Housing Tenure, Uncertainty, and Taxation 

Harvey S. Rosen 

Princeton University 

Kenneth T. Rosen 

University of Ca 1iforn ia 

Do ug 1a s Ho1t z-Ea k in 

Princeton University 

OTA Paper 54 February, 1983 

OTA Papers are circulated so that the preliminary findings of 

tax research conducted by staff members and others associated 

with the Office of Tax Analysis may reach a wider audience. 

The views expressed are those of the authors, and do not 

reflect Treasury policy. Comments are invited, but OTA 

Papers should not be quoted without permission of the 

authors. 

Office of Tax Analysis 

U.S. Treasury Department, Room 4040 

Washington, D.C. 20220 

Issued: February, 1984 

t 
I. 

11. c 

111. 

Iv. 

V. 

TABLE OF CONTENTS 

Introduction 

The Model 

Empirical Implementation 

Results 

A. The Basic Model 

B. Alternative Specifications 

C. Some Implications 

Conclusion 

1 

3 

6 

17 

17 

19 

22 

27 

29 

32 

35 

Appendix A 

Appendix B 

References 
. Housing Tenure, Uncertainty, And Taxation 

ABSTRACT 

Mod- empirical work on the choice between renting and owning focuses 

OZI the concept of the "user cost" of holl~hg~which intagrates into a single 

measure the various caorponents of housiag costs. The staadarct approach 

implicitly assumes that households know the user cost of housing,with 

certainty. &"ver8 the expost user cost measure exhibits substantial 

variabiUe over time, and it is highly unlikely that individuals believe 

themselves able to forecast these fluctuations with certaiaty. In this 

paper, we corurtruct and estimate a =del of the tenure choice that explicitly 

allows for the effects of =certainty. The results suggest that previous 

worlc which ignored uncertabty may have overstated the effects of the 

iaco" tax system upon the tenure choice. 

Harpay s. -sen rtenneth To Rosa Douglas Holtz-EaWn 

Department of Econdcs School of Business DepartmQnt of Economics 

Princaton University Uniwarsity of California Princeton University 

Princeton, IUJ 08544 Berkeley, CA 94720 Princeton, NI 08544 
1. 

I. Introduction 

The personal income tax provisions associated with homeownership have 

come under increasing scrutiny by both policymakers and academic researchers. 

This renewed interest has come about primarily because of the tremendous 

acceleration of real house prices in the past decade and the belief that 

Americans invest "too much" in owner-occupied housing relative to investment 

in more productive plant and equipment. (Feldstein C19821, Hendershott 

C19821.1 Both phenomena are blamed in part on the interaction of inflation 

2nd the treatment of owner-occupied housing in the federal income tax system. 

The non-taxation of implicit rental income, the deductibility of nominal 

interest payments and property taxes, and the virtual exclusion of housing 

capital gains from taxable income are all believed to provide incentives for 

households to become owner-occupiers. 

Modern empirical work on the choice between renting and owning focuses 

. 

. on the concept of the "user cost" of housing, which integrates into a single 

measure the various components of housing costs: interest rates, property 

and incone taxes, maintenance, depreciation, expected capital gains ,'etc. 

A typical approach is to compute the'ex-post value of the user cost of owner 

occupation each period, and then estimate a regression of the proportion of 

owner-occupiers in the population on the user cost and other variables. This 

approach has been fairly successful in explaining the movement of the homeownership ratio over time. (Rosen and Rosen C19801, Hendershott and Shilling C19803. ) 

The standard approach implicitly assumes that households know the user 

cost of housing with certainty. However, the -

ex post user cost measure

exhibits substantial variability over time, and it is highly unlikely that 

individuals believe themselves able to forecast these fluctuations with 
-- 

2. 

certainty. Since housing decisions are usually made over time horizons of 

several years, this uncertainty can have important consequences for behavior. 

Ignoring it can lead to incorrect predictions of how people will behave under 

certain conditions. Consider these two examples: 

1) During a period of time, housing prices increase substantially year 

after year. -

Ex post measures of the user cost of owner-occupation suggest

that families should become homeowners in order to reap the capital gains. 

Iiowever, individuals do not know ex ante that these gains will occur. Indeed, 

past price increases may increase their subjective uncertainty concerning 

future movements in price. To the extent that they are risk averse, this increase 

in uncertainty will discourage people from becoming homeowners a 1 

. 2) The government announces that it will begin taxing housing capital 

gains at the same rates as ordinary income. Focusing only on the ex post 

user cost suggests that such a policy will decrease the incidence of owneroccupation in the population. But the policy also lowers the variance of 

the user cost of homeownership--the government in effect becomes a silent 

partner, shzring both gains and losses. If individuals are risk-averse, this 

will tend to increase the attractiveness of owner-occupation, ceteris paribus. 

In this paper, we construct and estimate a simple model of the tenure 

choice that explicitly allows for the effects of uncertainty. Section I1 

presents the basic model and Section I11 discusses econometric issues involved 

in its estimation. Section IV presents the results and some of their 

implications. Price uncertainty is shown to have a statistically significant 

'In fact, during the 1970's, substantial increases in house prices 

occurred with barely any movements in the proportion of homeowners -- the 

figure in 1973 was 0.645; and in 1977, 0.648. (See Rosen C19811.) In 

the early 198O'S, the proportion of homeowners declined from 0.658 in 

1980 to 0.649 in 1982. (See U.S. Bureau of the Census C1980, 19821.) 
-- 

3. 

and quantitatively large impact on the percentage of owner-occupiers. The 

results suggest that previous work which ignored uncertainty may have overstated tax effects on tenure choice. Section V provides a summary and 

suggestions for additional research. 

11. The Model 

In this section we develop a model of household tenure choice which 

focuses on the role of price uncertainty. Assume that an individual's utility 

depends upon his consumption of housing services and of a composite of all 

other goods. Housing services are assumed available in either of two mutually 

exclusive modes; renting or owning. For simplicity, renting and owning are 

modelled as distinct commodities with characteristics which may differ. For 

examole, it may be difficult to rent a single unit with a large backyard. 

Similarly, it may be impractical for a homeowner to contract for the kind of 

maintenance services available to a renter. 

