

I.3 ALLOWANCE PLANS USED IN '!HE DEMAND EXPERIMENT

The Demand Experiment tested a number of cornb1.nat1.ons of payment formulas

and hous1.ng requirements and several var1.at1.ons W1.thin each of these

cornb1.nat1.ons. These var1.at1.ons allow some poss1.l>1e program des1.gns to

be tested d1.rectly. More importantly, they allow est1.rnation of key

responses such as part1.c1.pat1.on rates and changes 1.11. participant housing

1.11. terms of bas1.c program parameters such as the level of allowances;

the level and type of housing reqU1.rements; the In1.nimurn fraction of

1.ts own l.ncome that a household can be expected to contribute toward

housl.ng; and the way 1.11. wh1.ch allowances vary with household 1.ncome

and rent. 'lh es e response estimates can be used to address the pol1.CY

questions for a larger set of candidate program plans, beyond the plans

directly tested. l

Payment Formulas

TWo payment formulas were used in the Demand ExperllUent--Hous1.ng Gap

and Percent of Rent.

Under the Hous1.ng Gap formula, payments to households constitute the

d1.fference between a bas1.c payment level, C, and some reasonable fraction

of faIn1.1y 1.ncome. The payment formula 1.s:

P = C - bY

where P is the payment amount, C ~s the basic payment level, lib" is the

rate at which the allowance ~s reduced as ~ncome increases, and Y is

IThe bas1.c des1.gn and analysis approach, as approved by the HUD

Off1.ce of Policy Development and Research, 1.S presented 1.11. Abt AssoC1.ates

Inc., EXperllUental Des1.gn and Analysis Plan of the Demand ExperllUent,

Carnbr1.dge, Mass., August 1973, and 1.11. Abt Assoc1.ates Inc., Summary

Evaluat1.on Des1.gn, Carnbr1.dge, Mass., June 1973. Data1.1s of the operat1.ng

rules of the Demand Exper~ment are conta~ned ~n Abt Assocl.ates Inc4,

S1.te Operat1.ng Procedures Handbook, Carnbndge, Mass., Apr1.1 1973.

A-5
1 the net fam~ly ~ncome. The bas~c payment level, C, var~es with household

s~ze, and ~s proport~onal to C*, the est~ated cost of modest exist~ng

2 standard hous=g at each s~te. Thus, payment under the Hous~ng Gap

formula can be interpreted as mak~ng up the difference between the cost

of decent hous=g and the amount of ~ts own ~ncome that a household

3 should be expected to pay for hous=g.

Under the Percent of Rent formula, the payment ~s a percentage of the

household's rent. The payment formula ~s:

P = aR

where R ~s rent and "a" is the fraction of rent pa~d by the allowance.

In the Demand Exper1.ID.ent the value of "aIf rema~ned constant once a

4 household had been enrolled.

Housing Requirements

The Percent of Rent payment formula ~s tied directly to rent: a household's allowance payment ~s proport~onal to the total rent. Under the

Hous=g Gap formula, however, spec~f~c hous=g requirements are needed to

tie the allowance to housing. "Two types of hous=g re~rement were

used: Min~U11l Standards and M1.nlJIlum Rent.

lIn admtion, whatever the payment calculated by the formula,

the actual payment cannot exceed the rent pa~d.

2The hous=g cost parameter, C*, was established from es~ates g~ven by a panel of qualified hous=g experts = P~ttsburgh and Phoenix.

For more detailed mseuss~on regarding the der~vat~on of C*, refer to

Abt Assoc~ates Inc., Working Paper on Early F~nd~ngs, Cambr~dge, Mass.,

January 1975, Appenmx II.

3

As long as the~r hous=g met cert~n requ~rements (mscussed

below), Housing Gap households could spend more or less than C* for

housl.ng, as they desired, and hence contribute more or less than "bit

of their own 2ncome. ThJ.S 1.5 1.n contrast to other hous~g programs,

such as Sect~on 8 '~Exist=g) .

4

Fl.ve values of "a" were used 1.n the Demand ExperJ.Inent. Once a

fam~ly had been ass~gned its "a" value, the value generally stayed

constant J.n order to ~d experllflental analysJ.s. In a natl.onal Percent

of Rent program, "a" would probably vary w~th ~ncome and/or rent. Even

1.0 the exper~ent, if a famJ.ly's income rose beyond a certain pOl-nt, the

value of "a" dropped rap~dly to zero. S~=larly, the payment under

Percent of Rent could not exceed C* (the max~mum payment under the modal

Hous=g Gap plan), wmch effect~vely lim~ted the rents subsimzed to

less than C*/a.

A-6
Under the Minimum Standards requirement, partic~pants received the

allowance payment only ~f they occup~ed dwell~ngs that met cert~n

phys~cal and occupancy standards. Part~c~pants occupying un~ts that

~d not meet these standards e~ther had to move or arrange to ~prove

the~r current un~ts to meet the standards. PartJ.c~pants already l~ving

~n housmg that met standards could use the allowance to pay for better

housing or to reduce the~r rent burden (the fractJ.on of ~ncome spent

on rent) ~n the~r present un~ts.

If housmg qual~ty ~s broadly def~ned to ~nc1.ude all res~dentJ.al serv~ces,

and if rent levels are h~ghly correlated with the level of serv~ces, then

a straightforward hous~ng reqmrement (one that ~s relatively ~nexpens~ve

to a~n~ster) would be that recip~ents spend some minimum amount on

rent. Min= Rent was considered as an alternat~ve to M~nimum Standards

~n the Demand Exper;unent, in order to observe differences in response

and cost and to assess the relative mer~ts of the two types of requ~rements. Although the des~gn of the exper~ment used a f~xed m~nimum

rent for each household s~ze, a direct cash assistance program could

employ more flexible structures. For example, some features of the

Percent of Rent formula could be combined with the ~imum Rent require~

ment. Instead of rece~v~ng a zero allowance if the~r rent ~s less than

the M~nimum Rent, households might be p~d a fract~on of the~r allowance

depenmng on the fract~on of M~nimum Rent p~d.

Allowance Plans Tested

The three combinat~ons of payment formulas and housing requirements

used ~n the Demand Experiment were Housmg Gap Min=um Standards,

Housmg Gap M~n=um Rent, and Percent of Rent. A total of 17 allowance

plans were tested.

The twelve Hous~ng Gap allowance plans are shown ~n Table I-1. The

first n~ne plans mclude three var~ations in the bas~c payment level,

C (1.2C*, C*, and 0.8C*) and three variat~ons ~n hous~ng requ~rements

(M~n~um Standards, ~nimum Rent Low (0. 7C*), and ~nimum Rent H~gh

(0.9C*». The value of ''b''--the rate at wh~ch the allowance ~s reduced

as ~ncome ~ncreases--~s 0.25 for each of these plans. The next two

A-7
plans have the same level of C (C*) and use the MJ.n]JJ\um Standards Hous~ng

Requirement, but use d~fferent values of "b". In the tenth plan the

value of "b" ~s 0.15, and ~n the eleventh plan, 0.35. F~nal1y, the

twelfth plan ~s unconstra~ned, that ~s, ~t has no housing requireIrent.

This unconstra~ned plan allows a d1rect compar~son w~th a general incometransfer program.

Eligwle households that ~d not Ireet_ the housing requirement were sull

able to enroll. They rece~ved full payments whenever they met the

requirements dur~ng the three years of the experiIrent. Even before

rneet~ng the housing requirements, such households rece~ved a cooperauon

payment of $10 per month as long as they completed all report~ng and

~nterv1ew requ~rements.

Within the Hous~ng Gap des~gn, the average effects of changes in the

allowance level or hous=g requirements can be estJ.lIlated for all the

maJor responses. In ad~t~on, =teractions between the allowance level

and the hOUSJ.Ilg r~rement can be assessed. Responses to var1ations

in the allowance/income schedule (change.s in ''b'') can be es~ated for

the bas~c comb~nat~on of the Min~mum Standards hous~ng re~rement and

payments level of C*.

The Percent of Rent allowance plans consist of five var1ations 10 "all

(the proport~on of rent p~d to the household), as shown in Table I-I. 1

A demand funct~on for hous=g is estimated primar~ly from the Percent of

Rent observat~ons. Demand funct~ons descr~be the way = wh~ch the amount

people w~ll spend on hous~ng ~s related to their =come, the relative

pr~ce of hous~ng and other goods, and var~ous demograph~c character~sucs.

Such functions may be used to s~late response to a var~ety of posswle

rent subs~dy programs not ~rectly tested with~n the Demand Exper]JJ\ent.

Together w~th est]JJ\ates of supply response, they may also be used to

s]JJ\ulate the change ~n market pr~ces and hous~ng expen~tures over t~me

due to sh~fts ~n hous~ng demand or costs.

1

Desl.gnatl.on of multJ.ple plans for the same t1 a " value reflects

an early ass~gnment convent~on and does not =d~cate that the households

~n these plans were treated ~fferently for e~ther payment purposes or

analys~s.

A-8
Table I-1

ALLOWANCE PLANS TESTED

HOUSING GAP: IP = C - bY, where C IS a multiple of C')

HOUSING REQUIREMENTS

Minimum Minimum Rent Minimum Rent No

b VALUE C LEVEL Standards Low = 0.7C· High = O.SC· Requirement

b=0.15 C· Plan 10

1.2C· Plan 1 Plan 4 Plan 7 ,

b -0.25 C· Plan 2 Plan 5 Plan 8 Plan 12

o.se· Plan 3 Plan 6 Plan 9

.

b =0.35 C· Plan 11

Symbols b = Rate at which the allowance decreases as the Income Increases.

C· = BasiC payment level (vaned by family size and also by site).

PERCENT OF RENT IP = aR)

a=06. a=05 a=04. a=03 a=02.

Plan 13 Plans 14 -16 Plans 17 ·19 Plans 20·22 Plan 23

CONTROLS: With HOUSing

Information

I Plan 24

WithOUt HOUSIng

Information

Plan 25

A-9
Control Groups

In add1tion to the var~ous allowance plans, control groups were necessary

in order to establ~sh a reference level for responses, s~nce a number

of uncontrolled factors could also ~nduce changes ~n fam~ly behav~or

dur~ng the course of the expen.ment. Control households rece~ved a

cooperanon. payment of $10 per month. They reported the same wformat~on

as fam~l~es that received allowance payments, inclu~ng household

composition and ~ncome; they pe~tted hous~ng evaluations, and they

completed the Baseline Interv~ew and the three Periodic Interv~ews.

(Control famil~es were paid an ad~tional $25 fee for each Per~o~c

Interview. )

Two control groups were used ~n the Demand Experiment. Members of one

group (Plan 24) were offered a Houswg Information Program when they

Jo~ned the exper:unent and were paid $10 for each of f~ve sess~ons attended.

(Th~s program was also ,offered to households enrolled w the exper~ental

allowance plans but they were not p~d for their attendance.) The other

control group (Plan 25) was not offered the Houswg InfOl:mat~on Program.

All the households ~n the var~ous allowance plans had to meet a basic

income el~gw~l~ty requ~rement. Th~s l~~t was approximately the income

level at which the household would rece~ve no payment under the Housing

Gap formula:

C* Income EI~g~~lity L~~t = 0.25

In addit~on, households in plans with lower payment levels (Plans 3, 6,

9 and 11) had to have ~ncomes low enough at enrollment to receive

payment under these plans. Finally, only households w~th ~ncomes in

the lower th~rd of the elig~ble populat~on were elig~le for enrollment

~n Plan 13, and only those ~n the upper two-th~rds were el~gwle for

Plan 23.

I.4 FINAL SAMPLE

F~nal analys~s of the ~mpact of the houswg allowance will be based on

the hrst two years of exper~ental data. Thus, the key sample s~ze

A-lO
for thlS report and the other reports ln thlS serles lS the number of

households 1n the exper1ffient at the end of the f1rst two years. The

two-year sample Slze is shown In Table 1-2, and comprlses households

that were stlll actlve, In the sense that they were contlnulng to fulflll

reportlng requlrements. The sample Slze for a partlcular analysls may be

smaller. For example, analySls of the houslng expendltures of movers uses

only those households that moved dur1ng the f1rst two years after enrollment.

A-II
Table I-2

SAMPLE SIZE AFTER TWO YEARS

HOUSING GAP' IP = C - bY, where C IS a multiple of C*l

HOUSING REQUIREMENTS

Minimum Minimum Rent Minimum Rent I No

b VALUE C LEVEL Standards low 2 O.7C· High = 0.9C* Requirement

Plan 10

b=0.15 C* PIT = 45

PHX = 36

Plan 1 Plan 4 Plan 7

1.2C* PIT = 33 PIT = 34 PIT = 30

PHX = 30 PHX = 24 PHX =30

Plan 2 Plan 5 Plan 8 Plan 12

b-O.25 C* PIT= 42 PIT = 50 PIT=44 PIT = 63

PHX = 35 PHX = 39 PHX =44 PHX =40

Plan 3 Plan 6 Plan 9

O.BC* PIT = 43 PIT=44 PIT = 43

PHX" 39 PHX = 35 PHX = 35

-

Plan 11

b=0.35 C* PIT =41

PHX = 34

Total HOUSing Gap: 512 households In Pittsburgh, 421 households In Phoentx.

Symbols: b:= Rate at which the allowance decreases as the Income Increases.

C· = BaSIC payment level (vaned by family Size and also by SIte).

PERCENT OF RENT IP = aR) :

a=06 a = 0.5 a = 0.4 a=03 a =0.2

Plan 13 Plans 14-16 Plans 17 -19 Plans 20-22 Plan 23

PIT = 28 PIT= 109 PIT= 113 PIT = 92 PIT = 65

PHX = 21 PHX = 81 PHX = 66 PHX =84 PHX =46

Total Percent of Rent: 407 households In Pittsburgh, 298 households In Phoentx

CONTROLS. WIth HOUSing

Information

Plan 24

PIT = 159

PHX = 137

Without HOUSing

Information

Plan 25

PIT= 162

PHX = 145

Total Controls' 321 households In PIttsburgh. 282 households In Phoentx.

NOTE ThIs sample Includes households that were active, although not necessarily receiving payments, after two

years of enrollment; households whose enrollment lMcome was above the eligibilitY hmlts or that moved IOto subsidiZed houslOg or thelr own homes are excluded. While data on the excluded households may be useful for special

analyses. particular analyses may also require the use of a stili more restricted sample than the one shown here

A-12
APPENDIX II

DESCRIPTION OF THE SAMPLES

USED FOR ANALYSIS

Th~s append~x d~scusses the households selected for analys~s ~n th~s report

and explores some of the factors affect~ng the exclus~on of households from

a part~cular sample. In add~t~on, s~nce the f~nal analyt~c sample ~s smaller

than the orlglnal sample at enrollment, the comparablllty of the flnal and

or~g~nal samples ~s ex~ned.

1 Table 11-1 shows the samples used ln thlS report. The sample of enrolled

households ~s ~ncluded to demonstrate attrlt~on durlng the course of the

exper~ent. The sample of households actlve at two years ~s used for most

of the analysls ln thlS report. The samples of households that moved or

dld not move over the two-year exper~ental perlod are examlned separately

as well. The Percent of Rent sample is presented broken down by treatment

group ln Table 11-2.

Table 11-3 sets out demographlc characterlstlcs for the ellglble enrolled

and act~ve populat~ons.

lStlCS. )

(See Appendlx III for deflnltlons of the characterCompar~son of the pre-experlffiental (basel~ne) character~st~cs of Exper~ental

and Control households at enrollment and at two years after enrollment shows

that the sample characterlstlcs remaln baslcally the same throughout the

2

course of the experunent. One except~on was the percent of Rent group

recelvlng a 60 percent rent rebate; only households In the lower third of

the ellglble lncome range could partlclpate In thlS group. In any event,

1

All samples exclude households enrolled wlth lncomes above the

ellglb~llty llmlt. In general, households were not allowed to enroll in

the experlment lf thelr verlfled lucorne exceeded the el~glblilty lLmlt for

thelr treatment group. Verlflcatlon of lncome took up to two months,

dependlng on the speed wlth WhlCh lncorne sources (e.g., employers, welfare

agencles, and penslon funds) replled to requests for lnformatlon. Towards

the end of the enrollment perlod, lt was more efflclent to enroll some

households prlor to the completlon of verlf~catlon and exclude them from

the sample lf they were later verlfled to be QVerlnCome, Slnce thlS allowed

the enrollment perlod to be closed (and hence the experunental operatlons to

begln) two months earller.

2

The sample Slzes ln Table 11-3 are Sllghtly smaller than those In

Tables 11-1 and 11-2 due to mlss1ng values on some demographlc varlables.

A-13
Table II-I

OVERVIEW OF SAMPLES USED FOR ANALYSIS IN THIS REPORT

TREATMENT TYPE

SAMPLE

PERCENT

OF RENT UNCONSTRAINED CONTROL TOTAL

Enrolled households

Households act~ve at

two years a

Households that moved

between enrollment

and two years a

Households that d~d not

move between enrollment

and two years a

Enrolled households

Households act~ve at

two years

a

Households that moved

between enrollment

a and two years

Households that d~d not

move between enrollment

a and two years

510

407

153

254

490

298

182

116

PITTSBURGH

PHOENIX

75

63

25

38

70

40

23

17

434

321

112

209

525

282

148

134

1,019

791

290

501

1,085

620

353

267

DATA SOURCES: payments f~le and perlOd~c Interv~ews.

NOTE: Samples exclude households wl.th enrollment l.UCOrnes over the

el~g~b~l~ty l~~ts.

a. Excludes households ll.vl.ng l.n thel.r own homes or in subsl.dized

housJ.ng.

A-14
Table 11-2

PERCENT OF RENT SAMPLE AT TWO YEARS

USED FOR ANALYSIS IN THIS REPORT

NUMBER OF HOUSEHOLDS

ACTIVE AT TWO YEARS

PERCENTAGE REBATE P~ttsburgh Phoenl.x

60% 28 21

50% 109 81

40% 113 66

30% 92 84

20% 65 46

SAMPLE: Percent of Rent households act~ve at two years after enrollment, excludl.ng those wl.th enrollment l.ncames over the ell.gl.bl.llty Ilffil.ts

and those ll.vl.ng l.n the1r own homes or l.n SUbsldized houslng.

DATA SOURCE: Payments f~le.

A-IS
Table II-3

SELECTED HOUSEHOLD CHARACTERISTICS AT BASELINE FOR

THE ELIGIBLE, ENROLLED, AND TWO-YEAR ACTIVE SAMPLE

MEAN MEAN PERCENTAGE

MEAN MONTHLY HOUSEHOLD PERCENTAGE PERCENTAGE FEMALE- SAMPLE

SAMPLE RENT INCOME SIZE ELDERLY MINORITY HEADED SIZE

PITTSBURGH

El1gJ.ble Households $107 $335 2.8 37' 20' 5.- (2,948)

Enrolled Households

percent of Rent 111 377 3.0 28 25 49 (480)

Percentage

rebate20' 108 427 3.2 27 33 56 (86)

3D' 112 364 3.1 25 24 43 (115)

40' 114 416 3.1 25 27 46 (133)

50' 110 341 2 8 32 20 50 (113)

60' 107 254 2.7 36 12 67 (33)

Control 114 389 3.2 23 20 50 (403)

Households ActJ.ve at

Two years a

percent of Rent 112 384 3.0 28 21 50 (3S2)

Percentage

rebate

20' 109 426 3 0 30 30 60 (60)

3D> 110 360 2.9 26 2l 47 (89)

40> 118 449 3.3 22 21 43 (104)

50' 111 345 2.8 31 19 49 (102)

60' 107 260 2.8 33 11 63 (27)

Control 115 399 3.3 2l 19 51 (297)

PHOENIX

ElJ.gJ.ble Households $128 $417 3.2 22> 34' 3.- (2,956)

Enrolled Households

Percent of Rent 134 442 3.2 20 31 37 (454)

percentage

rebate.

20' 138 450 2.8 31 25 35 (SO)

3D' 135 455 3 5 19 31 29 (I25)

40' 133 438 3.1 17 27 39 (106)

50' 138 469 3 4 16 33 34 (115)

60' 101 266 3.2 21 45 79 (28)

Control 131 434 3 4 18 31 36 (474)

Households ActJ.ve at

Two years a

percent of Rent 130 429 3.3 23 36 43 (274)

Percentage

rebate:

20' 128 424 2.6 42 30 44 (43)

3D> 128 436 3.8 25 39 39 (75)

-IC~ *:0 .155 3.2 1.7 " 43 (58)

50' 138 442 3.4 19 34 36 (SO)

60' 106 266 3.6 11 61 89 (18)

Control 124 420 3.4 22 36 44 (257)

uATA SOURCES Household Events LJ.st, InJ.tJ.al and monthly Household Report Forms, and payments fJ.le

~OTE Samples exclude households ~J.th enrollment J.ncomes over the elJ.gJ.bJ.1J.ty lLmJ.ts

a. Excludes households lJ.vJ.ng J.n theJ.r own ~omes or J.n subsJ.dJ.zed housJ.ng.

A-16
the relevant characterlstlcs of thlS group appear to remaln constant over

the course of the experlment.

Not all households offered enrollment 1n the experlmental houslng allowance

program accepted the offer. Overall acceptance by el~g~ble households

offered enrollment ~n p~ttsburgh

holds and 60 percent for Control

was 75 percent for Percent of Rent house1 households. In Phoen~x, 83 percent of

the Percent of Rent and 75 percent of the control households accepted.

Acceptance rates appear unrelated to the percent of Rent d15COunt level

(see Table 1I-4) .

Of all the households accept~ng the enrollment offer, 98 percent of the

Percent of Rent households ~n both s~tes actually enrolled in the program.

The flgures for the control households are somewhat lower, 85 percent in

2 P~ttsburgh and 93 percent ~n Phoen~x.

F~nally, of the enrolled households, 74 percent of the P~ttsburgh Control

households and 80 percent of the P~ttsburgh Experimental households rema~ned

actl.ve 1n the program for the full two years. In Phoenl.x, a smaller percentage rema~ned: 54 percent of the Control and 61 percent of the Percent of

Rent households. Table 1I-5 shows that there may have been an exper~mental

effect on attrJ.tlon, as attrltl.On rates tended to decrease as the SubSldy

3 level lncreased.

1

The baslc ellglblIl.ty crlterlon for admlsslon luto the Demand

Experlment was an lucame threshold WhlCh varled by household SlZe. Nevertheless, for admlnlstratlve reasons, there were some households offered

admlsslon to the program who were above the lncorne llmlt at the tlme of

the Basellne Intervlew. ThlS was especlally true for the Control group.

Some of the Iloverlncomell households later fell below the lncome 11rnlt

durmg the course of the experJ.Il1ent.

2

Most of the households that accepted the enrollment offer but

that were not actually enrolled were deemed lnellg1ble because thelr verlf~ed ~ncomes were too h~gh (see Hoagl~n and Joseph, 1978).

3

Posslble blas due to acceptance and attrltlon 1S dealt wlth In

Sect~on 6.2 and Append~x XI.

A-17
Table II-4

ACCEPTANCE RATES OF PERCENT OF RENT AND

CONTROL HOUSEHOLDS OFFERED ENROLLMENT

PITTSBURGH PHOENIX

, NUMBER OF NUMBER OF

HOUSEHOLDS HOUSEHOLDS

OFFERED PERCENTAGE OFFERED PERCENTAGE

SAMPLE ENROLLMENT ACCEPTING ENROLLMENT ACCEPTING

Control 678 60% 662 75%

Percent of Rent 521 75 603 83

Percentage

rebate:

20% 152 70 115 77

30% 152 76 167 81

40% 172 78 141 89

50% 167 75 130 86

. 60% 54 72 50 82

SAMPLE: Percent of Rent and Control households that received an

enrollment offer exc!ud1ng those w1th enrollment 1ncomes above the e11g1­

b~l~ty llIU~tS.

DATA SOURCE: Household Events List.

A-18
Table II-5

RATES OF CONTINUED ENROLLMENT FOR PERCENT OF RENT

AND CONTROL HOUSEHOLDS FOR THE FULL TWO YEARS

PITTSBURGH PHOENIX

NUMBER OF PERCENTAGE NUMBER OF PERCENTAGE

HOUSEHOLDS ACTIVE AT HOUSEHOLDS ACTIVE AT

SAMPLE ENROLLED TWO YEARS ENROLLED TWO YEARS

Control 434 74% 525 54%

percent of Rent 510 80 490 61

percentage Rebate

20% 92 71 84 55

30% 118 78 140 60

40% 145 78 118 56

50% 121 90 116 70

60% 34 82 32 66

SAMPLE: percent of Rent and Control households that enrolled,

excluding those wlth.enrollment lnCOmes over the eliglbl1lty Ilmits.

DATA SOURCES: Household Events List, Inltlal and monthly Household

Report Forms, and payments flle.

A-19
REFERENCES

Hoaglin, David C. and Cather~ne A. Joseph, Income Reporting and Verif~cat~on

in the Hous~ng Allowance Demand Exper~ment, Canibr~dge, Mass., Abt

Associates Inc., April 1978 (revised June 1980).

A-20
APPENDIX III

DATA SOURCES AND MAJOR VARIABLES

USED IN THE ANALYSIS

II!.1 DATA SOURCES

Table III-l ind~cates the data sources used ~n the derivation of each of the

var~ables used for the analys~s in this report. If a household's record is

~sslng from any of the data sources required for the derlvation of a variable, that partlcular varlable is asslgned a rrasslng value code and the

household J...8 removed from the sample for analyses involvJ...ng that varl.able.

Other reasons for :rru.SSJ...ng value codes l.nciude nonresponses i udan' t know"

responses; out of range responses; and data that are inconsl.stent between data

sources. The maJor data collectl.on instruments used are dl.scussed below.

Initial Household Report Form

Init~al Household Report Forms were completed for all enrolled households as

part of the enrollment l.nterview. Enrollment l.nterviews were conducted between

April 1973 and February 1974. Detailed ~formation was collected on each households' composition, housing expenditures (rent, utl.lities, furnishings, and so

forth), and asset holdings (savings bonds, stocks, and so forth), as of the

time of the interv~ew. Income data were collected for each of the previous 12

months for each type of ~ncome (e.g., wages, Soc~al Security, welfare) for each

household member 18 years of age or over. Household expenses (e. g ., al=ony,

ch~ld care, med~cal) were also collected for the 12 most current months. Data

from the In~tial Household Report Form were used operat~onally to determ~ne

whether ~nit~al household composition and ~ncome eligibility requirements had

been met. Analyt~cally, these data have been used to describe the household's

demographl.c characteristics and income Just prior to part1cipation in the program.

Monthly Household Report Forms

After households were enrolled, they were requ~red to complete monthly Household Report Forms wh~ch collected deta~led informat~on on the household's composJ..tion, housJ.ng expenditures, and J.ncome for the previous month. The information was sim~lar to that collected on the Init~al Household Report Form and

A-2l
Table III-l

DATA SOURCES USED TO DERI.VE KEY VAlUABLES

DATA SOURCES

VARIABLES Enrollment Two years

Income

Net ~ncome for analys~s In~t~al Household Report 24-month h~story from HouseForm hold Report Form

Net mcome for ehgl.b~hty

Demograph~cs

Race/ethn~cJ.ty BaselJ.ne IntervJ.ew --- Educat~on of head of household

Age of head of household

Sex of head of household InJ.tJ.al Household Report 24-month hJ.story from HouseHousehold Form hold Report Form sJ.ze

Household composJ.t~on

Rent InJ.tJ.al Household Report Household Report Form; ThJ.rd

Form, Baselme IntervJ.ew perJ.od1c Interv~ew

Rent Burden In~t~al Household Report Household Report Form;

Form, BaselJ.ne Interv1ew payments f11e; Thud

Per10dl.c Intervl.ew

SatJ.sfact1on var1ables Basel1ne IntervJ.ew ThJ.rd PerJ.odJ.c Interv1.ew

Housmg QUahty

Housmg standards HouSJ.ng Eva1uatl.on Form HouSl.ng Evaluatl.on Form

for enrollment

Housl.ng adequacy Housl.ng Evaluatl.on Form HousJ.ng Evaluatl.on Form

for enro1lnent

HeOOnLC l.ndex Hous~ng Evaluatl.on Form, Housmg Evaluat~on Form;

census data, Base1~ne census data, T!nrd Per~ocllc

IntervJ.ew, other sJ.te Interv~ew, other Sl.te data

data

OCcupancy InJ.tJ.al_ Household Report Household Report Form;

Form, HOUS1ng Eva1uat~on Hous~ng Evaluat~on Form

Forr>

Move Status --- In~t].al Household Report

Form, F1rst, Second, and

'nard PerJ.ocllc Intervl.ew

Current Payment Status In1tJ.al Household Report 24-month h~story from

Form, payments £11e Household Report Form,

payments £1.1e

A-22
was used to determine the household's monthly payment. Analytically, these

data are used to describe the household's housing expenditures, demographic

characteristics, and ~ncome dur~ng the course of the experiment. In add~tl.on,

annual supplements collected information on assets and taxes.

Payments Data

After each monthly payment cycle, the household's current payment status, reasonS for the status (if other than Full Payments status), payment period

number, payment amount, and the intermediate var~ables used to calculate the

payment were extracted from the operational payments system and entered ~nto

an analytic payments file.

Basell.ne Interview

Baseline Interviewslwere administered to all households before offers to enroll in the program occurred, and were completed between March 1973 and January

1974. Data were collected in the following general categor~es: housing expenditures and consumption; location and housing search; nel.ghborhood and

housing preferences and satl.sfaction; maintenance and upgrading; household

compoSl.tioni household assets, l.ncome, and expenses; and participatl.on 1.0 other

government programs. The interv~ews prov~ded measures of the household's

position pr~or to the experiment.

Periodic Interviews

Periodic Interviews were admin~stered to all enrolled households at approximately

six months, one year and two years after enrollment. Data were collected on a

number of subjects ~ncluded in the Basel~ne Interview. Subject areas included

housing expendJ..tures and consumptl.on; location and hansl.og search; preferences

and satl.sfactl.Oni maintenance and upgrading; and partl.cipation in other government programs. In addit~on, the Period~c Interviews included quest~ons relat~ng

to participant expectations at the time of enrollment and impressions of various

IThis ~nterview, as well as the Exit Interview for Non-Participants,

and the First, Second, and Third Periodic Interviews, were des~gned by Abt

Associates Inc. and administered in the f~eld by the National Op~nion Research

Center; some Baseline Interviews were conducted by Westat" Inc.

A-23
aspects of the program, such as the Housing Information Program, the housing and

reporting requirements, and the amount and variability of the allowance payment.

Housing Evaluat~on Form

Housing evaluations were conducted for all dwelling units occupied by households

that accepted the enrollment offer. Un~ts were evaluated at enrollment and

whenever a partic~pant moved or upgraded the1r current unit to meet either

Minimum Standards or Minimum Rent housing requ1rernents. In addition, all Wlits

were re-evaluated at least once a year. Households with a Minimum Standards

requirement also could request evaluat10ns of new units before deciding to move

to see 1£ these units met the requirement. The Hous1.ng EValuatJ..on FOrIn, used

to collect these data on hous1ng qual1ty, provides 1nformation on basic housing

serv1.ces, safety hazards, structure and surface condit1on, and other ind1.cators

of housing cond1t10n.

Census Data

Census variables for Allegheny and Maricopa count1es were extracted from the

1970 Census of Population and Housing Fourth Count Suromary Tapes. The var~ables

that were selected ~ncluded descriptors of the tract and its housing stock and

soc~o-economlC characterlstics of the population. Household-level Census tract

assignments were made using standard geocoding programs at the time of enrollment and each of the Per~odic Interviews. When the location by tract was determined, the Census var~ables for that tract were posted to the household file.

III. 2 KEY VARIABLES

Key variables used in thlS report include lucerne and demographic variables,

rent, satisfaction, housing standards, occupancy measures, an hedonic index

measuring housing services, move status, and current payment status. Definlt~ons of the var~ables used ~n th~s report are discu~sed below. Table III-l

summarlzes the data sources for these varlables.

Income

A maJor varl.able used in the analysls in this report is "Net Income for Analysis,"

a measure of household disposable income. Net Income for Analysis 1.5 an estl.­

mate of the annual l.ucame recel.ved by all household members age 18 or over; it

A-24
PITTSBURGH

White

Black

is the swn of earned and other income net of taxes and alimony paid. A complete

11st of all income components included in the definit10n of net 1ncome and its

relation to two other income measures- (the income definltion used to determine

e11gibility for the experimental program and that used by the census) are g1ven

1 1n Table 111-2.

Net Income for E11gibility defines an annual net disposable income for eligibi11ty and payment purposes which 1S easily and accurately measured and which is

defined as equitably as poss1ble for demographically different households that

rece1ve income from a variety of sources (see Table 111-3 for e11g1bi11ty limits).

Net income for e11gibi11ty was derived by adding the annual 1ncomes of all

household members who were at least 18 years of age, and Subtracting taxes,

work-related expenses, alimony paid, and maJor medical expenses. Table 111-2

compares tms def1n1t1on with the census def1nit1on and the analytic defin1tion

of income.

Demograph1c Var1ables

Race/ethn1city. The following categories are used in th1s report for each s1te:

PHOENIX2

Wh1te

Black

Span1sh American

Classifications are based on interviewer observat~ons of the head of household,

except for the Spanish Amerlcan deslgnatlon, WhlCh 18 based on surname accordlng

to Census conventions.

Age of head of household. The age of head of household is defined according

to Census conventions.

Sex of head of household. The Census convention is used. To establish the

Census designated head of household, the sex and relationship of each household member to the respondent who is designated head is checked. Unless the

household has a s1ngle female head, 1t 1S class1f1ed as having a male head of

household.

IHouseholds with annual 1ncome less than $1000 were excluded from the

analys1s. Elasticity estimates were not affected by this exclusion.

2

In some analyses beth black and Spanish Amer1can households in Phoen1X

were classified as minorlty households.

A-25
Table III-2

COMPONENTS INCLUDED IN THE DEFINITION OF NET INCOME FOR ANALYSIS

AND COMPARISON WITH CENSUS AND PROGRAM ELIGIBILITY DEFINITIONS

COMPONENTS

I GROSS INCOME

A. Earned Income

1 Wages and Sa1ar1es

2. Net Bus1ness Inc~e

B. Income-Cond1t10ned Transfers

1. A1d for Dependent Ch11dren

2. General ASs1stance

3 Other Welfare

4. Food stamps SubS1dy

C. Other Transfers

L Supplemental secur1ty Income (Old Age

Ass1stance, A1d to the Bl1nd, A1d to

the D1sabled)

2. Soc1a1 secur1ty

-3 Unemployment Compensat10n

4. Workmen's Compensat10n

5. Government Pens.l.ons

6. Pr1vate PenS.l.ons

7. veterans penS.l.ons

D. Otner Income

1. Educat.l.on Grants

2. Pegular Cash Payments

3 Other Regular Income

4 Al.l.mony Rece.l.ved

5. Asset Income

6. Income from Roomers and Boarders

II. GROSS EXPENSES

A.

