d f f b

U.S. Department of Housing and Urban Development

Office of Policy Development and Research

American Housing Suvey 

Combining the 

American Housing Survey and the 

American Community Survey to 

Produce Information Useful in Public 

Emergency Situations: 

An Exploratory Analysis 
Visit PD&R’s Web Site 

www.huduser.org

to find this report and others sponsored by 

HUD’s Office of Policy Development and Research (PD&R). 

Other services of HUD USER, PD&R’s Research Information Service,
 

include listservs;special interest, bimonthly publications (best practices, significant studies 

from other sources); access to public use databases; hotline 1-800-245-2691 for help 

accessing the information you need.
 
American Housing Survey 

Combining the 

American Housing Survey and the 

American Community Survey to 

Produce Information Useful in Public 

Emergency Situations: 

An Exploratory Analysis 

Prepared for: 

U.S. Department of Housing & Urban Development 

Office of Policy Development & Research
 

Prepared by: 

Frederick J. Eggers 

Econometrica, Inc. 

Bethesda, Maryland 

Contract No. C-CHI-00976 

Order No. CHI-T0001 

Project No. 1026-001 

December 2009 
Acknowledgements 

The author is indebted to several persons for their help on this challenging task. Dr. Fouad 

Moumen of Econometrica, Inc., assisted in developing the independent and dependent variables 

used for all the regressions and carried out many of these analyses. Dr. Fred Bellemore and Mr. 

Chris Holleyman of Econometrica, Inc., performed the fractional logit analyses using STATA© 

and provided advice and other assistance. Dr. Albert Lee of Summit Consulting provided highly 

useful critiques of the regression analyses and suggested the use of fractional logit. Dr. David A. 

Vandenbroucke of the Office of Policy Development and Research at HUD helped identify 

policy-useful dependent variables and offered other important guidance throughout the project. 

The contents of this report are the views of the contractor and do not necessarily reflect the views 

or policies of the U.S. Department of Housing and Urban Development or the U.S. Government. 
Table of Contents
 

Acknowledgements....................................................................................................... v
 

Executive Summary ..................................................................................................... vi
 

I. The Analytical Framework ..................................................................................... 1
 

Small Area Estimation .............................................................................................. 2 

National vs. Metropolitan AHS ................................................................................. 2 

Unit Data vs. Data Grouped by Metropolitan Area ................................................... 3 

II. Emergency-Relevant AHS Variables .................................................................... 3
 

III. Data Issues ............................................................................................................. 8
 

Metropolitan Geography ........................................................................................... 8 

Small Sample Sizes ............................................................................................... 10 

Choice of Statistical Technique .............................................................................. 12 

IV. Covariates for Modeling ...................................................................................... 13
 

ACS Approximations of the AHS Condition ............................................................ 13 

Covariates to Distinguish Among Metropolitan Areas on Non-Housing Factors .... 15 

Covariates Related to Local Housing Markets and Economic Conditions .............. 16 

V. Statistical Models ................................................................................................. 17
 

VI. Conclusions.......................................................................................................... 21
 

Appendix A: ACS and AHS Metropolitan Areas .................................................... A-1
 

Appendix B: Correlation Matrix for Independent Variables .................................. B-1
 

Appendix C: Fractional Logit Estimates for the Other Dependent Variables ...... C-1
 

iv 
List of Tables 

Table 1: Types of Information Published by the AHS and the ACS ................................ 4 

Table 2: Correlations among the AHS Condition Variables ............................................ 9 

Table 3: Sample Sizes and Descriptive Statistics for the AHS Condition Variables ..... 11 

Table 4: Correlations among AHS Condition Variables and their ACS Approximations15 

Table 5: Chi-squared and R2

 Statistics ........................................................................ 17 

Table 6: Regression Results ........................................................................................ 19 

Table 7: Predicted Values of PCTHSHLDNEED and PCTRENTINS ........................... 20 

v 
Executive Summary 

This research project explores the possibility of using small area statistical techniques to generate 

for areas not covered by the American Housing Survey (AHS) information that would be useful 

in preparing for or responding to a disaster and that is available only in the AHS. 