2 Algebraically, if G = quantity 

of the composite good, H = quantity of housing services consumed in owneroccugation mode, and R = housing services consumed in rental mode, then 

U = U(G,H,R) 

where U(*> is the utility function, and HxR = 0 . At the time the tenure choice is made, the future real prices of both modes - are uncertain. As will be shown below, the real cost of owner-occupation (PI 

depends inter alia upon future housing capital gains, interest rates, and 

2Henderson and Ioamides c19831 provide a useful discussion of the 

distinctions between renting and owning. 
4. 

federal income tax rates; none of which is known with certainty. Similarly, 

in the absence of long run indexed leases for rental housing, uncertainty 

' 

also surrounds its real price (Q) . The price of the composite good is 

assumed to be known with certainty, and is equal to unity. 

The individual makes his choice by comparing the outcomes of two subaroblems. The first is maximizing utility, assuming that owner occupation 

is selected, and the second is maximizing utility assuming that renting is 

selected. Let Vh '(P,y) be the maximum utility associated with owning,

- and fl(Q,y) be the maximum utility associated with renting; where y is permanent 

income over the planning period. An individual elects to own if: 

Defining the expected prices of homeownership and renting as -P and 

-

Q, respectively, and taking a second-order Taylor series expansion of . 

$(;, y) around the point (7,y) yields: 

where Vllh =- -a'v" and a2 3 E(; - y12 . Similarly:

ap2 

a 2P where Z - and 62 Z E(&Q)2 . Hence, we can write: 

a q2 

One thus expects that (to a second order approximation) the 

tenure choice will depend upon: i>the expected prices of the 

nodes (v, q).and ii) the variation of actual prices about the 

I 
--- 

5. 

2 forecast (0 and d2Io3 Tbese latter terms (referred to herein as the forecast 

error variances) figure importantly in our test of the relevance of uncertainty 

4

to tenure choice. 

Our focus has been on the tenure choice at an individual level. Aggregation 

presents the usual difficulties, but may be motivated by considering a 

population with heterogeneous tastes and incomes, but identical expectations 

for future prices. For individual i , define 

where A i is a vector of taste parameters., Integrating over the joint 

distribution of y 

i and Ai in the population for year t yields the 

relation 

where et 

is the aggregate proportion of homeowners. 

-. 

For, purposes of empirical implementation, a specific functional form must 

be adopted for (2.1). We assume the convenient specification 

1-Ot = Bo t B P t B 2t 13 [ -1 f B' 02 + 346t2 + f5Yt f Et 3 (2.2) It 3t 

wherq is a random error. To the extent that changes in the prices 

of the respective tenure modes induce the same changes in utility levels, 

ceteris paribus, expected prices and forecast error variances affect the 

3Note that as a consequence of the assumption that renting and ownership 

are mutually exclusive, the covariance between the prices does not enter.- ­ Further, it is assumed that permanent income is independent of the priceP, Q 

4it should be stressed. that the variance terms are consequences of 

underlying uncertainty in the price of housing, and not the result of asset 

portfolio considerations The, interaction of housing and financial decisions is 

beyond the scope of this paper. 
tenure decision in a symmetric fashion.' Symmetry is clearly an empirical 

issue. For now, we merely note that it implies: 

8, = -B3 

These restrictions will be tested below. 

111. Empirical Implementation 

We estimate equation (2.2) with annual U.S. data for 1956 to 1979. In 

this section we explain the construction of empirical counterparts to the 

theoretical constructs of Section 11. The sources of all data are documented 

in an appendix available upon request. 

I. The proportion of homeowners (3,) 

Jaffee and Rosen [19791 argue that demographic changes in Uie U.S..population have had a major effect on the rate of household formation and 

homeownership, and that meaningful comparison of homeownership rates over 

time requires that such changes be taken into account. We adapt the Jaffee­

~osenprocedure, which consists of creating a series which controls for 

the changing mix of household types due to changes in the age.distribution 

of the population and alterations in marriage and divorce patterns. 

.-

2. The expected priie of owner-occupation CP ) tComputation of the price of owner-occupation is complicated by the fact 

that owners do not pay 'm explicit annual rent for housing. An important 

part of the annual cost of owner-occupied housing services is the unobservable 

'In terms of our theoretical model, a sufficient condition for symnetry is 

that Vh(*) and Vr(*) be identical up to an additive constant. 
..- . --.. . -----._.--- ,. 

opportunity cost of the owner's equity in the house. Moreover, the federal 

incorne tax lowers the effective cost by allowing ded&tions of mortgage 

interest payments and local property taxes.' Finally, like any other asset, 

anticipated capital gains on a house (either positive or negative) have an 

impact upon its effective rental price. Readers familiar with the neoclassical 

investment literature will recognize the similarity between constructing the 

?rice of owner-occupied housing services and the "user cost of capital." 

(See e.g. , Jorgenson C19711 1 

The construction of user costs for housing is now familiar, and there is 

no need to go through the derivation again in detail.' Let Vt = the market 

value of a house in period t, rct = the individual's opportunity cost of 

capital, rmt= the mortgage rate, Dt = depreciation,, M t = maintenance, and 

Tt = prooerty taxes. If the share of owner's equity in the house is yt' 

then the real annual cost of owner-occupied housing services in year t , 

?* is 

(l-rt)CytrctVt t (1-Y>r V t Ttl t Dt t M - V .. 

Pt -

- t mt t t t (3.1) 

where tt 

is the marginal income tax rate in period t, Vt is the expected 

ca?ital gain in period t, and PLt is an index of the general price level..8 

Dzta on mortgage rates are not available for the entire sample period, nor 

is there sufficient information to allow calculation of yt. We therefore .-

6See Congressional Budget Office C19811 for a detailed discussion of the tax 

provisions related to housing. 

Dougherty and Van- Order C19821 provide a careful derivation. - -. 'Expression (3.1) ignqres transactions costs. The 'fact that b is not 

multiplied by (l-t.,) reflects the reasonable approximation that housing capital 

gains are untaxed. (See Congressional Budget Office C198ll.) Vt is measured - as (L-V t where Vt+l is the optimal prediction of Vttl generated by 

pn ARIMA model. In some versions, a seoarate ARIMA model is used to compute -

Vttl; in others, the same ARIMA model is applied to all components of 

equation (3.J). AS shown in Section IV below, the substantive results a-ne 

essoztially unchanged by the difference. (All expectations are computed in 

real terms.) 