1. Federal Tax W.l.thheld

2. state Tax W.l.thhe1d

3. FICA Tax W.l.thhe1d

B. Work-Condl.tl.oned Expenses

1. Ch.l.ld Care Expenses

2. Care of S1ck at Home

3. Work Related Expenses

C. other Expenses

1. Al.l.mony Pa.l.d OUt

2. MaJor Med1cal Expenses

NET INCOME FOR

ELIGIBILITY

x

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X'

X'

X'

X'

X

-X

X'

X

X

NET INCOME

FOR ANALYSIS

X

X

X

X

X

X'

X

X

X

X

X

X

X

X

X

X

X

X'

X'

X'

X'

X

CENSUS

(GROSS INCOME)

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X'

*The amounts of these .l.ncome and expense J.tems are der.l.ved uS1.ng data reported by the household.

All other amounts are 1.ncluded 1.0 the 1.ncome varJ.abl ....s exactly as reported by the household.

A-26
Table III-3

INCOME ELIGIBILITY LIMITS AT ENROLLMENT

FOR PERCENT OF RENT AND CONTROL HOUSEHOLDS

HOUSEHOLD SIZE

DESIGN POINTa 1 2 3,4 5,6 7+

PITTSBURGH

Treatment Groups

12, 14-23 $5,050 $5,800 $6,750 $7,700 $9,150

Treatment Group 13 3,002 3,600 4,537 5,060 5,257

Treatment Groups

24, 25b 12,500 12,500 12,500 12,500 12,500

PHOENIX

Treatment Groups

12, 14-23 $6,000 $7,450 $8,650 $10,600 $12,750

Treatment Group 13 2,700 4,100 4,500 4,700 5,400

Treatment Groups

24, 25b 15,500 15,500 15,500 15,500 15,500

NOTE: Ind~cated amounts are $500 greater than formal el~g~b~l~ty

l~~ts. A $500 marg~ of error is allowed. only households w~th ~ncomes

more than $500 above the formal l~lts are consldered to be overlncome.

a. Refer to the summary exper~mental des~gn ~n Append~x I for

ldentiflcatlon of these groups.

h. These amounts were used as crlterla 10 the actual enrollment

process. Note, however, that households 10 these treatment groups are

conSldered to be overlncome for thlS lncome ellglblilty status at enrollment ~f the~r ~ncome ~s greater than the Income El~gib~l~ty L~~ts for

Treatment Groups 12 and 14-23

A-27
Household size. The definition of household s~ze includes all persons living

with the household except roomers and boarders.

Household compos~t~on. This var~able ident~f~es the structure of the household based on the relationships of household members to the head. Two classificat~ons are developed from the data.

Bas~c Classif~cation:

One-person household

Single head with children; no relatives

S~ngle head with children and relatives

Single head with no children; relatives present

Marrled couple; no children, no relat~ves

Married couple Wlth chl1dreni no relatlves

Married couple with children and relat~ves

Married couple with no children, but with relatives

Abbreviated Classification (eight basic categories collapsed ~nto three):

S~ngle-person

Single adult with children or others present

Married couple with or without others present

Rent

Analysis of participant expend~tures on housing takes two bas~cally different

approaches:

How much do households spend on rent?

How much does ~t cost to rent a dwelling unit with part~cular characteristics?

These d~fferences in approach require variat~ons ~n the analyt~cal definitions

of rent. For example, reductl.on in rent for contrl.butions from roomers and

boarders ~s appropriate for the first approach but not the second.

Analyt~cal adJusted contract rent ~s bas~cally def~ned as the monthly payment

for an unfurn~shed dwell~ng un~t ~ncluding bas~c ut~lities. The formula is

AdJusted Contract Rent = Contract rent + ut~lities - furnishings +

work 10 lieu of rent adJustment.

The components included are discussed below:

Contract rent. Contract rent 15 adJusted to a monthly amount

to provl.de a common rental perl-od.

A-28
util~ties adjustment. If the costs of utilities are not included 1n the household1s contract rent, utlllt~es adJustments are added to contract rent. AdJustments are made Vla

slte-speclflc tables for electrlc1ty, gas, heat, water, garbage, and trash. The amount of the adJustments depends on

the numbers of rooms reported 1n the Housing Evaluat10n Fonn.

No adJustment 1S made for any other utJ.l1hes or serv1ces,

such as park1ng. Allowance is made for 1ncreased utll1ty

costs over the two-year experlInenta1 perlod.

Furn1shlngs

1S made for

Work 1n 11eu of rent adJustment. If the contract rent

pa~d by the household ~s reduced because a household member

works for the landlord, the amount of the reduct~on ~s added

to contract rent. The adJustment has not been added to

~ncome, although ~t should ~n theory be added.

The analyt~cal adJusted contract rent used ~n th~s report for the analys~s

of hous~ng expendltures refers

contr~but~ons from roomers and

Rent Burden

to shelter costs borne by

2 boarders are subtracted.

the household, so

Rent burden was calculated as the ratlo of analytlc rent to net lncome for

analyslS, adJusted for allowance payments. Rent burden lS thus def~ned as

Net Rent/Net Income:

Rent Burden = contract Rent-Allowance

Net Income for Analys1s

3 Payment

(monthly)

Rent burden statlst~cs are hlghly sensltlve to the deflnitlon of ~ncome used.

Statlstlcs calculated from dlfferent sources uSlng dlfferent def1nltlons of

lncome may have to be recalculated or adJusted before comparlsons may be

made. The Houslng Allowance Demand Experlment data appear to be unique 1n

both attemptlng to use an analytlc deflnltlon of net dlsposable lncome and

1n havlng the data to do so. In general, the source of varlation 10 rent

burden statlstlcs result prlmarlly from dlfferences ln lncorne def1n~tlons.

See Budd~ng (forthcom~ng) for further d~scuss~on of th~s problem.

1

For more spec1flc deflnltlons of these adJustments, refer to Abt

Assoc1ates Inc., Worklng Paper on Early FJ..nd1nQS, January 1975, Appendlx IV.

2

Households w~th rents less than $40 per month were excluded from

the sample. ThlS exclus10n was based on a Judgment that gross rent fJ..gures

below thlS cutoff may be erroneous. ElastJ..c1ty estlmates were not affected

by this exclusJ..on.

3

For Control households, the $10 cooperat~on payment was deducted

from the contract rent amount.

A-29
Sat1sfact10n var1ables

Both hous1ng un1t and ne1ghborhood sat1sfact1on are measured on a four-point

scale:

very sat~sfied

Somewhat sat1sf1ed

Somewhat d1ssat1sf1ed

Very d~ssatisf~ed.

Program Housing and Occupancy standards

Th1s sect10n descr~es the hous1ng and occupancy measures used 1n the analys1s.

These measures are based on the M1n~um Standards hous1ng requ1rements used 1n

one part of the experlffient. They were developed from elements of the Amer~can

pub11c Health Assoc1at10njPubl1c Health Serv2ce, Recommended Hous2ng Ord1nance

(1971).1 Table III-4 l~sts the M~nlffium Standards hous~ng requ~rements as

they apply to the dwell~ng un~t ~tself. The requ~rements are grouped ~nto

15 components made up of related 1tems.

Two phys1cal standards and one occupancy standard are used 1n th1S report.

The 1I10w standard" applies to bas1c systems in and the exterJ.or of the un1t

while the "program standard" 1ncludes the 1nterJ.or and other features. The

standards that must be met to meet th~s low level of standard are complete

plumb1ng, complete kJ.tchen fac111ties, presence of the core rooms, adequate

heat1ng equ1pment, roof structure, and exterJ.or walls (numbers 1, 2, 3, 6,

13, and 14 ~n Table III-4).

Occupancy requlrements are separate from the physJ.cal requJ.rements I1sted

~n Table III-4. However, the requ~rements for l~ght/vent~lation, ce~l~ng

height, and electr1cal serVlce are applied to bedrooms 1n determ1n1ng the

number of adequate bedrooms for the program occupancy requJ.rement. The

occupancy requJ.rement sets a maxJ.mum of two persons for every adequate

bedroom, regardless of age. A studio or effJ.cJ.ency apartment J.S counted

as a bedroom for occupancy standards. An adequate bedroom J.S a room that

can be completely closed off from other rooms and that meets the following

program hous~ng standards: ce~l~ng he~ght, l~ght/vent~lat~on, and electr~­

cal serVlce. In addltl0n, the room must meet the housing standards for the

condlt1on of room structure, room surface, floor structure, and floor

Isee Abt Associates Inc. (1975) for more deta~l on the development

of the M~lffium Standards.

A-30
Table III-~

co.."'lPONENTS OF MINIMUM STANDARDS

(Program Oef~~t10n)

1 COMPLETE PLUMBING

Pr1vate to~let fac~l~t~es, a shower or tub w~th hot and cold runn~g water, and a washbaS1n wJ.th

hot and cold runn~ng water wJ.ll be present and workJ.ng condJ.tJ.on

2. COMPLETE ~TCHEN FACILITIES

A cook~ng stove or range, refr~gerator, and h.J.tchen sJ.nk .....~th not and cold rumung .....ater .....1,11

be present and 1,n work1,ng cond1,t1,on.

LIVING ROOM, BATHROOM, KITCHEN PRESENCE

A l1,v1,ng room, bathroom,_ and k1,tchen .....1,11 be present. (Th1s represents the dwellwg un1,t "core,"

wh1ch corresponds to an eff1,c1,ency un1,t.)

4. LIGHT FIXTURES

A ce1,1~n9 or wall-type f1,xture w1ll be present and work1ng 1n the bathroom and k1,tchen.

5. ELECTRICAL

At least one electr1C outlet w1ll be present and operable J.n both the 1l.vJ.ng room and k1tchen

A work1ng wall sW1,tch, pull-chaJ.n IJ.ght sw1,tch, or add1t1onal electr1cal outlet w1ll be present

~n the l1,vJ.ng rocm. a

6 HEATING EQUIPMENT

Un1ts wJ.th no heat1ng equJ.pment, WJ.th unvented room heaters whJ.ch burn gas, oJ.l, or kerosene,

or wh1,ch are heated maJ.nly wJ.th portable electrJ.c room heaters w1l1 be unacceptable

7. ADEQUATE EXITS

There .....J.ll be at least two eX1,ts from the dwellJ.ng unJ.t leadJ.n9 to safe and open space at

ground level (for mUlt1,famJ.ly bU1ld1ng only) Effect1ve November, 1973 (retroactJ.ve to program

~ncept10n) th1S requJ.rement was modJ.f1ed to perm1t overr1de on case-by-case basJ.s where 1,t

appears that f1re safety 15 met de5p1te lack of a second eX1t.

8. ROOM STRUCTURE

Ce1l1nq structure or .....all structure for all rooms must not be 1n condJ.t10n requU'J.ng replacement

(such as severe bucklJ.ng or lean1ng)

9. ROOM SURFACE

Ce111ng surface or wall surface for all rooms must not be 1,n condl.t10n requJ.r:rng replacement

such as surface mater1,al that J.S loose, contaJ.nJ.ng large holes, or severely damaged)

10 CEILING HEIGHT

LJ.vJ.Dg room, bathroom, and k~tchen ce111ngs must be 7 feet (or hJ.gher) 1n at least one-half of

the room area. a

11. FLOOR STRUCTURE

Floor structure for all rooms must not be 1n cOndJ.t1on requU"J.ng replacement (such as large

holes or m1,ssJ.ng parts)

12. FLOOR SURFACE

Floor surface for all rooms must not be J.n condl.t10n requJ.r1.ng replacement (such as large holes or mJ.sSJ.Dg parts).

13 ROOF STRUCTURE

The roof structure must be fJ.rm.

14 • EXTERIOR WALLS

The exter10r wall structure or exter10r wall surface must not need replacement (For structure

thJ.s would ~nclude such cond1t~ons as severe lean1ng, buck11ng, or sagg1ng, and for surface

condJ.t10ns such as excess~ve cracks or holes.)

15 LIGHT/VENTILATION

The unJ.t wJ.ll nave a 10 percent rat10 of w1ndow area to floor area and at least one openable

.....1ndow 1n the l1,v1ng room, bathroom, and k1tchen or the equ1valent ~n the case of properly

vented k1tchens and/or bathrooms. a

a. ThJ.s hOUS1ng standard 1,S app11ed to bedrooms 1n determ1n1ng the number of adequate bedrooms for

the program occupancy standard.

A-31
surface. If the dwell~ng unit contains four or more adequate bedrooms, ~t

~s Judged to meet occupancy standards; th~s reflects the actual program

operat1ng rule, wh1ch set this ce111ng to occupancy standards at the requ1rement for an e1ght-member household. (Roomers and boarders are added to

household S1ze when determ1n1ng whether a household meets occupancy standards, because all the rooms 1n the dwel11ng unit are taken 1nto account.)

HousJ.ng Adequacy Measure

The housing adequacy measure class1fies UIutS 1nto one of three categor1es:

clearly 1nadequate, at least nu.nimally adequate, or ambJ.guous. The measure

~s closely related to the M1.n~mum Standards measure in that the adequacy

measure ~ncludes all but one (bathroom window adequacy) of the M1.n~mum

Standards ~nfucators plus only two adfut~onal indicators (presence of rats

and w~ndow condition). See Chapter 5 and Budding (1978) for a more deta~led

descrJ.pt10n.

Hedon1c Index of Hous1ng ServJ.ces

The hedon1c 1ndex 15 a summary measure of housJ.ng serv1ces. ThJ.s J.ndex

est1mates the market value of a un1t 1ll terms of the attributes of the un1t

J.tself, the neJ.ghborhood and the qual1ty of publ1c and pr1vate servJ.ces

ava~lable. See Chapter 5 and Merr~ll (1977) for a more deta~led descr~ption.

Move Status

Determ1nat1on of a move 15 always based on the compar1son of addresses rather

than on the household's response to ~nterv~ew questions regard~ng mov~ng. A

household 1S class1f1ed as hav1ng moved dur1ng the experJ.ment 1f the address

on the In1t1al Household Report Form 15 d1fferent from any of the addresses

reported by the household dur~ng the two-year exper~mental per~od.

Current Payment Status

Status of the household ~s def~ned as one of the follow~ng:

Act~ve full payments

Act1ve rn1nlmum payments

A-32
Inact~ve, react~vated for later cycles (for example,

households that moved out of county and then moved

back ~nto the county)

Inact~ve, never react~vated ~n later cycles

Term~nated.

Posslble reasons for m~n~mum payments status are:

Household owns home

Household l~ves ~n subs~d~zed hous~ng

Rent rece~pt not returned

Fa~lure to meet hous~ng requ~rements (hous~ng Gap M~n~mum

Rent and M~n~um Standards groups only).

posslble reasons for lnactlve or termlnated status are:

Move out of county

Inellglble household composltl0n

Resldlng In lnst~tut~on

Cannot locate

per~odlc Intervlew refused

Houslng Evaluatl0n refused

M~sslng Evaluatlon refused

Mlss~ng Household Report Forms

New household members refused to comply wlth requ~rements.

Addltlonal posslble reasons for termlnat~on are:

Household deceased

Inel~g~le household spl~t

Fraud

Recelved lnellg~ble relocatlon beneflts

Termlnatlon other (confl~ct of lnterest)

Reverlflcatlon refused

Qu~t (voluntary term~nat~on).

A-33
REFERENCES

Abt Assocl.ates Inc., Working Paper on Early FindJ.ngs, Cambrl.dge, Mass.,

January 1975.

Budding, David, W., Housl.ng Depnvatl.on Among Enrollees in the Housing Allowance Demand Experiment, Cambridge, Mass., Abt Associates Inc. I November 1978 (revised June 1980).

Marrl.ll, Sally R., Hedonic IndJ.ces as a Measure of Housing Quality, Cambrl.dge,

Mass., Abt Associates Inc., December 1977 (revised June 1980).

A-34
APPENDIX IV

HOUSING PROGRAM EFFICIENCyl

(1) E =

One cr~ter~on for evaluatlng a houslng program 15 the extent to WhlCh payments are translated lute increased houslng expendltures. In these terms,

program "e fflCl.ency" may be narrowly deflned as the ratl.O of the change 1n

total rental expend~tures to the payment amount, or

RI-RO

S

where

E = subs~dy eff~c~ency

S the amount of the allowance payment

Rl = total rental expend~tures (after subs~dy), and

RO = total rental expend~tures (before subs~dy).

Thus, 1£ none of the subsl.dy is used to l.ncrease rental expendl.tures l.ts

efficl.ency wlll be zero; 1£ the entl.re subsl.dy

rental expendltures, l.ts efflCl.enay wl.ll equal

is added to pre-existing

2

one.

Under a percent of Rent housl.ug allowance, the payment is equal to a fractJ.on,

n a ," of rent, so that

(2)

Effl.cl.encycan be computed based on the log-ll.near housl.ng demand functl.on,

(3)

where

R = total rental expendl.tures

y d~sposable l.ucame

PH prJ.ce of hOUSlUg, and

", III , 112 = demand funct~on parameters.

1Th~s append~x ~s drawn from Mayo (1977).

2 . . Ef£l. Cl.ency ~s not cons tra~ned to the zero-one range.

A-35
Equ~l~br~um rental expend~tures after the percentage pr~ce SUbS1dy are

related to egu~l~br~um rental expend~tures before the subs~dy by

(4)

1 Subst~tuing Equat~on (4) ~nto Equat~on (2) g~ves

(5) E =

Sz (I-a) -1

ail-a) Sz = 1 -Sz [1- (I-a) 1• a

Thus, the eff~clency of a percent of Rent payment lS determ~ned by two parameters--the percentage rebate, "a," and the price elast1clty, f32. Table IV-l

presents values of subs~dy eff~c~ency for several hypothetlcal comb1natlons

of percentage rebate and pr~ce elastlclty.

Table IV-l

SUBSIDY EFFICIENCY OF PERCENT OF RENT SUBSIDIES

FOR DIFFERENT SUBSIDY RATES AND PRICE ELASTICITIES

PRICE ELASTICITY OF DEMAND (Sz)

SUBSIDY RATE (a)

0.2

0.4

0.6

-0.25

0.27

0.30

0.34

-0.50

0.53

0.56

0.61

-0.75

0.77

0.80

0.83

-1.00

1.00

1.00

1.00

The table lnd~cates, for example, that at 40 percent rent rebate and a prlce

ela5t1c1ty of -0.50, the efflc1ency 15 0.56. In other words, 56 percent of

the payment goes toward 1ncreas1ng total rental expend1tures. The table

111ustrates that the eff1c~ency of the SubS1dy 15 an 1ncreas1ng funct10n of

the absolute value of the pr1ce elastlclty, SZ. As the pr~ce elast~city

approaches -1.0, the entlre SubSldy wll1 be used to lncrease rental

Sz (I-a) -1

ail-a) Sz·

A-36
expend~tures and subs~dy eff~c~ency approaches 1.0 regardless of the subs~dy

1 rate.

If the pr~ce elastlclty 18 greater than one In absolute value, not only wlll

the subs~dy be ent~rely spent on hous~ng, but the household w~ll sh~ft some

of ltS before-subsldy lnCame from other goods to housing. In such cases,

the calculated subs~dy eff~c~ency w~ll be greater than 1.0. As the price

elastlclty lncreases In absolute value, the calculated SUbSldy ef£lclency

2 approaches an upper l~~t of l/a. F~gure IV-l ~llustrates the relationsh~p

among SubSldy efflclency, SubSldy rates, and prlce elastlclty.

Figure IV·'

EFFICIENCY AS A FUNCTION OF PERCENT OF RENT REBATE RATES

AND PRICE ELASTICITY

a = Percentage rebate

2.00

> 1.50 "

c.,

U

.;::

w 1 00

75

50

25

.00

00 -50 -100 -1.50 -200

a = 0.20

a = 0.40

a = 0.60

Proce ElastIcIty of Demand

1

For the prlce elastlcltles less than one In absolute value, efflclency also lncreases as the SubSldy rate lncreases.

2

From Equat~on (5),

E = [l-(1-al-S2 J.

a

S~nce (I-a) ~s less than one, ~n the l~m~t the bracketed term approaches one

or,

a

A-37
The relat2ve ~pact on rental expend2tures of unrestr2cted 2ncome transfers

and pr~ce subs~d~es of equ~va1ent magnitude may be compared based on the

analys2s above a A straightforward compar~son 2S possible because unrestricted

~nCOme transfers operate through income elast2c2t2es of demand and price subsid1es operate through pr2ce elast2cities of demand.

A pr2ce subsidy should always produce a greater 1ncrease 1n hous2ng expend2­

tures than an equal 2ncome subsidya W2th an equal income subsidy, the household can purchase the same amounts of hous2ng and other goods as 2t purchases

under the pr~ce subs~dy. However, under the ~ncome subs~dy ~t st~11 faces the

orig2nal, h~gher price for hous1ng and so may be expected to buy less hous2ng

than under the pr1ce subs~dy, wh1ch offers the ~ncent1ve to lower prices a

The extent of the d~fference ~n hous~ng expend~tures under the two types of

subs1dy depends on the 1ncome and pr1ce elast1c1t1es and the or1g1nal rent1ncome rat10a The pr1ce sUbs2dy, S , needed to ach1eve a g2ven level of

p

hous1ng expend1tures, Rl , 1S

( 6)

from Equat~on (4). The rent ach1eved under an 1ncome subs1dy, S , 1S

Y

s = R [l + --y. ] 13 1.

o Y

Thus the ~ncome subs~dy necessary to ach~eve R1 = (1-a)132

Ro , ~s g~ven by

S

(7) (1_a)132R = R [1 + -y ]131

o 0 Y

Thus,

(8)

comb~n~ng Equat~ons (6) and (8), the rat~o of the subs~dy needed under a

pr1ce subs1dy to that needed under an income subs1dy 15

(9) , or

A-38
(10)

-82(1--1) -82J-l

[I-a) 81 - (I-a)

where -B2 15 posltlve. Slnce the change 1n rent is the same 1n both cases,

S /s ~s also the rat~o of the subs~dy eff~c~ency under an ~ncome subs~dy p y

to that under a pr~ce subs~dy. The relative effic~ency of pr~ce subs~d~es

15 generally larger (for a glven lnltlal rent-lncame ratlO) as the prlce

elasticity 18 larger 1n absolute value, and 18 larger as the lucame elast~city is smaller.

A-39
REFERENCES

Mayo, Stephen K., Hous~ng Expend~tures and Qual~ty, Part I: Hous1ng Expend1­

tures Under a percent of Rent HOUS1ng Allowance, Cambr1dge, Mass.,

Abt Assoc~ates Inc., January 1977.

A-40
APPENDIX V

THE ECONOMICS OF THE

FOOD STAMP HOUSING SUBSIDY

The max~mum poss~ble Food Stamp subs~dy (S) ~s equal to:

(1)

where

S

=c ::Y-(R-. 3Y)] =A-a (1. 3Y-R)

for R

for R

< .3Y

>.3Y

A = the value of food that can be bought with the

full Food Stamp allotment, where A = PFFs (F = the max~um anount of food that

ca~ be bought with the subs~dy when the

pr~ce of food ~s PF)'

a = the contribution rate (a 0.3),

Y net household ~ncome after deduct1ons, and

R = hous=g expend~tures (rent); where R = PHH

(p = the price of hous~ng, and H = the

amilunt of housing).

The subs~dy moves the ~n~t~al budget constra~nt (y = PFF + PHH + PZz, where

F 18 actual food consumptlon, Pz 18 the prlce of other goods, and Z represents

-other goods). Four cases can be dlstlngulshed.

Case (a) pFF > A, R 0.3Y

In th~s case the household purchases more food than ~s covered by ~ts Food

Stamp allotment. The bUdget constra~nt becomes

Subst~tut~ng for the subs~dy, S, Equat~on (2) becomes

(3)

In thlS case the relatlve prlces of food, houslng, and other goods are all

unchanged. The program s~mply acts to ~ncrease ~ncome by the amount of the

Food Stamp subs~dy (A-aY).

A-41
Case (b) P F > A, R > O.3Y

F

Here aga~n, the household purchases more food than ~s covered by ~ts Food

Stamp allotment. Now, however, ~t 18 spend1ng enough on houslng to brlng

the shelter deduction ~nto effect. Using Equation (2) and aga~n subst~tut~ng

~n for the subs~dy, S, the budget constra~nt becomes

(4)

The effect here ~s to ~ncrease ~ncome by (A - a(l.3)Y) and reduce the pr~ce

of hous~ng from PH to (l-a)PH·

Case (c) P F < A, R < O.3Y

F -

If a household purchases less food than the amount poss~ble w~th a full

allotment, ~t ~s allowed to purchase a fract~on of ~ts full allotment (onequarter, one-half, or three-quarters). It 15 assumed here that the household can purchase the actual fract~on des~red (PFF/A) by averag~ng ~ts

fractl0nal purchases over several months. The budget constralnt becomes

PFF

(5) Y + (A - crY)T pFF + PHH + PZZ

or

(6)

In th~s case, the pr~ce of food ~s reduced from PF to (~ PF ). (This must

decrease the pr~ce of food, s~ce the subs~dy [A - cry] > 0 for rec~p~ents.)

Case (d) p

F

F:5.. A, R O. 3Y

In thlS case, the budget constralnt becomes

(7)

or,

Y + [A - cr(l.3Y-R)]

(8)

ThlS functl0n 18 nonllnear 10 food and houslng. Prlces (net CO&t per addltlonal unlt) are no longer constant. The lmpllcatlons of thlS are dlscussed

further below.

A-42
I Three of the four cases are ~llustrated ~n F~gure V-I. For cases (a) and

(b), the ~mpact of the Food Stamp program on hous~g expend~tures can be

analyzed us~ng the hous~ng demand funct~on alone. As long as the household

spends more than ~ts coupon allotment for food, the effect of the program

18 s~ply to ralse ltS income and/or reduce the prlce of housing. Sluce

housing 15 a normal good, the amount of houslng consumed will lncrease as

lucame increases. There wl11 also be an lncrease in houslng consumptlon

due to the decrease ~n the relat~ve pr~ce of housing for households spend~ng

more than 30 percent of the~r net ~ncome on rent [case (b)].

Figure V-2 111ustrates lucerne and prlce effects for several dlfferent

sltuatl0ns uSlng lndlfference curves to represent a household's equl11b2 rlum posltl0n. Flgure V-2a lilustrates an lncrease 1n houslng consumptlon

due solely to the income effect. F~gure V-2b ~llustrates a s~tuat~on ~n

WhlCh houSlng consumptlon lncreases due to both lncOffie and prlce effects.

Note that the lucame effect alone may cause households to lncrease thelr

rent-to-net lucame ratlo to above 30 percent, maklng It ellglble for a prlce

subs~dy. (The household could also have been spend~ng more than 30 percent

in~t~ally.)

In the rema~nlng two cases, 10 WhlCh households spend less than thelr allotment on food, the Food Stamp program leads to changes in the pr~ce of food

as well as changes 10 lucame and, 10 case (d), the prlce of housing. Thus,

these cases cannot be analyzed solely 10 terms of the houSlng demand functlon

est~ated 10 thlS report. However, as mentloned 1n Chapter 2, cases (a)

and (b) probably account for the bulk of Food Stamp rec~p~ents.

IF~gure V-I assumes that expenditures on all other goods ~s f~xed at ZO(pz = 1). In~t~al income ~s yo. F~gure V-I also assumes that there

~s range of hous~ng for wh~ch the household ~s pay~ng more than 30

percent of ltS net lucame for rent. (If thlS were not true, analysls could

be restr~cted to cases (a) and (c).) S~nce ~n the low-~ncome populat~on

enrolled as Demand Exper~ment Control households more than half of the

households were pay~ng more than 30 percent (the med~an was 32 percent),

and s~nce 74 percent of Food stamp households took the shelter deduct~on,

the sltuatlon depleted seems reasonable.

2Each lndlfference curve represents the combinatlons of houslng and

food wh~ch make the household equally well off. A household would prefer to

be on a hlgher lndl£ference curve Sluce thlS would enable them to consume

more of at least one good. Consumptlon wlll lncrease to the p0l0t where

the budget ~s completely spent.

A-43
Figure v-,

FOOD STAMP BUDGET CONSTRAINTS

Amount of Food

budget constraint

r case (a) [slope = -PH/PFl

)

,

"-"-,

"-,,­"-

I

I

I

I

I

I

budget constraint

case (bl [slope = - (1 - a)PH/PFl

IOttlal budget --z...,,;

constraint

[slope = PH/PFl

I

I

I "- --------------1----'-

I 'I,

I I',

: '.... budget constramt

I "-,,~ case (d) [slope = -A PH/a (1 3Y - PHH)PFl

I

I

A

F =­

s P

F

(Yo - Zol

PF

(7Y - Zo + 51

PF

(1-13a) Yo-Zo+A

(1 -a)PH

Amount of Housmg

Yo

Zo

S

A

Fs

PF

H

PH

a

Income

consumption of nonhousmg goods

value of the Food Stamp subsidy to the household

the value of food that can be bought with the full coupon allotment

the maximum amount of food that can be bought with the subsidy

the pnce of food

the amount of housmg

the price of hOUSing

the benefit reduction rate

A-44
Figure V-2

INCOME AND PRICE EFFECTS OF FOOD STAMPS ON HOUSING

Amount of HOUSing

Ca)

I

I

I

I

1

I

1

I

I

I

I

I

I

I

I

-----T-I

I I -';;::,,,,,--._

_______ I I " -I -I --- ,-

I ' I

I'," "

Amount

of

Food

Amount

of

Food

Amount of Housmg

initial consumption of hOUSing

consumption of hOUSing due to Income effect of food stamp subsidy

consumption of hOUSing due to Income and price effect of food stamp subsidy

Note" See Figure V· Jfor additional dlagramatlc detail.

A-45
Tabulat~ons from the 1976 Survey of Income and Education, shown ~n Table

V-I, indicate that 94 percent of Food Stamp rec~p~ents purchase the~r full

Food Stamp allotment. Of these, 65 percent say they spend more on food

than ~s covered by their Food Stamp allotment. Thus, at least 61 percent

of Food Stamp recip~ents (0.94 x 0.65) clearly fall ~nto case (a) or (b).

Furthermore, most of these rec~p~ents report expenditures well above their

allotment.1

Cases (a) and (b) apply as well to households that would purchase no less

than full allotment ~f the budget l~ne d~d not curve down for food purchases

of less than the allotment (see F~gure V-I). There ~s no ready way to tell

what proport~on of the full allotment households that report spending all

of their allotment fall ~nto th~s category.

1MacDonald (1977) est~mates that roughly two-th~rds of all rec~p~ent

households are effect~vely unconstrained by the program.

A-46
Table V-I

COMPARISON OF FOOD PURCHASES AND FOOD STAMP ALLOTMENT

Number

Percentage of total rec~pients

Spend more on food than ~s covered

by Food Stamps

percentage of total rec~p1ents

Spend more by

less than $5 per month

$5 to $15

$16 to $25

more than $26

don't know

PURCHASE FULL

ALLOTMENT

4,869,687

94%

3,151,900

61%

71,992

696,049

727,733

1,627,581

28,544

PURCHASE LESS THAN

FULL ALLOTMENT

307,782

6%

187,531

4%

5,579

34,306

29,407

117,814

426

SOURCE: Unpubl~shed data from 1976 Survey of Income and Educat~on,

uned~ted data tabulated by U.S. Bureau of the Census, Table 1 (weighted to

represent the U.S. population).

A-47
APPENDIX VI

AN ALTERNATIVE ESTIMATION

OF EXPERIMENTAL EFFECTS

Chapter 4 descr~bed est~t~on of demand fUnct~ons w~th the effect of

Percent of Rent rebates spec~f1ed as a l~near funct~on of In(l-a). Th1s

appendlX uses a less form-constralned method to evaluate the ~pact of rent

rebates qn expendltures.

vr.l DEVELOPMENT OF THE METHODOLOGY

ExperImental effects are measured under the assumption that the actual houslUg expendltures of percent of Rent households at two years after enrollment,

R, can be decomposed luto two parts--the normal houslng expendltures that

would have been made In the absence of the rebates and an addltl0nal amount

wh~ch ~s ~nduced by the rebates. Thus

(1)

where

R actual expendltures two years after enrollment

=

=

normal expendltures two years after enrollment, and

the exper1mental effect on expendltures.

The experlrnental effect can be measured elther as the dlfference between

actual and normal expendltures or as thelr ratio

(2)

R

R

N

=

For conslstency w~th the log-llnear demand funct~ons est2mated ~n Chapter 4,

and for conven~ence, throughout th1S append1x the experImental effect 18

measured 1n terms of the ratlO of actual to normal expendltures.

Exper~ental effects are estlmated under the assumpt10n that the rat10 of

actual to normal hous1ng expendltures lS functlonally related to experlmental varlables and a random error, speclflcally

A-49
(3)

R

-= exp(XS + e),

or

(4) XS + e,

where

x = a vector of experlffiental varlables

S a vector of experlmental effects, and

e a random error term d~str~buted N(O,a2 ).

e

The coeff~c~ents S of Equat~on (4) may be ~nterpreted as the

change 10 rent assoclated wlth a unlt change 10 the relevant

percentage

1

varlable, x.

Sluce In(~) 15 no~observable~-lt 15 estlmated uSlng Control households

(wh~ch have not been affected by rent rebates).

The log-llnear speclflcatlon for houslng expendltures 15 chosen for convenl.ence:

(5) In(R~) i = a + S In(Y ) + e

where yl. 15 l.ncome.

eO

Least Squares (OLS) est~mat~on

An asymptotically more eff~c~ent

If the residuals over the two t~e per~ods,

equat~on would be ~neff~c~ent.

chastic

and e l ,

of th~s

equatl.on concerns the partl.cular assumptl.ons about

error term, et.

are correlated, then the Ordl.nary

Gl.ven the speclfJ.catJ.on of Equatl.on (S) and the fact that observatl.ons on

each household 11).11 are aval.lable for two tl.me perl.ods, t=O (enrollment)

and t=l (two years), a crJ.tl.cal J.ssue J.O estLmatl.ng the parameters of the

the nature of the stoest~mat~onJtechn~que, Seem1ngly Unrelated Regress10n (SUR), developed by

Zellner (1962), ~s used here. Tak~ng account of ~n~t~al pos~t~on through

eO 1mproves pred1ct10n.