The study experienced difficulty in identifying variables that would be of obvious help in 

disasters situations. It looks at nine conditions that might be useful to measure: 

 the percent of households with needs—households that (a) are poor, (b) have an elderly 

householder or spouse, (c) are single-parent households, or (d) have a householder or 

spouse who is a recent immigrant 

 the proportion of occupied units with severe physical problems 

 the proportion of occupied units with either severe or moderate physical problems 

 the proportion of occupied units that have severe physical problems and are occupied by 

households with needs 

 the proportion of occupied units that have severe or moderate physical problems and are 

occupied by households with needs 

 the proportion of occupied units built prior to 1940 and are occupied by households in 

need 

 the proportion of occupied units that are mobile homes and are occupied by households in 

need 

 the proportion of owner-occupied units with homeowners’ insurance 

 the proportion of renter-occupied units with renters’ insurance. 

The research chose to use fractional logit to estimate these conditions using variables measured 

for all metropolitan areas by the annual American Community Survey (ACS). Three types of 

independent variables were used: ACS approximations of the AHS-measured conditions, 

covariates to distinguish among metropolitan areas on non-housing factors, and covariates 

related to local housing markets and economic conditions. 

The results are only mildly encouraging. Of the nine equations estimated, only two were 

statistically meaningful using the Chi-squared test. However, the R2

s for these two equations 

indicate that using the predicted values may be a worthwhile improvement over assuming that all 

metropolitan areas have the same values, that is, using the sample mean. Out-of-sample 

predictions using these two equations suggest that conditions may vary substantially across 

metropolitan areas. 

Equations with better statistical properties might result from using household-level data rather 

than metropolitan-level data. This would involve using microdata from the AHS to estimate the 

equations and microdata from the ACS public use files to use the equations for predictive 

purposes. 

vi 
The next major disaster may very well indicate what AHS information is crucial. Unfortunately, 

if such an event were to occur, there may not be time to carry out the desired microdata analysis. 

If so, the techniques explored in this paper might be a valuable second-best approach. 

vii 
 

 

 

 

Combining the American Housing Survey and the American 

Community Survey to Produce Information Useful in Public 

Emergency Situations: An Exploratory Analysis 

In October 2008, Econometrica, Inc., and its partner, ICF International, entered into a contract 

with the Department of Housing and Urban Development (HUD) to support the American 

Housing Survey (AHS). Task C of that contract required the Econometrica team to use the 

information from the 2007 AHS surveys of seven metropolitan areas to produce information for 

those areas that might be useful to federal, state, or local agencies in preparing for or responding 

to natural disasters or other emergencies. For Task D, Econometrica suggested exploring the 

possibility of using small area statistical techniques to generate information available only in the 

AHS to areas not covered by the AHS. ICF International performed the analysis under Task C; 

Econometrica carried out the work under Task D. 

This paper reports in six sections what was learned in Task D: 

 Section I translates the Task D idea into research terms. 

 Section II looks for information available only in the AHS that might be useful in 

emergency situations. 

 Section III discusses relevant data issues and statistical issues. 

 Section IV identifies the covariates to be used in regression analysis to estimate AHS 

variables using American Community Survey information. 

 Section V reports the model results. 

 Section VI provides brief concluding observations. 

I. The Analytical Framework 

A simple concept underlies Task D: 

At present, the American Community Survey (ACS) produces detailed information 

annually on people and housing for all geographical units with 20,000 or more persons.1 

Beginning in late 2010, the ACS will provide the same information for all places and for 

census tracts and census blocks as well.2 Federal, state, and local agencies preparing for 

1

 For places with more than 65,000 persons, the ACS publishes information using data collected in the preceding 

year. For places with more than 20,000 persons (including places with more than 65,000 persons), the ACS 

publishes information using data collected in the preceding 3 years.

2 For places with fewer than 20,000 persons and for census tracts and blocks, the ACS will publish information 

using data collected in the preceding 5 years. Information based on the same time period will also be published for 

all places, including those with populations greater than 20,000. Once the ACS is fully implemented in 2010, the 

statistics available annually from the ACS by size of place are as follows: For places with populations greater than 

65,000, the Census Bureau will release three different data sets, one based on data collected in the preceding year, 

one based on data collected in the preceding 3 years, and one based on data collected in the preceding 5 years. 

Places with populations greater than 20,000 but less than 65,000 will have two data sets, one based on data collected 

1 
 

 

 

or responding to natural disasters or other emergencies should find ACS information very 

valuable. The AHS contains more detailed information on housing units and the 

households living in those units than the ACS. This additional information might also be 

valuable to those dealing with emergencies. However, AHS data are generally not useful 

in emergency situations because AHS data are available only at the national or regional 

level. Task D explores whether statistical models using information from the ACS can 

produce satisfactory estimates of AHS variables for metropolitan areas for which AHS 

data are not available. 