C 
ex 

8. 

assume that rmt = r , which makes yt irrelevant. For r , the AAA 

ct Ct 

corporate bond rate is used. No tine series data are available on the 

depreciation and maintenance costs of the stock of owner-occupied housing. 

Following general real estate practice, we take depreciation and maintenance 

each to be 1 percent of the house value, Vt' 

as the average noncommercial property tax per 

term Tt is the average marginal tax rate on 

[1981]. 9 Pbt is the implicit price deflator 

with base year 1972. ' (pL1972 = 1.0.) 

Property taxes are computed 

owner-occupied dwelling. The 

income as calculated by Joines 

for total consumption expenditures 

Substituting all of these variables into (3.1) gives us only the post - cost of owner-occupation in year t , while our theory suggests that tenure 

decisions are based upon the ex?ected annual cost over the relevant horizon.10 

Only if expectations are myopic will people expect the current red pvice to 

continue into the future. Because expected housing prices are not directly 

observable, they must be constructed on the basis of some model. There has 

been a long and sometimes acrimonious debate on just how expectations are 

formed. (Much of the discussion is reviewed bv Friedman r19791.1 We use 

.. 

9~~r a vmie~05 reasons, it is difficult t? say exact4y which jax rats

is relevant. First Of all, not all homeowners ltemlze their deductions. 

Secondly, Hendershott and Slemrod [1981] note that the appropriate variable 

is the average tax savings Per dollar due to homeownership. We believe that 

- the marginal rate used here provides a good approximation. - .-

"Specifically, the decision is based upon the future costs of a unit purchased 

in the present period. For inaividuals who finance their entire purchase with a 

fixed rate mortgage, the borrowing cost component (r t) is constant over the 

relevant horizon. However, as we noted in Section IIIf.2, in the absence of 

complete time series data on the aggregate loan to value ratio for new purchases, 

we set rmtequal to the Aaa corporate bond rate (ret) , which does vary over 

the horizon. The larger the equity proportion of house value, the more accurate 

will be our approximation. As a practical matter, however, this issue is not 

of much importance. For historic values of yt from 1960-1976, we 

find that over a typical five-year horizon, the ference between the 

average user cost using our procedure, and one distinguishing between rct 

and rmt , is only about $48. .. 

A related issue is whether +ha aono*anity coat of .%rids might be better 

ye?resented by some other interest rate, such as the return on tax exempt 

securities. We found that inclusion of the rate on municipal bonds instead 

I 
9. 

the optimal ARIMA forecasting procedure suggested by Box aTd 

.. . .. Jenkins C197'01. The Box-Jenkins model produces forecasts of a variable 

base6 only on past values. Conditional on this information, the forecasts 

are rztional. In principle, one might want to forecast using a completely 

specified econometric model. This 9 however 9 would require forecasting all of 

:he Gadel's exogenous variables into the future. In a similar context, 

Feldsrein and Summers [1978] argue, "There' is no reason to expect that the 

more general procedure that requires estimates of monetary and fiscal policy 

for :any years ahead would yield better forecasts than the simpler Box-Jenkins 

procedure. I' (pp . 2-6 1. 

Forecasts made at any given time are based only on information available 

at tkst time. (Current year prices are not included in the information set, 

but all lags are.) Thus, it is necessary to estimate a separate forecasting 

equa:ion for each year, based upor! observations prior to that year. It is 

not cbvious how far into the past the observatiolis for each forecasting 

equation should go. One possible procedure is to choose some arbitrary length 

of the (say 10 years) and assume that individuals use data only within that 

period to make their forecasts. Each 'year a new observation is added, and 

simultaneously the observation at the end of the sample is dropped. This 

method is sometimes called "rolling regression. lt1l 

Another possibility is that as more information becomes available over 

time, individuals employ it, but continue to use the older information as 

well. Thus, the number of observations grows each year. People 

believe that the basic economic structure generating the observations remains 

of ret rriade little difference. Finally, it might be the case tb.:rt the 

relevant opportunity cost might be investment in another house. This possibility 

is ruled out by our assumption that each individual can own only one dwelling. 

in a more general model which viewed the housing choice as part of a portfolio 

decision, this possibility could be analyzed. See Section V below. 

. 6 . -.\ 

11Some justifications for rolling regression are discussed by Friedman 

[1973]. Yelastein and Sunmers 119781 use it to generate a time series of 

expected inflation rates. 
-- 

10. 

the same, but they use new information to update their estimates of the 

structure's parameters. For practical purposes, a starting point is 

needed. If World War I1 is perceived as an important breaking point in 

economic history, then starting somewhere in the late 1940's is sensible. 

Essentially, this is no different than the typical practice of using all 

avalleble post-War data to estimate macroeconomic relationships. 

There is not much theoretical basis for choosing between the two assumptions 

on how information is processed. We tried both and found that the second 

performed better in the sense of lbading to a statistically superior 

explanation of the tenure choice. The results presented below are based on 

this method. 

P.fter some preliminary analysis of 'the time series on Pf , we selected 

an ARIM (l,l,O) equation to make forecasts in year T : 

.where u is a normally distributed white noise error and 4(T) is a 

t 

parameter to be estimated.12 Again, note that (3.2) is re-estimated each year 

T with observations from year 0 to T-1 . Within a given time period $(T) 

is constant, but as the time period changes, so does O(T) . (In practice, 

year 0 is 1946, and the first 4 is estimated for 1956.) 

Given an estimate of +(TI , say ;(TI , equation (3.2) can be solved 

recursively to generate forecasts of the price of homeownership for as many 

I 

'?It is possible to view the ARIMA(1,1,0) mndll of equation (3.2) as 

the AR(2) model Pt = +lPt-l t d2Pt-2 + ut with the constraint 4,. t +2 = I. 