1Note that

a[In(RI~) 1

ax

Thus, B~ measures the proport~onal change 10 (R/~) ~n response to a un~t

change ~n X •

A-50
The SUR procedure consists of estunat~ng Equat~on (5) for the two tune

per~ods separately us~ng OLSi then computlng P, the correlatlon between

..... 1 A1

the est1mated reslduals, eO and 6

1 , WhlCh 15 a consistent est~ate of the

true serlal correlatlon coefflClent, p. The estlmate p 18 then used to

transform the ~ndependent and dependent var~ables ~n Equat~on (5) ~n order

to prov~de General~zed Least Squares (GLS) estunates of the parameters.

As Chapter 2 demonstrated, there are large dl£ferences between changes 10

hous~ng expend~tures of households that moved and those that stayed ~n

thel.r enrollment unltS. Thus, the predl.ctlon of nonnal housl.ug expendl.­

tures lncorporates movlng behavlor. S~ce l.t is poss~le that the rent

rebates lnduced reSl.dentlal moblilty, the estlmatlon of normal rent does

not depend on whether a household had actually moved after enrollment.

Rather, the estllnatl.on 18 based on the normal probablJ.llty of movl.ng,

est~mated from the sample of Control households. F~gure VI-l descrilies

thedisposltion of Percent of Rent households notl.ng that a Percent of

Rent household may have been ~nduced to move. The normal expend~ture of

any household, i, is then

( 6)

where

the normal probab~l~ty of mov~ng (absent

the experunent)

tne normal log expend~ture of household ~,

~f ~t were not to move, and

the normal log expend~ture of household ~,

~f ~t were to move.

Chapter 2 ~ndlcated that the response of movers and nonmovers d~ffered ~n

J.Inportant ways. Mover and nonmover households can be exanuned separately.

If all Percent of Rent households that d~d not move would not have moved ~n

1

the absence of the experJ.Inent, the normal expend~ture for nonmovers 1S

sunply

1It 1S poss1ble, In theory, that Percent of Rent rebates could

~nduce some households that would have moved to less expenslve unltS to

retaln thelr orlg~nal units.

A-51
Status

at

Enrollment

Figure VI - 1

DISPOSITION OF EXPERIMENTAL HOUSEHOLDS BY MOBILITY STATUS

N

MobJi,ty

Behavior

Over Experimental

Period

Stay

(1- Pm) N

Normal

Behavior Over

Experimental

Penod

(11

Induced

Stay to Move Move

(1-P m) N Pm - Pc) N Pc N

Normal

Expenditure

R

NM NM

R

MV

Pattern R

N N N

Notes

Pm Proportion of Experimental households that moved

Pc Proportion of Control households that moved (normal mobility)

N Total number of households

NM

R Normal expenditure of Control households that did not move

N

MV

R Normal expendIture of Control households that moved

N

A-52
(7) r

N (nonmover)

Normal expendl.ture for movers 18 more complex due to l.nduced mobl.ll.ty (see

Fl.gure VI-I), 51-nee some movers would normally have been nonrnovers:

(8) r

N (mover)

where p ~s the probab~hty that a Percent of Rent

m

«p - p ) ~s thus the ~ncrease ~n the probab~l~ty m c

household w~l1

1 of mov~ng).

move

vr.2 EMPIRICAL ESTIMATION OF EXPERIMENTAL EFFECTS

As the prevl.OUS sectl.on descr1bed, normal expendl.ture equatl.ons are estl.mated

2 us~ng Control households. The probab~l~ty of mov~ng equat~ons are obta~ned

from Mac~llan (1978). Table VI-l presents the est~ated exper~ental effect.

The estl.mates of l.ncrease 1n rent above normal conform to expectations,

shawl-ug an l.nCrease wl.th the percentage rebate, both overall and for movers

(assunung el.ther no or some J.nduced mobl.ll.ty). For nonmovers there J.8 no

exper~mental effect at all--apparently the rent rebate d~d not ~nduce any

additl.onal housl.ng expendl.ture by nonmovers.

The d~fference between actual and pred~cted In(rent) can be regressed on the

exper~mental var~able In(l-a) to approx~ate the log-l~near response funct~on

est~mated ~n Chapter 4. As ~n Chapter 4, the coeff~c~ent of the var~able

3 In (I-a) ~s ~nterpreted as a pr~ce elast~c~ty. Table VI-2 presents the

rent are, for movers,

- Pln(Yt_l~ + pln(Rt _l )

predictl.on equatl.ons for normal

In(Rt ) "1 - P"O + S~n(Yt)

1 (Pc/Pm) ~s the fract~on of movers that would normally have moved;

«p~-p~)/p~) ~s the fract~on that would normally have stayed. Results are

also presented below under the assumpt~on p~ = p~ (all mobil~ty ~s normal,

none 1.8 l.nduced).

2

These

and, for nonrnovers,

(u) y + 6ln(R 1) tThe coeff~c~ents est~ated from Control households are presented in Append~x

Table X-45. In these equat~ons ~-l and are rental expend~tures at

enrollment and two years after enrollment"respect~vely. S~~larly Yt - l and

Yt are household's current ~ncome at enrollment and two years after enrollment.

3

See Footnote 1 on second page of thlS appendlx.

A-53
Table VI-l

EXPERIMENTAL IMPACT OF RENT REBATES

(Med1an percentage Increase 1n Rent Above Normal)

DISCOUNT RATE

SAMPLE

HOUSEHOLD GROUP 20% 30% 40% 50% 60'1< SIZE

PITTSBURGH

Overall -1.0 2.3 4.6 4.6 11.2* (382)

(3.0) (2.7) (2.4) (2.5) (5.0)

Movers

No ~nduced -3.3 3.9 8.3 8.2 17.8 (144)

mob~l~ty assumed (7.7) (5.8) (5.2) (6.0) (11.6)

Induced -2.9 4.4 . 8.7 9.1 19.9 (144)

mob~l~ty assumed (7.7) (5.8) (5.2) (6.0) (11. 9)

Nonmovers 0.3 -0.9 1.9 2.4 2.1 (248)

(1. 9) (1.8) (1. 7) (1.6) (3.2)

PHOENIX

Overall 7.6* 6.2* 5.8 9.6** 16.2** (275)

(4.0) (3.0) (3.4) (3.1) (6.4)

Movers

No lnduced 10.5 15.5** 16.1** 13.9** 17.9** (165)

mob~l~ty assumed (5.7) (4.7) (5.2) (4.1) (7.6)

Induced 11.5* 16.2** 17.0** 14.8** 20.1** (165)

mob~l~ty assumed (5.6) (4.6) (5.2) (4.1) (7.6)

Nonrnovers 1.0 2.1 -0.4 -0.6 2.1 (115)

(3.3) (2.3) (2.7) (2.9) (6.5)

SAMPLE: Percent of Rent households actlve at two years after enrollment, excludlng those wlth enrollment lucornes over the ellgibl11ty l~ltS and

those I1vlng 1n thelr own homes or 1n Subsldlzed houslng.

DATA SOURCES: In~tial and monthly Household Report Forms, and payments

f~le.

NOTE: Standard errors 1n parentheses.

* t-stat~stic s~gn~f~cant.at the 0.05 level.

** t-statlstlc slgnlflcant at the 0.01 level.

A-54
Table VI-2

PRICE ELASTICITY ESTIMATES

FROM NORMAL EXPENDITURES

HOUSEHOLD GROUP PITTSBURGH PHOENIX

Movers

No lnduced -0.134** -0.230**

moblllty assumed (0.049) (0.035)

Induced -0.146** -0.245**

moblllty assumed (0.049) (0.035)

SAMPLE SIZE (144) (165)

SAMPLE: Percent of Rent movers actlve at two years after enrollment, excludlng those wlth enrollment lucornes over the ellg1billty limltS

and those I1vlng In thelr own homes or In SUbsldlzed houslng.

DATA SOURCES: Inltlal and monthly Household Report Forms, and

payments flle.

NOTE: Standard error In parentheses.

** t-statistic significant at the 0.01 level.

A-55
result~ng pr~ce elast~c~ty est~mates for mover households. The est~ates

are s1m~1ar to (and not s~gn~f~cant1y d~fferent1y from) those presented ~n

1 Chapter 4.

1These were -0.211 ~n p~ttsburgh and -0.219 ~n Phoen~x.

A-56
------------------------------- -

REFERENCES 

MacM1.11an, Jean, Mobihty in the Housing Allowance Demand Exper~ment, Cambr~dge, Mass., Abt Assoc~ates Inc., June 1978 (rev~sed June 1980). 

Zellner, Arnold, "An Efficient Method of Estimahng See=ngly Unrelated 

Regress~ons and Tests for Aggregation BJ.as, n Journal of the 

Amer~can Statistical Assoc~at~on, vol. 57, 1962, pp. 348-367. 

A-57 
APPENDIX VII

A DISEQUILIBRIUM MODEL OF MOBILITY

ThlS appendlx focuses on the ~pllcatlons of household dlsequl11brium 10

houSJ.ng consumptlon for adJustments 10 hOUSlng consumptlon Vla resldentlal

mob~l~ty. Three factors prompted th~s analys~s--a concern about the problem

of select~ng movers, the possibility of shedd~ng some light on the effects

of experImental duratlon, and an lnterest 10 testing some further 1mpllCat~ons of the consumer demand theory presented ~n Chapter 3. The analys~s

is adm~ttedly preliminary and as such ~s only suggestive of further analys~s

tasks. It presmnes baslc knowledge of the rnJ.croeconomlCS of household

behavlor and J.5 of J.nterest to those concerned wlth applled mlcroeconomics.

The eXlstence and persJ.stence of household dJ.sequllibrJ.um requJ.res expllclt

recognJ.tJ.on of the reasons for dlsequJ.librlum and the sources of frlctJ.on J.n

the market for hous~ng. Sect~on VII.l presents a s~ple model of adJustment

(res~dent~al mOb~lity) when there are no transact~ons (mov~ng) costs.

Sect~on VII.2 presents emp~rical results of est~at~ng such a model w~th

sJ.gniflcant transactJ.ons costs, uSJ.ng the empirlcal demand functlons estJ.­

mated ~n th~s report.

VII.l THEORETICAL DEVELOPMENT OF A MOBILITY MODELl

ConsJ.der the conventional resldentlal locat~on models wh~ch der~ve the equ~l~br~um pattern of location and consumpt~on of hous~ng serv~ces ~n a metropol~tan

area (see Alonso, 1964 or Muth, 1969). The results der~ved from such models

are lIequil~br~umll 1n the sense that under unchanged cond~tJ.ons, households

have no lncentive to adjust the1r location or houslng consumptlon.

In the absence of transact~on costs a household would be expected to adJust

J.ts hous1ng consumpt10n J.n response to changes J.n varJ.ables affectJ.ng the

equ~l~rium consumpt~on of hous~ng. Thus, changes ~n the relat~ve pr~ce of

hous~ng, a householdls J.ncome, or compos~tJ.on would be expected to result J.n

changes J.n housJ.ng consumpt~on, and usually J.n moving.

1

The model and dJ.Scusslon presented ~n th~s sectJ.on draws on Qu~gley

and We~nberg (1977).

A-59
Such adJustments are 1mplaus1ble 1n the real world because the costs of

mOv1ng are substantlal. These costs lnclude not only the cost of searchlng

for and moving to a new res~dence but also loss of any long-term tenancy

discount that m~ght exist at the old res~dence. The ex~stence of substantial

transact10ns costs (lnclud1ng both monetary and more general psychic costs),

immediately suggests that, having chosen an equil~brium pos~t~on, households

w~ll drift out of equ~l~brium as small changes render the~r choice of hous~ng

nonopt1ffial for their part1cular household characterlst1cs. Such drlfts wl11

result 1n ut111ty losses.

In pr1nclple, the utl11ty ga1n foregone by a household in not moving to its

equ1libr1um may be measured by uS1ng the concept of the compensating 1ncome

var1atlon--the max1mum amount of money households could spend on mov1ng costs

glven the preva1l1ng prlces and lncome and stll1 be as well off after the

1

move as they were beforehand. If the "lucome compensat10n" lS larger than

the actual costs assoclated wlth movlng, the household should, 1n theory,

prefer to move.

Household behav10r can be formallzed uS1ng the same model of utll1ty maXlmlzatlon lntroduced In Chapter 3, and the lncome compensatl0n of any dlsequ1l1brlurn can be computed uSlng the parameter est1mates obtalned from the demand

functlons dlscussed In Chapter 4. A household 1n any period lS assumed to

maxlmlze ltS utlilty, U(H,Z), where H represents houslng serVlces and Z

represents other goods, subJect to a budget constralnt. ThlS maX1ffilzatlon

lmplles an equlllbrlurn demand functlon for houslng

(1)

where

PH the relatlve prlce of houslng, and

Y = household lncome.

In the absence of transactl0ns costs, the lncome compensatlon 15 5lmply the

addltional lncome, IC, that 1£ subtracted from a household's own lncome, would

make such a household as well off w1th 1tS current nonoptlmal houSlng (consumlng HO wlthout movlng) as It would be lf lt were to consume the optlmal

1

A slmllar concept lS the equlvalent lncame varlatlon--the amount of

money requ~red to supplement the quant~ty of other goods wh~ch would make the

household as well off as lts current locatlon as 1t would be 1£ It were to

consume lts preferred qu?ntlty of houslng serVlces.

A-60
amount Hi after a mOve. The value of IC LS obtaLned by solving EquatLon (2):

(2)

where

R* = 1 rental expend~tures for

of houslng serVlces Hithe desLred amount

1 The derLvatLon of IC LS Lllustrated Ln FLgure VII-I. The household LS

assumed to be Ln equLILbrLum in perLod to wLth Lncome YO and UtLILty UO.

For 111ustratlon, 10 perlod t 1 the householdls income lncreases from YO to

Y

l • If no adJustment LS made, the household utLILty wLll now be Ul • If the

opt~al posltlon (Hi> 18 chosen, however, the maXlmum moving costs allowlng

the household to have utLILty Ul LS the value of IC for WhLCh the associated

utLlity functLon [U(YI-IC, PH)] has a maXLrnum equal to Ul •

The household wLll move Lf movLng costs for that household (M) are less than

IC--ln other words, 1£ the net galn from movlng 18 posltlve. For a partlcular

household, rnovLng wLll not be perfectly correlated wLth the sign (plus or

mLnus) of dLfference (IC - M), however. UncertaLnty about the future,

~perfect lnformatl0n and the dlstrlbutlon of tastes across households wlll

destroy any exact relatLonshLp. It should stLll be true, though, that the

probabLlLty of movLng LS posLtLvely related to the benefits to be gaLned and

lnversely related to the costs.

For a well-deflned utll1ty functlon, the exact (Hlckslan) measure of the compensatLng Lncome of any dLsequLILbrLurn can be derLved dLrectly (from Equation

(2». Take, for example, the Stone-Geary form already dLscussed Ln Chapter 3.

(3) U(H,Z) = (H-e l)b(z-e2)1-b

The compensatlng varlatlon, I~, that would make the household as well off

consumlng ltS lnltlal houslng, HO' paYlng rent, RO' as It would be 1£ It

were to consume ~ts opt~mal hous~ng, H*, at rent R*, given exogenous ~ncome

YO' LS obtaLned from solvLng EquatLon (4):

(4)

1

Each ut~l~ty curve reaches a max~mum because for any given ~ncome

and prices, there ~s a comb~nat~on of hous~ng and nonhousing goods that

maXLmLze utilLty wLthLn the feasLble bUdget set.

A-61
UtIlity

lUI

U\

Figure VII·'

COMPENSATING INCOME VARIATION

Ho 100tiai housing consumption

Hi the opt,mal (maximum utility) level of housmg consumption under Prices, PH, and

mcome, (Y1 - Ie)

Yo initial Income level

y 1 current Income level

PH the Price of housmg

Ie compensating Income vanatlon needed to make the household as well off after the move

as before he, ach,eve utility level U1)

A-62

Housing

(H)
Rearrang~ng terms and express~ng everyth~ng ~n terms of rental expenditures

g~ves

(5)

[ y -R*-6 ] o 0 2

Alternatively, ~f the household demand funct~on (but not the ut~l~ty funct~on)

~s known, say PH = D(H), the Marshall~an compensation, a close approx~at~on

to the exact Hickslan compensat2on, can be computed.! It is slmply the

dlfference 10 consumer surplus between enJoYlng the equl11brlum level of houslUg serVlces, H* (and spendlng R* on rent), and the

sum~ng HO housing serv~ces (and spend~ng RO on rent

ThlS dlfference 10 consumer surplus is defined as

lnltlal posltlon of con2

at the preva~l~ng pr~ces).

=

(6) IC =K/H~(H)dH) - R~ H*

f (D(H)dH) + (RO-R*).

HO

For example, 1£ the demand curve for houslng servlces is log-llnear as 10

Equat~on (7): ,

(7) In(H) = In(K) + a In(Y) + b In (PH) ,

subst~tut~on ~nto Equat~on (6) y~elds

(8) [ IC

H* l/b J

LL = f (Ha ) dH

HO kY

1

W~ll~g (1976) demonstrated that ~n many pract~cal situat~ons the

Marshaillan and Hlckslan measures of lucome compensatl0n are numerically

very close. The dlstlnctlon 18 that the Hlckslan measure uses a compensated demand curve while the Marshaillan measure uses an uncompensated

one. For the data used 10 thlS seetlon, the apprOXLmatlon error ~s under

2 percent.

2

Consumer surplus results from the fact that ~nd~v~dual demand curves

are downward slop~ng. Because there ~s typ~cally one pr~ce at WhlCh the household buys all lts demand, lt ~s In fact spendlng less on each lnframarglnal

unlt that It would be wllling to. Consumer surplus measures thlS dlfference

for each unlt.

A-63
1

In terms of rent, th~s can be wr1tten as

(9)

Any pre-exper~enta1 hous~ng d~sequ~l~br~um would be expected to alter the

effects of rent rebates, WhlCh change the effectlve relative pr1ce of houslng

faced by reClp1ents. Ignor1ng movJ..ng costs for the sake of exposJ..tlon, In

the case of 1n1t1al underconsumptJ..on, actual hous1ng HO 15 less than the

deslred amount H

O(see Flgure VII-2a). S1ID11arly, In the case of lnltial

overconsumpt10n, H

o

15 larger than HO(see FJ..gure VII-2b). The householdls

ut~l~ty ga~n of mov~ng ~s (UO- UO)' W~th the ~ntroduct~on of the pr~ce

d1SCOunt, the utl11ty level of consumlng He lncreases to U

e

and the ut111ty

of consum~ng the des~red level of housing (H*) becomes U*.2 The ut~l~ty e e

ga1n from movlng (u* - U ), may be decomposed lnto three parts: e e

(10)

1The results of the ~ntegrat~on of Equat~on (8) are

Mu1t~p1y~ng

(b+1) /b (b+1) /bJ

H* -Ho

(n) ICLL (~:apHb+1)1/b (b~l) [(PHH*) (b+1)/b

- (PHHO}b+1)/b] - R* + R

O

Reca11~ng that R* = kyapHb+1, Equat~on (~~) can be wi~tten as

Equat~on (9).

2Note that those overconsumlng relatJ..ve to the1r ln1tJ..al equl1ibrlum

could already be consum1ng H* and have no 1ncent1ve to adJust the1r hous1ng e (u* = U). H* w11l always be greater than HO

* because houS1ng 18 a normal

e e e good.

A-54
Utility

(UI

Figure VII-2

INITIAL AND INDUCED DISEQUILIBRIUM FOR PERCENT OF RENT

HOUSEHOLDS (NO MOVING COSTS)

Utility

(UI

U;

Ue

•Ue

Ue

-----~--

(a) Underconsumptlon

H~ Ho H;

(bl OverconsumptIon

Housing

(H)

-z..- U(y, PH (l-a))

Housing

(H)

Ho actual pre-experimental housing consumption

H~ optimal pre-experimental housmg consumption

H; optImal housing consumptIon given the percentage rebate, a

y 1 current Income level

PH the Price of houSing

a the rebate level

A-55
The term (U~ - UO) represents the exper~entally ~nduced change ~n equillbr~um ut~l~ty levels; the term (UO- Uo) represents the pre-exper~ental

d~sequ~libr~um; and the term (Ue - Uo) represents the household's actual

ut~l~ty ga~n at ~ts ~nit~al pos~t~on. Th~s decompos~t~on of the ut~l~ty

gq~n ~nto its components may be relevant because of the l~~ted durat~on of

the experiment. The household m~ght respond differently to an exper~entally

~nduced d~sequil~br~um than to a nonexperimental d~sequ~llbr~um. The compensat~ry income var1atlons of these separate components of utl11ty

computed, allowlng hypotheses about thelr separate effects to be

galn can be

I tested.

VII.2 EMPIRICAL ANALYSIS OF MOBILITY

Theoretlcal development of the beneflt measures was presented 1n the prevlous

sectl0n. Speclflcatlon of the cost measures 15 less compllcated. Costs of

rnovlng should lucinde not

that must be borne by the

only the out-of-pocket

2 household.

costs but also any losses

I

For the log-llnear demand functlon, these varlatlons are, from

Equation (7),

(a) ~) rR* - b+l L: 0

(b+l)/b

(b)

(c)

b H*

= (b~l) ICLL = J e~(H)dHJ- (l-a)R* - R* H* e 0 0

[ (b+l)/b -b(l/b)

RaJ - R* R* (I-a) R* + R*

e 0 e 0

c = JHO~(H)~_ (I-a) RO + RO ICLL = aRO'

H

O

Siml1arly, Equatlon (5) can be used to derlve the lucome compensatlons for

the Stone-Geary utll~ty funct~on.

2

Not all movlng costs can be measured, however. Such costs luclude

psyahle costs due to such factors as ne1ghborhood social attachment.

A-66
Out-of-pocket costs of mov1ng possess1ons 1S the cost most closely assoc1ated

with moving. S1nce the household makes 1tS dec1S10n pr10r to actually exper1­

encing the costs, 1t 1S the expected moving costs that matter. Actual mov1ng

costs for movers were taken from the Second and Th1rd Per10d1c Interv1ews

(g~ven at one year and two years after enrollment, respect~vely). Household

demograph1c character1st1cs for movers were used as

a regress10n equat10n to pred1ct prospective mov1ng

~ndependent

1

costs.

varlables 1n

The second type of movlng costs used here 1S search costs. Once aga1u th1s 1S

a prospect1ve measure. Reported t~e spent f1nd1ng the household enrollment

dwell~ng (on the Baseline Interv~ew) was regressed on the same household

characteristics as was out-of-pocket mov1ng costs and the resultant equat10n

2 used to pred~ct expected search t~e.

F~nally, a var~able used to approx~ate the loss of monthly rent d~scount

attr~butable to long-term occupancy (a max~mum of about $15 ~n Pittsburgh

and $22 10 Phoen1x) was obta10ed from an hedon1c regresslon of rental expend1­

tures on hous1ng components and household character1stics (see Merr11l, 1977).

The est~mates of out-of-pocket

The estLmat1ng regress10ns had

costs and search t~e

2

very low R and small

are adm~ttedly ad hoc.

3 theoretlcal rat10nale.

Nor do these costs, even 1f pred1cted accurately, pretend to capture all or

1

The mean out-of-pocket movlng costs reported by movers answer1ng the

quest~on on the Second Per~od~c Interv~ew was $54.06 ~n P~ttsburgh and $12.59

1n Phoen1X. The costs are low 1n phoen1x because 85 percent moved the1r

belong1ngs uS1ng the1r own or a borrowed veh1cle or no veh1cle at all (the

correspond~ng f~gure in P~ttsburgh was 35 percent). In order to get a monthly

cost, the expected mov1ng cost should be amort1zed over the householdls

expected tenure 1n the new un1t. Inclus10n of expected mov1ng costs as

predlcted from the regress10n equat10n as a separate term w1ll allow the

sample 1tself to determ1ne slmultaneously the amort1zat1on rate and 1tS

effect on mob~l~ty.

2The mean search time reported on the Baseline Intervlew was 95

days ~n P~ttsburgh and 33 days ~n Phoen~x. When ~ncluded ~n the mob~l~ty

equation, this measure's coeff1clent could implic1tly measure the (amortized)

pr1ce of search t1me.

3In addit~on wh~le search t~me data was taken from the Basel~ne Interv.l.ew, data on out-of-pocket mov1ng costs was collected from Per10d.l.c

Interviews of households that moved dur~ng the exper~ent. Thus to the

extent that movers tend to be households with lower than average costs,

this method will underest~ate the potent~al out-of-pocket mov~ng costs

of a randomly selected household.

A-67
even most of the costs of search and movlng. They are only 1ntended to

provlde a beg1nn~ng ~nd1cat~on of the role of moving costs.

Pract~cal reasons prohLb~ted the use of the Stone-Geary ~ncome compensat~on

1 as a measure of benef~ts. Rather than apprOX1matlng the Stone-Geary form

2 w~th a Cobb-Douglas form, the Marshallian ~ncome compensat~ons der~ved for

the log-linear case are used instead.

As suggested ~n Sect~on VII.l, two specif~cat~ons of benef~t measures were

used: Model I--a measure partltl0nlng the household1s d1sequllibr1um 1nto

an ln1tlal d1sequl11br2Uffi (that 15, pre-experlmental disequll1brlum) and

an experlmentally lnduced dlsequl11brlUffi (the latter 1S zero for Control

households); and Model II--an overall measure. Households may dlscount the

exper1ffiental dlsequllibr1Uffi, so the lnltlal and lnduced equlllbrlUffi may have

d1fferent ~pacts on mob111ty. The hypothes1s of equal ~pacts w111 be

3 tested.

The medlan, mean, standard devlat1on, and range for each of the measures of

4 costs and beneflts are presented 1n Tables VII-I and VII-2, respectlvely.

The most surpr1s1ng element of the tables 1S the remarkably small magn1tude

of the potent1al benef1ts from mov1ng compared to the potent1al costs. Wh1le

out-of-pocket costs and search tLme spent are one-tlme expendltures that can

be amortlzed over the expected tenure at the new unlt, the tenure dlscount

1S a monthly cost. Espec1ally notable 1S the neg11g1ble d1sequ111br1urn

lIn the formula [Equation (5)], the d1fference between rent and

PHSI 15 ralsed to a fractl0nal power. When a household's equlllbr1Uffi or

actual rent lS less than PHSl' thlS number 1S 1maglnary and the compensatlng

lncome varlatl0n 1S undef1ned.

2

The Cobb-Douglas form constra1ns 81 = 82 = O. Th1S 1mp11es a un1tary

lucome elastlc1ty, WhlCh, as shown 10 Chapter 4, 1S lnapproprlate for houSlng.

3

The 1n1t1al pos1t1on (1973) 1S character1zed 1n terms of 1975 dollars

by 1nflat1ng 1n1t1al rent by 15 percent 1n P1ttsburgh and 10 percent 1n

Phoen1x 1n order to permlt dlrect comparlson wlth equ111brlU1U expendlture

est1rnates 1n 1975 dollars. These numbers are based on the f1nd1llgs of

Merr1l1 (1977). The results were not senS1t1ve to changes 1n the 1nflat1on

rate. Equll1brlUffi rent 1S pred1cted using a serlal correlatlon model of

expend1ture (see Append1x VI).

4

The max1murn 1S m1sleading--only 2 of 701 households 1n P1ttsburgh and

6 of 563 1n phoen1x had 1ncome equ1valents worth more than $300. Each of these

households was spendlng less than half of ltS equ1l1brlUffi houslng expendlture.

A-68
--------------------------

Table VII-l

CHARACTERISTICS OF COST MEASURES

USED IN ANALYSIS OF MOBILITY

STANDARD

MEASURE MEDIAN MEAN DEVIATION MINIMUM MAXIMUM

PITTSBURGH

Expected out-of-pocket

movJ.ng cost 58.70 61.05 15.82 0.0 137.98

Expected search tlffie •

(days) 60.76 59.97 16.37 0.0 105.33

Current tenure dJ.scount 5.12 6.25 5.59 0.0 15.04

SAMPLE SIZE (701)

PHOENIX

Expected out-of-pocket

mov~ng cost

Expected search t1me

(day)

Current tenure dlscount

SAMPLE SIZE

16.84

36.14

4.02

16.38

36.32

7.05

4.97

17.87

7.54

(563)

0.0

0.0

0.0

38.72

87.63

22.72

SAMPLE: percent of Rent and Control households actlve at two years

after enrollment, excludlng those wJ.th enrollment lUCornes over the e11g1­

bl11ty 11mltS and those 11vlng In thelr own homes or In Subsldized houSlng.

DATA SOURCES: In~t~al and monthly Household Report Forms, Basel1ne

amd Perl0dlc Intervlews.

A-69
Table VII-2

CHARACTERISTICS OF BENEFIT MEASURES

USED IN ANALYSIS OF MOBILITY

PITTSBURGH

In~t~al D~sequ~l~r~um

STANDARD

DEVIATION MINIMUM MAXIMUM

Percent of Rent households

Percentage

rebate

200

300

400

SO,

60.

Control households

Induced D~sequ~l~br~um

Percent of Rent households

Percentage

rebate

20'

30>

40.

50\

60'

Contrcl households

Overall D~sequ11~r~um

percent of Rent households

percentage

rebate

20'

30>

40.

SO>

60.

control households

Sample S1.ze

Percent of Rent households

percentage

rebate·

20'

30'

400

SO.

60.

control" households

16.12 28 96 36.85 0.00 276.96

15.36 24 94 28.18 0.02 140 83

15 76 30 24 40.02 0.01 233.64

16.97 33.25 46.17 0.02 276.96

15.06 26.49 29.32 0.06 172.32

17.16 26.56 27 15 a 00 93 44

17 82 34.38 47.49 0.00 421.10

4.33 3 60 11.27 -50 76 31.98

2.48 1.96 5.04 -13.17 10.74

3.75 2.40 8 70 -31.09 19 29

4.30 271 12 74 -50.76 30 30

8.13 3.80 12.92 -31.60 28.56

5 25 6.12 14.24 -24.59 31.98

a 00 0.00 0.00- 0.00 0.00

22.33 32.56 36.52 a 69 307.26

20.45 26 90 27 44 0.69 152.57

18.04 32.65 39 84 1 54 249.94

23.43 35.96 45.74 2.61 307.26

22.45 32.29 28.86 3.52 198.92

24 02 32 67 28.65 5.19 116.45

17.82 34.38 47.49 0.00 421.10

(398)

(63)

(88)

(Ill)

(108)

(28)

(303)

SAMPLE: Percent of Rent and Control households actl.ve at two years after enrol1me"lt, exclud~ng

those w~th enrollment 1.ncomes over the el~g~l.ll.ty 11.m~ts and those l~v~g ~n thel.r own homes or 1.n

subs~dl.zed housl.ng.

DATA SOURCES· In1.tl.al and monthly Household Report Forms, payments f1.1e, Th~rd per1.od~c Intervl.ew.

a. Income equl.valent of ll.sted measure

A-70
Table VII-2 (contmued)

CHARACTERISTICS OF BENEFIT ~URES

USED IN ANAL~SIS OF MOBILITY

PHOENIX

a STANDARD

MEASURE MEDIAN MEAN DEVIATION MINIMUM MAXIMUM

InJ.tJ.al DJ.sequJ.lJ.brJ.UIn

Percent of Rent households 17 92 33.48 63 46 0.00 802 99

Percentage

rebate

20% 17.60 34 68 50.30 021 317.19

30t 16.96 27.82 37.26 0.00 197 55

40% 17 .14 29.49 52.62 0.00 399.63

50% 20 62 29.70 31.48 0.00 167 14

60' 20.87 79 55 179 47 0.02 802 99

Control households 19.11 37.81 57.60 o 02 565.46

Induced DJ.sequJ.lJ.brJ.UIn

Percent of Rent households 6.16 6.18 11.35 -27.03 65 67

Percentage

rebate:

20t 3.43 1 99 4.95 -9 90 8.77

30t 6 21 4 64 7 39 -25.93 16.99

40% 9.78 8.10 9.65 -18.12 35.62

50' 872 6.05 13.68 -27 03 39.23

60' 12.74 16.05 20.20 -20.02 65.67

Control households 0.00 0.00 0.00 0.00 0.00

Overall DJ.sequJ.IJ.brJ.UIn

percent of Rent households 25 23 39.67 67.93 l.18 868 66

Percentage

rebate

20t 22.42 36.66 51.03 1.71 325.95

30% 21.42 32.46 37.74 1.18 212.56

40t 23 73 37.60 56.70 2 90 435.25

SOt 29 31 35.75 32.10 4.24 206.37

60' 29.72 95.60 194.30 6.22 868 66

Control households 19.11 37.81 57.60 0.02 565 46

Sample SJ.ze

percent of Rent (291)

Percentage

rebate

20t (45)

30t (83)

40t (63)

SOt (79)

60\ (21)

Control households (272)

SAMPLE Percent of Rent and Control households actJ.ve at two years after enrollment, excludJ.ng

those wJ.th enrollment Lncomes over the elJ.gJ.bJ.lJ.ty IJ.mLts and those l~vJ.ng J.n theLr own homes or J.n

subsJ.dJ.zed nousJ.ng.

DATA SOURCES InJ.tLal and monthly Household Report Forms, payments fJ.le, ThJ.rd PerJ.odJ.c IntervJ.ew.

a. Income equJ.valent of IJ.sted measure.

A-71
1 ~nduced by the rent rebates. Apparently, households would be about as well

off adJusting to the~r ~n~t~al equ~l~br~um (HO) and accept~ng the percentage

of rent associated w~th that un~t as they would be ~f they adJusted all the

way to the~r experLmental posltl0n

movlng (such as pSychlc costs) are

{H*}. In addltl0n, unmeasured costs of

e

l~kely to ~nh~b~t moving as well.

The modest Slze of the beneflts to be galned from movlng thus suggests that

households are unllkely to respond 10 a slgnlflcant way, though one would

stlll expect a posltlve relatl0nshlp between movlng and the lucame equlvalents. Table VII-3 presents the results of est~at~ng th~s benef~t/cost

model of mobl11ty uSlng lOglt analysls. The overvall explanatory power of

th15 model 15 lower than a model based solely on soclo1og1cal-demographlc

determlnants (see MacMl11an, 1978). The cost measures perfor:m well at both

sltes--slgnlflcantvarlables have the expected (negative) s~gn. The most

~mportant cost var~able ~s the tenure d~scount. Increas~ng th~s tenure

d~scount by $1 a month w~ll decrease the probabil~ty of mov~ng by about 2.6

2

percentage po~nts ~n p~ttsburgh and 2.1 percentage po~nts ~n Phoen~x.