Small Area Estimation 

“Small area estimation” is the term applied to a set of statistical methods that have been 

developed in recent years to solve problems such as the one posed in the preceding paragraph, 

namely, to produces estimates for “areas” or “domains” for which the sample sizes available in a 

“national” sample are too small for direct estimation. An example of small area estimation is the 

Bureau of Labor Statistics (BLS) Local Area Unemployment Statistics (LAUS) series that uses 

the national Current Population Survey to generate estimates of labor force participation, 

employment, and unemployment for small areas. Because of the considerable work that went 

into the creation and testing of the statistical models used in LAUS, the BLS is confident enough 

in their reliability to release LAUS estimates on a monthly basis for jurisdictions with 

populations as small as 10,000. The goal of this task is considerably more modest. HUD does 

not intend to publish any estimates from the models created in this task. The goal is simply to 

test the feasibility of developing techniques that could be applied quickly in an emergency 

situation to generate information useful to those responding to the emergency. 

A variety of statistical tools are used to solve small area estimation problems. The author uses 

one of the most frequently employed techniques, regression analysis, but the regression 

equations used here are considerably simpler than the models used to create publishable small 

area statistics. Two reasons explain the choice of simpler models: the limited scope of the task 

and the objective of creating techniques that could be replicated quickly and simply, even with 

different dependent variables or different levels of geography. 

Translating this concept into a framework suitable for statistical modeling involves answering 

the two questions discussed below. 

National vs. Metropolitan AHS 

Should the analysis be based on the national AHS or on metropolitan AHS surveys? 

The AHS surveys 21 metropolitan areas on a once-every-six-year schedule. The public use files 

(PUFs) contain data at the household level with location identified down to “zones,” which are 

units of geography containing no fewer than 100,000 people, created especially for the AHS.3 It 

in the preceding 3 years and one based on data collected in the preceding 5 years. Places with populations less than
 

20,000 will have only one data set based on data collected in the preceding 5 years. 

3

 “Zones” are not available for the New York, Los Angeles, Chicago, Detroit, and Philadelphia metropolitan areas 

and for the group of metropolitan areas surveyed in the AHS as “Northern New Jersey.” 

2 
 

 

might be useful to project AHS-type information down to smaller levels of geography such as 

census tracts or blocks. The author chose not to pursue this option for two reasons. First, the 

author could not do this without access to information on the location of AHS sample units that 

the Census Bureau does not make available to the public. While it would be possible to petition 

the Census Bureau for access to this information, the process of obtaining the needed clearances 

seemed to be beyond the timeframe of this Task. Second, ACS data are not yet available at the 

census tract level. While the author could use 2000 decennial census data, this information 

would be 9 years old. For these reasons, the author chose to use the national AHS data. 

Unit Data vs. Data Grouped by Metropolitan Area 

Should the analysis use household-level data or metropolitan-level data? 

The AHS publishes information at the national and regional levels. In addition, the Census 

Bureau makes all of the AHS data available in a public use file (PUF) that identifies 144 

metropolitan areas.4

 The ACS publishes data for various levels of geography, including most 

metropolitan areas. The Census Bureau also releases a PUF for the ACS containing roughly a 

million cases at the level of Public Use Microdata Area (PUMA), which are units of geography 

containing no fewer than 100,000 people and created especially for the ACS. 

The first option would involve using the AHS PUF data to model relationships at the housingunit level. Then one could apply the AHS models to PUMA geography using microdata from 

the ACS PUF. The second option would involve using the AHS PUF to group AHS data by 

metropolitan area, and then build models that use AHS information at the metropolitan level as 

dependent variables and ACS published information at the metropolitan level as independent 

variables. Then one could apply these models to other metropolitan areas and conceivably to 

lower levels of geography for which ACS published information could be used for independent 

variables. 

The author chose the second option because it could be implemented quickly if an emergency 

arose. A model created using published ACS data could be applied swiftly to produce an 

estimate of AHS variables for any metropolitan area. As explained in the next section, there was 

little consensus about what AHS variables would be most useful to those responding to an 

emergency situation. The simple models based on area-level data developed in this task could be 

easily replicated using different AHS variables as dependent variables. Finally, if the estimated 

models appear to be robust and if the exigency were great, one could even apply the model to 

lower levels of geography quickly using published ACS data. 