A test on this constraint using observations from 1939 to 1979 indicated that 

it was consistent with the data--F(1,37) = 2.08, while the critical level at a 

0.05 significance level is 4.08. Note also that with the normdity assumption, the distribution of P can be characterized by its mean and variance with no 

element of approximatih. 
-- 

-- 

11. -

. -----__L 

future years from time T as desired. This raises the question of the 

horizon people consider when making their tenure choice decisions. One 

possibility is that individuals look only to the end of the current year, 

reasoning that they can always change tenure status after that time. More 

realistically, substantial transactions costs are involved in movingJ3 and 

one exgects that people are concerned about the course of prices at least 

several years into the future. We assume that people form expectations not 

only for the current year but four years into the future, and base their 

tenure choice on the five year average. That is, if we denote F-Tt5 as 

the simple average of the first five forecasts generated by the Tth version 

of equation (3.21, then F- is entered as the observation for Y i n

T+5 t 

equation (2.2). To test the sensitivity of our substantive results to this 

assuxption on horizon length, we also estimated the tenure choice equation 

assming that decisions are made on a one-year basis. These results we also 

reported below. --_.- I 

- - -

Figure 3.1 shows the value of $(TI for each year. Note that the estimates 

1. vary substantially as new information becomes available. Hence, attempts 

,2. f to rodel expectations formation on the basis of a single ARIMA model.estimated 

,-.L r - for the entire period would likely produce misleading inferences. To the 

extent there is a trend, the value of $(TI tends toward zero. As equation 

(3.2) indicates, a decrease of +(TI in absolute value suggests that relatively 

more weight is being placed on the most recent observation. This may be due 

to the increased volatility in Pt which occurred during the 1970's. This 

phenomenon, associated mainly with movements in nominal interest rates and 

capital gains, reduced the value of "old" information. The negative values 

... . _.- . - -.-_.*- .. ,... I' :.. .. ,. . ... .. . .. . .. of Q(T) suggest that housing expectatjons are "regressj.ve" in the sense that 

if prices have gone up in the past, people expect them to return toward some 

"normal" value. 

1'

"For a3 estimate of the transactions costs associated with moving, see 

Venti and Wise [1982]. 
FIGURE 3.1 

ESTIMATES OF PHI OF EQUATIONS (3.2) . 

-0. 

P 

H 

-0 * 

-0. 

1955 1958 L36L L964 1367 1970 L973 1975 1379 

I EAR 

I 
-- 

-- 

12. 

Figure 3.2 exhibits for each year the expected price of owner-occupation 

. - over a five year period, PT+5 , and compares them to the average of the 

- . - actual (ex -post) prices for the same period. Over the period 1956-19'96, ae - .I : 

average ex post value of FT+5 

was $652.62; the average ex ante value was 

$736.14. Due to the nature of the learning process imposed by equation (3.21, 

individuals react to turning points with a one period lag. Note that 

in the 1970'~~people often expected the cost of housing to be higher thur 

its --ex oost:value. This may help explain the relatively small change in 

the homeownership rate during that decade. 

It should be noted that our procedure assumes that people form 

expectations of the real user cost, Pt, as a whole. It is also plausible 

that agents forecast each component of the user cost and then aggregate. 

The latter procedure,however, is difficult to implement. The investigator 

must specify and estimate an ARIMA model of each component. Correctly,. 

aggregating involves, at a minimum, computing the covarianceS between 

separate ARIMA models. The non-linear nature of equation 3.1 complicates 

matters further. For these reasons, our simpler procedure was adopted 

for the bulk of the analysis. 

.Also reported below, however, are estimates based on 

a moCel in which real capital gains are the only source of uncertainty. This 

assucption has been used in earlier studies of tenure choice (Hendershott 

and Shilling Cl9821, Rosen and Rosen C19801) and studies of business 

investment (Jorgenson Cl971.3). 

3. The forecast error variance of the price of owner occupation (u2 I. 

tThe same equations used to generate the expected price of owner occu?ation 

can be used to produce a series of the forecast error variances. From 
-- 

,O01 

L 

-L 

A 

A 

5 

FiGURE 3.2 

EX POST AND EX ANTE VALUES OF Pz: 

EX POST (SOiID)

EX ANTE (OASiiED) 

11004 

too03 

9001 800

/ \ I 

7001 / \I 

I V 

I 

I 

500 I 

-1OCj 

-6OOj 

-7004 

-8001 

-9ooj 

I955 L956 1961 136q 19 67 L97C 1973 , 1976 1979 
--- 

13 

- - - - equations (3.2), at the start of year T, the one year ahead forecast, PT ,is 

The true value one year hence (conditional on 3.2) is 

- ihe error in the one year ahead forecast made at the start of year T is (PT - PT)$ 

and its variance a; v -

- 2 where u (TI is the year T estimate of the variance of UT' 

Two simplifying assumptions can be made: 

(a) The covzriance of $(TI with tSe data on which it is estimated 

(?l,...,?T,l) is zero. To compute it is burdensome, and it is plausible 

that people ignore this source of error. In this case, equation (3.4) 

redxes to 

(3.5) 

- '

2 

$(TI where is the estimated variance of $(TI, computed as usual as

(b) = 0 .' This simplifying assumption is made in virtually all 

AXYA forecasting. (See Nelson C19731.1 Intuitively, it is assumed that 

there are enough observations so that errors of estimation are of second order 

importance relative to the inherent uxertainty ( uT )in the world. We 
14 

Then find 

2uT = A2 (TI (3.6) 

Expressions (3.5) and (3.6) give alternative values for the forecast 

error variance of a one year forecast. Our framework, however, requires 

coTpQting the variance for a five year average. This leads to two complications: 

a. It must be assumed that ;(TI is known with certainty. Recall that 

in the case of the one-year forecast, one can choose between assuming 

1 

that $(TI is known.with certainty or uncertainty. For the former, equation 

(3.6) is used; for the latter, equation (3.5) is relevant. Once we forecast 

further into the future, the computational problem becomes intractable unless 

we assume that u

2 

G(~) 0 . This is because each forecast error variance= .5 

contains ex2ectations of third and higher order moments of +(T) . 

In an attempt to gauge the importance of assuming ;(TI is known with 

, certainty, we estimated two different tenure choice equations with the 

naintained hypothesis that -one-year ahead forecasts were appropriate. In

::?e first u T was esthated using (3.5); in the second, (3.6). The . 

results, which are presented below, indicate that the substantive results.are 

unaffected. Of course, we do not know that this would continue to be the 

case for the five-year horizon; but the result is suggestive. 
b. The variance of the five year average is not simply the average of the 

five variances. The computation must take into account the cova2iances between 

the fcrecast errors for the various years. Some tedious but straightforward 

calculations yield the following fornula for the five year average forecast 

error variance, 14 2u-:Tt5 

2 4 2 

u-- - 3 c;~(T) z ail T+5 i=O 

where 

Figcze 3.3 shows how the five year average forecast error variance changed 

over the. Its mean value over the sanple period was 366,676, and the general 

tendency has been for it to fall. l5 This is reflective of the pattern of actual C . 