The benef~t measures add s~gn~f~cantly to the explanatory power of the equat~on only ~n P~ttsburgh. All the coeff~c~ents have the expected (pos~t~ve)

s~gn at both s~tes. The magn1tude of these effects are small, wlth the

effect of an exper~mentally 1nduced d1sequ~11brlum larger than that of an

already eX1stlng one. An lncrease of $10 In the lnduced dlsequ111br~um w111

have an effect on mob~l~ty of 3.7 percentage po~nts ~n P~ttsburgh (1.2 ~n

Phoen~x) but the pre-ex~stlng d~sequ~llbrlum has an effect of ~ncreaslng the

probabl1l1ty of mov~ng by only 1. 0 po~nt ~n P~ttsburgh (and 0.1 po~nt ~n

phoen1x). Glven the small average s~ze of the lnduced dlsequl1~br1um,

nelther effect 15 very ~mportant.

G~ven the mean value of the lnduced dlsequll~r~um for Percent of Rent

households shown In Table VII-3, the estlmated mean effect of the Percent

of Rent offers lS very small ~ndeed--about 1 percentage pOlnt ln each slte

and s~gn~f~cant only ~n P~ttsburgh. MacM~llan (1978) us~ng a d~rect log~t

1

The lnduced equ~llbrlum does tend to be larger for households w~th

larger dlSCOuntS (hlgher Ilalf level). Of course, for a glven household 1n

equ~llbrlum, a larger dlscount would lead to a larger d1sequll1br~um.

2

These values are partlal derlvatlves evaluated at the mean of the

sample.

A-72
Table VII-3

DISEQUILIBRIUM LOGIT MODEL OF TWO-YEAR MOBILITY

PIT!'SBURGH PHOENIX

INDEPENDENT VARIABLES MODEL I MODEL II MODEL I MODEL II

Constant 0.2821 0.2844 1.0983 1.1123

(0 62) (0 63) (3 12) ** (3 06) **

Cost Measures

Expected out-af-pocket mov~ng costs -0.0091 -0.0089 0.0140 0.0140

(1.80lt (1. 77) t (0 85) (0 83)

Expected search t~e 0.0030 a 0029 -0.0133 -0.0135

(0.57) (0.56) (2.77) ** (2.81) **

Current tenure d~scount -0.1146 -0.1125 -0.0859 -0.0856

(8.11)"'* (8.02)** (7.67)** (7.50) **

Benef~t Measuresa

In~t~al d~sequ11ibr1um 0.0041 0.00044

(2.14)* (0.29)

Exper~entally Lnduced d1sequ11ibr1um 0.0162 0.0051

(1. 77)t (O~56)

Overall d1sequ11ibr1um 0.0043 0.00053

(2.25)* (0.36)

Ch1-square of benef1t b 6.48c 4.88d a 32C O.12d measures

(sJ.gm.fJ.cance) (0.05) (0.05) (Not sJ.gm.- (Not sJ.gnJ.-

hcant) fJ.cant)

ProportJ.on mov~ng 0.359 0 563

Coeff~c~ent of determ~nat~on (02 ) 0.072 0.070 o 092 0.092

Sample s~ze (701) (563)

SAMPLE. Percent of Rent and Control households act~ve at two years after enrollment I excludlllg

those w~th enrollment 1ncomes over the elJ.gLb~I~ty l~~ts and those l~vJ.ng ~n the~r own homes or 1n

subs1d~zed hous1ng

DATA SOURCES InJ.tJ.al and monthly Household Report Forms.

NOTE: ASymptot1C t-stat~st~c J.n parentheses below coeffJ.c1ent.

a. See text for measurement I'Iethod.

b. When only one benefJ.t measure 1S added, the chJ.-square stat1st1c g~ves the same s1gnJ.f~cance

level as the asymptotJ.c t-stat1st~c.

c. W~th two degrees of freedom.

d. W1th one degree of freedom.

t t-stat~st~c sJ.gn1f~cant at the 0.10 level

* t-stat~st~c sJ.gn~f1cant at the 0 05 level.

** t-stat1st1c sJ.gn~f1cant at the 0 01 level.

A-73
est~mate of mob~l~ty d~fferences between percent of Rent and Control households, w~th a var~ety of demograph~c covar~ates found s~gn~f~cant effects of

5 percentage po~nts ~n p~ttsburgh and 11 percentage po~nts ~n phoen~x (though

her analysls also lndlcated that attrltlon bias mlght account for 2 to 3

percentage pOlnts of the effect 1n each slte). These estimates are small,

1 but much larger than the 1 percentage po~nt effect est~ated here.

One ObVl0US pOSSlbl11ty 15 that the contlnuous dlsequl11brlum varlables do

not fully capture the difference between percent of Rent and Control households. Comparlsons of actual and predlcted rates for these groups are

presented ~n Table VII-4, us~ng the est~ates from Table VII-3. The pred~cted

values are close to the actual values and fluctuate around them for the different rebate levels, wlth no apparent pattern (and certalnly are not 51gnlflcantly

dlfferent from the actual values). Nevertheless, there 15 a Sllght underpredlctlon of Percent of Rent mobl11ty and Qverpredlctlon of Control mobl11ty

10 each slte. The net effect 15 an underpredlction of the actual difference

between the two groups of 3.3 percentage po~nts ~n p~ttsburgh and 7.6

percentage po~nts ~n Phoen~x (us~ng Model II), wh~ch ~s enough to account for

most of the d~fference from MacMl11an ' s flnd~ngs.

VII.3 SUMMARY

In th~s append~x, a cost-benef~t model of mob~l~ty was proposed and tested.

The maJor flnd1ng lS that cost measures, as d1s1ncent1ves,do better at

expla1n1ng mOblllty than do benef1t measures. This relterates a flndlng of

lotherwlse, MacMillan's results were conslstent w1th the results of

Table VII. She also found a negat~ve effect for length of tenure (though

It was slgn1f1cant only 1n Plttsburgh), even when pr10r moblilty was also

included 1n the lOglt. Like th1S model, MacMlllan 's model follows the bas1c

conceptual scheme of mob~l~ty as determ~ned by the benef~ts of hous~ng change

and the costs of search and mov1ng. Her analys1s does not lnvolve any pr10r

speciflcat10n or measure of dlsequ111brlum and is focused more on develop1ng

proxles for various costs, and barr1ers 1n the search process.

The f~nal model est~mated by MacM~llan reflects maJor variables found to

affect mobl11ty 1n prev10us studles and extenslve emplrical testlng of

alternatlve forms and varlable sets. Her overall coefficlent of determ1natlon

us~ng a 17 var~able model was about twice as h~gh as the 5 var~able model of

Table VII-3--0.165 ~n p~ttsburgh and 0.206 ~n phoen~x.

A-74
Table VII-4

PREDICTIVE POWER OF MOBILITY EQUATION

Percent of Rent households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

percent of Rent households

Percentage rebate:

20%

30%

40%

50%

60%

control households

OBSERVED AVERAGE PREDICTED

PROPORTION PROBABILITY OF MOVING SAMPLE

MOVING Model I Model II SIZE

PITTSBURGH

0.377 0.362 0.358 (398)

0.286 0.321 0.323 (63)

0.398 0.364 0.364 (88)

0.432 0.356 0.354 (111)

0.352 0.387 0.377 (108)

0.393 0.376 0.366 (28)

0.337 0.355 0.360 (303)

PHOENIX

0.612 0.580 0.576 (291)

0.578 0.570 0.570 (45)

0.530 0.562 0.560 (83)

0.587 0.582 0.577 (63)

0.696 0.609 0.606 (79)

0.762 0.557 0.546 (21)

0.511 0.545 0.548 (272)

NOTE: Percent of Rent and Control t-statlstlcs show that all observed

proportlons could have could from a normal distrlbutlon wlth mean p (the

average predlcted probablilty) and varlance p(l-p)/N, where N = sample SlZe.

a. Predlcted uSlng coefflclents reported ln Table VII-3.

A-75
Goodman (1976). In h1S more rud~entary model, Goodman quant1f1ed benef1ts

us~ng d~sequ111br1um measures der1ved from average group character1st1cs.

Nevertheless, the stat1stically s1gn1f1cant coeff1c~ents for the benefit

measures 1n P1ttsburgh do 1nd1cate that households are at least part1ally

mot1vated by econom1C cons1derat10ns when they conS1der mov1ng. G1ven the

prelkm1nary nature of the models, the results are encourag1ng for future

work.

A-76
REFERENCES

Alonso, W~ll~arn, Locatl0n and Land Use, Cambrldge, Mass., Harvard Unlverslty

Press, 1964.

Goodman, John L., Jr., "HouSJ.ng Consumptl0n Equl1J.brJ.UIn and Local ResJ.dentJ.al

Mobl.ll.ty," EnVl.rOIllnent and Housl.ng I vol. 8, 1976.

MacMillan, Jean, MobJ.lJ.ty J.n the Housing Allowance Demand Experiment, CambrJ.dge, Mass., Abt AssocJ.ates Inc., June 1978 (revised June 1980).

MerrJ.ll, Sally R., HedonJ.c IndJ.ces as a Ms!asure of Housing QualJ.ty, CambrJ.dge,

Mass., Abt AssoCJ.ates Inc., December 1977 (reVJ.sed June 1980).

Muth, Rlchard F., Cltles and HouSl.ng, Chlcago, Ill., Unl.versl.ty of Chlcago

Press, 1969.

QUl.gley f John M. and Danlel H. Welnberg I IIIntra-Urban Resl.dentl.al Mobl.ll.ty:

A Revl.ew and SynthesJ.s," InternatJ.onal Regl.onal SCl.ence RevJ..ew,

vol. 2, no. 1, Fall 1977, pp. 41-66.

WJ.lllg, Robert D., IIConsumers I Surplus WJ.thout Apology, 11 Amarl.can Econonl1C

Revlew, vol. 66, 1976.

A-77
APPENDIX VIII

THE EFFECT OF DEMOGRAPHIC VARIABLES ON THE

HOUSING EXPENDITURES OF THE OVERALL SAMPLE

Demograph~c Varlables as Covariates

Under the approach used ~n th~s report, demographic var~ables were ~ncluded

as dummy varlables 10 the demand equatl0n~ The varlables lncluded were those

1

lndlcatlng mlnorlty status and household composltlon. Models that luciude

Just a mlnorlty varlable, Just household composltlon varlables, and comblnations of the two are presented ~n Tables VIII-l and VIII-2.

At both s~tes the spec~f~cat~on that allows a separate ~ntercept for each of

the six groups created by interactlng minorlty status wlth household composJ.­

tion do=nates all others (as ~nfucated by the R2 statist~c adJusted for

degrees of freedom). For thlS speciflcatJ.on, 10 PJ.ttsburgh nonnu.norJ.ty households headed by only one adult and minority s~ngle-person households appear to

have lower hOllSJ.ng expenfutures than the reference group of nonnunorJ.ty households headed by a couple. In Phoenix, all categor~es of minonty households

and nonnu..norlty sJ.ngle-person households have lower expenditures than the

reference group.

StratJ.fJ.catJ.on

The covar~ate analys~s showed that each of the s~x demograph~c groups should

have a separate J.ntercept. The specJ.fJ.catJ.on dJ.scussed there assumes that

all the groups have the same pr~ce and ~ncome elast~c~t~es. Strat~f~cat~on

allows these to vary--separate equat~ons were estimated for each group (see

Tables VIII-3 and VIII-4). The hypothesis of homogene~ty of elast~c~t~es

when the ~ntercepts are d~fferent was tested us~ng a variance-rat~o test.

At both s~tes th~s test stat~st~c was small and less than ~ts cr~t~cal value.

ThUS, the hypothes~s that the ~ntercepts

are equal across the groups could not be

are d~fferent but the elast~c~t~es

2 reJected.

1

Other covar~ates (age, sex, and education of the head of household

and household s~ze) were exam~ned and reJected as 1ns1gn~flcant.

2

The value of the F-statist~c was 1.30 ~n P~ttsburgh and 1.01 ~n

Phoen~x, both ins~gnif~cant at the 0.05 level.

A-79
Table VIII-1

LOG-LINEAR DEMAND FUNCTIONS USING DEMOGRAPHIC VARIABLES

AS COVARIATES FOR THE OVERALL SAMPLE

(PI'l"'l'SBURGH)

INDEPENDENT VARIABLES

Constant

Income elast~c1ty

Pr1ce elast1c1ty

M1nor1ty householda

a S1Dgle-person household

S1ngle head of household W1th

othersa

NOnInJ,.nor1ty s1ngle-person

householda

NOIUlU.nOr1ty s1ngle head of

household W1 th ot.'lersa

M1nor1ty s1ngle-person householda

M1DOr1ty s1ng1e head of household w1th othersa

M1nor1ty household headed by

a couplea

R

2

AdJusted R2

SEE

Sample s1zeb

NO

COVARIATES

2.865**

(0.170)

0.328**

(0.028)

-0.178**

(0.038)

0.178

o 176

0.28

(669)

MINORITY

STATUS

2.895**

(0.169)

0.326**

(0.028)

-0.175**

(0.037)

-0.095**

(0.027)

0.193

0.189

0.28

(G69)

HOUSEHOLD

COMPOSITION

3.027**

(0.224)

0.300**

(0.036)

-0.174**

(0.038)

-0.053

(0.038)

0.032

(0.026)

0.187

0.182

0.28

(669)

ADDITIVE

EFFECTS

3.039**

(0 221)

o 301*

(0 035)

-0.171**

(0.037)

-0.110**

(0.028)

-0.051

(0.038)

0.050

(0.026)

0.206

0.200

0.28

(669)

COMPLETE

INTERACTION

3.030**

(0.222)

0.301**

(O.035f

-0.171**

(0.037)

-0.030

(0.039)

-0.058*

(0.029)

-0.228**

(0.070)

-0.056

CO 038)

-0.059

(0.049)

0.209

a 202

0.28

(669)

SAMPLE

w1th enrollment

hous1ng

percent of Rent and Control households act1ve at two years after enrollment, exclud1ng those

1ncomes over the el~g1b1l1ty 1~1ts and those l1v1ng the1r own homes or 1n subs1d1zed

DATA SOURCES In1t1al and monthly Household Report Forms, and payments f1le.

NOTE. Dependent var1able: In (Rent), Standard error 1n parentheses.

a. Denotes dummy var1able.

b. Sample sue d1ffers from prev10us tables due to add1t10nal select10n on demograph1c var1ables.

"" t-stat1st1c s1gn1f1cant at the 0.05 level.

"""" t-stat1st1c s1gn1f1cant at the 0.01 level.

SEE = Standard Error of Est~ate.

A-80
Table V'III-2

LOG-LINEAR DEMAND FUNCTIONS USING DEmGRAPHIC VARIABLES

AS COVARIATES FOR THE OVERALL SAMPLE

(PHOENIX)

INDEPENDENT VARIABLES

Constant

Income elast~c~ty

Pr~ce elast~c~ti

M~or~ty householda

S~nqle-person householda

S~ngle head of household w~th

othersa

NOIUllJ.nor~ ty s~ngle-person

householda

NOIUllJ.nor~ty s~nqle head of

household Wl.th othersa

M~nor~ty s~ngle-person householda

M~nor~ty sl.ngle head of household w~th othersa

Ml.nOrl.tyahousehold headed by

a couple

R2

AdJusted R2

SEE

sample sl.zeb

NO

COVARIATES

2.265**

(0.197)

0.441**

(0.033)

-0 235**

(0.050)

0.278

0.275

0.33

(521)

MINORITY

STATUS

2.466**

(0.195)

0317**

(0.032)

-0.248**

(0.048)

-0.166

(0.030)

o 319

0.315

o 32

(521)

HOUSEHOLD

COMPOSITION

2.210**

(0.234)

o 447**

(0.038)

-0 231**

(0.050)

-0.015

(0.045)

0.065*

(0.034)

0.285

0.279

0.33

(521)

ADDITIVE

EFFECTS

2.603**

(0.235)

0.394**

(0.037)

-0.245**

(0 048)

-0.190**

(0.031)

-0.086*

(0.045)

0.060t

(0.033)

0.335

0.329

0.32

(521)

COMPLETE

INTERACTION

2.530**

(0 235)

0.411**

(0.038)

-0.241**

(0.048)

-O.Ul*

(0.048)

-0.004

(0.041)

-0.267**

(0.091)

-0.099*

(0.048)

-0.268**

(0.042)

0.345

0.336

0.31

(521)

SAMPLE Percent of Rent and Control households actl.ve at two years after enrollment, excludl.ng those

wJ.th enrollment J.ncomes over the elJ.gl.bJ.l~ty 1lll1~ts and those IJ.Vlllg III theJ.r own homes or J.n subsJ.dJ.zed

housJ.ng.

DATA SOURCES InJ.tJ.al and monthly Household Report Forms, and payments fJ.le.

NOTE Dependent varJ.able: In(Rent), Standard error J.n parentheses. a. Denotes dummy varJ.able.

b. Sample sJ.ze dJ.ffers from prevJ.ous tables due to addJ.tJ.onal se1ectJ.on on demographJ.c varJ.ables.

t t-statJ.stJ.c sJ,gnJ.fJ,cant at the 0.10 level.

* t-statJ.stJ,c sJ.gnJ.fJ.cant at the 0.05 level.

** t-statl.stJ.c sJ.gnl.fJ.cant at the 0.01 level.

SEE = Standard Error of Est~ate.

A-81
Table VIII-3

STRATIFIeD LOG-LINEAR EXPENDITURE FUNCTIONS

FOR THE OVI:RALL SAMPLE

(PITTSBURGlI)

ALL HOUSI:nOLDS NONMINORITY HOUSEHOLDS MINORITY HOUSEHOLDS

Income Pr~ce Income Pr~ce Income Pr~ce

r:las- ElasR

2 Elas- ElasR2 Elas- ElasR2 INDEPENDENT VARIABLeS Constant t1c~ty t~c~ty SEE Constant bc~ty t~c~ty SEE Constant tiCl.ty tl.C~ty SEE

All households 2.865** 0.328** -0 178** o 28 o 178 2.893** 0.326** -0 171** 0.28 o 179 2.805** o 324** -0 197* 0.28 0.179

(0.170) (0 028) (0 038) (N=669) (0.189) (0.031) (0.041) (N"'536) (0.381) (0.063) (0 088) (N"'133)

S~ngle-person households 2 596** o 370** -0.161t 0.32 o 129 2.517** 0 388** -0 164t o 32 o 129 3 244** o 219 -0 186 0.25 0.133

(0 480) (0.086) (0 091) (N=133) (0.559) (0 100) (0.097) (N"'1l3) (0 867) (0 157) (0 220) (N=20)

Slongle heads of house- 4 009** o 141* -0.149* 0.28 0.0425 3.839** o 175** -0 153* o 27 0.063 4 183** o 103 -0 087 0.29 0.014

hold w~th others (0 346) (0 051) (0.059) (N::=:257) (0 390) (0.066) (0 066) (N=182) (0.726) (0.120) (0.127) (N=75)

Households headed by 2.345** 0 408** -0 221** 0.26 0.196 2.302** o 417** -0.199** o 27 o 183 2 579** 0.356** -0.357* 0.24 0.300

a couple (0.325) (0 052) 10.057) (N"'279) (0.369) (0.059) (0 062) (N=241) (0.666) (0.107) (0 135) (N=38)

ELDERLY

Income Prloce

Elas- ElasR2 INDEPENDENT VARIABLE Constant bcity tic~ty SGE

1111 households 2.795** o 327** -0 223* 0.33 0.115

(0.551) (0.099) (0.102) (N"'1l2)

SN1PLE P~ttsburgh Percent of Rent and Control households actLve at two years after enrollment, exclud~ng those w~th enrollment loncomes over

the el~g~b~l~ty l~mlots and those l~v~ng lon thelor own homes or ~n subs~dlozed hous~ng.

DATA SOURCES In~t~al and monthly Household Report Forms, and payments f~le

NOTE. standard error lon parentheqes

t t-stat~st~c s~gnl.£locant at the 0.10 l(>vel

* t-statistloc s~gn~f~cant at the 0.05 level.

** t-stat~st~c s~gn~flocant at the 0 01 level

SEE '" Standard Error of r:st~mate.
Table VIII-4

STRATIFIED LOa-LINEAR EXPENDITURE FUNCTIONS

FOR THE OVERALL SAMPLE

(PHOENIX)

ALL HOUSEHOLDS NONMINORITY HOUSEHOLDS MINORIT¥ HOUSEIIOLDS

Income PrJ.ce Income PrJ.ce Income Price

Elas- ElasE2 Elas- ElasE2 Elas- ElasINDEPENDENT VARIABLCS Constant tl.Cl.ty tl.Cl.ty SEE Constant tl.Cl.ty tl.city SEE Constant t~CJ.ty t~cJ.ty SEE E2

All households 2.265** o 441** -0.235* 0.33 0.278 2.138** 0470"* -0 263** 0.30 o 341 2 836** 0.327** -0 227* 0.36 0171

(0.197) (0.033) (0.050) (N=521) (0 228) (0.038) (0 057) (N=339) (0 350) (0.059) (0 088) (N"'182)

s~ngle-person households 1.752** o 529*'" -0.162 0.30 o 371 2.430*'" o 412** -0.172 0.29 o 253 o 283 o 775** -0.304 0.30 0.678

(0 407) (0 072) (0 117) (N=98) (0.475) (0 084) (0.122) (N=83) (0 858) (0.154) (0 343) (N=15)

Single heads of house- 2.461*"* o 417** -0.207 0.33 0.220 2.339** 0.440** -0.290** 0.29 0.270 3 223** o 278* -0 136 0.37 0.087

hold wJ.th others (0.361) (0 061) (0 076) (N=184) (0 473) (0.078) (0.092) (N",105) (0.837) (0.111) (0 126) (N=79)

Households headed by 2.340** o 424** -0 279** 0.34 o 202 2. 466*'" 0 419** -0.286** 0.30 0.247 2 720** 0.334** -0.313* o 33 a 166

a couple (0 390) (0 063) (0 079) (N",239) (0 419) (0 067) (0 090) (N=151) (0.710) (0 116) (0.127) (N=88)

ELDERLY SPANISH AMERICAN BLACK

Income Pr~ce Income Pr~ce Income Prl.ce

Elas- Elas- 2 Elas- ElasE2 Elas- ElasE· INDEPENDCNT VARIABLG Constant t~cJ.ty tl.C~ty SEC E Constant ticity tl.city SEE Constant bc~ty t~c~ty SEE

All households 1.962** 0 489** -0 163 o 31 a 247 2 702** 0.352** -O.l71t 0.35 a 178 3.477** 0.204 -0.459* 0.39 0.18

(0 553) (0 100) (0.135) (N=81) (0.403) (0.067) (0.097) (N=138) (0.774) (0.136) (0 204) (N=44)

SAMPLE Phoen~x Percent of Rent and control households act~ve at two years after enrollment, exclud~ng those w~th enrollment l.ncomes over the

el~gJ.bilJ.ty IJ.mJ.ts and those IJ.v~ng ~n theJ.r own homes or J.n sUbsJ.dJ.zed housl.ng.

DATA SOURCES InJ.tJ.al and monthly Household Report Forms, and payments file.

NOTE standard error J.n parentheses

t t-statJ.stJ.c s~gnJ.f~cant at the 0 10 level

* t-statJ.stic sl.gn~f~cant at the 0 05 level

** t-stat~stJ.c sJ.gn~f~cant at the 0.01 level

SEE = Standard Error of Est~mate.
APPENDIX IX

COMPARISON OF ELASTICITY ESTIMATES

FROM FIRST-YEAR DATA ANALYSIS AND THIS REPORT

Chapter 4 noted that the ~ncome and pr~ce elast~c~t~es estimated by Mayo ~n

the report on the first-year of data (Mayo, 1977) were different than the

results presented here. Some dlfferences are to be expected, as the samples

used were not ldentlcal--

• for the overall sample, Chapter 4 used the sample of households actlve at two years after enrollment excludlng those

that had rents less than $40 per month or ~ncomes less than

$1,000 per year, wh~le Mayo used the sample of households

active at one year after enrollment wlth no other exclUSlons;

• for the mover sample, Chapter 4 ~n addit~on selected households

movlng between enrollment and two years after enrollment, while

Mayo used only those households mov~ng dur~g the f~rst year

after enrollment.

Tables IX-l and IX-2 present the steps taken to reconc~le the two est~ates

for the overall and the movers samples, respectlvely. The flrst 11ne 10

each table represents the numbers reported ~n Chapter 4. Succeed~ng l~nes

f~rst add some low-rent households excluded from the analys~s of Chapter 4,

then change the lucame varlable from the three-year average lucerne used III

Chapter 4 to the two-year average ~ncome used ~n Mayo (1977), then change

the dependent var~able to rent at one year (and, ~n Table IX-2, the sample

to households that moved ~n the f~rst year), and then sh~fts from the sample

of households act~ve at the end of two years to the sample act~ve at the end

of one year. The f~nal l~ne g~ves the est~ates reported by Mayo.

Re-estlrnatlng Mayo's exact speclflcatlon uSlng the two-year data base stlll

leaves some dlfferences Sluce the two-year data base lncludes some lnformatlon on some households that was mlsslng from the one-year data base.

However, thlS dlfference is not maJor. Dlfferences In est~ates essentlally

reflect dlfferences In the est1mated response for movers and occur for two

reasons:

A-8S
1) Second-year movers In Plttsburgh had a hlgher response than

d1d f1rst-year movers, wh1!e the reverse was true 1n Phoen1x

(See Table 6-2), and

2) In Plttsburgh, households that dropped out of the sample

dur1ng the second year had somewhat lower than average

f1rst-year responses.

A-86
Table IX-1

COMPARISON OF ELASTICITY ESTIMATES' FINDINGS FROM FIRST-YEAR DATA

ANALYSIS VS. THIS REPORT (OVERALL SAMPLE)

PITTSBURGH PHOENIX

RENT INCOME INCOME PRICE SAMPLE INCOME PRICE SAMPLE

SAMPLE VARIABLE VARIABLE ELASTICITY r::LASTICITY SIZE ELJ\STICITY ELASTICITY SIZE

(1) A2,R,Y Two-Year Three-Year 0.333 -0.178 (674) 0.435 -0.234 1532)

Average (0.028) (0.038) (0.032) (0.049)

(2) A2,Y Two-Year Three-Year 0.360 -0.178 (684) 0.445 -0.246 (543)

Average 10.028) (0.039) (0.032) (0.049)

(3) A2,Y Two-Year Two-year 0.336 -0.176 (684) 0.423 -0.243 (543)

Average (0.029) (0.039) (0.032) (0.050)

(4) 1\2,Y One-Year Two-Year 0.345 -0.135 (696) 0.418 -0.237 (532)

Average (0.028) (0.037) (0.033) (0.053)

(5) Al,y one-Year Two-Year 0.354 -0.126 (781) 0.422 -0.217 1675)

:r- Average (0.026) (0.035) (0.030) 10.047)

I

00 (6) Al a (764) 0.400 -0.234 (657) ..., One-Year Two-Year 0.338 -0.109

Average (0.026) (0.036) (0.029) (0.048)

SAMPL~S: Al - Percent of Rent and Control households active at one year after enrollment, exclud1ng

those w1th enrollment incomes over the elig1b1lity l1mits and those liv1ng in their

own homes or 1n subs1d1zed housing.

A2 - Percent of Rent and Control households active at two years after enrollment, excluding

those w1th enrollment 1ncomes over the e11g1b1l1ty 11m1ts and those living 1n the1r

own homes or 1n subsid1zed housing. •

R - Sample also excludes households w1th rent less than $40 per month.

Y - sample also excludes households w1th 1ncomes less than $1,000 per year.

DATA SOURCES For samples 1-5, est1mates are from Chapter 4 of th1s report, for sample 6, estimates

are from Table 4-1 1n Mayo (1977).

NOTES' F1rst-year data analys1s refers to Mayo, 1977 (sample 6), in wh1ch the maJor sample used was

households act1ve at one year after enrollment, th1s report focuses on those households act1ve at two years

after enrollment. See Appendix IX text for a discuss10n of further sample d1fferences.

standard errors 1n parentheses.

a. The analytic rent def1n1t10n used 1n Mayo (1977) used or1ginal ut11ity adJustments and

1ncluded the reported contribut10n of roomers, th1s report d1d not. Neither of these differences affected

the results.
Table IX-2

COMPARISON OF ELASTICITY ESTIMATES FINDINGS FROM FIRST-YEAR DATA

ANALYSIS VS. THIS REPORT (MOVERS SAMPLE)

PITTSBURGH PHOENIX

RENT INCOME INCOME PRICE SAMPLE INCOME PRICE SAMPLE

SAMPLE VARIABLD VARIABLE ELASTICITY ELASTICITY SIZE ELASTICITY ELASTICITY SIZE:

(1) A2,M2, Two-Year Three-Year 0.363 -0 211 (236) o 364 -0 219 (292)

R,1 Average (0.052) (0.063) (0.042) (0.059)

(2) A2,M2, Two-Year Three-Year 0.448 -0.212 (244) 0.380 -0.238 (299)

1 Average (0.055) (0 069) (0.042) «).060)

(3) A2,M2, Two-Year Two-Year o 383 -0.199 (244) 0.343 -0 349 (299)

1 Average (0.056) (0.072) (0.042) (0.075)

:J> (4) A2,M1, One-Year Two-Year 0.412 -0.111 (177) 0.346 -0.314 (222) I

'" 1 Average (0.059) (0.080) (0.051) (0.065)

'" (5) Al,MI, One-Year Two-Year 0.401 -0 059 (198) 0.355 -0.312 (317)

1 Average (0.056) (0.075) (0 046) (0 066)

(6) Al,Ml One-Yeara Twa-Year o 365 -0.045 (189) 0.348 -0 354 (291)

Average (0.059) (0.077) (0.044) (0.060)

SAMPLES Al - Percent of Rent and Control households active at one year after enrollment, excluding

those w~th enrollment incomes over the el~gibil1ty limits and those living in the1r

own homes or 1n subsid1zed hous1ng.

1'1.2 - Percent of Rent and Control households act1ve at two years after enrollment, exclud1ng

those with enrollment incomes over the eligibi11ty limits and those 1iv1ng 1n their

own homes or 1n SUbs1d1zed hous1ng

R - Sample also excludes households w1th rent less than $40 per month.

Y - Sample also excludes households w1th incomes less than $1,000 per year.

MI - Move between enrollment and one year after enrollment.

M2 - Move between enrollment and two years after enrollment

DATA SOURCES For samples 1-5, est1mates are from Chapter 4 of th1S report; for sample 6, estimates

are from Table 4-2 1n Mayo (1977).

NOTES. F1rst-year data analys1s refers to Mayo, 1977 (sample 6), 1n which the maJor sample used was

households act1ve at one year after enrollment, th1S report focuses on those households active at two years

after enrollment. See Appendix IX text for a d1Scuss1on of further sample differences

Standard errors 1n parentheses.

a. The analytic rent def1n1t10n used 1n Mayo (1977) used or1g1nal ut111ty adJustments and

1ncluded the reported contr1but10n of roomers; thJS report d1d not. Ne1ther of these differences affected

the results
REFERENCES

Mayo, Stephen K., Hous~ng Expend~tures and Quality, Part I: Hous~ng Expend~­

tures Under a percent of Rent Hous~ng Allowance, Cambr1dge, Mass.,

Abt Assoc~ates Inc., January 1977.

A-89
l\PPENDIX X

DETAILED TABLES

nus appendix contains the following detal.led tables from wh~ch some of the

tables and bndings in Chapters 2 through 6 have been extracted.