II. Emergency-Relevant AHS Variables 

While the ACS contains a considerable amount of useful information on housing, the AHS 

provides substantially more information on housing units, including detailed information on 

amenities, housing costs, and the condition of housing units. The following table is excerpted 

4

 The number of sampled households in each of the identified metropolitan areas ranges from 8 to 1,274. The PUF 

contains information on over 35,000 households throughout the United States. 

3 
 

 

from Comparison of Housing Information from the American Housing Survey and the American 

Community Survey, a report prepared for HUD by Econometrica in 2007.5 

Table 1: Types of Information Published by the AHS and the ACS 

The italic entries represent housing characteristics available in published tables from the AHS 

that are not available in published tables from the ACS. 

American Housing Survey 

(national survey) American Community Survey 

Status of unit 

 Seasonal, year-round, 

occupied/vacant, reason vacant 

 Owner/renter 

 Seasonal, occupied/vacant, 

reason vacant 

 Owner/renter 

Structure 

characteristics 

 Units in structure 

 Year built 

 Stories in structure 

 Lot size (single unit and mobile homes 

only) 

 Units in structure 

 Year built 

Unit 

characteristics 

 Number of rooms 

 Number of bedrooms 

 Number of bathrooms 

 Square footage 

 Heat equipment and heating fuel 

 Source of water and sewage disposal 

 Number of rooms 

 Number of bedrooms 

 Heating fuel 

Unit quality 

 With all kitchen facilities—by specific 

facility 

 With all plumbing facilities—by 

specific facility 

 Selected amenities, includes: 

o Telephone service 

o Air conditioning 

o Fireplace 

o Washing machine 

o Clothes dryer 

o Dishwasher 

o Disposal 

o Deck 

o Garage or car port 

 With all kitchen facilities 

 With all plumbing facilities 

 Telephone service 

 Selected deficiencies, includes: 

o Selected structural 

deficiencies, e.g., leaks or 

holes in floors or ceilings 

o Selected plumbing problems 

o Selected electrical problems 

o Selected upkeep problems 

 Summary measure of severe and 

moderate physical problems 

 Occupants rating of unit on scale of 1 

to 10 

Neighborhood 

characteristics 

 Type and age of housing in 

neighborhood 

 No national-level tables 

 Beginning in 2010, researchers 

5

 This report is available at http://www.huduser.org/intercept.asp?loc=/publications/pdf/comparison_hsg.pdf. 

4 
 

 

American Housing Survey 

(national survey) American Community Survey 

and quality  Adequacy of schools, shopping, and 

public transportation 

 Problems with: 

o Crime 

o Traffic noise 

o Odors 

o Abandoned buildings 

o Litter 

 Occupants rating of neighborhood on 

scale of 1 to 10 

will be able to obtain for 

individual census tracts 

information on type and age of 

housing in census tract, housing 

costs in census tract, home 

values in census tract, and 

household characteristics in 

census tract 

Renter housing 

costs 

 Contract rent 

 Utilities and other housing costs 

 Gross rent—contract rent plus utilities 

and other housing costs 

 Ratio of gross rent to income 

 Whether unit receives housing 

assistance 

 Contract rent 

 Gross rent 

 Ratio of gross rent to income 

Owner housing 

costs 

 Utilities and other housing costs 

 Real estates taxes 

 Mortgage payments 

 Monthly housing costs 

 Ratio of monthly housing costs to 

income 

 Real estates taxes 

 Monthly housing costs 

 Ratio of monthly housing costs 

to income 

Value of owneroccupied 

housing 

 Purchase price 

 Source of downpayment 

 Owner estimate of value 

 Value by income 

 Ratio of value to income 

 Price asked for vacant units 

 Owner estimate of value 

 Value by income 

 Ratio of value to income 

 Price asked for vacant units 

Mortgage 

 With or without prime mortgage 

 How obtained 

 Year originated 

 Government insurance 

 Payment type, e.g., fixed-rate 

 Mortgage payment 

 Interest rate 

 Remaining years 

 Outstanding principal amount 

 Current loan as percent of value 

 Second mortgage 

 Home equity line of credit 

 With or without prime mortgage 

Despite all the extra information available in the AHS, the author found it difficult to identify 

information unique to the AHS that would obviously be useful in emergency situations. The 

author used the literature review produced for Task C, discussions with HUD analysts, previous 

work by the author on permanent losses,6

 examination of information produced in the past by 

6 The Destruction of Housing Capital: A Preliminary Exploration into Demolitions and Disasters. This 2004 ICFEconometrica report was produced for HUD and can be found at 

http://www.huduser.org/datasets/ahs/ahsReports.html#1. 