, -

- " 

1'- - prices depicted in Figure 3.2. Although prices in the beginning of the period 

- ,1 -r 

.- ;- moved less than those at the end, they did so in a less "predictable1' way. 

'n Details are provided in an appendix available upon request. 

''A general downward trend interrupted in about 1975 was also found in 

the forecast emor variances generated by the "rolling regression1' model. 
FIGURE 3.3 

FIVE YEAR FORECAST ERROR VARIANCE 

COO535-

T 

H 

0 

!.I 

S UOC- \ 

R 

N 

0 

S 

- 0 300-

0 

2GO-

. 

100-

0 " ' " ' ~ " " ' I " " ' i " " ' ( . . "',"'","".~ 

1955 ~3sa I,E6 L L964 1967 L2.70 1,073 LS76 L979 

TEAR 
-- 

-- 

16. 

4. The expected value and forecast error variance of the price of rental 

2 housing, qt and 6% . The sane strategy is used to compute 5 and 6 2 

as was used for 7 

t t t 

and G: above. A series of equations of the form 

(3.7) 

are estimated, and the results are used to generate expected values and 

variznces.'6 Unlike the case of owner occupation, it is not necessary to 

construct a time series on Qt' Explicit rents are paid to landlords, 

and data on them are easily avai1able.l' 

Cver the period, the -ex post rea1"price of renting rises smoothly, 

as does the forecast value. (The mean ex post value is $1103; the mean 

ex ante value is $1066.) The forecast error variances of renting are very 

small compared to that associated with owney-occupation. It seems likely 

that risks associated with owning are most important to the tenure decision. 

5. Other variables 

Our theoretical discussion suggested that permanent income should have 

an effect on housing decisions. Muth cl960, p.301 and others have noted that 

Again, this time series process was selected after preliminary investigation. 

"S?ecifically, Q, was constructed on the basis of census data on the median 

rent of renter-occupied units. Further details are provided in a data 

qpentix available upon request, There are, of course, a number of government 

programs that implicitly and explicitly subsidize rental housing. However, 

all that matters from our point of view is the market price facing consumers, 

and this is precisely what the published data are intended to reflect. 
. --.--.--__ . - ._. 17. -- -- 

current consumpion is probably a better "proxy" for permanent income that is 

current izcome. We therefore include per capita real 'consumption, C, , as c 

a righthazd side variable. 18 

An inc3rtant issue in the housing literature is the extent to which credit 

rationing influences housing denand decisions. (See Arcelus and Meltzer 

C13721 and Swan C19731.1 A rigorous examination of the impact of credit 

raticning on the tenuze decision would require specification and estimation 

zf a disequilihium model as suggested by Fair and Jaffee C19721. A simpler 

apTroach is.to include ainong the regressors a measure of the avail&ility 

of mcrtgage market funds. For this purpose, we create the variable CREDt , 

2eiined as the real growth in deposits at thrift institutions (mutual 

savings banks and savings and loan associations) between years t-l and t. 

3ne expects that if credit availability has been a factor in the homeownership 

decision, then CREDt will have a positive sign. 

A. The Basic Model 

In our basic equation, expected prices and their forecast emor variances 

Ere compuyed over a 5 year horizon. In terms of equation (2.2), F' = -

L TJ , L

2 - T+ 5 , and Qt and bt2 

are defined analogously. Under these assumptions, ut=u19

and iinposing constraints (2.31, ordinary least squares estimation of (2.2) 

'%he consumption variable includes expenditures on housing. Conceptually , this is appropriate, because the idea is to proxy permanent income, and all 

conponents of the consumption stream Ifbelong." Simultaneity is not likely to 

be an important issue because the dependent variable is a function ofthe 

homeownership ratio, notbusing expenditures per se. In any case,when consumption 

net of housing expenditures is used the results ape essentially unchanged. 

19Preliminary investigation indicated that the hypothesis chat constraint 

(2.3) is applicable could not be rejected by the data. The F-statistic for 

the test was 3.28, and the critical value is F(2, 18-1 = 3.55 (5%) or 6.01 (1%).

In the unconstrained equation, the coefficients on Qt and 6: were insignificantly different from zero, a phenomenon likely due to insufficient 

variability within the sample period. The fact that there were fewer degrees 

35 f-eedcn aJailable in the unconstrained regression may also have contributed 

fo the inaility to estimate the coefficients precisely. 

2 
la. 

yields : 

CI 

- 26.89 - at) + 2.04 cct 10-41 

(1.74) (0.30) 

D.W. = 1.44 

R2 = .989 

The nunbers in parentheses are standard errors. The Durbin-Watson statistic 

is ixonclusive at 5% and does not reject the null hypothesis at a 1%level. 

In any case, when a first-order correction for autocorrelation is made, the 

outcome is virtually unchanged. 

- - T:-.e coefficient on (P, - 3,) is negative and statistically sip-ificant L 

at csmentional levels. When the expected excess of the cost of owning over 

renting increases, the proportion of owner-occupiers decreases. The elasticity 

- of 3

t Kith respect to (Ft - Q,) Is -G.053.20 This result is qualitatively 

consis:ent with earlier research. 

The key new variable introduced in our specification is the difference in 

2

the forecast error variances of the costs of owning and renting, (ut2 - 6t). 

The coefficient on this term is negative and exceeds its standard error by 

nearly a factor of 4. Greater uncertainty in the price of owning reduces 

the proportion of homeowners, ceteris paribus. The elasticity of with 

2 respect to (a: - 6t) is -0.188. 

The coefficient of the consumption variable is positive and statistically 

significant, with an implied elasticity of 0.707. As in previous work using 

20A11 elasticities are evaluated at the average sample values for 1975-79. 

Because of the substantial volatility in the underlying data, the elasticity 

calculated for any single year might be misleading. 
19. 

both cross sectional and time series data, there is a positive relationship 

between real per capita permanent income (as proxied by personal consumption 

expenditures) and the tendency to choose owner-occupier status. 