Table X-I

Table x-2

Table x-3

Table X-4

Table X-S

Table X-6

Table X-7

Table X-8

Table X-9

Table" X-IO

Table X-ll

Table X-12

Table X-13

Table X-14

Table X-IS

Table X-16

Table X-17

Table X-18

Changes in Rent From Enrollment to Two Years After Enrollment

Changes ~n Median Rent Burden From Enrollment to ~o Years

Change ~n Mean Rent Burden From Enrollment to ~o Years

Percentage Distribution of Rent Burden

Changes ~n Rent From Enrollment to ~o Years After Enrollment

for the Mover Sample

Changes ~n Rent From Enrollment to ~o Years After Enrollment

for the Nonmover Sample

Change in Rent Applying Selective Income Ehgili~l~ty L~=ts

to Control Households

Change ~n Rent Apply~ng Selective Income EI~gibility Linute

to Control Households for Mover Sample

Olange in Rent Applying Selective Income EI~g~b~lity Li=ts

to Control Households for Nonmover Sample

Proportion of Allowance Payment Allocated to Increased Rental

E'IP" nfutures

Enrollment Rent Burden by Income Class for COllllnned S~tes

Overall Characterist~cs of Var~ables Used in Regression 1\nalys~s

Log-Linear Expenditure Functions

unear E'IP"nmture Functions

Log-Linear Demand Function Allow~ng Variable Price Elast~city

Log-Linear Expenditure Functions - Sites Pooled

Log-L~near Demand Functions for Movers Sample Strat~bed by

Median Monthly Income

Log-unear Demand Funct~ons for Mover Sample Est~mated Us~ng

Income Spline

A-91
Table X-19

Table X-20

Table X-2l

Table X-22

Table X-23

Table X-24

Table X-25

Table X-26

Table X-27

Table X-28

Table X-29

Table X-30

Table X-3l

Table X-32

Table X-33

Table X-34

Log-~near Expend1ture Funct10ns Using Demographic Var1ables

as Covar~ates for the Mover Sample

Mean Monthly Hous1ng Expend1tures at Enrollment and at Two

Years After Enrollment for the Mover Sample by Race/Ethnicity

Strat1f1ed Log-L1near Expenditure Funct10ns for the Movers

Sample

Rent for Movers by Stratified Demograph1cs Pooled Sites

Changes in Rates of Pass1ng Lowest Hous1.ng Standards From

Enrollment to Two Years for Control and Percent of Rent

Households

Changes in Rates of PassJ.ng Program HousJ.ng Standards From

Enrollrrent to Two Years for Control and Percent of Rent

Households

Changes 1.n Rates of PassJ.ng Program Occupancy Standards From

Enrollnent to Two Years for Control and Percent of Rent

Households

Changes in Rates of Passing Lowest Housing Standards From

Enrollment to TWo Years for Control and Percent of Rent

Households for the Movers Sample

Changes 1n Rates of Pass1ng Lowest Hous1ng Standards From

Enrollment to Two Years for Control and Percent of Rent

Households for the Nonmover Sample

Changes in Rates of Passing Program Housl.ng Standards From

Enrollment to Two Years for Cbntrol and Percent of Rent

Households for the Mover Sample

Changes in Rates of Pass1ng Program Hous1ng Standards From

Enrollment to Two Years for COntrol and Percent of Rent

Households for the Nonmover Sample

O1anges 1.n Rates of Passing Program Occupancy Standards From

Enrollment to Two Years for Control and Percent of Rent

Households for the Mover Sample

Changes 1n Rates of Pass1ng Program Occupancy Standards From

Enrollment to Two Years for Control and Percent of Rent

Households for the Nonmover Sample

Changes in Hous1ng Adequacy From Enrollment to Two Years for

Control and Percent of Rent Households

Changes 1n Hous1ng Adequacy From Enrollment to Two Years for

Control and Percent of Rent Movers

Changes in Hous1ng Adequacy From Enrollment to Two Years for

Control and Percent of Rent Nonmovers

A-92
Table X-35

Table X-36

Table X-37

Table X-38

Table X-39

Table X-40

Table X-4l

Table X-42

Table X-43

Table X-44

Table X-45

Change in Hedon1.c Housing Services Index From Enrollment to

Two Years for Control and Percent of Rent Households

O1anges ~n Hedon1.C Hous1.ng ServJ.ces Index From Enrollment to

Two Years for Control and Percent of Rent Households for the

Mover Sample

O1anges ~n Hedonic Hous~ng Services Index From Enrollment to

Two Years for Control and Percent of Rent Households for the

Nonmover Sample

Search Effort for Last Move

Demand for Rent Components

Strat1.f1.ed Log-Linear Hous1.ng Serv1.ces Functions for the

Overall Sample

Strat1.f1.ed Log-L1.near Hous1.ng Serv1.ces Functions for the

Mover Sample

J-Ean Monthly Hous~ng Ser=ces at Enrollment and at Two Years

After Enrollment for the Mover Sample by Race/Ethnic~ty

Strat1.f1.ed Log-L1.near Housl.ng Expenditures, Housl.ng Services,

and Hedonic Res~duals Elastic~ties for the Mover Sample

Log-LJ.near Expenditure FunctJ.ons for Hous1.ng Services USl.ng

Full Sample and Submarket Hedonic Inilices for Phoenix

Est~mate of Log (Normal Rent) at Two Years After Enrollment

A-93
TABLE X-l

CHANGES IN RENT FROM ENROLLMENT TO WO YEARS AFTER ENROLLMENT

MEAN RENT MEAN CHANGE IN RENT

At PERCENTAGE

Enroll- At Two Mean of Rat~o of SAMPLE

TREATMENT GROUP Ment Years AMOUNT Rat~o Means SIZE:

PITTSBURGH

All Percent of

Rant Households $114 $139 $25 26% 22% (385)

Percentage rebate:

20% 109 126 17 17 16 (62)

30% 112 136 25 25 22 (82)

40% 122 148 26 27 21 (108)

50% 114 140 27 27 24 (l05)

60% 109 142 33 39 30 (28)

Control households 115 133 18 18 16 (289)

UnconstraJ.ned

households 107 128 21 22 20 (59)

PHOENIX

All Percent of

Rent households 132 162 30 26 23 (280)

Percentage rebate:

20% 133 156 23 24 17 (44)

30% 125 152 27 24 22 (79)

40% 136 166 30 24 22 (59)

50% 141 172 31 24 22 (77)

60% 112 157 45 45 40 (21)

Control households 128 145 17 18 13 (252)

Unconstral.ned

households 135 165 30 35 22 (37)

SAMPLE: Percent of Rent, Control, and Unconstra~ned households actl.ve

at two years after enrollment, exclufung those Wl.th enrollment 1ncomes over

the elJ.gJ.bl.ll.ty IJ.IlU.ts and those IJ.vl.ng l.n their own homes or l.n subs1.dJ.zed

housing.

DATA SOURCES: In~t~al and monthly Household Report Forms. and payments

f~le.

A-94
TABLE X-2

CHANGES IN MEDIAN RENT BURDEN

FROM ENROLLMENT TO TWO YEARS

MEDIAN RENT BURDEN

At At Two MEDIAN CHANGE SAMPLE

TREATMENT GROUP Enrollmenta Yearsb IN RENT BURDEN SIZE

PITTSBURGH

All Percent of Rent

households 0.32 0.21 -0.11 (388)

Percentage rebate:

20% 0.29 0.22 -0.06 (62)

30% 0.33 0.25 -0.09 (83)

40% 0.31 0.20 -0.11 (109)

50% 0.33 0.17 -0.15 (106)

60% 0.40 0.18 -0.22 (28)

Control households 0.29 0.26 -0.04 (290)

Unconstra~ned households 0.35 0.20 -0.17 (59)

PHOENIX

All Percent of Rent

households 0.32 0.24 -0.09 (282)

Percentage rebate:

20% 0.37 0.31 -0.01 (45)

30% 0.31 0.26 -0.06 (79)

40% 0.31 0.22 -0.11 (59)

50% 0.33 0.20 -0.14 (78)

60% 0.39 0.19 -0.18 (21)

Control households 0.32 0.30 -0.02 (256)

Unconstra~ned households 0.33 0.13 -0.23 (38)

SAMPLE: Percent of Rent, Control, and Unconstralned households

actlve at two years after enrollment, excludlng those wlth enrollment

lncornes over the el191blilty Ilmlts and those Ilvlng In thelr own homes

or In Subsldlzed houslng.

DATA SOURCES: In~t~al and monthly Household Report Forms, and

payments f~le.

a. Rent burden at enrollment 15 deflned as the ratlo of enrollment

rent to enrollment lncame.

b. Rent burden at two years ~s def~ned as the rat~o of net twoyear rent (gross rent rnlnus allowance payment) to two-year income.

A-95
TABLE X-3

CHANGE IN MEAN RENT BURDEN

FROM ENROLLMENT TO TWO YEARS

MEAN RENT BURDEN

At At Twg MEAN CHANGE SAMPLE

TREATMENT GROUP Enrollmenta Years IN RENT BURDEN SIZE

PITTSBURGH

All Percent of Rent

households 0.36 0.23 -0.14 (388)

Percentage rebate:

20% 0.35 0.26 -0.09 (62)

30% 0.34 0.27 -0.08 (83)

40% 0.36 0.22 -0.14 (109)

50% 0.38 0.20 -0.18 (106)

60% 0.44 0.19 -0.26 (28)

Control households 0.33 0.29 -0.04 (290)

Unconstra~ned households 0.39 0.20 -0.19 (59)

PHOENIX

All Percent of Rent

households 0.37 0.27 -0.10 (282)

Percentage rebate:

20% 0.37 0.34 -0.03 (45)

30% 0.35 0.30 -0.06 (79)

40% 0.35 0.25 -0.11 (59)

50% 0.38 0.24 -0.15 (78)

60% 0.41 0.22 -0.19 (21)

Control households 0.35 0.34 -0.01 (256)

unconstralned households 0.38 0.09 -0.29 (38)

SAMPLE: Percent of Rent, Control, and Unconstralned households

actlve at two years after enrollment, exc!udlng those wlth enrollment

lucornes over the ellglbl11ty lLmlts and those Ilvlng 1n thelr own homes

or 1n subsidlzed houslng.

DATA SOURCES: In~t~al and monthly Household Report Forms

a. Rent burden at enrollment 15 deflned as the ratlo of enrollment

rent to enrollment lucame.

b. Rent burden at two years 15 deflned as the ratlo of net two-year

rent (gross rent mlnus allowance payment) to two-year lucame.

A-96
TABLE X-4

PERCENTAGE DISTRIBUTION OF RENT BURDEN

PITTSBURGH PHOENIX

RENT BURDEN RANGE

Control Households

<10%

10-20

20-25

25-30

30-40

40-50

>50

Totala

Sample size

Percent of Rent Households

<10%

10-20

20-25

25-30

30-40

40-50

>50

Totala

Sample s~ze

Unconstra~ned Households

<10%

10-20

20-25

25-30

30-40

40-50

>50

Totala

Sample s~ze

AT

ENROLLMENT

0%

13

19

22

20

15

11

100

(290)

o

11

13

20

25

15

17

101

(387)

o

8

12

14

32

14

20

100

(59)

AT TWO

YEARS

0%

21

18

16

21

13

12

101

(301)

7

44

19

13

12

3

2

100

(389)

9

37

16

18

14

4

4

102

(57)

AT

ENROLLMENT

1%

14

15

13

29

17

11

100

(254)

o

13

14

14

28

12

19

100

(281)

o

14

8

19

32

8

19

100

(37)

AT TWO

YEARS

0%

11

12

20

27

14

16

100

(256)

5

32

20

12

16

9

6

100

(285)

20

17

20

13

20

3

7

100

(30)

SAMPLE: Percent of Rent, Unconstralned, and Control households

actlve at two years after enrollment, excludlng those wlth enrollment

lucornes over the ellglblllty IlffiltS and those Ilvlng 10 thelr own homes

or 10 SubSldlzed houslng.

DATA SOURCES: In~t~al and monthly Household Report Forms, and

payments f~le.

a. Total may not add to 100 percent due to round~ng.

A-97
TABLE X-5

CHANGES IN RENT FROM ENROLLMENT TO '!.WO YEARS

AFTER ENROLLMENT FOR THE MOVER SAMPLE

MEAN RENT MEAN CHANGE IN RENT

At PERCE:NTAGE

Enro11- At two *>an of Ratio of SAMPLE

TREATMENT GROUP ment years AMOUNT Ratio Means SIZE

PITTSBURGH

All Percent of

Rent households $114 $156 $41 45% 36% (142)

Percentage rebate:

20% 110 135 25 27 23 (17)

30% 107 150 43 44 40 (33)

40% 128 167 39 43 30 (46)

50% III 157 45 49 41 (35)

60% [98] [154] [56] [74] [57] (11)

Control households 120 147 26 29 22 (94)

Unconstrained

households 109 145 36 39 33 (22)

PHOENIX

All Percent of

Rent households 135 179 44 38 33 ( 169)

Percentage rebate :

20% 122 158 36 37 30 (26)

30% 137 181 44 37 32 (40)

40% 142 191 50 40 35 (33)

50% 143 184 41 32 29 (54)

60% 114 170 56 57 49 (16)

Control households 132 160 28 30 21 ( 123)

Unconstrained households 128 175 48 55 38 (21)

SAMPLE: Percent of Rent, Control, and Unconstrained movers active at

two years after enrollment, excluding those w~th enrollment incomes over the

el~g~bl.lJ.ty 11.Inl.ts and those livl.ng l.n thel.r own homes or l.n subsJ.dized hous­

~ng.

DATA SOURCE:S: Ini t~a1 and monthly Household Report Forms, and payments file.

NOTE: Brackets indicate entnes based on 15 or fewer observations.

A-98
TABLE X-6

CHANGES IN RENT FROM ENROLLMENT TO TWO YEARS

AFTER ENROLLMENT FOR TIlE NONMOVER SAMPLE

MEAN RENT MEAN CHANGE IN RENT

At PERCENTAGE

Enroll- At two Mean of Ratlo of SAMPLE

TREATMENT GROUP ment years AMOUNT Ratio Means SIZE

PITTSBURGH

All Percent of

Rent households $114 $130 $16 15% 14% (243)

Percentage rebate:

20% 109 123 14 13 13 (45)

30% 115 128 12 12 10 (49)

40% 117 134 17 15 15 (62)

50% 115 132 17 17 15 ( 70)

60% 116 134 18 16 16 (17)

Control households 112 127 14 13 13 (195)

Unconstrained

households 106 119 13 12 12 ( 37)

PHOENIX

All Percent of

Rent Households 127 134 8 7 6 (111)

Percentage rebate:

20% 148 154 6 5 4 ( 18)

30% 112 122 10 10 9 ( 39)

40% 129 135 5 5 4 (26)

50% 137 143 7 6 5 (23)

60% [108] [116] [9 ] [9] [8] (5)

Control Households 125 132 7 7 6 (129)

Unconstral.ned

houpeholds 145 151 7 8 5 (16)

SAMPLE: Percent of Rent, Control, and Unconstra1ned nonmovers acc.ve

at two years after enrollment, exclud1.ng those W1th enrollment incomes over the

elig:Lbil~ty luuts and those liVJ.ng ~n the~r own homes or in subsifuzed hous~ng.

DATA SOURCES: In~tial and =nthly Household Report Forms, and payments

f~le.

NOTE: Brackets J.nd1.cate entries based on 15 or fewer observatJ.ons.

A-99
TABLE X-7

CHANGE IN RENT APPLYING SELECTIVE

INCOME ELIGIBILITY LIMITS TO CONTROL HOUSEHOLI:S

MEAN RENT MEAN CHANGE IN RENT

TREATMENT GROUP

At

Enrollment

At Two

Years

PERCENTAGE

Mean of Ratio of

AMOUNT Ratw Means

SAMPLE

SIZE

PITTSBURGH

Percentage

rebate = 20% $105 $120 $16 16% 15% (39)

Control households 119 139 20 19 17 ( 179)

Percentage

rebate = 60% 108 136 28 32 26 (23)

Control households 107 123 16 18 15 (111)

PHOEIUX

Percentage

rebate = 20% 146 166 20 19 14 (30)

Control households 140 156 17 15 12 (166)

Percentage

rebate = 60% 117 155 38 36 32 (17)

Control households 106 120 15 21 14 (88)

SAMPLE: Percent of Rent households 1n Treatment Groups 13 and 23 and

Control households act~ve at two years after enrollnent, exc~ufung those w1th

enrollment ~ncomes over the el~g~bJ..lJ.ty IJ.nu.ts ~d those 1J.VJ.ng J.n theJ.r own

homes or J..n subsidized housJ.ng.

DATA SOURCES: 1mtial and monthly Household Report Forms, and payments

file.

NOTE: See Appenfux Table 111-3 for the 1ncome elig1b11ity 11ffi1ts

appl1ed to these households.

A-IOO
TABLE x-8

aIANGE IN RENT APPLYING SELECTIVE INCOME ELIGIBILITY

LIMITS TO CONTROL HOUSEHOLDS FOR MOVER SAMPLE

MEAN RENT MEAN aIANGE IN RENT

TREATMENT GROUP

At

EnrollmentAt Two

Years

PERCENTAGE

Mean of Rat~o of

AMOUNT Rat~o Means

SAMPLE

SIZE

PITTSBURGH

Percentage

rebate = 20%

Control households

Percentage

rebate = 60%

Control households

[$lOOJ

125

[104J

114

[$133J

155

[146J

138

[$33J

29

[43J

24

[33%J

32

[56J

29

[33%J

23

[41J

21

(7)

(47)

(9)

(48)

Percentage

rebate = 20%

Cbntrol households

Percentage

rebate = 60%

Control households

. [140J

145

[119J

112

PHOENIX

[l77J

171

[167J

135

[37J

26

[48J

23

[34J

23

[45 J

34

[26J

18

[40J

21

(15)

(77)

(13)

(49)

SAMPLE: Percent of Rent movers ~n Treatment Groups 13 and 23 and

Control Il'K)vers act~ ve at two years after enrollment, exelufung those WJ.th

enrollment lncornes over the ellgJ.bJ.lJ.ty IJ.~ts and those living in theJ.r own

homes or 1n subsJ.cuzed housing.

DATA SOURCES: Init~al and monthly Household Report Forms, and payments f~le.

NOTE: Brackets ~nd~cate entr~es based on 15 or fewer observat~ons.

See Append~x Table 111-3 for the ~ncome el~q~b~l~ty requirements appl~ed to

these households.

A-IOI
TABLE X-9

CHANGE IN RENT APPLYING SELECTIVE INCOME ELIGIBILITY

LIMITS TO CONTROL HOUSEHOLDS FOR NONMOVER SAMPLE

TREATMENT GROUP

Percentage

rebate = 20%

Control households

MEAN RENT MEAN CHANGE IN RENT

At PERCENTAGE

Enroll- At Two Mean of Rat~o of SAMPLE

ment Years AMOUNT Rat~o Means SIZE

PITTSBURGH

$105 $117 $12 12% 11% (32)

117 133 16 15 14 (132)

Percentage

rebate = 60%

Control households

Percentage

rebate = 20%

Control households

Percentage

rebate = 60%

Control households

[110]

102

[151]

135

[112]

98

[129]

112

PHOENIX

[155]

144

[118]

101

[18]

10

[4]

9

[6]

4

[17]

10

[4]

8

[7]

5

[16]

10

[3]

7

[5 ]

4

(14)

(63)

(15)

(89)

(4)

(39)

SAMPLE: Percent of Rent nonnovers ~n Treatment Groups 13 and 23 and

Control nonmovers act1ve at two years after enrollment, excludlug those Wlth

enrollment lucornes over the ell.gl.bl.ll.ty luruts and those ll.vl.ng 1ll thel.r own

home:s or in subsl.dJ.zed housl.ng ..

DATA SOURCES: In~t~al and monthly Household Report Forms, and payments

f~le.

NOTE:

Append~x Table

households •

Brackets l.ndJ.cate entrl.es used on 15 or fewer observatl.ons.. See

111-3 for the ~ncorne el~g~~l~ty requ~rements appl~ed to these

A-102
TABLE x-IO

PROPORTION OF ALLOWANCE PAYMENT

ALLOCATED TO INCREASED RENTAL EXPENDITURES

HOUSEHOLD GROUP

All Households

Nonrnovers

percentage rebate~

20'

30>

40>

50>

60.

Movers

percentage rebate·

20>

30,

40.

50'

60%

MEAN CHANGE

IN RENT

ABOVE NORMALa

PITTSBURGH

$ 7-

2

-1

-2

3

3

4

15

-1

17

15

19

[301

PHOENIX

PROPORTION USED

FOR INCREASED SAMPLE

MEAN PAYMENT EXPENDITURESb SIZE

$49 14> (391)

46 4 (248)

23 -4 (46)

35 -6 (52)

50 6 (62)

58 5 (71)

74 5 (17)

56 27 (143)

27 -4 (17)

40 43 (33)

59 25 (47)

70 27 (35)

[87J [34J (ll)

All Households

Norunovers

Percentage rebate:

20>

30'

40>

50'

60.

Movers

Percentage rebate:

20>

30>

40>

50.

60>

$14

1

-1

3

-1

-1

[2J

16

12

18

24

15

30

$59 24>

46 2

28 -4

35 9

51 -2

69 -1

[66J [3J

68 24

29 41

53 34

69 35

88 17

100 30

(285)

(ll4)

(18)

(40)

(27)

(24)

(5)

U7l)

(27)

(40)

, (33)

(55)

(16)

SAMPLE. Percent of Rent households act~ve at two years after enrollment, exclud~ng those w~th enrollment

~ncomes Qver the el~gw~l~ty l.UlU.ts and those l~v~ng ~n the~r own homes or ~n subs~d~zed hOUSlllg.

DATA SOURCES: In~t~al and monthly Household Report Forms, and payments f~le.

NOTE: Brackets ~nd~cate entr~es based on 15 or fewer observat~ons.

a. Th~s ~s computed as the mean change for Experllllental households m~nus the mean change for Control

households.

b. Th~s ~s computed as the mean change above normal d~vJ.ded by the mean payment. It ~s ~ntended to

represent a program average rather than a household average.

A-I03
TABLE X-11

ENROLLMENT RENT BURDEN By

INCOME CLASS FOR COMBINED SITES

MONTHLY MEAN MEAN MEAN RENT SAMPLE

INCOME RENT INCOME BURDEN a SIZE

"$83.3-150 $ 86 $129 0.69 (159)

151-250 101 203 0.50 (625)

251-350 115 301 0.38 (709)

351-450 126 398 0.32 (694)

451-550 137 498 0.28 (585)

551-650 149 595 0.25 (311)

651-750 162 694 0.23 (120)

751+ 157 864 0.18 (77)

Total 123 385 0.37 ( 3348)

SAMPLE: Expenmenta1 and Control enrollees, exc1ud~ng those w~th

enrollment ~ncomes over the e11g1b111ty l~ltS.

DATA SOURCES: In~t~a1 Household Report Fonns.

a. Mean rent burden lS deflned as the mean of rent at enrollment

dlvlded by lncame at enrollment.

A-104
TABLE x-12

OVERALL CHARACTERISTICS OF VARIABLES

USED IN REGRESSION ANALYSIS

AJ,J~ 1I0USEHOLDS MOVERS

PITTSBURGH PHOENIX PITTSBURGH PHOENIX

Standard Standard Standard Standard

Equahons W~C1n DovJ.atJ.on Sample Mean DeV1.at1.on sample Mean Deviation Sample Mean Dev1.at1.on sample

Log-11.near Expend1.tures

Equat1.on

Log (rent) 4.869 0313 (674) 4.966 0.385 (532) 4.977 0.308 ( 236) 5 085 o 347 (292)

Log (average monthly

J.ncome) 5 958 0.395 (674) 5.982 o 442 (532) 5.968 0.356 (236) 5.998 0.426 (292)

Log (current monthly

l.ncome) 6 040 0 452 (674) 5.999 0.491 (532) 5 968 o 416 (236) 6 006 0.478 (292)

Log (1-') -0.292 0 294 (674) -0.265 0.291 (532) -0.311 o 294 (236) -0.305 0.306 (292)

Linear EXpend1.tures

Equahon

Rent 136.72 44 43 (674) 153.89 56 02 (532) 152.08 48.76 (236) 171.13 56.62 (292)

Average monthly

l.ncome/(l-a) 573 69 266 91 (674) 588.07 303.01 (532) 579.81 243.50 (236) 617.93 305.59 (292)

Current monthly

l.ncome/(I-a) 638 84 334.19 (674) 612.90 362 26 (532) 652.54 312.48 (236) 640 70 377.73 (292)

l/(1-a) 1 400 o 435 (674) 1 362 0.429 (532) 1.426 0.435 (236) 1.423 0.459 (292)

Log-linear HouS1.ng

SerV1.ces Equation

Log (hedonJ.c 1.ndex

of housJ.ng serv1.ces) 4.739 0.235 (635) 4.931 0.325 (486) 4.783 0.251 (214) 5.005 o 329 (257)

Log (average monthly

income) 5.954 0.393 (635) 5.986 0.438 (486) 5.954 0.354 ( 214) 6 001 0.422 (257)

Log (I-a) -0.291 0.293 (635) -0 264 o 289 (486) -0.313 0.292 (214) -0 304 0.302 (257)

SAMPLE' Percent of Rent and Control households act1.ve at two years after enrollment, excluding those w1.th enrollment J.ncomes over the

e1ig1.bJ.11.ty 11.m1.ts and those 11.v1.ng 1.n the1.r own homes or l.n subs1.d1.zed hous1.ng.

DATA SOURCES In1.t1.al and monthly Household Report Forms.
TABLI: X-I3

LOG-LIN~~R EXPE~DITURE FUNCTIONS

PITTSBURGH PHOENIX

Income PrJ.ce

R

2 Sample Income Price

R

2 Sample

HOUSEHOLD GROUP Constant ElastJ.city Elasticity SEE Sl.ze Constant Elast1c1ty Elastl.cl.ty SEE S1ze

All Households

Current 1ncome 3 065** o 291** -0.164** 0.08 o 28 (674) 2.678** 0.371** -0.239** 0.25 0.33 (532)

(0 149) (0 024) (0.037) (0.179) (0 030) (0 050)

Average l.ncome 2 835** 0.333** -0.178** 0.18 0.28 (674) 2.303** 0.435** -0 234** 0.27 0.33 (532)

(0.169) (0 028) (0 038) (0.195) (0.032) (0.049)

Mover Households

Current l.ncome 2.955** 0.324** -0 195** 0.20 0.28 (236) 3.065** 0.325** -0 219** 0.23 0.31 (292)

(0 271) (0.044) (0.062) (0.229) (0 038) (0 059)

Average 1ncome 2.744** o 363** -0.211** o 18 0.28 (236) 2.834** 0.364** -0 219** o 23 0.31 (292)

(0.317) (0.052) (0 063) (0.256) (0 042) (0 059)

SAMPLE Percent of Rent and Control households actl.ve at two years after enrollment, excluding those wl.th enrollment 1ncomes over the

elig1b11ity l1m1ts and those I1v1ng 1n the1r own homes or 1n subs1d1zed hous1ng.

D~TA SOURCES: Inl.t1al and monthly Household Rp.port Forms, and payments f1le.

NOTE Standard Error 1n parentheses. The model used here 1S

In (Rent) = ~O + ~l In (Income) + 62 In(l-a),

where "a" 18 the percentage rebate

** t-8tat1st1c s1gn1f1cant at the 0.01 level

SEE = standard ~rror of Est1mate.
TABLE X-14

LINEAR EXPENDITURE FUNCTIONS

ESTIMATED COEFFICIENTS STONE-GEARY COEFFICIENTSa STANDARD

Income Price B PHI\ '2 R2 ERROR OF SAMPLE

HOUSEHOLD GROUP Constant Coeff~cient Coeff~cient ESTIMATE SIZE

PITTSBURGH

All Households

Current ~ncome 115.47** o 0577** -11.15** 0.0577 122.54 193.24 o 16 40.9 (674)

(5 36) (0.0053) (4.10)

Average l.ncome 113 98** 0.0714** -13.00** o 0714 122 74 182.07 0.14 41.2 (674)

(5.431 (0.0069) (4.26)

Mover Households

Current income 120.79** 0.0804** -14 86* 0.0804 131 35 184.83 0.22 43.3 (236)

(9.83) (0 0102) (7 34)

Average income 117 41** o 1027** -17.43** 0.1027 130.85 169.72 0.21 43 7 (236)

(10.03) (0.0136) (7.63)

PHOENIX

All Households

Current income 122 80** 0.0745** -10 69** 0.0745 132.69 143.49 0.20 50 2 (532)

(7 25) (0.0069) (5 80)

Average l.ncome 120 11** o 1021** -19.28** 0.1021 133.77 188 83 o 24 49 0 (532)

(7.09) (0.0083) (5.89)

Mover Households

Current income 138 60** 0.0733** -10.14 0.0733 149.56 138 34 0.21 50.6 (292)

(9 69) (0.0090) (7.42)

Average 1.ncome 133.25** 0.1018** -17.57* o 1018 148.35 172.59 0.24 49 7 (292)

(9.55) (0 0114) (7 58)

+ B (InCOme) + 1-a

SAMPLE Percent of Rent and Control households actl.ve at two years after enrollment,

ell.gl.bill.ty ll.rnl.ts and those 11.vl.ng l.n thel.r own homes or 1.n subsidl.zed housing.

DATA SOURCeS Inl.tl.al and monthly Household Report Forms, and payments fl.1e

NOTE' Standard Error l.n parentheses. The model used here l.S: Rent = A( l=a)

Stone-Geary utl.l1.ty Functl.on B 1-B a. U (H-a where B B 1 ) (z-a2 ) ,

PHel C'I (I-B)

·2 -AlB

* t-statl.stl.c sl.gnl.f:I.Cant at the o 05 level

** t-statJ.stl.c sl.gnl.fl.cant al the 0.01 level

exc1udl.ng those w1.th enrollment l.ncomes over the

C', where "a" is the percentage rebate.
TABLE X-IS

LOG-LINEAR DEMAND FUNCTION

ALLOWING VARIABLE PRICE ELASTICITY

INDEPENDENT

VARIABLE PITTSBURGH PHOENIX

Constant 2.803** 2.864**

(0.322) (0.261)

Ln(1ncome) 0.354** 0.358**

(0.053) (0.043)

Log(O.8) for households 0.055 -0.242

rece~vlng 20% rent rebate (0.334) (0.299)

Log(O.7) for households -0.117 -0.324*

recelvlng 30% rent rebate (0.160) (0.157)

Log(O.6) for households -0.288** -0.310**

recelvlng 40% rent rebate (0.099) (0.118)

Log (0. 5) for households -0.174* -0.206**

recelvlng 50% rent rebate (0.081) (0.073)

Log(O.4) for households -0.195* -0.196*

recelvlng 60% rent rebate (0.010) (0.090)

2 0.191 0.230 R

Standard error of estlinate 0.28 0.31

Sample S1ze (236) (292)

SAMPLE: Percent of Rent and Control movers actlve at two years after

enrollment, excludlng those wlth enrollment lucornes over the eliglbl11ty

llinltS and those 11vlng 10 thelr own homes or 10 SubSldlzed housing.

DATA SOURCES: In1t1al and monthly Household Report Forms.

NOTE: Standard Error 1n parentheses. The R2 for a speclflcation

that constralns the prlce elastlclty to a 810g1e value over the entlre range

of pr1ce d1scounts (the one used 1n Chapter 4) was 0.183 1n P1ttsburgh and

0.225 10 PhoenlX. F-tests could not reJect the assumptl0n of a 510g1e prlce

~last1c1ty (F=0.566 1n P1ttsburgh, F=0.370 1n Phoen1x, both 1ns1gn1f1cant).

* t-stat1st1c s1gnif1cant at the 0.05 level.

** t-stat1st1c s1gn1f1cant at the 0.01 level.

A-I08
TABLe )(-16

LOG-LINEAR EXPF,NDI'l'U~ f'UNC'l'IONS ­

SITE:S POOLED

POOLED SITE INTERCEPT DIFFeRENT SI'l'E INTERCEPT

Income Prl.ce

R2 Sample Phoem.x Income Prl.ceR2 Sample

HOUSEHOLD GROUP Conbtant E1astJ.c1.ty E1ast1c1.ty 'EE SJ.ze Constant oworny I:1ashcity I:1ast1c1.ty SEE Size

All llouseho1ds

Current 1ucome 2 907** 0.324** -0 189** o 20 0.31 (1206) 2 817** 0.117** o 330** -0 199** 0.23 o 31 (1206)

(0 117) (0 019) (0.031) (0 116) (0 018) (0 019) (0 030)

Average l.n<.ome 2 544** o 387** -0 200** 0.23 0.31 (1206) 2 517** 0.094** 0.38511<* -0 207** o 24 0.30 (1206)

(0 129) (0 021) (0.030) (0 128) (0 018) (0 021) (0 030)

Mover Households

Current l.ncome 306811<* o 316** -0.205 o 20 o 30 (528) 2.942** o 128** o 325** -0 209** 0.24 0.29 (528)

(0 177) (0 029) (0.044) (0 175) (0 026) (0.028) (0 043)

Average l.ncome 2 765"'* 0.369** -0 215** 0.21 0.30 (528) 2 738*'" 0.09811<* 0.364** -0 216** o 23 0.29 (528)

(0.200) (0 033) (0.044) (0.197) (0 026) (0.033) (0 043)

SAMPLE percent of Rent and Control households act1.ve at two years after enrollment, exclud1.ng those W1.th enrollment l.ncomeS over the

el1.gib1.!J.ty 11.m1.ts and those lJ..v1.ng 1n the1.r own homes or 1.n subs1.d1.zed housing

DATA SOURCES In1.t1.al and monthly Household Report Forms, and payments f1.le

NOTE Standard Error 1.n parentheses F-tests of overall homogeneity (pooled S1.te intercept versus separate regressions as in Appendix Table

IV-I) 1.nd1.cate re]ect1.on 1.0 all four cases for each S1.te at the 0 01 level F-tests of homogeneity of the elast1.c1.t1.es (allow1.ng for d1.fferent S1.te

l.ntercepts) l.ndJ.cate rCJect1.on only for all households (at the 0 05 level).

Overall Homogene1.ty

F-stat1.st1.c Degrees of Freedom

Different Elast1.c1.ties

F-stat1.st1.C Degrees of Freedom

All-current l.ncome

All-average 1.ncome

Movers-current l.ncome

Movers-average l.ncome

** t-stat1.st1.c s1.g111.f1.cant at the 0 01 level

SEC Standard error of Est1.mate.

16.111

11 535

8.203

4.825

(3,1200)

(3,1200)

(3,522)

(3,522)

2.804

3 161

0.035

0.001

(2,12011

(2,1201)

(2,523)

(2,523)
TABLE X-17

LOG-LINEAR DEMAND FUNCTIONS FOR MOVERS SAMPLE

STRATIFIED BY MEDIAN MONTHLY INCOME

PITTSBURGH PHOENIX

LOWER HALF UPPER HALF LOWER HALF UPPER HALF

INDEPENDENT OF INCOME OF INCOME OF INCOME OF INCOME

VARIABLE DISTRIBUTION DISTRIBUTION DISTRIBUTION DISTRIBUTION

Constant 2.343** 2.322** 2.877** 2.512**

(0.692) (0.775) (0.542) (0.816)

Log (l-a) -0.167* -0.268** -0.217** -0.222*

(0.082) (0.100) (0.081) (0.087)

Log (average income) 0.439** 0.427** 0.357** 0.415**

(0.121) (0.123) (0.096) (0.129)

2

R 0.12 0.13 0.13 0.09

Standard error

of est~m.ate 0.27 0.29 0.31 0.31

Sample s~ze (118) (118) (136) (156)

SAMPLE: Peroent of Rent and Control movers actlve at two years after

enrollment, excludlng those wlth enrollment lUCOrnes over the ellg1bl11ty l~ltS

and those I1ving In thelr own homes or In subsidlzed houslng.

DATA SOURCES: In~t~a1 and monthly Household Report Forms.

NOTE: Standard error In parentheses.

* t-stat~st~c s~gn~f~cant at the 0.05 level.

** t-stat~stic s~gn~f~cant at the 0.01 level.

A-110
TABLE X-18

LOG-LINEAR DEMAND FUNCrrONS FOR

MOVER SAMPLE ESTIMATED USING INCOME SPLINE

INDEPENDENT

VARIABLE PITTSBURGH PHOENIX

Constant 2.673** 2.955**

(0.599) (0.443)

Log (I-a) -0.211** -0.220**

(0.064) (0.059)

Log (average ~ncome) 0.376** 0.342**

(0.104) (0.077)

Log(average 1ncome) m~nus -0.024 0.053

log (meihan income) a (0.172) (0.159)

R

2 0.18 0.23

Standard error of estimate 0.28 0.31

Sample s~ze (236) (292)

SAMPLE: Percent of Rent and Control movers act1ve at two years

after enrollment, exclud1ng those with enrollment 1ncomes over the e11g1­

b~l~ty l~its and those l~v~ng ~n the~r own homes or ~n subs~d~zed hous~ng.

DATA SOURCES: In~t~al and monthly Household Report Forms.

NOTE: Standard error ~n parentheses.

a. For households W1th average income> median 1ncorre (the

independent variable is zero otherwise) .