5 
 

 

 

 

 

 

HUD using the AHS, and considerable introspection and still failed to find variables that would 

be unquestionably useful. As frequently happens, it is difficult to anticipate whether something 

might be useful in the abstract. In discussing this difficulty, David Chase noted that, in the early 

days of geocoding data, it was difficult to get policymakers and even analysts to specify what 

maps would be useful until the policymakers and analysts became familiar with what mapping 

could do. 

The author selected two measures of deficient housing that are unique to the AHS: 

 PCTSEVPROB: the proportion of occupied units with severe physical problems.7 

Housing with severe physical problems may be more susceptible to damage or, if 

damaged, may be deemed unfit or not valuable enough to repair. However, analysis using 

data on individual units in The Destruction of Housing Capital did not find an association 

between units with severe physical problems and permanent losses through demolition or 

disasters. 

 PCTSEVMODPROB: the proportion of occupied units with either severe or moderate 

physical problems. 

Having either moderate or severe physical problems was related statistically to permanent 

losses through demolition or disasters in The Destruction of Housing Capital. Units with 

problems of these types may be more susceptible to damage or, if damaged, may be 

deemed unfit or not valuable enough to repair. In either case, provision for new housing 

must be made. 

The cited research on permanent losses also found statistical relationships of varying strength at 

the individual unit level between permanent losses through demolition or disasters and the 

following AHS variables:8 

 Having been built prior to 1920 – a consistently strong statistical relationship 

 Having been built between 1920 and 1939 or having been built between 1940 and 1959 – 

consistent statistical relationships of varying strength 

 Midwest location – consistent statistical relationship of varying strength 

 Renter-occupancy – consistently strong relationship 

 Vacancy – consistently strong relationship.
 

The ACS provides information on all these variables, and therefore the author does not model 

them. 

7

 For definitions of severe and moderate physical problems, see pages 1,043 and 1,044 of the AHS Codebook at 

http://www.huduser.org/intercept.asp?loc=/Datasets/ahs/AHS_Codebook.pdf. Changes to the questionnaire in 2007 

eliminated the questions needed to assess the adequacy of hallways. 8 The Destruction of Housing Capital also found a consistent and strong statistical relationship between an 

occupant’s rating of his or her housing unit and permanent losses through demolition or disaster. This variable 

(HOWH) is not available in the ACS, but its granularity (it is scored on a 1-10 scale) makes it difficult to create an 

appropriate summary variable for an entire metropolitan area. 

6 
 

 

 

 

The author created a measure of households in need: 

 PCTNEEDHSHLD: the percent of households that (a) are poor (below poverty-level 

income), (b) have an elderly householder or spouse, (c) are single-parent households, or 

(d) have a householder or spouse who is a recent immigrant (came to this country in 

2002 or later). 

The information on households with needs could be obtained from the ACS PUF, so the AHS is 

not a unique source.9 The author used the AHS to identify households in need so that the author 

could create variables that link housing problems and household needs. However, the author 

decided to estimate this variable as well, because it might be useful to have an equation that 

estimated this percentage without having to use the ACS PUF. 

The author linked being a household in need with specific housing features in the following four 

variables: 

 PCTSEVPROBNEED: the proportion of occupied units that have severe physical 

problems and are occupied by households with needs. 

 PCTSEVMODPROBNEED: the proportion of occupied units that have severe or 

moderate physical problems and are occupied by households with needs. 

 PCTOLDHSNEED: the proportion of occupied units built prior to 1940 and are occupied 

by households in need. 

 PCTMHNEED: the proportion of occupied units that are mobile homes and are occupied 

by households in need. 

The author focuses on older housing units because of the relationship found in The Destruction 

of Housing Capital between the age of a unit and permanent losses through demolition or 

disaster. The author focuses on mobile homes because of their susceptibility to wind damage. 

Because the ACS contains information on both year built and type of structure, the author 

estimates only the intersection of these structural characteristics and household needs. 