One potential difficulty with our estimates is that they may be inconsistent 

due to sixultaneity bias. If increases in the proportion of owner occupiers 

drives up the price of owner-occupied housing, then there will be correlation 

- between (F?- Q,) and the error term E 

to Recently, Plosser, Schwert and 

'vThite [iss2] proposed a specification test which can be used to investigate 

whether this is a serious problem. Their procedure requires 

estimating the model in levels and differenced form. Under the null hypothesis 

that E

t is i.i.d. and there is no simultaneity bias, the estimates will 

be identical. The test statistic, chi-squared distributed with 3 degrees 

of freedon, is 1.324, indicating a failure to reject the null hypothesis by 

a wide margin. 

,B. Alternative Specifications 

To test the robustness of the basic model several additional specifications 

were estixated. In the first, the credit variable (CR2DtI described earlier 

was added to the basic equation. The results are shown in column (2) of 

Table I. (Column (1)reproduces the results of the basic equation for convenience.) 

The results in column (2) show that the addition of CXED leaves the basic 

t 

results essentially unchanged. The CEDt term itself is insignificant. At 

least in our formulation, the availability of real mortgage credit does not . influence the homeownership decision. As stressed earlier, we do not regard 

this as lecisive llproofll that rationing is unimportant in the housing market. 

The basic model assumed that households used a five-year horizon for 

tenure choice decisions. We estimated two alternative equations where a one-
rl(3 

n cu Q) cum r0m o h or0 (3m I o m .. .. I O d mcu cuo .. Iw W 00 Y 

n n 3- rlm cum a a Pcu cvrl I Ob E .. .. I 0 0 (34 cy0 .. z IY W 00 & W a 

n h n O)Q cur0 dcu (00

.. am . . .. I 

I 44 

mli rlo 00 W W Y 

2 

Q

h 

aa n n .coo tb n O'd 00 4 3 eucI 40 00 lid .. . . ?? cuo 1 -

.. 0 0 14 W Y 

IY 

n n m m

om 

to 

I cy1 

.. I ?? 

cuo 00 W Y 

n 

f 

I U

rl 

0 3 

X ,u vl 

U,

U 3 c 

u 0 8 U 

I 
21'. 

jTear decision horizon was postulated. The results in column (3) are based on 

the assum?tion that the autoregressive parameter in the equation that 

generates price expectations is known with certainty. Hence, t = -PT; * ct = aT of equation ( 3.6 1; and 

t and 62t are computed analogously. 

Colum 4 Is based on the assumption that the autoregressive parameter is 

xn certsin--a 

t 

2 

= 'T 

2 of equation (3.51, and d 2

t is computed analogously. 

Taken togrther, the results of columns (3) and (4) show that: (i)the basic 

estimates of column (1) are not very sensitive to reasonable changes in the 

time horizon, and (ii)neither are they sensitive to the assumption that the 

rutoregressive parameter in the price expectations equations is known with 

ceyt ainty .21 

Column (5) shows the results when the user cost of home owning is computed 

under the "traditional" assumption that the only unknown component is the 

expecte? real capital gain. Specifically, we estimated a series of ARIMA 

models for real capital gains, and used them to compute the expected value 

and forecast error variance over 5-year horizons, just as was done for the 

entire user cost in Section 111, The other components of P, were assumed 

known with certainty. As the results indicate, not much changes. This.is 

not too surprising, since much of the variability in the Pt series is 

associated with changes in house value. 

Finally, we estimated a version of the model trying to take into account 

changes in the qualities of owner-occupied and rental housing over the period. 

The only dimension of housing quality for which time series data are available 6 

is the average size of rental and owner-occupied units. Column (6) reports 

results when the user costs were scaled by average number of rooms for owneroccupied and rental housing. (A five-year horizon is again assumed.) The 

qualitative results are similar to those previously obtained, although the 

2be also estimated an equation'in which the planning horizon for owning 

was five years, and the horizon for renting was one year. These results, which 

are avallakde upon request, are es-cntially identical to those reported in 

column (1). 
22. -

coefficients differ as a result of the scaling. Of course, this is a crude 

adjustment for quality change, but it is the only one available over the time 

period. 

C . Some Implications 

To get a better feel for the quantitative significance of our results, 

it is useful to employ them as the basis for a number of simulations. 

Tnically, simulations of the inpact of changes in the housing environment 

focus exclusively on the effects upon the user cost of housing. However, 

any exogenous force which changes mean expected prices will also affect the 

forecast error variances. To accommodate this problem, the following 

sinulation procedure was adopted: 

1) A counterfactual was posed. For instance, "What would have been the 

e5fezt upon the homeownership ratio if the growth rate of real house values 

had bem constant over the sample period?" (discussed below) .. 

2) An artificial ex post user cost series was calculated by evaluating 

equatlm (3.1) under.the counterfactual hypothesis. 

3) Equatiom (3.2 were re-estimated on the artificial data series, 

resulting in new estimates of +(TI. These were used to calculate expected 

prices of home ownership and forecast error variances under the counterfactual. 

4) The counterfactual series of price differentials and forecast error variance 

differentials were substituted into the estimated behavioral eqution .-.* 

(SnciiLon 'I (4.l))to predict the homeownership ratio which would have obtained

under the counterfactual. To avoid peculiarities associated with any 

particular year,comparisons of actual and simulated homeownership ratios are 

p=.esenTed on the basis of 5 yea? averages over 1975-1979. 

The first proposition considered was the effect of a constant growth rate 

in real house values((VtlFLt 1 in equation (3.1)). To investigate this, we 

created an pificial series whose endpoints matched the historical record, 
23. 

but which grew smoothly at the rate of 3.1% yearly, and then followed the 

simulation procedure outlined above. 

The results indicate that a steady real growth rate in housing prices 

would have increased the proportion of owner-occupiers in the late 1970's 

by +0.0334. It is useful to "decompose" this figure into the parts due to 

the change in the expected price difference, and the part due to the change in the 

difference.in the forecast error variances. If ut2 is held at its actual 

value and the artificial value of t is substituted into equation (4.11, we 

find that the proportion of owner-occupiers -falls by 0.0072. Under the

simulation, capital gains in the latter part of the period are smaller than 

historical values, so on the basis of expected price alone, owner-occupation 

is less desirable than it was in reality. On the other hand, if Ft is 

held at its actual value, and the artificial value of the forecast error 

varlance is used, then the proportion of owner-occupiers increases by 0.0406. 