** t-sta~stic sign~ficant at the 0.01 level.

A-lll
Table X-19

LOG-LINEAR EXPENDITURE FUNCTIONS USING DEMOGRAPHIC VARIABLES

AS COVARIATES FOR THE MOVER SAMPLE

(PITTSBURGH)

INDEPENDENT VARIABLES

Constant

Income elast~c~ty

Pr~ce e1ast~c~ty

M~nor~ty head of household

S~ngle-person household

S1ng1e head of household w~th

others present

Norum.nonty s~ngle-person

household

Norum.nonty s~ngle head of

household w~ th others present

~nor~ty s~ngle-person household

M~nor~ty s~ngle head of household

w~th others present

MJ.nor~ty household headed by a

couple

Standard error of estJ.Ill.ate

Sample s~ze

NO

COVARIATES

2.768**

(0.322)

0.359*""

(0.053)

-0.213

(0.064)

0.178

0.177

0.28

(234)

MINORITY

STATUS

2.768**

(0.323)

0.359**

(0.053)

-0.213**

(0.064)

-0.005

(0.050)

0.178

0.177

0.28

(234)

HOUSEHOLD

COUPOSITION

2.540**

(0.401)

0.391**

(0.064)

-0.2I9**"

(0.064)

0.031

(0.067)

0.075t

(0.043)

0.189

0.188

0.28

(234)

ADDITIVE

EFFECT

2.542**

(0.402)

0.391**

(0.064)

-0.218**

(0.064)

--0.015

(0.050)

0.030

(0.067)

0.076 t

(0.043)

0.189

0.188

0.28

(234)

COMPLETE

INTERACTION

2.534**

(0.405)

0.393**

(0.065)

-0.220**

(0.065)

0.014

(0.070)

0.073

(0.047)

0.143

(0.171)

0.055

(0:070)

-0.044

(0.081)

0~192

0.188

0.28

(234)

SAMPLE: Percent of Rent and Control movers act~ve at two years after enrollment, exclud~ng those w~th

enrollment ~ncomes over the el~giliJ..1~ty lJ.nUts and those l~vJ.ng ~n the~r own homes or ~n subSJ.d~zed housJ.ng.

DATA SOURCES InJ.tJ.al and monthly Household RepOrt Porms, and payments hIe.

NOTE' Standard enor ill parentheses. Dependent varJ.able: In (Rent)

t t-stat~st~c sJ.gnJ.f~cant at the 0.10 level.

** t-statJ.stJ.c sJ.gnJ.fJ.cant at the 0.01 leveL

A-HZ
TABLE X-19, cont1.nued

LOG-LINEAR EXPENDITURE FUNCTIONS USING DEMOGRAPHIC VARIABLES

AS COVARIATES FOR THE MOVER SAMPLE

(PHOENIX)

INDEPENDENT VARIALBES

Constant

Income ~last~c~ty

Pr~ce elast~c~ty

M~nor~ty head of nousehold

S1ngle-person household

S~ngle head of household w~th

others present

NOnm:Lnor~ty s1ngle-person

housenold

NOnm:Lnon.ty s1ngle head of

household W1 th others present

M1nor1ty s1ngle-person housenold

M1nor1ty s1ngle head of household

Wl.th others present

M~nor1ty household headed by a

couple

AdJusted R2

Standard error of est1mate

Sample S1ze

NO

COVARIATES

2.796**

(0.260)

o 370**

(0.043)

-0.219**

(0.060)

0.230

0.225

0.31

(285)

z.lINORITY

STATUS

2.993**

(0.258)

0.345**

(0.042)

-0.237**

(0.059)

-0 153**

(0.038)

0.272

0.264

0.30

(285)

HOUSEHOLD

COMPOSITION

2.700**

(0.303)

0.384**

(0.048)

-0.222**

(0.061)

0.031

(0.067)

0.024

(0.042)

0.231

0.220

0.31

(28S)

ADDITIVE

EFFEcr

2.968**

(0.302)

0.348~*

(0.048)

-0.236**

(0.059)

-0.157**

(0.039)

-0.016

(0.066)

0.024

(0.041)

0.274

0.261

0.30

(285)

COMPLETE

INTERACTION

2.915**

(0.299)

0.365**

(0.048)

-0.226**

(0.058)

-0.080

(0.071)

-0 064

(0.049)

-0.065

(0.139)

-0.105t

(0.058)

-0 .289**

(0.054)

0.303

0.285

0.39

(2a5)

SAMPLE. Percent of Rent and Control movers actJ.ve at two years after enrollment, excludl.ng those wJ.th

enrollment ~ncomes over the e11g1b11~ty lxm2ts and those 11v1ng 1n the~r own homes or 1n subsJ.d1zed housJ.ng.

DATA SOURCES. 1m.hal and monthly Household Report Forms, and payments £1le.

NOTE. Standard error J.n parentheses. Dependent var1able. In(Rent)

7 t-stat1st~c s1gnJ.fl.cant at the 0.10 level.

** t-statJ.stl.C SJ.gnl.f1cant at the 0.01 level.

A-l13
TABLE X-20

MEAN MONTHLY HOUSING EXPENDITURES AT ENROLLMENT

AND AT TWO YEARS AFTER ENROLLMENT

FOR THE MOVER SAMPLE BY RACE/ETHNICITY

MEAN mANGE IN

HOUSING EXPENDITURES

MEA.'l HOUS ING

EXPENDITURES PERCENTAGE

TREATMENT GROUP

At

Enrollment

At Two

Years

Mean of Rat~o of

AMOUNT the Rat~o the Means

SAMPLE

SIZE

No~nor~ty households

Percent of Rent

households

Control households

UnconstraJ.ned

households

~nont:y (black)

households

Percent of Rent

households

Control households

UnconstraJ.ned

households

Nonminor~ty households

Percent of Rent

households

Control households

UnconstraJ.ned

households

( cont~nued)

$115

120

114

115

114

[90J

$146

141

[138]

PITTSBURGH

$156

147

145

159

141

[142J

PHOENIX

$192

166

[175]

$41

27

31

44

26

[52]

$46

25

[37]

44%

29

33

50

29

[57]

37%

22

[42]

36%

23

27

38

23

[58J

32%

18

[30J

( 121)

(81)

(16)

(22)

( 18)

(5)

( 106)

( 81)

(12)

SAMPLE: Percent of Rent UnconstraJ.ned and Control movers actJ.ve at two

years after enrOllment, exc!udJ.ng those wJ.th enrollment J.ncomes over the e11.g1.­

bJ.IJ.ty l~J.ts and those IJ.vJ.ng 1.0 theJ.r own homes or 1.n Subs1dJ.zed housJ.ng.

DATA SOURCES: In~t~al and monthly Household Report Forms.

A-1l4
TABLE X-20 (cont1.nued)

MEAN MONTHLY HOUSING EXPENDITURES AT ENROLLMENT

AND AT TWO YEARS AFTER ENROLLMENT

FOR THE MOVER SAMPLE BY RACE/ETHNICITY

MEAN CHANGE IN

HOUSING EXPENDITURES

MEAN HOUSING

EXPENDITORES PERCENTAGE

At At Two Mean of Rat1.o of SAMPLE

TREATMENT GROUP Enrollment Years AMOUNT the Rat1.o the Means SIZE

PHOENIX (cont1.nued)

M1.nor1.ty households

Percent of Rent

households $114 $156 $42 39% 37% (61)

Control households 113 144 31 42 27 (43)

Unconstra~ned

households [114] [176] [62] [72] [54] (9)

Black households

Percent of Rent

households [108] [154] [46] [43] [43] (15)

Control households [114] [125] [11] [26] [10 ] (15)

Unconstra~ned

households [127] [224] [97] [76] [76J (1)

Span~sh-Amer~can

households

Percent of Rent

households 116 156 41 38 35 (46)

Control households 113 155 42 50a 37 (28)

Uncons tra~ned

households [112] [170] [58] [71] [52] (8)

SAMPLE: Percent of Rent Unconstra~ned and Control movers act~ve at two

years after enrollment, exclud~ng those w~th enrollment lncornes over the ellglblilty Ilmlts and those Ilvlng 10 thelr own homes or 10 SubSldlzed houslng.

DATA SOURCES: In1.t1.al and monthly Household Report Fonns.

a. El1.rn1.nat1.ng one Control household W1.th an abnormally large change

(361 percent) reduces th1.S volume to 37 percent.

A-US
'rABLE X-21

STRATIFIED LOG-LINEAR EXPENDITURE FUNCTIONS

FOR THE MOVERS SAMPLE

(PITTSBURGII)

AI,L HOUSEHOLDS NONMINOlUTY HOUSEHOLDS MINORITY HOUSEHOLDS

Inc.oma Pn.ce Income prl.ce Income Prl.ce

r,las- r,labR

2 Elas- Elas- 2 Elas- Elas- 2 INDEPENDENT VARIABLeS const-ant tl raty tl.Cl.ty seE Constant tl.Cl.ty tl.Cl.ty SEC R Constant tl.Cl.ty tl.Cl.ty SEE R

-

All households 2 768** a 359** -0.213** 0.28 o 178 2 606** o 386""'" -0 210** 0.28 o 204 3.643""'" o 212 -0 204 0.30 o 0705

(0 322) (0.053) (0.064) (N=234) (0 346) (0 057) (0.069) (N=196) (0 899) (0.148) (0.179) (R:'38)

Sl.ng1e-person households 3.272** 0.274 -0 077 o 28 o 069 3 352** 0.258 -0.072 0.30 0.053 Only 3 observatl.ons

(1 048) (0 184) (0 189) (N=33) (1.196) (0.210) (0.202) (N=30)

Sl.ngle heads of house- 3 958** 0 165 -0 1561 0.27 0.051 3.881** o 182t -0.121 o 25 o 057 4 121t 0.133 -0.303 0.35 0.058

hold with others (0 605) (0 102) (0 092) (N=98) (0.629) (0 107) (0 096) (N=77) (1 845) (0.307) (0.296) (N=21)

Households headed by 1 131* 0 613** -0 364** o 27 o 333 0.792 0.668""'" -0 377** 0.27 0.368 3.059t o 301 -0.193 0.27 0.128

a couple (0 566) (0 090) (0.096) (N=103) (0.622) (0.100) (0.104) (N=89) (1.506) (0.237) (0 279) (N=14)

ELDERLY

Income Price

E1as- E1as- 2 INDCPENDENT VARIABLE Constant tl.Cl.ty bcity SEE R

1\11 households 3.391* 0.237 -0 211 o 31 o 049

(1.470) (0.256) (0.256) (N=24)

SAMPLE: percent of Rent and control movers actl.ve at two years after enrollment, exclud1ng those wl.th enrollment l.ncomes over the e11gl.bl.lity

ll.ml.ts and those ll.vl.ng l.n the1r own homes or 1n subsl.dl.zed housl.ng.

DATA SOURCES In1tl.al and monthly Household Report Forms and payments hIe

NOTE Standard error l.0 parentheses Dependent Varl.able In (Rent)

t t-statl.stl.c sl.gnl.fl.cant at the 0.10 level.

* t-statl.stl.c sl.gnl.fl.cant at the 0.05 level

** t-statl.stl.c sl.gnl.fl.cant at the 0.01 level.

STIr: =Standard Error of I:stl.mate
TABLe X-21, continued

STRnTIFIED LOG-LINEAR EXpeNDITURE FUNCTIONS

FOR THE MOveRS SAMPLE

(PHOENIX)

- ALL HOUSEHOLDS NONMINORITY 1I0USEHOLnc:; MINORITY HOUSEHOLDS

Income Pr:LCe Income Price Income Pr~ce

Elas- Elas- 2 Elas- Elas-

.2

Elas- Ela"l- 2 INDEPeNDENT VARIABLES Constant tJ.<".1 t y hc~ty SEE • constant tlC.lty tlclty SEE constant tlClty tJ.cJ.ty SEE •

All households 2 796** o 370** -0.219** 0.31 0.230 2 463** o 431** -0 287** o 27 0.347 3 643 0.177* -0 179 o 34 o 072

(0.260) (0 043) (0 060) (N=28S) (0.2861 (0.047) (0 068) (N=185) (0 493) (0 083) (0 105) (N·I00)

S~ngle-person households 2 179** 0 480** -0 2451 o 20 o 566 2 407** o 444** -0.147 o 21 o 455 Only 5 observatJ.ons

(0 457) (0 080) (0.138) (N=32) (0.570) (0.099) (0 157) (N·27)

Slng1e heads of house- 2 995** o 342 -0 128 o 31 o 165 2.563** 0.410** -0 297* 0.29 o 256 3.771** 0.213 0 029 0.32 0.054

hold wlth others (0 429) (0 072) (0 087) (N=12I) (0 555) (0.091) (O.US) (N-71) (0 757) (0 1321 (0 132) (N::::I50)

Households headed by 2 669** 0 383** -0 327** o 33 0.192 2 739** o 390** -0.290** o 27 0.257 3 415** o 227 -0 415* o 34 o 154

a couple (0 518) (0 083) (0.100) (N=132) (0.503) (0.080) (0 104) (N=87) (1 0921 (0.178) (0 177) (N::::I45)

ELDERLY SPANISH ArtERICAN BLACK

Income Prlce Income Pr~ce Income Prlce

Elas- Elas-

.2

Elas- Elas-

.2

Elas- Elas-

.2 INDEPENDENT VARIABLE Constant t:LClty tlc~ty SEE Constant ticlty ticlty SEE constant tlClty tlClty SEE

All households 2.559'" 0.422t -0.018 0.21 0.202 4.148** 0.133 -0.137 o 33 0.04 3 524** o 224 -0 255 0.37 o 12

(1 121) (0.206) (0.184) (N=20) (0.606) (0.101) (0.122) (N=72) (0.965) (0 188) (0 217) (N=28)

SAMPLE Percent of Rent and Control movers actlve at two years after enrollment, e~cludlng those wlthlenrollment lnComes over the ellg~b~l~ty

llrnlts and those llvlng In thelr own homes or in SUbsldized hous~ng.

DATA SOURCES Inltlal and monthly Household Report Forms and payments flle

NOTE Standard error In parentheses Dependent varlable' In (Rent)

t t-statlstlC slgnlf~cant at the 0 10 level

'" t-statistlC slgnlf~cant at the 0 05 level.

*'" t-stat~stlC slgnlf~cant at the 0 01 level

SEE =Standard Error of Estlmate
TABLE X-22

RENT FOR MOVERS BY STRATIFIED DEMOGRAPHICS

POOLED SITES

INCOME PRICE SAMPLE

INDEPENDENT VARIABLES CONSTANT PHOENIX ELASTICITY ELASTICITY SEE R

2 SIZE

All households 2.723** 0.096** 0.366** -0.217** 0.30 0.230 (519)

(0.201) (0.026) (0.033) (0.044)

Nonminority households 2.433** 0.145** 0.413** -0.249** 0.27 0.325 (381)

(0.219) (0.028) (0.036) (0.048)

M1nor1ty households 3.818** -0.006 0.184** -0.183* 0.33 0.072 (138)

:r (0.431) (0.063) (0.071) (0.089)

I-'

I-' S1ngle-person households 2.389** 0.111t 0.426** -0.175 0.25 0.337 (65) 00 (0.473) (0.064) (0.083) (0.116)

S1ngle heads of house- 3.210** 0.066t 0.294** -0.137* 0.29 0.125 (219)

hold with others present (0.345) (0.040) (0.058) (0.063)

Households headed by 2.032** 0.111** 0.468** -0.327 0.30 0.264 (235)

a couple (0.382) (0.040) (0.061) (0.070)

SAMPLE: Percent of Rent and Control movers active at two years after enrollment, exclud1ng those w1th

enrollment 1ncomes over the e11g1b111ty I1mits and those I1v1ng 10 their own homes or 10 Subs1dized housing.

DATA SOURCES: In1tial and monthly Household Report Forms, and payments file.

NOTE: Standard error in parentheses. Dependent var1able: In (Rent)

t t-stat1stic s1gn1f1cant at the 0.10 level.

* t-statist1c s1gnificant at the 0.05 level.

** t-statistic s1gn1ficant at the 0.01 level.

SEE = Standard Error of Est1mate.
TABLE X-23

CHANGES IN RATES OF PASSING LOWEST HOUSING STANDARDS

FROM ENROLLMENT TO TWO YEARS FOR

CONTROL AND PERCENT OF RENT HOUSEHOLDS

TREATMENT GROUP

PERCENTAGE PASSING

LOWEST HOUSING STANDARDS

At At Two

Enrollment Years

PITTSBURGH

CHANGE IN

PERCENTAGE

PASSINGa

SAMPLE

SIZE

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstra~ned households

81%

82

77

78

86

79

81

74

PHOENIX

84%

84

77

86

87

89

80

77

+3 (391)

+2 (62)

0 (88)

+8 (106)

+1 (107)

+10 (28)

-1 (299)

+3 (61)

1\11 Percent of Rent

households 72 75 +3 (279)

Percentage rehate:

20% 73 75 +2 (44)

30% 67 68 +1 (79)

40% 74 84 +10 (62)

50% 78 78 0 (77)

60% 59 65 +6 (17)

Control households 66 74 +8 (258)

Unconstrained households 62 82 +20 (39)

SAMPLE: Percent of Rent and Control households act~ve at two years

after enrollment, exclud~ng those w~th enrollment ~ncomes over the ellglbillty

ll.mits and those 11vlng J.n theJ.r own homes or 1.n subsJ.dl.zed housing ..

DATA SOURCES: Hous~ng Evaluat~ons Forms.

NOTE: See Append~xIII for full descr~pt~on of lowest phys~cal hous~ng

standards.

a. Percentage pOJ.nts.

A-119
TABLE X-24

CHAillGES IN RATES OF PASSING PROGRAM

HOUSING STANDARDS FROM ENROLLMENT TO TWO YEARS

FOR CONTROL AND PERCENT OF RENT HOUSEHOLDS

TREATMENT GROUP

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstralned households

All Percent of Rent

households

percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstralned households

PERCENTAGE PASSING

PROGRAM HOUSING STANDARDS CHANGE IN

At At Two PERCENTAGE SAMPLE

Enrollment years PASSINGa SIZE

PITTSBURGH

37% 34% -3% (391)

27 31 +4 (62)

39 2r -12 (88)

30 37 +7 (106)

47 39 -8 (107)

39 32 -7 (28)

33 29 -4 (299)

25 31 +6 (61)

PHOENIX

33 40 +7 (279)

30 48 +18 (44)

27 39 +11 (79)

39 44 +5 (62)

38 39 +1 (77)

24 29 +5 (17)

28 36 +8 (258)

28 41 +13 ( 39)

SAMPLE: percent of Rent and Control households act~ve at two years

after enrollment, excludlng those wlth enrollment lucornes over the ellglbillty

11.ID1.ts and those 11.v1.ng l.n the1.r own homes or In subs1.d1.zed housing.

DATA SOURCES: Hous~ng Evaluat~on Forms.

NOTE: See Append~x III for full descr~pt~on of program phys~cal hous~ng

standards.

a. Percentage pOl-nts.

A-I20
TABLE X-25

CHANGES IN RATES OF PASSING PROGRAM OCCUPANCY STANDARDS

FROM ENROLLMENT TO TWO YEARS FOR CONTROL AND

PERCENT OF RENT HOUSEHOLDS

TREATMENT GROUP

PERCENTAGE PASSING

PROGRAM OCCUPANCY STANDARDS

At At Two

Enrollment Years

PITTSBURGH

CHANGE IN

PERCENTAGE

PASSINGa

SAMPLE

SIZE

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstra1ned households

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

COntrol households

Unconstra~ned households

49%

44

48

51

51

54

46

46

PHOENIX

43%

43

42

37

54

24

38

46

47% -2% (390)

47 -3 (62)

48 0 (87)

50 -1 (106)

42 -9 (107)

46 -8 (28)

41 -5 (299)

44 -2 (61)

55% +12% (279)

52 +9 (44)

53 +11 (79)

58 +21 (62)

58 +4 (77)

35 +11 (17)

53 +15 (258)

64 +18 (39)

SAMPLE: Percent of Rent and Control households act~ve at two years after

enrollment, excludlng those wlth enrollment lucornes over the ellgibl11ty Ilmlts

and those I1vlng In thelr own homes or In subsidlzed housing.

DATA SOURCES: In~t~al and monthly Household Report Forms, Hous~ng

Evaluatlon Forms.

NOTE: See Append~xIII for full descr~pt~on of program occupancy

standards.

a. Percentage pOlnts.

A-121
TABLE X-26

CHANGES IN RATES OF PASSING LOWEST HOUSING STANDARDS

FROM ENROLLMENT TO TWO YEARS FOR CONTROL AND

PERCENT OF RENT HOUSEHOLDS FOR THE MOVERS SAMPLE

TREATMENT GROUP

PERCENTAGE PASSING

LOWEST HOUSING STANDARDS

At At Two

Enrollment Years

PITTSBURGH

CHANGE IN

PERCENTAGE

PASSINGa

SAMPLE

SIZE

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstra~ned households

75%

81

77

68

86

[55]

82

70

PHOENIX

85%

88

71

91

89

[91]

79

87

+10% (142)

+7 (16)

-6 (35)

+23 (44)

+3 (36)

[+36] (11)

-3 (98)

+17 (23)

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstra~ned households

69 77 +8 (163)

64 72 +8 (25)

67 77 +10 (39)

68 82 +14 (34)

74 79 +5 (53)

[67] [67] [0] (12)

67 82 +15 (126)

59 95 +36 (22)

SAMPLE: Percent of Rent and Control movers act~ve at two years after

enrollment, exclud~ng those wlth enrollment lucornes over the ellg1bl11ty lLffiltS

and those 11vlng 10 thelr own homes or in Subsldlzed houslng.

DATA SOURCES: Hous1ng Evaluat10n Forms.

NOTE: See Append1xIII for full descr1pt1on of lowest hous1ng standards.

Brackets lndlcate entrles based on 15 or fewer observatlons.

a. Percentage pOlnts.

A-122
TABLE X-27

CHANGES IN RATES OF PASSING LOWEST HOUSING STANDARDS

FROM ENROLLMENT TO TWO YEARS FOR CONTROL AND

PERCENT OF RENT HOUSEHOLDS FOR THE NONMOVER SAMPLE

TREATMENT GROUP

PERCENTAGE PASSING

LOWEST HOUSING STANDARDS

At At Two

Enrollment Years

PITTSBURGH

CHANGE IN

PERCENTAGE

PASSINGa

SAMPLE

SIZE

72 -5 (ll6)

79 -5 (19)

60 -8 (40)

86 +4 (28)

75 -13 (24)

[60] [+20] (5)

67 +2 (132)

65 0 (17)

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstrained households

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

control households

Unconstrained households

84%

83

77

86

86

94

81

76

PHOENIX

77

84

68

82

88

[40]

65

65

84%

83

81

82

86

88

81

71

0 (249)

0 (46)

+4 (53)

+4 (62)

0 (71)

-6 (17)

0 (201)

-5 (38)

SAMPLE: percent of Rent and Control nomnovers act~ve at two years after

enrollment, excludlng those wlth enrollment lUCornes over the ellg1bl11ty l~ltS

and those liVlng in thelr own homes or In SUbsldlzed houSlnga

DATA SOURCES: Housl.ng Evaluation Forms.

NOTE: See Appendl.x III for full descrl.ptl.on of lowest housing standards.

Brackets lndlcate entrles based on 15 or fewer observatlons.

a. percentage pOlnts.

A-123
TABLE X-28

CHANGES IN RATES OF PASSING PROGRAM

HOUSING STANDARDS FROM ENROLLMENT TO TWO YEARS FOR CONTROL

AND PERCENT OF RENT HOUSEHOLDS FOR THE MOVER SAMPLE

TREATMENT GROUP

PERCENTAGE PASSING

PROGRAM HOUSING STANDARDS

At At Two

Enrollment Years

CHANGE IN

PERCENTAGE

PASSINGa

SAMPLE

SIZE

PITTSBURGH

All Percent of Rent

households 30% 37% +7

percentage rebate:

20% 19 44 +25

30% 43 26 -17

40% 18 46 -28

50% 36 36 0

60% [36] [27] [-9]

Control households 32 29 -3

Unconstra~ned households 17 35 +18

PHOENIX

All Percent of Rent

households 31 42 +11

percentage rebate:

20% 20 44 +24

30% 28 54 +26

40% 38 41 +3

50% 34 38 +4

60% [33] [25] [-8]

Control households 25 38 +13

Unconstra.1ned households 18 45 +27

(142)

(16)

(35)

(44)

(36)

(11)

(98)

(23)

(163)

(25)

(39)

(34)

(53)

(12)

(126)

. (22)

SAMPLE: percent of Rent and Control movers actlve at two years after

enrollment, excludlng those wlth enrollment lncornes over the ellg1hlllty I1mlts

and those I1vlng 10 thelr own homes or 1n SUbSldlzed houslng.

DATA SOURCES: HousJ.ng EvaluatJ.on Fonns.

NOTE: See AppendJ.x III for full descrJ.ptJ.on of program physJ.cal houSJ.ng

standards. Brackets lndlcate entrles based on 15 or fewer observatl0ns.

a. Percentage pOlnts.

A-124
TABLE X-29

CHANGES IN RATES OF PASSING PROGRAM

HOUSING STANDARDS FROM ENROLLMENT TO TWO YEARS FOR CONTROL

AND PERCENT OF RENT HOUSEHOLDS FOR THE NONMOVER SAMPLE

TREATMENT GROUP

PERCENTAGE PASSING

PROGRAM HOUSING STANDARDS

At At Two

EnrolLment Years

CHANGE IN

PERCENTAGE

PASSINGa

SAMPLE

SIZE

PITTSBURGH

All Percent of Rent

households 41% 32% -9%

Percentage rebate:

20% 30 26 -4

30% 36 28 -8

40% 39 31 -8

50% 52 41 -11

60% 41 35 -6

Control households 34 29 -5

Unconstra1.ned households 29 29 0

PHOENIX

All Percent of Rent

households 34 38 +4

Percentage rebate:

20% 42 53 +11

30% 25 22 -3

40% 39 46 +7

50% 46 42 -4

60% [0] [40] [+40]

Control households 30 33 +3

Unconstra1.ned households 41 35 -6

(249)

(46)

(53)

(62)

(71)

(17)

(201)

(38)

(116)

(19)

(40)

(28)

(24)

(5)

(132)

(17)

SAMPLE: Percent of Rent and Control nonmovers act~ve at,twQ years after

enrollment, exclud~ng those w~th enrollment ~ncomes over the el~gibl11ty Ilmits

and those Ilvlng In thelr own homes or In SUbsldlzed houslng.

DATA SOURCES: Hous1ng Evaluat10n Forms.

NOTE: See Append1x III for full descr1pt1on of program phys1cal hous1ng

standards. Brackets lndlcate entlres based on 15 or fewer observatlons.

a. Percentage pOlnts.

A-125
TABLE X-30

CHANGES IN RATES OF PASSING PROGRAM OCCUPANCY STANDARDS

FROM ENROLLMENT TO TWO YEARS FOR CONTROL AND

PERCENT OF RENT HOUSEHOLDS FOR THE ·MOVER SAMPLE

TREATMENT GROUP

PERCENTAGE PASSING

PROGRAM OCCUPANCY STANDARDS

At At Two

Enrollment Years

PITTSBURGH

CHANGE IN

PERCENTAGE

PASSINGa

SAMPLE

SIZE

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstral.ned households

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

UnconstraJ.ned households

44%

38

43

50

42

[36]

36

17

PHOENIX

44

40

49

32

53

[25]

36

41

47% +3% (142)

62 +24 (16)

49 +6 (35)

50 0 (44)

39 -3 (36)

[36] [0] (11)

31 -5 (98)

39 +22 (23)

53 +9 (163)

52 +12 (25)

62 +13 (39)

53 +21 (34)

55 +2 (53)

[25] [0] (12)

59 +23 (126)

59 +18 (22)

SAMPLE: Percent of Rent and Control movers active at two years after

enrollment, exclud1ng those W1th enrollment 1ncornes over the eligibi11ty limats

and those I1ving 1n the1r own homes or 1n Subs1d1zed housing.

DATA SOURCES: In~t~al and monthly Household Report Forms, Hous~ng

Evaluation Forms.

NOTE: See Append~x III for full descr~ption of program occupancy

standards.

Brackets 1nd1cate entr1es based on 15 or fewer observat1ons.

a. Percentage p01nts.

A-126
TABLE X-31

CHANGES IN RATES OF PASSING PROGRAM OCCUPANCY STANDARDS

FROM ENROLLMENT TO TWO YEARS FOR CONTROL AND

PERCENT OF RENT HOUSEHOLDS FOR THE NONMOVER SAMPLE

TREATMENT GROUP

PERCENTAGE PASSING

PROGRAM OCCUPANCY STANDARDS

At At Two

Enrollment Years

PITTSBURGH

CHANGE IN

PERCENTAGE

PASSINGa

SAMPLE

SIZE

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstrained households

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstra~ned households

53%

46

52

52

5E

65

51

55

PHOENIX

43

47

35

43

58

[20]

39

53

46% -7% (248)

41 -5 (46)

48 -4 (52)

50 -2 (62)

44 -12 (71)

53 -12 (17)

46 -5 (201)

47 -8 (38)

56 +13 (116)

53 +6 (19)

45 +10 (40)

64 +21 (28)

67 +9 (24)

[60] [+40] (5)

48 +9 (132)

71 +18 (17)

SAMPLE: Percent of Rent and Control nonmovers act~ve at two years after

enrollment, excluding those with enrollment incomes over the elig~b~lity l~m~ts

and th9se living ~n the~r own homes or in subs~d~zed hous~ng.

DATA SOURCES: In~t~al and monthly Household Report Forms and

Hous~ng Evaluat~on Forms.

NOTE: See Append~x III for full descr~pt~on of program occupancy

standards.

Brackets ~nd~cate entries based on 15 or fewer observations.

a.. Percentage po~nts.

A-127
TABLE X-32

CHANGES IN HOUSING ADEQUACY

FROM ENROLLMENT TO TWO YEARS FOR

CONTROL AND PERCENT OF RENT HOUSEHOLDS

TREATMENT GROUP

PERCENTAGE IN

MINIMALLY ADEQUATE

At At Two

Enrollment Years

HOUSING

a Change

PERCENTAGE IN

CLEARLY INADEQUATE

At At Two

Enrollment Years

HOUSING

a Change

SAMPLE

SIZE

All Percent of Rent

households

percentage rebate:

20%

30%

40%

50%

60%

Control households

Unconstr~ned

households

All Percent of Rent

households

Percentage rebate:

20%

30%

40%

50%

60%

Control households

UnconstraJ..ned

households

31%

24

29

27

40

36

29

19

36

42

28

40

44

14

35

27

28%

22

20

32

33

32

25

32

39

51

32

48

35

29

37

46

PITTSBURGH

-3%

-2

-9

+5

-7

-4

-4

+13

PHOENIX

+3

+9

+4

+8

-9

+15

+2

+19

41%

52

38

42

34

43

38

46

44

42

54

38

35

67

45

54

35%

40

41

32

29

39

35

34

39

33

46

33

35

52

41

30

-6%

-12

+3

-10

-5

-4

-3

-12

-5

-9

-8

-5

o

-15

-4

-24

( 391)

(63)

(85)

( 109)

(106)

(28)

( 301)

(59)

(284)

(45)

(80)

(60)

( 78)

(21)

(256)

( 37)

SAMPLE: Percent of Rent and Control household act~ve at two years after

enrollment, exclu~ng those w~th enrollment ~ncomes over the el~gib~l~ty l~~ts and

those l.1.v1.ng .1.0 theJ.r own homes or J.n subs.1.d.1.zed hous.1.ng.

DATA SOURCES, Hous~ng Evaluat~ons Forms.

NOTE: See AppendJ.x III for full descrl.ptl.on of the adequacy measure 4

a. Percentage pOl.nts.

A-128
TABLE X-33

CHANGES IN HOUSING ADEQUACY

FROM ENROLLHENT TO TWO YEARS FOR

CONTROL AND PERCENT OF RENT MOVERS

PERCENTAGE IN PERCENTAGE IN

MINIMALLY ADEQUATE HOUSING CLEARLY INADEQUATE HOUSING

At At Two At At TwO SAMPLE

Enrollment Changea Enrollment Years Changea TREATMENT GROUP Years SIZE

PITTSBURGH

All Percent of Rent

households 22% 35% +13% 45% 31% -14% (143)

Percentage rebate:

20% 18 41 +23 53 24 -29 ( 17)

30% 33 21 -12 42 42 0 ( 33)

40% 13 43 +30 51 32 -19 (47)

50% 26 34 +8 34 23 -11 (35)

60% [27] [36] [+9] [45] [27; [-18] (11)

Control households 25 26 +1 43 32 -11 (100)

unconstraJ.ned

householdb 14 41 +27 55 23 -32 (22)

PHOENIX

All Percent of Rent

households 32 40 +8 48 38 -10 (170)

Percentage rebate:

20% 30 44 +14 52 37 -15 ( 27)

30% 25 42 +17 50 32 -18 (40)

40% 30 42 +12 42 42 0 (33)

50% 43 37 -6 43 37 -6 (54)

60% 19 31 +12 69 44 -25 (16)

Control households 37 43 +6 45 31 -14 (127)

Unconstralned

households 19 57 +38 62 19 -43 ( 21)

SAMPLE: Percent of Rent and Control movers actlve at two years after enrollment, exc!udlng those wlth enrollment lucornes over the ellg1bl11ty Ilmlts and those

Ilvlng In thelr own homes or In Subsldlzed houslng.

DATA SOURCES: Houslng Evaluatl0ns Forms.

NOTE: See Append~x III for full deSCrl.ptlon of the ajequacy measure.

A-129
TABLE X-34

CHANGES IN HOUSING ADEQUACY

FROM ENROLLMENT TO TWO YEARS FOR

CONTROL AND PERCENT OF RENT NONMOVERS

PERCENTAGE IN PERCENTAGE IN

MINIMALLY ADEQUATE HOUSING CLEARLY INADEQUATE HOUSING

At At Two At At Two SAMPLE

TREATMENT GROUP Enrollment "Years Changea Enrollment Years Change a SIZE

PITTSBURGH

All Percent of Rent

households 36% 24% -12% 38% 38% 0% ( 248)

Percentage rebate:

20% 26 15 -11 52 46 -6 (46)

30% 27 19 -8 35 40 +5 (52)

40% 37 24 -13 35 32 -3 (62)

50% 46 32 -14 34 32 -2 ( 71)

60% 41 29 -12 41 47 +6 (17)

Control households 31 25 -6 36 36 0 (201)

UnconstraJ..ned

households 22 27 +5 41 41 0 ( 37)

PHOENIX

All Percent of Rent

households 42 38 -4 39 40 +1 (114)

Percentage rebate:

20% 61 61 0 28 28 0 (18)

30% 30 22 -12 58 60 +2 (40)

40% 52 56 +4 33 22 -11 ( 27)

50% 46 29 -17 17 29 +12 (24)

60% [0] [20] [+20] [60] [80] [+20 ] (5)

Control households 33 30 -3 46 51 +5 (129)

UnconstraJ..ned

households 38 31 -7 44 44 0 (16)

SAMPLE: Percent of Rent and Control nonmovers actJ..ve at two years after enrollment, excludJ..ng those wJ..th enrollment J..ncomes over the elJ..gJ..bJ..lJ..ty IJ..mJ..ts and

those IJ..vJ..ng J..n theJ..r own homes or J..n subsJ..dJ..zed housJ..ng.