Clearly, the encouraging effect of less uncertainty dominates the outcome. 

For reference, these results are recorded in column (1)of Table 11. 

'de next gauged tne impact of several proposed changes 

in the tax treatment of housing. Suppose that during our sample period the 

deduction of mortgage interest and property taxes had been disallowed, but 

everything else had been the same. The results are recorded in column (2) 

of Table 11. Elimination of these deductions would have decreased the 

proportion of owner-occupiers by 0.0040. Most of the effect (.0036) comes 

via changes in the expected price; elimination of the deductions does not 

hae nuch inpact upon the forecast error variance .22 

22The magnitude of this effect is somewhat smaller than that found in 

earlier studies such as Hendezshott and Shilling [i982j and Rosen and Rosen 

C19801. This is due in part to the fact that the marginal income tax rates 

used in those studies exceed.those computed by Joines [1981], which me the 

ones used here. Hence, removal of any given tax deduction has a smaller 

dollar effect on the user cost of housing in this paper than in its 

predecessors. 
+ .) 

rl 

m 

rQ, 

I 

v) 0 In 3 F f (3 0 Q). 0 0 0 

0 0 0 rlal

> 

I I I 

vla 

O A

k o

0 

rcc

rl v) In 

(3 CI 

0 0 0 0 0 0 0 

+ + + 

a H (3 Q, cy 4 0 In Q) v) o a H 0 0 rl E

Y 0 0 0 

7u 

a 0

m + I + d 

U -rd a 

E.. 'r' 

v) rl In 0 v) v) rl 0 rl 0 '0 0 

+ I + 

0 In 

3 z? (3 0 0 0 0 0 0 0

. I I I 

cual 3 cy rr) 5( G ' (3 F 0 m a (3 0 f 0 0 0 

+ 1 

+

. 

01 

a 

CI

mal 

40 

d Q +Jh rlc Ok ec1 t..w Q 
25 

Another tax reform possibility is to tax housing capital gains at ordinary 

rates, but leave the other deductions in place. As shown in column (3) of 

Table 11, this change would have increased the proportion of owner-occupiers 

by 0,0105. This is a surprising result, but the other figures in ~cdumn(3) 

reveal its source. On the basis of expected price alone, we would have 

preZicted a decrease of -.0051. However, the encouraging effect of the taxinduced reduction in the forecast error variance dominates the outcome. 

This kind of result is familiar from the literature on taxation and 

uncertainty (Tobin E19583). As far as we know, its relevance to the issue 

of housing tenure choice has not been established before. 

Column (4) records the results when the interest an4 property tax - deductions are removed -

and housing capital gains are taxed. On balance,

there is a very small increase in the proportion of owner-occupiers. The -. 

variance effect so strongly present in column (3) is mitigated to some extent 

by the expected price effect of column(2) 

Recently, a number of suggestions have been made to change the current 

income tax into a "flat tax." Generically, a flat tax is an income tax with 

a constant marginal tax rate and a broadly defined tax base. However, a 

number of quite different proposals have been labeled as flat taxes. In __ 

particular, the various proposals have differed substantially with respect 

to the tw treatment of housing--some would leave it virtually unchanged, 

while others would eliminate most of the current benefits. Clearly, one 

cannot simulate the inipact of "the" flat tax. We therefore simulate the 

effects on tenure choice of three different proposals: 
a) Institute a tax with constant marginal rate of 24%, but which allows 

the current deduction of interest payments and property taxes, and which 

continues rhe current exemption of housing capital gains. The figure of 24% 

is based on Slemrod and Yitzhaki’s C19831 estimate that it would best 

balance efficiency costs with minimal changes in the distribution of tax 

Swdens. According to the results in column (51, there would not be much 

of an impact on the homeownership ratio. This is due mostly to the fact 

that the flat rate of 24% does not differ all that much from the average of 

historical marginal tax rates. More disaggregated data would allow us to 

examine how differential changes in tax rates within the population might 

affect the tenure choice. Unfortunately, such data are not available. 

S) Stipulate a constant marginal tax rate of 0.24, but eliminate the 

mortgage interest and property tax deductions. However, capital gains are 

still untaxed. As indicated in column (6), this regime induces a slight 

decrease in the incidence of homeownership, most of which is due to the 

increase in the user cost associated with the loss of the deductions. 

c) Institute a constant marginal tax rate of 0.24, eliminate interest 

and property tax deduction, and tax housing capital gains. The results, in 

column (71, show a slight stimulative effect on the homeownership ratio. This 

result is not unexpected given our previous discussion of column (3)--taxing 

capital gains makes housing more expensive, but this effect is overwhelmed 

by the reduction in risk associated with the tax’s introduction. 

Finally, we consider briefly the effects that indexing the income tax 

might have upon the homeownership ratio. From the point of view of constructing a counterfactual time series on the user cost of owning, indexing presents 
27. 

enormous difficulties. What real rates would have been built into the tax 

system? Would deductions and exemptions have been computed in real terms 

zs well? If so, what price index would have been used? 

In the absence of any obvious way to answer these questions, a reasonable 

?rocedure is to assume that the ultimate effect of indexing would simply 

3e somewhat lower marginal tax rates. In column (81, we assume that under 

indexing, marginal tax rates would have been 10 per cent smaller in each 

year than the historical values. The results suggest a very small depressing 

effect on the homeownership ratio--when the marginal tax rates decreases, 

the tax advantageassociated with homeownership are worth less, so the user 

cost increases 

V. Conclusions 

In this paper, we invest%gate the effects of price uncertainty on the 

tenure choice decision. Estimates on data from 1956-1979 indicate thatuncertainty over the course of relative prices has significantly depressed 

the aggregate proportion of homeowners. 

Proposals to modify the tax treatment of housing affect both the expected 

price differential between renting and owning and the difference in the ­ foreczst error variances. Previous analyses of policy changes may be misleading -

because the two effects can work in opposite directions. For example, our 

results suggest that taxation of capital gains at marginal personal income 

tax rates would have increased the homeownership rate, despite the increased 
28. 

expected cost of owning. The reduction in price variance is sufficiently 

attractive to dominate the outcome. Other results indicate that eliminating 

property tzx acd interest payment deductions would have reduced the homeownershi? 

rate, but that the combination of no deductions with czpital gains taxation 

would have resulted in a slightly higher proportion of homeowners. 