DATA SOURCES: Hous~ng Evaluat~ons Forms.

NOTE: See Append~x III for full descr~pt~on of the adequacy measure.

a. Percentage poJ..nts.

A-l30
TABLE X-35

OlANGE IN HEDONIC HOUSING SERVICES INDEX

FROM ENROLLMENT TO TWO YEARS

FOR CONTROL AND PERCENT OF RENT HOUSEHOLDS

At

TREATMENT GROUP Enrollment

MEAN HEDONIC INDEX

At

Two

Years

MEAN CHANGE IN INDEX

PERCENTAGE

Mean of Ratto of

AMOUNT Rat~o Means

SAMPLE

SIZE

PITTSBURGH

All percent of Rent

households $114 $121 $ 7 9% 6% ( 353)

Percentage

rebate:

20% 107 116 9 9 8 (58)

30% 114 119 5 6 4 (80)

40% 116 123 7 9 6 ( 100)

50% 116 123 7 8 6 (90)

60% 115 127 12 16 10 (25)

Control households 114 120 5 6 4 (273)

Unconstra.l.ned

households 106 116 11 12 10 (52)

PHOENIX

All Percent of Rent

households 132 149 17 16 13 (241)

Percentage

rebate:

20% 135 150 15 20 11 (36)

30% 130 142 12 11 9 (71)

40% 135 153 19 15 14 (54)

50% 136 153 17 14 13 (65)

60% [110] [141] [31] [37] [28] (15)

Control households 128 144 16 17 13 (231)

UnconstraJ..ned

households 132 158 26 34 20 (34)

SAMPLE: Percent of Rent and Control households act~ve at two years

after enrollnent, excludl.ng _those with enrollment l.ncomes over the eligJ.bl.lity

ll.mits and those livJ.ng J.n their own homes or J.n subs1dized housl.ug.

DATA SOURCES: In~tial and monthly Household Report Forms, Hous~ng

Evaluation Forms, 1970 census of Populat~on, and Base1~ne and Th~rd Per~ofuc

IntervJ.ews •

NOTE: Brackets indicate entries based on 15 or fewer observatl.ons.

A-131
TABLE X-36

alANGES IN HEDONIC HOUSING SERVICES INDEX

FROM ENROLLMENT TO TWO YEARS FOR CONTROL AND

PERCENT OF RENT HOUSEHOLDS FOR THE MOVER SAMPLE

MEAN HEDONIX INDEX MEAN CHANGE IN INDEX

At PERCENTAGE

At Two ~an of Rat~o SAMPLE

TREATMENT GROUP Enrollment Years AMOUNT Ratio of Means SIZE

PITTSBURGH

All Percent of Rent

households $111 $128 $17 19% 15% ( 121)

Percentage

rebate:

20% [106] [121J [15] [17] [14] (12)

30% 112 124 12 15 11 (30)

40% 114 130 17 19 15 (41)

50% 112 130 18 18 16 (29)

60% [103] [130] [27] [40] [26] (9)

Control households 114 126 12 13 11 (92)

Unconstra~ned

households 105 131 27 31 26 ( 19)

PHOENIX

All Percent of Rent

households 133 157 24 22 18 (134)

Percentage

rebate:

20% 127 146 18 29 14 ( 19)

30% 138 159 21 17 15 ( 38)

40% 138 165 27 20 20 ( 30)

50% 135 157 22 18 16 (42)

60% [106 ] [147] [41] [49] [39] ( 10)

Control households 126 155 30 32 24 (109)

Uncons trro.ned

households 125 166 41 50 33 ( 18)

SAMPLE: Percent of Rent and Control movers act~ve at two years after

enrollment, excludang those W1th enrollment lncomes over the eliglbl11ty lxmltS

and those I1VJ..ng 10 thelr own homes or 1n subSlfuzed houslng.

DATA SOURCES: IIllhal and monthly Household Raport Fonns, Hous~ng

Evaluatl0n Forms, 1970 census of Population, and Baseline and Th1rd Perlodic

Intervlews .

NOTE: Brackets indicate entrles based on 15 or fewer observatl.ons.

A-132
TABLE X-37

CEANGES IN HEDONIC HOUSING SERVICES INDEX

FROM ENROLLMENT TO WO YEARS FOR CONTROL AND

PERCENT OF RENT HOUSEHOLDS FOR THE NONMOVER SAMPLE

At

TREATMENT GROUP Enro11nent

MEAN HEDONIC INDEX

At

Two

Years

MEAN CHANGE IN INDEX

PERCENTAGE

Mean of Rat~o of

Al-I0UNT Rat~o Means

SAMPLE

SIZE

PITrSBURGH

All Percent of Rent

households

Percentage

rebate:

20%

30%

40%

50%

60%

Cbntrol households

Unconstrained

households

$115

108

115

117

118

122

114

106

$118

115

116

118

120

125

116

108 .

$ 2

7

1

1

2

3

2

1

3%

7

1

3

3

3

2

1

2%

6

1

1

2

2

2

1

(232)

(46)

(50)

(59)

(61)

(16)

(181)

( 33)

All Percent of Rent

households

Percentage

rebate:

20%

30%

40%

50%

60%

Cbntrol households

unconstrm.ned

households

131

144

123

131

137

[118]

130

139

PHOENIX

139

156

128

139

146

[129]

134

149

8

12

5

8

9

[11]

4

10

7

9

5

9

7

[12]

5

14

6

8

4

6

7

[9]

3

7

(107)

(17)

(38)

(24)

(23)

(5)

(122)

(16)

SAMPLE: Percent of Rent and Control nonmovers act1ve at two years

after enrollment, exclufung those Wlth enrollment incomes over the elJ..gJ.b11ity

l1mits and those living 10 their own homes or 1n subsid1zed hous1.ng.

DATA SOURCES: Initial and monthly Household Report Forms, Hous~ng

Evaluation Forms 1 1970 census of Population, and Baseline and Third PerJ.Delle

Interviews.

NOTE: Brackets .l.nfucate entrJ.es based on 15 or fewer observatJ.ons.

A-133
TABLE X-38

SEARCH EFFORT FOR LAST MOVE

MEAN SEARCH TIME

(days)

MEAN NUMBER

OF UNITS SEEN

MEAN NUMBER

OF CALLS MADE SAMPLE SIZE

Control

Households

Percent

of Rent

Households

Control

Households

Percent

of Rent

Households

Control

Households

Percent

of Rent

Households

Control

Households

percent

of Rent

Households

HOUSEHOLD

GROUP

All Movers

Nonm~nority movers

Black movers

All Movers

Nonminor~ty movers

All m1nority

movers

Span1sh Amer1can

movers

97

97

98

34

31

40

28

119

117

129

46

37

62

a

76

PITTSBURGH

6.6 7.8

6.6 7.3

6.5 9.8

PHOENIX

6.3 6.2

7.1 7.6

4.8 3.7

4.4 4.5

13.2

13.5

12.1

10.2

12.6

5.5

b

6.0

16.0

16.4

14.3

8.1

10.4

4.0

5.4

(143)

(118)

(25)

(162)

(108)

(54)

(40)

(102)

(82)

(20)

(140)

(90)

(50)

(31)

SAMPLE: Percent of Rent and Control movers act1ve at two years after enrollment, excluding those w1th enrollment 1ncomes over the elig1b11ity 11m1ts and those 11v1ng in the1r own homes or in subs1dized houS1ng.

DATA SOURCES: Init1al and monthly Household Report Forms, and period1c Interv1ews.

a. T-test compar1ng means of Percent of Rent and Control Span1sh American households significant at the 0.05

level (one-tail test), t = 1.81.

b. T-test comparing means of nOnffi1nOr1ty and Spanish Amer1can Percent of Rent households sign1f1cant at the

0.05 level (one-tail test). t = 1.74.
TABLE X-39

DEMAND FOR RENT COMPONENTS

INDEPENDENT VARIABLE STANDARD

DEPENDENT VARIABLE a In (MonthlY)bERROR OF

R

2 Constant In (I-a) Income ESTIMATE

PITTSBURGH

Rent (expend~tures 2.893** -0.230** 0.338** 0.27 0.18

defin~t~on) (.324) (.065 ) (.054)

Hedonic ~ndex of 3.402** -0.113* 0.226** 0.24 0.10

hous~ng services (.287) (.057) (.047)

Hedon~c resldual -0.462* -0.159** 0.089* 0.20 0.06

( .236) (.047) (.039)

Tenure characterlstlcs -0.065 0.027* 0.019t 0.05 0.04

(.063) (.013) (.010)

Def~n~t~onal d~ffer- 0.018 0.000 0.004 0.05 0.01

ences in rente (.063) ( . 013) (.010)

Sample s~ze (214)

level.

level.

level.

0.10

0.05

0.01

SAMPLE: Percent of Rent and Control moverS actlve at two years

after enrollment, excludlng those wlth enrollment lucornes over the ellgibillty I1mQtS and those Ilvlng 10 thelr own homes or 10 SubSldlzed houslng.

DATA SOURCES: In~t~al and monthly Household Report Forms, and

payments f~le.

a. a = percentage rebate.

b. Three-year average lucame 15 used here as a measure of

permanent lUCame.

c. Between the expendltures deflnltlon and the de£lnltlon used

for estkmatlon of hedonlc lndex.

t t-stat~st~c sign~f~cant at the

* t-statlstlc slgnlflcant at the

** t-statlstlc slgnlflcant at the

A-135
TABLE X-39, cont1nued

DEMAND FOR RENT COMPONENTS

INDEPENDENT VARIABLE STANDARD

a In (MonthlY)b ERROR OF 2 DEPENDENT VARIABLE Constant In (I-a) Income ESTIMATE R·

PHOENIX

Rent (expend~ture 2.901** -0.215** 0.353** 0.31 0.21

def~n~t10n) (.278) (.064) ( .046)

Hedonlc lndex of 2.739** -0.045 0.375** 0.29 0.23

houslng serVlces (.259) ( .060) (.043)

Hedonlc res~dual 0.097 -0.193** -0.021 0.23 0.06

( .208) ( .048) (.034)

Tenure characterlstlcs 0.029 0.017 0.001 0.06 0.01

(.050 ) (.011) (.008)

Deflnltl0nal dlffer- 0.035 0.005 -0.002 0.04 0.00

ences ln ~ent c (.031) (.007) (.005)

Sample s~ze (257)

level.

level.

level.

0.10

0.05

0.01

SAMPLE: Percent of Rent and Control movers actlve at two years

after enrollment, excludlng those with enrollment lncomes over the eliglbll~ty llmlts and those I1vlng In thelr own homes or In Subsldlzed houslng.

DATA SOURCES: In~t~al and monthly Household Report Forms, and

payments hIe.

a. a = percentage rebate.

b. Three-year average lncorne lS used here as a measure of

permanent lncorne.

c. Between the expendltures deflnitl0n and the deflnltl0n used

for estllnatlon of hedonlc lndex.

t t-stat~st~c s~gn~f~cant at the

* t-statlstlc slgnlflcant at the

** t-statlstlc slgniflcant at the

A-136
TABI.C X-40

STRATIrIED LOG-LINeAR HOUSING SERVICES FUNrTIONS

FOR TilE OVERALL SAMPLE

(PITTSBURGU)

--

"LL 1l0USEliOLDS NONMINORIT'l nonSEIiOLDS MINORITY HOUSEHOLDS

Im.orne Pr:Lce Income Prl.ce Income Price

Elas- ElagR

2 Elas- Elac;-

R2 Elas- Elac;-R2 INDEPENDENT VARIABLES Constant bC:L ty tl.Clt-y SEC Constant bCl.ty t:LC:Lty SEE Constant bC:Lty tH'] ty SEE

All households 3.378** o 224** -0 106** o J2 0.142 3 319** o 234** -0 172** o 21 o 167 3.622** 0 181** -0 019 0.25 0.076

(O 115) (0 022) (0 030) (N=635) (0 144) (0.024) (0 031) (N",,<;09) (0 343) (0 057) (0 OB3) (N,=126)

S:Lngle-person households 2 870** 0 310** -0 188** o 24 o 158 2.725** 0.340** -0 202** o 24 o 179 3 664** 0.143 -0 093 0.24 o 065

(0 390) (0 070) (0 072) (N=128) (0.432) (0.077) (0 074) (N=109) (0.814) (0.148) (0 218) (N=19)

sUlgle heads of house- 4 131** 0 103* -0.042 o 22 o 022 3.700** 0.174** -0 092 t o 21 0.073 5 407** -0.103 0.147 o 22 0.040

hold w:Lth others (0 27<» (0 047) (0 048) (N=241) (0.315) (0.053) (0.053) (N=l71) (0 571) (0 094) (0 103) (N=70)

Households headed by 2 696** 0.329** -0 140** o 20 0.213 2.647** 0.339** -0 125** o 19 o 221 2 949** 0.277* -0.235 0.24 0.191

a couple (0.248) (0 040) (0 044) (N=26s) (0 268) (0.0431 (0.045) (N::229) (0.676) (0.109) (0 144) (N=37)

ELDERLY

Income Pr:Lce

Elas- ElasR

2 INDEPENDENT VARIABLE Constant bcity tl.C:Lty SEE

All households 2 914** o 298** -0.248** 0.25 0.173

(0.430) (0 077) (0 080) (N=107)

SAMPLE Pittsburgh Percent of Rent and Control households actl.ve at two years after enrollment, exclud1ng those w1th enrollment lncornes over

the el1g1bl.ll.ty I1ml.ts and those I1v1ng :Ln the1r own homes or 1n subs1d1zed housl.ng

DATA SOURCeS In1t1al and monthly Household Report Forms, Housl.ng Evaluation Forms, 1970 Census of populat10n, and Basellne and Per1od1c

Interv1ews

NOTE Standard error 1n parentheses

t t-statist1c s1gn1f1cant at the 0.10 level

* t-statist1c s1gn~f1cant at the 0 05 level

~* t-statist1c s1gnl.f1cant at the 0.01 level

SEE = standard Error of Estl.mate.
TABLE X-40, continued

STRATIFICD LOG-LINEAR HOUSING SERVICES FUNCTIONS

FOR TilE OVERALL SAMPLE

(PHOENIX)

ALL nOUSEIlOLDS NONMINORITY HOUSEHOLDS MINORITY HOUSEHOLDS

Income Pr:tce Income Pr:tce Income pr:tce

c1as- ClasR2 Elas- ElasR

2 Elas- ElasR2 INDEPENDENT VARIABLES Constant t:I.cJ.ty t:I.C1.ty SEE Constant tl.city hcity SEE Constant tl.Cl.ty tJ.cJ.ty SEE

All households 2 776** o 359** -0 090* 0.28 0.238 2 616** o 391** -0.125* o 25 0.305 3.417** o 228** -0.071 0.30 o 112

(0.178) (0 030) (0 045) (N-486) (0 205) (0.034) (0.051l (N=319) (0 303) (0.051) (0 076) (N=167)

S:tngle-person households 2 669** o 376** -0.101 o 29 o 246 3.333** 0 265** -0 047 0.28 0.118 1 245t 0.589** -0.645* o 20 0.746

(0 399) (0.070) (0.117) (N=93) (0.487) (0 086) (0 126) (N=78) (0 578) (0.1041 (0 231) (N=15)

SJ.ngle heads of house- 2 558** 0.401** 0.047 0.27 0.2S9 2.141** 0.475** -0.150t 0.23 0.354 3.933** O.ISH 0.033 0.28 0.042

hold W1.th others (0 310) (0.052) (0.066) (N=173) (0 407) (0.067) (0.077) (N=98) (0.502) (0.087) (0.100) (N=75)

Households headed by 2 554** 1 385** -0 128** o 29 o 189 2.463** a 412** -0 156* o 25 0.292 3 258** 0.247* -0 123 o 31 0.076

a couple (0.350) (0 056) (0 071) (N=220) (0.350) (0.056) (0.076) (N=143) (0.711) (0.116) (0 123) (N-77)

ELDERLY SPANISH AMERICAN BLACK

Income PrJ.ce Income Price Income Price

Elas- ElasR2 Elas- ElasR2 Elas- E1asR2 INDEPENDENT VARIABLE Constant t1.C1.ty tJ.CJ.ty SEE Constant tiCJ.ty t1.cJ.ty SEE Constant tJ.C1.ty tJ.C1.ty SEE

All households 2 520** 0.405** -0 096 o 24 0.209 3.234** 0 261** -0 057 0.29 0.135 3.477** 0.204 -0.459* o 39 a 182

(0.515) (0.093) (0 129) (N=109) (0.361) (0 060) (0.087) (N=124) (0 774) (0 136) (0.204) (N=44)

SAMPLE Phoen1Y Percent of Rent and Control households act1.ve at two years after enrollment, exc1udJ.ng those w1th enrollment 1ncornes over the

el1.gibl.ll.ty !J.m1ts and those 11v1ng J.n the1.r own homes or 1.0 subsidl.zed housJ.ng.

DATA SOURCES In:I.tlal and monthly Household Report Forms, HousJ.ng EvaluatJ.on Forms, 1970 Census of populat10n, and Basel~ne and PerJ.odic

Interviews

NOTD: Standard error in parentheses.

i t-statl.st1.C eign:tf).cant at the 0 10 level.

* t-statl.stic sJ.gnificant at the 0 05 level.

** t-statl.stJ.c signl.f1.cant at the 0.01 level

SEE = standard Error of Est1.mate.
TABLB X-41

STRATIFIED LOG-LINEAR HOUSI~G SERVICES FUNCTIONS

FOR THE MOVER SAMPLE

(PITTSBURGII)

ALL HOUSEHOLDS NONMINORlTY HOUSEHOLDS MINORITY HOUSEHOLDS

Income Pr1.ce Income PrJ.ce Income Prl.ce

Elas- ElasR

2 Elas- ElasR2 Elas- ElasR2 INDEPENDENT VARIABLES Constant tl.Cl.ty t1.Cl.ty SEO Constant tl.C1.ty tl.C1.ty SOE Constant tl.C1.ty tl.Cl.ty SEE

All households 3.402** 0.226** -0.1131 0.24 0.101 3 126** 0.269** -0.143* a 22 o 1585 4 922** -0.012 0.067 0.30 0.004

(0 287) (0.047) (0 057) (N=214) (0.291) (0.048) (0 057) (N=180) (0.923) (0.151) (0 201) (N=34)

Sl.ngle-person households 3.338** o 241 -0.118 a 25 o 073 3 135** o 275 -0.112 a 25 0.084 Only 3 observatl.ons

(0 929) (0 163) (0.168) (N:::32) (1 025) (0.180) (0 174) (N=29)

S1.ngle heads of house- 3. 745'1l:1r 0.181t -0.038 a 23 o 0425 3.316** 0.245* -0.121 0.22 0.096 6.639** -0 273 o 275 a 18 0.227

hold W1.th others (0 562) (0.095) (0.085) (N=87) (0 627) (0.107) (0.091) (N=69) (0.993) (0 165) (0.166) (N=18)

Households headed by 1.681** 0.489"'* -0.246** 0.21 0.322 L 742** o 484** -0.202** 0.19 0.349 o 941 0.5751 -0.611 0.31 0.338

a couple (0 473) (0.076) (0 080) (N=9S) (0 471) (0.075) (0.077) (N=82) (1. 738) (0 274) (0 353) (N=13)

ELDERLY

Income Pr1.ce

Elas- ElasR2 INDEPENDENT VARIABLe Constant tl.C1.ty ticl.ty SEE

All households 3.387* 0.222 -0 215 a 26 o 067

(1. 246) (0.217) (0 219) (N=23)

SAMPLE Pl.ttsburgh Percent of Rent and Control movers act1.ve at two years after enrollment, excludl.ng those w1.th enrollment l.ncomes over the

ell.gl.b1.11.ty 11.m1.ts and those 11.vl.ng 1.n thel.r own homes or l.n subs1.dl.zed hous1.ng

DATA SOURCES. In1.tl.al and monthly Household Report Forms, Housl.ng Evaluat1.on Forms, 1970 Census of Populat1.on, and Base11.ne and perl.od1.c

Interv1.ews

NOTE Standard error 1.n parentheses

t-stat1.stl.c s1.gnl.fl.cant at the 0.10 level

* t-stat1.stl.C sl.gnl.fl.cant at the 0.05 level

** t-statl.stl.c sl.gnl.fl.cant at the 0 01 level

SEE::: Standard Error of estl.mate.
TABLE X-41, cont~nued

STRATlrIED LOG-I.INEAR 1I0USINC. SERVICCS rUNCTIONS

rOR THC MOVER SAMPLE

(PHOENIX)

- ------- - ________~_L IIOUSL:IIOLDS NONMINORITY UOUSC!tOLDS MINORITY 1I0USEIIOLDS

Tne-ome f'r~cc Income Pr~ce Ine-orne Pr1ce

J::la<;- ElasR

2 E1as- ElasR2 Elas- r.:las- 2 INDCPENDENT VARIABI,CS COllstD.llL h<"lty tl.Clty SEE Constant t1C1ty t1C1ty SEC Cooc,tant t1C1ty t~c~ty SEC R

- 1\11 households 2.739* 0 375** -0 045 o 29 o 232 2 379** 0 440** -0 129* o 24 o 377 3 962** o ] 541 o 023 0.32 o 038

(0 259) (0 043) (0 050) (N=257) (0 272) (0 045) (0.065) (N=168) (0.501) (0 085) (0 106) (N=89)

S1ngle-per'3on household,; 2 201** 0 464** -0 3661 o 25 0.478 2 309** 0 454** -0 249 o 25 0.396 Only 5 obscrvat10n,;

(0 578) (0 101) (0 197) (N=29) (0 711) (0 123) (0 225) (N=24)

S1nq1e heads of house- 2 549** 0 416** 0.045 o 27 o 270 2 042** 0 497** -0 145 o 24 o 381 3 752** 0 '05t o 185 0.29 o 101

hold w1th others (0 401) (0 067) (0 001) (N=lll) (0 497) (0 082) (0.101) (N=64) (0 704) (0 122) (0 125) (N=47)

Households headed by 2 753** 0 365** -0 121 0.31 o 154 2.315** 0 448** -0 123 0.25 0.325 4.906** -0 012 -0 120 o 35 0.011

a couple (0 510) (0 082) (0 098) (N"'1l7) (0 464 (0 074) (0 097) (N=80) (1.229) (0_199) (0 193) (N=37)

ELDERI;i SPANISH AMERICAN BLACK

Income Prl.ce Income Prl.ce Income PrJ.ce

r:1<1';- ClasR

2 Elas- ElasR

2 Elas- r:lasR2

INDCPENDENT VARIABLE Constant L1C1.ty t1C1ty SeE Constant t1Cl.ty t1.C1.ty SEE Constant bC1ty tJ.CJ.ty SEE

•All households 0.92' 0 714* -0 207 o 26 o 315 4 345** o 100 0 116 o 31 o 033 3 818** o 159 -0 136 o 35 o 59

(l 490) (0 272) (0 297) (N=18) (0.611) (0 102) (0 121) (N=62) (0 949) (0_165) (0 218) (N=27)

SAMPLE Phoenl.x P0rcent of RenL and Control households act1.vc at two years after enrollment, excluding those w1th enrollment l.ncomes over the

cligJ.b1.l1ty l1m~ts and thosc 11.V1ng 1.n th(ur own homes or ~n subSJ.d1zed hous~ng.

DATA SOURCES IllJt1al and monthly Household Report Forms, Hou';1ng Evaluat10n rorm<>, 1970 Census of populat1on, and BaseJ1ne and Perl.Od1C

Interv1ews.

NOTE Standard error ~n parentheses

t t-statLst1.C s1.gn1.fLcant at the 0 10 level

* t-statl.stJ.c s1gnl.f1cant at the 0 05 level

** t-stat~stic sl.gnl.fl.cant at the 0 01 level.

Sr:E = Standard r:rror of EstJ.matc.
TABLE X-42

MEAN MONTHLY HOUSING SERVICES AT ENROLLMENT

AND AT 'IWO YEARS AFTER ENROLLMENT FOR THE

MOVER SAMPLE BY RACEjETHNICITY

MEAN CHANGE IN

HOUSING SERVICES

MEAN HOUSING

SERVICES PERCENTAGE

At At Two Mean of Rat~o of SAMPLE

TREATMENT GROUP Enrollment Years AMOUNT the Rat~o the Means SIZE

PITTSBURGH

Non~nor1ty households

Percent of Rent

households $113 $126 $13 15% 12% ( 102)

Control households 114 125 10 11 9 ( 76)

Unconstralned

households [104] [132] [2S] [35] [27] (14)

M~nor~ty (black)

households

Percent of Rent

households 103 136 34 41 33 (19)

Control households [110] [128J [18] [22] [16] (15)

Unconstra1ned

households [105] [132 J [27] [26] [26] (4)

PHOENIX

Nonmlnorlty households

Percent of Rent

households $145 $168 $24 21% 17% (86)

Control households 137 162 25 24 18 (68)

unconstra1ned

households [142J [169 J [27] [27] [19] (9)

( cont~nued)

SAMPLE: Percent of Rent Unconstralned and Control movers actlve at two

years after enrollment, excludlng those Wlth enrollment lncornes over the e11g1­

bl11ty l1rnlts and those I1vlng 1n thelr own homes or 1n Subsldlzed houslng.

DATA SOURCES: In~t~al and monthly Household Report Forms.

A-141
TABLE X-42 (cont~nued)

MElIN MONTHLY HOUSING SERVICES AT ENROLLMENT

lIND AT TWO YEARS AFTER ENROLLMENT FOR THE

MOVER SAMPLE BY RACE/ETHNICITY

MElIN CHANGE IN

HOUSING SERVICES

MElIN HOUSING

SERVICES PERCENTAGE

At At Two Mean of Rat~o of SAMPLE

TREATMENT GROUP Enrollment Years AMOUNT the Rat~o the Means SIZE

PHOENIX (cont~nued)

M~nor~ty households

Percent of Rent

households $111 $134 $23 23% 21% (46)

Control households 102 142 40 49 39 (38)

Unconstra~ned

households [108] [163] [55] [74] [51] (9 )

Black households

Percent of Rent

households [118] [131] [13] [11] [11] (11)

COntrol households [90] [124] [33] [57] [37] (12)

Unconstra~ned

households [106] [189] [83] [79] [79] (1)

Span~sh-Amer1can

households

Percent of Rent

households 109 135 26 28 24 (35)

Control households 108 151 43 46 40 (26)

Unconstra1ned

households [109] [160] [51] [74] [47] (8)

SAMPLE: Percent of Rent Unconstra1ned and Control movers act1ve at two

years after enrollment, exclud1ng those w1th enrollment 1ncomes over the e11gib111ty 1~1ts and those 11v1ng 10 the1r own homes or in Subs1d1zed hous1ng.

DATA SOURCES: In~t~al and monthly Household Report Forms.

A-142
----------------------------------------------

TABLE X-43

STRATIFIED LOG-LINEAR HOUSING EXPENDITURES, HOUSING SERVICES, AND

HEDONIC RESIDUALS ELASTICITIES FOR THE MOVER SAMPLE

PITTSBURGH PHOENIX

I~DEPENDENT VARIABLES

All Households

EXPENDITURESHOUSING

SERVICES

HEDONIC

RESIDUAL

SAMPLE EXPENDI- HOUSING

SIZE TURES SER~ICES

HEDONIC

RESIDUAL

SlIMPLE

SIZE

Income elast1C1ty

P~1ce elast1c1ty

SJ,nqle-person douseholds

IncOme elast1c1ty

Pr1ce elast1c1ty

S1ngle Heads of Household

w:J,th Others

Income elast1c1ty

Pr1ce elast1C1ty

Households Headed bv

a Couple

IncOme elast1c1ty

prJ,ce elast1c1ty

Nornm.nOrI.ty Fiouseholds

Income elastJ.cJ.ty

prJ,ce elastJ.cJ.ty

IncOme elastJ.cJ.ty

PrJ.ce elastJ.cJ.ty

Blac~ ~ouseholds

Income elastJ.cJ.ty

PrJ.ce elastJ.cJ.ty

SoanJ.sh AmerJ.can Households

Income elastJ.cJ.ty

0.338**

(0.054)

-0230'"

(0065)

o 283

(0 180)

-0.055

(0.185)

0.222*

(0.105)

-0 216*

(0 093)

o 560**

(0094)

-0 349**

(0099)

0.358**

(O 059)

-0.233**

(0 070)

a 232t

(0.136)

-0 207

(0181)

a

0.226**

(O 047)

-0.113*

(0.057)

o 241

(0163)

-0 118

(0 168)

0.1.81+

(0.095)

-0.038

(0.085)

o 489**

(0.076)

-0.246**

(0 080)

o 269**

(0048)

-0 143*

{O 057}

-0.012

(0.151)

0.067

(0 201)

o 089*

(O 039)

-0 159**

(O 047)

o 143

(0.032)

o 032

(0094)

-0.021

(0089)

-0.245**

(O 079)

o 085

(0.067)

-0.137+

(0.071)

o.on.... (0.038)

-0 13'3**

(0 045)

0194

(0.140)

-0 280

(O 187)

(214)

(32)

(87)

(95)

(l80)

(34)

0.353**

(O 046)

-0 215**

(O 064)

o 476**

(0 079)

-0 404**

(0 l54)

0.321**

(0076)

-0.073

(0.092)

0.364**

(0 088)

-0 356**

(O 106)

o 406**

(O 050)

-0 290**

(O 073)

o 169T

W.09l)

-0.154

(0.115)

o 214

(0.1?3)

-0.277

(0228)

o 113

(O 113)

_0 081

(0 136)

o 375**

(0 043)

-0 045

(0060)

o 464**

(0 101)

-0 366T

(0 197)

o 416**

(0 067)

o 045

(O 08l)

o 365**

(0.082)

-0.121

(0 098)

o 440**

(0.045)

-0.129*

(0065)

o 154+

(0 085)

o 023

(0.106)

0159

(0165)

-0 138

(0 218)

o 100

(0 102)

0.116

(O.12l)

-0 021

(0.034)

-0.193**

(0.048)

0.011

(0058)

-0 111

(0112)

-0 086

(0.058)

-0 129+

(0 070)

0.005

CO 065)

-0 272**

(O 078)

-0 042

(0 038)

-0 197**

(O 056)

o OL~

(0.071)

-0.180*

(0.090)

0.003

(0160)

-0 132

(0.211)

o 058

(0.080)

-0 211*

(O 096)

(257)

(29)

(111)

(117)

(l68)

(89)

(27)

(62)

SAMPLE. Percent of Rent and Control movers act~ve at t~ years after enrollment, exc1ud~ng those w~th

enrollment lncomes over the el~g~b~l~ty ll.nl1ts and those lLvl.ng ~n the~r own homes or ~n subs~d~zed nouS~l'g

DATA SOURCES InLtLal and monthly Household Report Forms, HouSLng Evaluat~on Forms, 1970 Census of

populat~on, ard BaselLne and perLodLc I~tervLews.

NOTE Standard error Ln parentheses. ISE LndLcates that the overall F-statLstLc for the ~quatLon was

not sLgnLfLcant at the 0 10 level or less.

a. All mJ.norLty households Ln PLttsburgh are black.

t t-statLstLc sLgnJ.fLcant at the 0.10 level.

* t-StatLstLC sLgnLfLcant at the 0.05 level.

** t-StatLStLC sLgnLfLcant at the 0.01 level.

A-143
TABLE X-44

LOG-LINEAR EXPENDITURE FUNCTIONS FOR HOUSING SERVICES

USING FULL SAMPLE AND SUBMARKET HEDONIC INDICES FOR PHOENIX

INDEPENDENT

VARIABLES

WHITE

HOUSEHOLDS

MINORITY

HOUSEHOLDS

SPANISH

AMERICAN

HOUSEHOLDS

Full Sample Index

Constant

Ln(l-a)

Ln(monthly lncome)

Standard error

of estl.mate

Sample Sl.ze

Spanl.sh Amerl.can

Submarket Index

Constant

Ln(l-a)

Ln (monthly lncome)

Standard error

of estimate

Sample Sl.ze

2.446** 3.883** 4.205**

(0.273) (0.488) (0.543)

-0.109 0.023 0.098

(0.067) (0.104) (0.120)

0.430** 0.167 0.122

(0.045) (0.083) (0.099)

0.37 0.04 0.04

0.25 0.32 0.31

(166) (91) (63)

2.401** 3.927** 4.182**

(0.284) (0.491) (0.063)

-0.1l7t 0.027 0.099

(0.070) (0.083) (0.122)

0.441** 0.164* 0.129

(0.047) (0.083) (0.101)

0.36 0.04 0.04

0.26 0.33 0.31

(166) (91) (63)

SAMPLE: Phoenl.x Percent of Rent and Control movers actl.ve at two

years after enrollment, excludl.ng those wl.th enrollment lucornes over theellgl.b111.ty 11.IDl.ts and those 11vlng In thelr own homes or lD subsl.dlZed

housl.ng.

DATA SOURCES: Inltlal and monthly Household Report Forms, Houslng

Evaluatlon Forms, 1970 Census of populatl.oD, Basell.ne and Perl.odl.c Intervl.ews.

NOTE: Standard error lD parentheses.

t t-statl.stl.C slgnl.flcant at the 0.10 level.

* t-statlstlc slgnlflcant at the 0.05 level.

** t-statlstlC slgnlflcant at the 0.01 level.

A-144
TABLE X-45

ESTIMATE OF LOG (NORMAL RENT) AT

TWO YEARS AFTER ENROLLMENT

PITTSBURGH PHOENIX

INDEPENDENT STANDARD STANDARD

VARIABLE COEFFICIENT ERROR COEFFICIENT ERROR

MOVERSa

Constant (two years) 3.848 (0.335) 3.026 (0.275)

Constant (at enrollment) 3.673 (0.322) 2.866 (0.272)

Log(monthly 1ncome) 0.178 (0.054) 0.328 (0.045)

Ser1al correlat~on 0.447 0.406

R2 0.32 0.34

Sample Sl.ze (95) (126)

NONMOVERSb

Constant 0.307 (0.153) 0.442 (0.160)

Log (enrollment rent) 0.959 (0.033) 0.919 (0.034)

R2 0.81 0.85

Standard error of estJ.lnate 0.14 0.16

Sample sJ.ze (200) (130)

SAMPLE: Control households actl.ve at two years after enrollment,

exclud1ng those wl.th enrollment l.ncomes over the e11gibl.ll.ty Ilml.ts and

those I1v1ng 1n the1r own homes or 1n subsl.dl.zed hous1ng.