These results provide some explanation for the puzzling behavior of the 

homeownersbip ratio in the late 1970’s. In that period -

ex post costs of

honeowning fell gleatly relative to renting. Despite this, the aggregate 

proportion of homeowners changed little. Our evidence suggests that this 

was largely due to the erratic nature of housing costs which made ownership 

commitments unattractive. 

The chief limitation of this analysis is its omission of the relationship 

between housing and other financial decisions. From a theoretical point of 

view, one cxpects that the housing decision will be part of a broader portfolio 

allocation problem. As an empirical issue, the relevance of this consideration 

is not clear -- in 1972, 80%of those under the age of 56 held less than $5000 

in financid assets. (Feldstein and Feenberg C19831). Nevertheless, this 

is a topic worthy of further investigation. 
29. 

Appendix A 

I 

This appendix details the calculations of the forecast error variance of 

a projection based on the simple average of the first five future observations. 

We ca2 write the process for generating prices as: 

where 4 is assumed to be known. 

Using the lag operator, (A.1) implies: 

Expanding (A.2) yields an expression for 

't+j as a weighted average.of 

past shocks : 

where 

c(k) Z 1 + 6 + 6 2+...+ (bk 

A

The expected price, Pt+j9 at time t is calculated by taking the 
30. 

expectation of (A.4) conditional on information known at time t (which 

excludes ut : 

OD 

'ttj = I: c(k1 u ~ ~ ~ - ~ k=j+1 

, Thus, the forecast error is: 

Let wOy wl, w2, w39 w4 be weights. Then the 5 period weighted average 

forecast error is : 

4 -

e: I: we 

i=O i tti 

4 

Collecting coefficients on the shocks': 

- 4 3 2 

e = u C w.c(i1 t uttl C w it1c(i1 + utt2 I: wit2c(i) I i=o 1 i=O i=O 

1 

Clearly E(;) = 0 . Thus Var(e> = E(;*). Since the u's are independently, 

ideEcically, distributed, all covariance terms disappear and the result is: 

where : 
b 

.I 31. 

In the case referred to in the text, wi = 1/5 for all i . 
32. 

Appendix B 

This appendix describes the methodology used to construct our data series. 

The source of our raw data is also documented. HS refers to Historical 

Statistics of the United States: Colonial Times to 1970 (1975) and SA refers 

to various editions of Statistical Abstract of the United States. 

1. Troport'ion of owner-occupied dwellings, adjusted for demogra?hic 

composition: ' 

Three different sources of data were utilized. From 1945 to 1959 the 

iterative perpetual inventory method described in Rosen and Rosen (1980) 

was used. From 1960 to 1973 data on the proportion of owner-occupied housing 

starzs wene taken from Housing Vacancy Survey, U.S. Bureau of the Census, 

Publication #111. From 1974 to 1980, the owner-occupancy data were taken .. 

from the Annual Housing Survey, U.S. Bureau of the Census and Department of 

Housing asld Urban Development. The okner-occupied rates were then adjusted 

for changing demographic composition of the population following Jaffee and 

Rosen (1979). 

2. Price of owner-occupied housing : Pt 

As noted in the text, the price of owner-occupied housing is: 

where rt5\is the AAA bond rate, Vt is the market value of a house, Tt 

is the property tax per single family housing unit, Dt is depreciation, 

Mt is maintenance, Vt is the expected capital gain, Tt is the marginal 

tax rate for the household with average taxable income, Yt is the 

share of owner's equity in the house,,and PLt is the implicit price deflator 

for total consumption expenditures.- $:It was assuied rct -

- - rt ' 
33. 

The AAA bond rate series was taken from HS and SA. Following actual 

=.ea1 estate practice, depreciation and maintenance were each set at 1 percent 

of the house's value. The tax rate Tt was taken from Joines, 61981, p. 2101. 

.:.fter 1975, the 1975 tax rate of .1479 was used. . The market .value of owner-occupied housing, Vt , was derived by first 

splicing two housing price series and using the results to compute annual 

rates of change of house prices, gt ' The values of gt were then applied 

to census-year numbers on the median value of owner-occupied units in order 

to derive an annual series comparable with the census-year numbers. In an 

iterative process, the values of gt were changed proportionately until the 

values of the 'constructed price series for census years exactly matched those 

the census. Median values of owner-occupied units in census years were 

lound in HS. For 1944 to 1966, gt was computed using MA sales price data 

as reported in various editions of the FHA Yearbook. For 1967 to 1980, gt 

xas calculated from various editions of Existing Home Sales, a publication of 

the National Association of Realtors c39801. 

The property tax per owner-occupied unit was calculated by dividing the 

residential portion of all federal, state, and local property taxes by the 

number of owner-occupied units: 

xhere PTTt is total property tax revenue, KRt is net private residential 

capit.al stock at current cost, KNt is net private nonresidential capital stock 

at current cost, and OSt is the number of owner-occupied units. For years 

pior to 1971, these series were taken from HS; for 1971 to 1980, they 

xe?e from SA. 
34. 

3. Price of rental housing: Qt 

An annual rate of change of the rental price of housing was computed using 

the rental component of the CPI (HS prior to 1971, SA for 1971 to 1980). 

This rate of change series was then applied to census-year numbers on the 

median rent of renter-occupied units in order to derive an annual series 

compazable with the census-year numbers. In an iterative process, the annual 

changes in rental prices were adjusted until they exactly replicated the 

census-year numbers. 

4. Real consumption : Ct 

Real per capital consumption expenditures were taken from the Economic 

Report of the President (1982 1. 

5. Xed growth in deposits at savings and loan associations and mutual 

savings banks: CREDt . The savings data were from HS for the 1949 to 1970 and from SA for-1971 

to 1980. 

6. Quality adjustment for rental and owner-occupied housing. 

A3 annual tine series on the number of rooms in renter and owner-occupied 

housing was developed from census data prior,to 1973, and from the Annual 

Housing Survey since 1973. The price variables for renter and owner-occupied 

housing were then recalculated on a per room basis. 
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.36e 

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.