DATA SOURCES: In1t1al and monthly Household Report Forms.

a. Est1ffiated uS1ng Seem1ngly unrelated Regress10n.

b. Estxmated uS1ng Ord1nary Least Squares.

A-145
APPENDIX XI

EVALUATION OF SAMPLE SELECTION BIAS

IN ESTIMATED PRICE ELASTICITIES~

The procedures used to select the sample of households offered enrollment ln

the Demand Experlment were carefully deslgned to provlde a probablllty sample

of a well-deflned, low-lucame populatlon 1n both sltes, randomly asslgned to

2

the varlOU5 Exper~ental and Control plans. The demand functlons presented

1n Chapters 4 and 5 were estlmated on a dlfferent sample of households--households that accepted the enrollment offer, were verlfied to be withln the lncome

ellglblllty l~lt, remalned 1n the exper1ffient, and moved sometlme between

enrollment and two years after enrollment. Each of these selectlon crlterla

may have lntroduced blas 1n the est~ated coefflClents, so that they may dlifer

from-the populatlon coeff.l.Clents, as follows:

Acceptance blas. Households offered hlgher payments may have

been more llkely to accept the enrollment offer than households

offered lower payments. Sluee, for each rebate level, payment

lncreased with houslng expendltures, households that accepted

the Percent of Rent offers may have tended to spend more for

houslng than Control households. In thlS case, cross-sectl0nal

comparlson of Percent of Rent and Control households mlght overestimate the effect of the rebate.

Attrltlon blas. Llkewlse, households may have been more l~kely

to remalU ln the program lf they recelved hlgher payments. Agaln,

Percent of Rent households that tended to spend more on houslng

regardless of the experlffient may have been more llkely to remaln

In the experlment.

Moblllty blas. In theory, households move to change thelr houslng

and hence should be, other thlngs equal, more llkely to move the

larger thelr deslred changes. Households may move ln order to

spend less or to spend more on houslng. The rent rebates offered

to Percent of Rent households would be expected to encourage movlng

1ThlS appendlx was wrltten by stephen Kennedy. He has beneflted

greatly from comments by walter stellwagen and Davld Hoaglln, as well as

many helpful dlScusslons wlth the authors of thlS report, Joseph Frledman

and Danlel Welnberg. The appendlx also reflects the helpful comments of

Davld Wlse on a more general dlScusslon presented at the summer meetlngs

of the Econometrlc Soclety (Kennedy, 1978). Responslblllty for errors,

of course, remalns w1th the author.

2Random asslgnment was modlf1ed for certain plans to reflect

spec1al ~ncome llm1ts. ThlS 1S accounted for ln the analysls.

A-147
by households that would have moved to lnCrease thelr spendlng.

Thus the sample of percent of Rent movers may not be comparable

to the sample of Control movers. l

Heckman (1976) prov1des a general framework for address1ng sample selection

bias for cases In whlch the selectlon process lS observed. ThlS appendlx

essent1ally appl1es a mod1f1ed version of Heckman's model to the sample

select10ns descr1bed above. Wh1le 1t 1S often d1fficult to f1nd the identifYlng varlables requlred for the Heckman Solutl0n, It appears that serlal

correlatlon can provlde a relatlvely slmple test for sample select~on. When

there lS serlal correlat10n, d1fferences 1n the normal consumpt1on levels of

selected and nonselected households w111 be reflected 1n proport10nal d1fferences 1n preprogram consurnpt10n levels. Unfortunately, the factor of propor.­

t10na11ty depends very much on the dynam1cs of the dec1s10n-maklng process

lnvolved 1n the selectlon. However, plauSlble models can be proposed wh1.ch

lead to the conven1ent factor of one.

The appendlx 1.S organlzed as follows. Sectl0n XI.l descr1.bes the sample

selectl0n problem and 1.nd1.cates problems 1.n the appl1.cat1.on of the Heckman

solut1.on. Sect1.on XI.2 der1ves a s~ple correct10n for sample select10n

based on ser1al correlat1.on and dlscusses 1tS SenS1.tlv1ty to assumpt10ns

concern1.ng the dynarn1cs of dec1slon-making. F1nally, Section XI.3 exam1nes

the emp1rlcal results concernlng the SlZe of the sample selectl0n blas and

the approprlate correctl0ns 1n the analyses of Chapters 4 and 5.

XLI THE SAMPLE SELECTION PROBLEM

The sample select10n problem has been n1cely descr1bed 1n Heckman (1976) and

also, follow1ng Heckman, by Hausman and W1se (1977). Spec1f1cally, cons1der

the log-llnear expendlture functl0n of Chapter 4:

(1) R = XI> + E

1

One other posslble blas 1S not consldered here. If the prlce

elast1C1.ty 1.S ltself stochast1.c, then households that moved dur1.ng the

f1.rst two years m1.ght tend to l.nclude mOre IIhl.gh responsell households.

Estl.mates based on these households would overest~ate the responses of

later movers. As dlscussed 1n Sect1.on 6.1, there 15 no conslstent eVldence of decl1.nlng response over t1.me.

A-148
where

R the logar~thm of hous~ng expendltures

X a matr1x of 1ndependent varlables (a constant,

In(Y), and In(l-a) , where Y ~s household ~ncome

and "all 1S the percentage rebate)

S = the vector of behav~oral parameters w~th elements

So (the constant), Sl (the ~ncome elast~c~ty), and

S2 (the pr~ce elast~c~ty), and

E = a stochast~c term, assumed to be lndependently

normally dlstrlbuted w1th mean zero and standard

dev~at10n (J • s

The potent~al select~on b~ases descr~bed above suggest that the probab~l~ty

that a household falls ~nto the selected sample var~es systemat~cally w~th

E and X, so that

(2) E(S/S) = Xy

where E(S/S) ~s the expected value of S for the selected sample, S, and y

lS a vector of parameters represent1ng the selectlon blas. In thlS case,

Ordlnary Least Squares estlmates of Equatl0n (I) wl1l be b1ased, Slnce

( 3) p

" = S + (X'X) -1X's

(4) E(sls) = S + y.

y •

2

the rebates on expendlIn words, 1£ Y2 1S non-zero, the est1mated pr1ce elastlc1ty, $2' w1ll confuse

the actual effects of the Percent of Rent rebates on expendltures, S2' w1th

the select~on of the h~gher expend1ture households at higher rebate levels,

Est1mated effects w~ll overstate the actual lffipact of

tures.

speclflcally, say that the probab111ty of belng selected, TI,lS some functlon

of the determ~nants of R (X and s) and other var~ables (Z):

(5) TI = 7T{X,Z,E).

Then

(6) E(s/X Z S) fsn(X,Z,s)f(s)ds , , fn(X,Z,s)f(s)ds

where f(s) 1S the dens1ty funct~on of s.

A-149
If the fonn of 1f ~s known, then the expected value of 'IT over €, 'IT

!n(X,Z,8)f(8)d8 can be est~mated. If ~n add~t~on, 8 ~s normally d~str~buted

and 1f can be wr~tten as a l~near funct~on ~n X, Z, and €, then as shown ~n

Note A:

(7)

lead~ng to

n (Xy + ze + I.e)

(8)

and

(9)

where

n(Xy + ze)

E(e!S,X,Z)

!n(Xy + ze + A8)f(8)d8

= A(J2 1 oiT{y) 8 -----

iT{y) oj;

y = Xy + ze.

Thus, 1f 'IT can be est~mated, under the assumpt~ons stated above, the b~as

In the expectat~on of E can be

.

1f, and the unknown coeff~clent

expressed

, 2 1

A(J •

8

In terms of the est~ated funct1on,

1Heckman (1976) and Hausman and W~se (1977) formulate the problem ~n

a sllghtly more restr~ct1ve way. They start by deflnlng 1f In terms of the

standard prob~t model:

n = prob (v > 0)

v Xy + ze + a

where a and 8 (the error term from Equat~on (1» are b~var~ate normal w~th

correlatlon

In thlS case

TI = 1 - F(-Xy-Ze),

!

2 f(-Xy-Ze) E (0 s,X, e) = \l a + (J a ---='l-=":F'""'(':=-""xy-'-=-=z"'eo-)

and

(v)

A(J

E(8!s,X,e) = _8 E(als,x,e).

(Ja

The formulat~on In the text lS Sllghtly more general, Slnce lt does not restrlct

the form of n to the prob~t d~str~but~on. More ~mportantly it may a~d model~ng

by emphas~z~ng the behavioral bas~s of the problem--the fact that 8 affects the

probab~l~ty of select~on. -

A-ISO
Equat~on (1) to y~eld

Heckman suggests two solut~ons to the select~on problem based on Equat~on (9)

for cases ~n WhlCh the selectl0n process 15 observed. Flrst, In a two-stage

procedure, 1£*18 estunated, then the varJ.able (~ ~~) may be added to

1f Cly

(

1 Cl-) (10) R = XB + A<J2 ::- + v <: 1f Cly

where V ~s uncorrelated w~th X ~n the selected sample. Second, the system

(11)

{

R = XB + <:

1f = !1f(Xy + ze + A<:)f(<:)d<:

may be estunated uSlng maxlrnum llkelJ.hood technJ.ques.

The crltlcal problem, In 61ther case, 15 flndlng the ldentl£lers, Z. In the

context of the expendlture functl0n estLmates of Chapter 4, Z varlables must

be factors that affect acceptance, attrltlon, or moblilty, but are known not

1

to affect houslng expendltures. No strong ldentlflers have been found.

Xr.2 SERIAL CORRELATION

Glven the dl£flculty In flndlng ldentlflers, an alternatlve 18 avallable 1£

the descrlptors, X, and the stachastlC term, €, only enter the part~c~pat~on

select10n process through the~r effect on R. In th1S case, may be wr~tten

as

(12) 1f = ~[A(XB+<:) + Z6J.

It ~s apparent that th~s w~ll prov~de enough ~nformat~on to ~dent~fy A and B.

unfortunately, however, th~s w~ll not generally be the case. Demograph~c

descr1ptors such as age or 1ncome seem qu1te l1kely to 1nfluence acceptance,

attr1t10n, and mob11ity apart from R.

One var~able that clearly would be expected to affect 1f ~n the say way as <:

1S past values of E. There 1S a strong ser1al correlat1on between present

and past values for E for hous1ng. If E can be wr1tten as

1

Dav1d W1se has p01nted out that there need not 1n fact be any

~dent~f~ers. The form (l/])(ai/ay)~s nonl~near ~n y and th~s w~ll often

be enough to estlffiate Band AUL ~n Equat~on (10). However, th~s puts a

<: heavy re11ance on the proper spec~f1cat10n of R{X) as a l1near form 1n the

f1rst place, someth1ng about Wh1Ch 11ttle 1S usually known.

A-lSI
where subscr~pts ~nd~cate tnne per~ods, then ~t seems reasonable to spec~fy

that1

But from Equat10n (13) 1t 1S 1mmed1ate that

(15)

where

(n)

Thus

(16) E(EOls,x,z) = TO E( E

1 Is ,x,z)

s~nce there ~s no d~rect select~on on EO (so that E(OO!S,X,Z) ~n Equat~on

2

(15) 1S zero).

1Hausman and W~se (1977) use such a spec~f~cat~on.

2

Equat10n (16) can also be der1ved from Equat10ns (9), (13), and (14).

then by Equat10n (9)

1 3" it 3y = O~O AT1 (E(EOls,x,z)

By Equat10n (13)

(111) E( E

1 Is ,x,z) T

1

E(EO[S,X,Z) + E(Ol IS ,X,Z).

SubSt1tutwg (11) 1nto (111)

(1V) E( E

1 Is ,x,z) = E(EOls,x,z) ~" ~). 02 T

But from Equat~on (13) EO 1

(footnote cont~nued)

(v)

A-152
Equat10n (16) offers a part1cularly easy test for sample select10n b1as. If

there are lnltlal observatl0ns on the full sample, then sample selectl0n on

8

1 may be tested by testlng for sample selectl0n on £O--l.e., by testlng the

equa11ty of the estllnated coeff1c1ents of Equat10n (1), based on the 1n1t1al

observatl0ns, for households that are subsequently selected and those that

are not. Llkewlse, the value of TO may be estllnated uSlng the entire sample,

by regresslng EO on 8

1 , SlUCe selectl0n on 81 should not d1sturb the regres510n of EO on 81 •

Thus, sample selectlon blas may be tested for by est1matlng

(17)

, for the entlre populatlon and then regresslng EO on X, for the selected

sample

(18)

where EO

estlmate

(19)

1 and Xl refer to observatl0ns for the selected sample.

of E(81Is,x) 1S then g1ven by

E( 8

1 Is,x) = y TO

A conslstent

. where TO 18 the estlmated regressl0n coefflClent of EO on 8

1 for the selected

sample. 2

(footnote cont1nued)

Notlce, however, that the dlrect proof presented 1n the text does not requ1re

that 8 be normally d1str1buted. Th1s can be useful. Analys1s of 1ncome

report1ng errors ~n the Demand Exper~ent, for example, 1nd~cated that the

d~str~but1on of errors was dec~dedly longer-ta1led than would be the case for

a normal d~str~but1on. Th~s hampered attempts to correct for truncat10n

effects. See Hoag11n and Joseph (1978).

1 2 - - -1 - - -1 - - __ -1 :h: es!~at=lY w111 then have var1ance

°

0 [(XiXl) -(XiXl) (XIXO)

(XOXO) (XbXl) (XiXl) ]. For the spec1al case of exper1ffiental effects, where

the exper~ental var~ables have the same value at both per1ods, y may be

obta1ned by s1ffiply tak1ng the d1fference 1n estllnated coeff1c1ents for thr fu~~_s~£le and the selected sample and the var1ance reduces to 0~[(X'X)­

-(XOXO) ].

2

More eff~clent procedures are undoubtedly avallab1e. For example,

Hausman and W~se (1977) 1ncorporate ser~al correlat1on lnto max~um 1~ke1hood

est1mates. These have not been cons~dered because, as d1scussed below, there

are reasons to be11eve that the mult1p11cat1ve factor 1n Equation (19) (liTO)

can be dropped.

A-153
There rema~ns an =portant problem, however. The model of Equat~on (13)

lnvolves only two perlods. As wl11 be seen below, this can be a crltical

assumpt~on ~n determ~n~ng the exact relat~on between E(EOls) and E(E1Is).

Most exper~ents and programs run for some tLffie before and after the pOlot

of analysls. It seems reasonable to suppose that selectlon does not s~ply

occur at the pOlot of analysls, but 15 an ongolng process. But 1£ selectl0n

deC1S10ns are based on normal expendlture levels 10 other periods as well as

to and t l (and hence select on other Et'S), then the rat~o of E(E1Is) to

E(EOls) w~ll no longer be '0-1as ~n Equat~on (16).

The rest of thlS seetlon explores several s1ffiple descrlptl0ns of dynamlc

deC1S10ns 10 order to explore thelr effect on the ratlo of E{81Is) to

E(EOls). It 15 shown that alternatlve models can generate a range of ratlos

-1

from '0 to the same t=e a plaus~ble case can be made for a '0· At ratlo

of one. Th~s y~elds a partlclliarly convenlent correctlon for selectl0n blas.

The descr1pt10ns are not 1ntended to be conv1nclng models of dec1s10n-mak1ng.

They are lntended to 1nd1cate the sens1tlv1ty of the ser1al correlat10n b1as

correct1on to dynamlc speclf1cat10ns.

Say, for example, that there lS attr1t1on 1n each per10d based on that

periodls values of R. Thus In each per1od, the mean value of E lS shlfted by

1 some amount, B, 1n add1t10n to the effects of attrltion In prev10us per1ods.

Assume further that value of E ln dlfferent perl0ds are serlally correlated

2 such that

(20)

In th1s case

(21)

assumed

EO and

1

The constancy of B 1S conven1ent, but not espec1ally plauS1ble.

For example, 1f EO lS normally d1str1buted, then the d1str1but10n of tt 1n

each succeed1ng per10d w1ll also be normal 1f the select10n probabl11ty,

n(Y+AE) ~s ~tself a normal d~str~but~on funct~on. The assumpt~on that the

add1tl0nal Sh1ft 1n the mean, B, 15 constant, however, requ1res that the

attr1t1on probab1l1ty change over t1ffie (for example, that A 1ncrease), Slnce

the moments of the net-of-prev1ous attr1t1on d1str1but10n wl1l be different

1n each t1ffie per10d.

2

For the rest of th1S sect10n, the var1ance of t over txme lS

constant so that TO = T

l = P where p 15 the correlatl0n between

A-154
where (E(Sllsl ... SN) ~s the expected value glven succeSSlve selectl0ns in

1 each per~od, t l to tN'

Notlce, however, that p 15 the one-perl0d correlatl0n rather than the carreN N lat~on between EO and EN (wh~ch ~s p). Thus, for a g~ven value of p , as

the number of selectlons assumed to have occurred becomes large, the appro2 pr~ate ~nflator for the E(EOls) approaches one.

Alternatively, conslder the sort of serlal correlatlon generated by a compoth nents-of-varlance model. Under thlS model, the error term for the 1 lndlvldual is the sum of a value for that lndlvldual, f plus a stochastlc term,

(22)

Suppresslng the tlme term, 6

t ,

(23)

Thus, the multlperlod and

3 model. In thlS case,

(24)

one-period correlatl0ns are the same for this

Agaln, for a glven correlatlon, as the number of perlods lnvolved grows

large, the factor appl~ed to E(EOls) in order to obta~n E(ENls) approaches

one.

and

1 Equat~on (21) ~s proved as follows:

N

I N-t E(EN Sl···SN) = L p B = 1

N l-p --Bl-p

(u)

N t l p B

1

N p(l-p )

l-p B •

2

Note also that ~f the ~n~t~al observat~on were subJect to the same

process, so that selectl0n also occurs on EO (as IDlght be the case for ~reprogram data on part~c~pants ~n an ongo~ng program),then E(EOls) = E(ENIS).

3

Equat~on (24) follows from

B [eN-I) p+l)

and

E(EN!Sl· .• SN)

E(EO Sl,.,SN) = B[(N-l)p].

A-ISS
Flnally, In elther of

that attr~t~on ~n the

the above models, lf attrltlon operates wlth a lag so

th perlod lS determlned by €t-l' the expresSlons 10

(25)

Equat~ons (21) and (24) reverse, so that

{

E(80Is) = E(8Nls) under Equat~on (20)

E(80Is) = 1 + 1 E(8N!S) under EquatlOn (23).

p (N-l)

The sort of repeated select1.ons descrlbed above may also be Justlfled lf

households only reassess thelr sltuat1.0ns from time to t1.me. In thlS case,

at any glven lnstant, the perlods on wh1.ch current part1.Clpants based the1.r

declsl0ns may be d1str1.buted over the past, glvlng for the "average" part1C1.­

pant, the equ1valent of repeated select1.ons. Alternat1.vely, 1.t mlght seem

reasonable that households base the1.r deC1.S10ns on longer-run cons1.derat1.ons.

But th1.s leads to the same sort of conclus1.on. Thus 1.n the components of

var1ance model, select1.on based on the expected value of R over many per10ds

wlll lead to select1.on 1n terms of the U term alone. But th1S aga1.n g1.ves

a s~tuat~on ~n wh~ch E(80 !S) equals E(8Nls).

Such arguments are hardly conclus1.ve. The1.r purpose 1.S to lnd1.cate some of

the problems ~nvolved ~n us~ng ser~al correlat~on to correct for sample

select1.on and to suggest that a case can frequently be made for adopt1.ng the

correct1.on

(26)

Th1.s 1.S clearly a very conven1.ent decls10n, Slnce (1.£ the varlance of E 1.S

constant over tlffie) l.t el1mlnates the necess1.ty of est1.mat1.ng TO to develop

the correct1.on 1n Equat1.on (19) and prov1des an unb1.ased est1.ffiate of the

correct10n term w1.th the usual small-sample d1.str1.but1.on propertles.

XI. 3 EMPIRICAL EVIDENCE

The emp1.r1.cal results show no eV1.dence of 1.rnportant bias due to sample

1 selectl0n. Table XI-l presents results for expend1.tures. There 1S a

S1.gn1.f1cant blas 1.n phoen1.x, 1nd1.cat1.ng that expendlture pr1ce elast1.c1.t1.es

may have been overest1.rnated 1n Phoen1.x. The numbers for P1.ttsburgh, wh1.1e

1

The regress1.ons from wh1.ch these numbers are taken are shown 10

Note B.

A-156
Table XI-l

SELECTION EFFECTS FOR EXPENDITURE PRICE ELASTICITIES

PITTSBURGH PHOENIX

Estimated Pr1ce Elast1c1t1es

-0.035 -0.010

(0.034) (0.038)

-0.048 -0.103*

(0.037) (0.049)

0.041 -0.098

(0.063) (0.062)

(2) Households actl.ve two years

after enrollment

(1) All enrolled households

(3) Households actl.ve two years

after enrollment that moved

between enrollment and two

years

Selectl.on Effect

Actl.ve households [(2)-(1)] -0.013

(0.015)

-0.093**

(0.031)

Movers [( 3) - (1) 1 0.076

(0.053)

0.087t

(0.049)

SOURCE: See Appendl.x XI, Note B.

NOTE: Standard error 1n parentheses.

t t-statl.stl.c sl.gnl.fl.cant at the 0.10 level.

* t-statl.stic sl.gnl.fl.cant at the 0.05 level.

** t-statl.stic sl.gnl.fl.cant at the 0.01 level.

A-157
not s~gn~f~cant, ~nd~cate an underest~ate for that s~te only somewhat less

than the overest~mate in Phoen1x. Wh11e only the phoen1x est1mates are

slgnlficant, the nearly opposite and equal effects In the two sites suggest

random no~se due to sampl1ng error more than they do systematic select10n.

Indeed, appl~cation of corrections 1n each slte would have little effect

on the average est1ffiated elasticity for the two sites.

USlng the model developed In Sectlon XI.2, the total correctlon for the estlmated elast1c~ty ~n each slte would be

(27)

where

C = -E - pE S I

correct~on

select10n effect

lnlt1al elast1clty, and

serlal correlat10n between res1duals at

enrollment and two years after enrollment.

Th1S ylelds an overall correct10n for the pr1ce elast1c1ty for movers of

-0.059 In plttsburgh and +0.092 In Phoenlx. Thus whlle the unblased Phoenlx

elastlclty might be smaller (In absolute value), the Plttsburgh elastlclty

m1ght be larger, leav1ng the two-slte average almost unchanged.

Much larger correct10ns would be 1ndlcated, of course, if the or1g~nal model

of Sectlon XI.2--whlch would requlre that E

S be dlvlded by p--were followed.

Nevertheless, 1n th1S case the correctl0ns for the two sites would aga~n

1 largely cancel.

Results for the hedon1c 1ndex of houslng serV1ces, presented 1n Table XI-2,

show no slgn1f1cant selectlon effect 10 e1ther slte. The overall correct10n

for movers (followlng Equatlon (27» would be -0.008 In plttsburgh and +0.052

10 Phoeolx. The d1fference 1n correctl0ns for expend1tures and for the

hedonlc lndex suggests that there may have been a small addltlonal shopplng

effect of about 0.05 In Plttsburgh; and further, about 0.04 pOlnts of the

effect in phoen1x may have been due to m1sestlmatl0n. These possible

correctlons are nevertheless well w1th1n the errors of est~ate 1nd1cated

in Chapter 5.

1

The correctlon would be -0.142 In Plttsburgh and +0.193 In phoenlx.

A-158
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~---

Table XI-2

SELECTION :J!:FFECTS FOR HOUSING SERVICES

PRICE ELASTICITIES

PITTSBURGH PHOENIX

Est1mated Pr~ce Elastic~tles

-0.068** 0.016

(0.026) (0.034)

-0.081** -0.030

(0.029) (0.044)

-0.032 -0.042

(0.049) (0.057)

(2) Households act~ve two years

after enrollment

(1) All enrolled households

(3) Households act~ve two years

after enrollment that moved

between enrollment and two

years

Select~on Effect

Act~ve households [(2)-(1)] -0.013

(0.013)

-0.046

(0.028)

Movers [(3)-(1)] 0.036

(0.042)

-0.058

(0.046)

SOURCE: See Append~x XI, Note B.

NOTE: Standard error ~n parentheses.

** t-statist~c s~gn~f~cant at the 0.01 level.

A-159
APPENDIX XI NOTE A

SUBSAMPLE MOMENTS WHEN THE

ERROR IS NORMALLY DISTRIBUTED

Say that the probab111ty that a household 1S observed, ~, can be expressed

as

(AI)

where E ~s a stochast1c term d1str1buted N(~/a) and y 15 some funct10n of

observed var1ables.

Def1.ne

(A2)

In theory, i(y) can be est~ated from observat10ns of the select10n process.

If £(8) 15 normal, then the moments of the stochast1c term, 8, 1n the observed

subpopulat1.ons, 8, can be descr1bed 1n terms of i , A, and the total populat10n

parameters of f(s), as shown below. If f(s) 1S normal, then

(A3)

Subst1tute

(A4) e y + AS

1n Equat10n (A2) so that

(AS)

Thus

(A6)

de

But the term 1n brackets 18 the d1fference between the expected values of E

1n the observed populat1on and 1n the ent1re populat1on. Thus

A-160
(A7) 

where 

E(Ely,s) =	 the mean value of E In the observed 

populatlon, S 

~la2 the	 mean and var~ance of 8 in the total 

populatlon 

A the coefflclent of E in [Equatlon (A2)], 

and 

*(y) the expected value of the probabillty that 

a household ~s observed, given y. 

Th~s procedure may be repeated to obta1n the subpopulatlon var1ance of s, 

(AB) E(E2jy,S) =02

* (A~)2 + 1) ,,2

\ay2 

or 

(A9) E(E2 /y,S)	 - (E(Ely,s»2 

= ,,2 + A2,,4 [~

Alternatlvely , 

(AIO) 

so that lf	A and are known, summlng Equatlon (AIO) across the values of y 

allows the	 subpopulatlon varlance to be used to form an estlmate of a2 • 

A-161

APPENDIX XI NOTE B

SOURCES OF TABLES XI-l AND XI-2

The follow~ng tables present the est~ted coefflClents for three regressl0ns

10 each 51-te , flrst for expendltures and then for the hedonlc index of houslng

serv1.ces.

Equat~on (1) estlffiated at enrollment ~s

(Bl)

where the superscrlpt, F, lndlcates that all enrolled households were used 1n

the estJ.Inatlon, YO 15 household lncame, and "all 15 the percentage rebate

offered the household. Tak~ng account of select~on

(B2) R

F = QA + QA 1 () QA 1 (1 ) ~O ~l n YO + ~2 n -a

where agaln the full sample was used, but a dummy varlable, dA , was used to

est1mate a separate lntercept and prlce elastlclty for households actlve at

two years after enrollment, and

(B3)

Elastic~ty:

wh~ch repeats Equat~on (B2) except that the dummy var~able, dM, now refers

to movers.

The numbers ~n Tables XI-l and XI-2 are constructed from the est~mates of

Equat~ons (Bl) through (B3) as presented ~n Tables XI-3 and XI-4 for expend~­

tures and hous~ng serv~ces respect~vely, as follows:

(1) pr~ce Elast~c~ty for All Enrolled Households

'F82

Error of Estlffiate:

A-162
Table XI-3

ESTIMATION OF THE SELECTION EFFECT FOR EXPENDITURES

COEFFICIENT

So

p.

S2

YO

Y2

2

R

F-stat~st~c

(s.l.gn~f.l.cance)

Standard error of

est.unate

sample S.l.ze

So

S.

62

YO

Y2

2

R

F-stat.l.st.l.C

(sJ.gnJ.fJ.-::ance)

Standard error of

estJ.mate

sample Sl.ze

EQUATION (Bl)

PITTSBURGH

3.031**

(O.141)

0.282**

(0.024)

-0.035

(0.034)

0.134

69.94

(0.01)

0.29

(904)

PHOENIX

2.686**

(0.133)

o 362**

<0.022)

-0.010

(0.382)

0.215

133.30

(0.01)

r. 0.33

(975)

EQUATION (B2) EQUATION (B3)

3.044** 3.026**

(0.141) (0.141)

0.281** 0.281**

(0.024) (0.024)

0.065 -0.064

(0.082) (0.041)

_0 009 0.043

(0.031) (0.031)

-0.118 o 105

(0.090) (0.750)

0.136 0.136

35.53 35.55

(0.01) (0.0l)

0.29 0.29

(904) (904)

2.790** 2.697**

(0.134) (0.133)

0.356** 0.362**

(0.022) (0.022)

o 108t 0.039

(0.061) (0.049)

-0.127** -0 053t

(0.028) (0.031)

-0.211t -0.137t

(0.078) (0 079)

o 231 0.218

73.02 67.64

(0.01) (0.01)

0.33 0.33

(975) (975)

SAMPLE: Enrolled Percent of Rent and Control households, exc!udJ.ng those W1.th l.ncomes over the

elJ.gLbJ.l1.ty l1.m1.ts.

DATA SOURCES In1.t1.al and montnly Household Report Forms, and Basel1.ne and PerJ.odJ.c IntervJ.ews

, t-stat~stJ.c s1.gnJ.fJ.cant at the 0.10 level (two-taJ.led test)

* t-stat.l.stJ.c sJ.gnJ.fJ.cant at the 0.05 level (two-taJ.led test).

** t-statJ.stJ.c sJ.gn1.fJ.cant at the 0.01 level (two-taJ.led test).

A-163
Table XI-4

ESTIMATION OF THE SELECTION EFFECT FOR HOUSING SERVICES

COEFFICIENT

'0

61

6,

Yo

Y2

.2

F-statJ.stl.C

(sJ.gnJ.fJ.cance)

Standard error of

estunate

Sample sJ.ze

60

61

62

YO

Y2

2

R

F-stat:::.stJ.c

(sJ.gnJ.fl.carce)

standard error of

esb.mate

Sample sJ.ze

EQUATION (B1)

PITTSBURGH

3.543**

(0.10l)

0.192**

(0 017)

-0.068**

(0.026)

0.124

64.89

(0.01)

0.22

(917)

PHOENIX

3.118**

(0.114)

0.286**

(0.019)

0.016

(0.034)

a 202

116.16

(0 01)

0.28

(921)

EQUATION (82) EQUATION (83)

3.551** 3 543**

(0.104) (0 101)

0.191** 0.192**

(0.017) (0.017)

-0.012 -0.088**

(0 055) (0.030)

-0.005 -0.019

(0.020) (0.023)

-0.069 +0.055

(0.062) (0.058)

0.126 0.129

32.80 33.84

(0.01) (0.01)

0.22 0.22

(917) (917)

3.181** 3.138**

(0.116) (0.114)

0.280** 0.285**

(0.019) (0.019)

0.067 0.037

(0.053) (0.043)

-0 059t -0.052t

(0.024) (0.027)

-0.097 -0.079

(0.069) (0 071)

0.207 0.205

59.78 59 08

(0 01) (0.01)

o 28 0.28

(921) 0 (921)

SAMPLE Enrolled Percent of Rent and Control households, excludl.ng those wJ.th J.ncornes over the

elJ.gJ.bJ.lJ.ty l].IDJ.ts.

DATA SOURCES InJ.tJ.al and monthly Household Report Forms, and Basell.ne and PerJ.odJ.c IntervJ.ews.

T t-statJ.stJ.c sJ.gnJ.fJ.cant at the 0.10 level (two-tal.led test).

* t-statJ.stJ.c sJ.gnJ.£J.cant at the 0.05 level (two-taJ.led test)

** t-statJ.stJ.c sJ.gnJ.fJ.cant at tne 0 01 level (two-taJ.led test).

A-164
(2) Pr~ce Elast~c~ty for Act~ve Households

AA .....A Elast~c~ty: S2 + Y2

I Error of Estxmate:

(3) Pr~ce Elast~c~ty for Mover Households

....M ....M Elast~c~ty: S2 + Y2

I Error of Est1ffiate:

F~nally, Table XI-5 glves the ser1al correlatl0n coefflc~ent between enrollment and two years for the expendlture and hedonlc lndex residuals, respectlvely~ These were est1ffiated, uSlng Control households only, by comparing

the correlatlon of reslduals (assumlng equal varlance) at enrollment and two

years after enrollment from the equatlon

(B4) Rt = SOt + SIt In(Yt ) + E

t

where

Rt log expenditures or log of the hedon~c index

of houslng serv1ces, and

Yt = household lncorne~

IThlS 18 an apprOX1ffiatl0n that 19nores any poss1ble covarlance in

separate est~ates for the two groups due to the COmmon lucame elastlclty.

A-165
Table XI-5

CORRELATION OF RESIDUALS FOR CONTROL HOUSEHOLDS

AT ENROLLMENT AND TWO YEARS AFTER ENROLLMENT

PITTSBURGH

Expend~tures

PHOENIX

All households

Sample sJ.ze

Households that moved between

enrollment and two years after

enrollment

Sample sJ.ze

HOUSLng ServJ.ces

All households

Sample Sl.ze

Households that moved between

enrollment and two years after

enrollment

Sample sJ.ze

0.701

(250)

0.478

(82)

0.666

(250)

0.415

(82)

0.642

(213)

0.461

(98

0.599

(213)

0.383

(98)

SAMPLE: Control households act1.ve at the end of two years after

enrollment, exc!udl.ng those wl.th enrollment l.ucornes over the elJ.gl.bl.ll.ty

l~l.ts and those liVl.og 10 thel.r own homes or 10 subSl.dl.zed housing.

DATA SOURCES: Init1.al and monthly Household Report Forms, Baseline

and perl.odJ.c Intervl.ews, and Housl.ng Evaluat10n Forms.

A-166
REFERENCES

Hausman, Jerry A. and David A. Wise, "Attrition 1.n ExperJ.mental and Panel

Data: The Gary Income Maintenance Experlll\ent," (mimeo), May 1977.

Heclonan, James J., "The Common Structure of Stat1.stJ.cal Models of Truncatl.on,.

Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models,n Annals of Economl.C and Social Measurement,

Vol. 5, no. 4, Fall 1976.

Hoaglin, David C. and Catherlne A. Joseph, Income Reporting and Verification

1.0 the Housing Allowance Demand Experl.rnent, Cambndge I Mass., Abt

Associates Inc., 1978 (revlsed June 1980).

Kennedy, Stephen D., "Sample Selection and the Analysls of Constralned

Transfers: Some Evidence from the Housing Allowance Demand

Experiment," paper presented at the summer meetings of the

Econometric Soclety, June 1978.

A-167