HUD suggested including a variable that identifies whether the household has homeowners’ or 

renters’ insurance. The percentage of owners with homeowners’ insurance is substantially 

greater than the percentage of renters with renters’ insurance.10 Therefore, the author decided to 

estimate two variables: 

9

 Table B17017 in the published ACS data contains counts of households by all of these conditions except being a 

recent immigrant; the information on being elderly in Table B17017 refers to the householder only. Separately, the 

ACS also contains information on household members with disabilities. The AHS will have this information
 

beginning in 2009.

10 Among the 118 metropolitan areas for which we calculate the percentages, 25 percent of renters had renters’ 

insurance and 95 percent of homeowners had homeowners’ insurance.
 

7 
	 PCTOWNINS: the proportion of owner-occupied units with homeowners’ insurance. 

	 PCTRENTINS: the proportion of renter-occupied units with renters’ insurance. 

Table 2 shows that, except for PCTSEVMODPROB and PCTSEVMODPROBNEED, the 

correlations between these seven AHS condition variables are relatively small. 

III. Data Issues 

The author confronted three data issues: how to reconcile the metropolitan areas reported in the 

AHS with those reported in the ACS, what to do about metropolitan areas where the AHS 

sample was small, and what statistical technique to use for the modeling. 

Metropolitan Geography 

The 2007 AHS PUF identifies 144 separate metropolitan areas using the variable SMSA and 

identifies an additional 3 geographical areas that are a combination of some of the 144 

metropolitan areas. The ACS publishes 2007 data on 310 metropolitan areas. Matching the AHS 

metropolitan areas with those found in the ACS involves taking into account changing 

definitions of metropolitan areas and the availability of published ACS data. Appendix A 

provides a list of the 118 metropolitan areas used in this analysis. These are areas for which the 

author had both data from the 2007 national AHS and published data from the 2007 ACS. 

For 103 of the 118 metropolitan areas, there was a one-to-one match between the areas identified 

in the AHS and those for which 2007 ACS data are published. There may, however, be 

differences in the boundaries of an AHS metropolitan area and the ACS metropolitan area with 

the same name. The author cannot correct for boundary differences. 

The remaining 13 metropolitan areas involved fitting together multiple AHS metropolitan areas 

or using ACS combined metropolitan areas. 

	 In four cases, the author had to use combined statistical areas when obtaining the 

published ACS data. 

o	 The AHS reports Johnson City-Kingsport-Bristol, TN-VA as one metropolitan 

area; the ACS reports them as separate areas and also publishes data for the two 

areas combined. 

o	 The AHS reports Raleigh-Durham as one metropolitan area; the ACS reports 

them as separate areas and also publishes data for the two areas combined. 

o	 Both the AHS and ACS recognize Orlando and Daytona Beach as separate 

metropolitan areas, but the ACS only publishes data for Orlando and for the 

combination of the two metropolitan areas. 

o	 Both the AHS and ACS recognize Greenville, SC and Spartanburg, SC as 

separate metropolitan areas, but the ACS only publishes data for Greenville and 

for the combination of the two metropolitan areas. 

8 
9 

Table 2: Correlations among the AHS Condition Variables 

PCTSEVPROB

PCTSEVMODPROB

PCTNEEDHSHLD 

PCTSEVPROBNEED

PCTSEVMODPROBNEED

PCTOLDHSNEED

PCTMHNEED 

PCTSEVPROB 1 PCTSEVMODPROB 0.5182 1 PCTNEEDHSHLD -0.0557 -0.0161 1 PCTSEVPROBNEED 0.6114 0.2742 -0.0272 1 

PCTSEVMODPROBNEED 0.3545 0.8188 0.2161 0.3388 1 

PCTOLDHSNEED -0.1143 -0.0711 0.3735 0.0240 0.1325 1 

PCTMHNEED 0.0700 -0.0189 0.2350 -0.0183 -0.1089 -0.1938 1 PCTOWNINS 0.0276 -0.4232 -0.2484 0.0446 -0.4092 -0.0432 -0.0766 PCTRENTINS -0.1213 -0.0653 -0.0923 -0.0866 -0.0572 0.0436 -0.1337 
 

 

 

 

 

	 The ACS New York City metropolitan area includes all of Long Island and most of 

northern New Jersey. The ACS definition encompasses seven metropolitan areas which 

the AHS identifies separately. In addition, the AHS separately identifies data that fall 

into one of the five northern New Jersey metropolitan areas without specifying which 

metropolitan area, and also data that fall into the New York City or Nassau-Suffolk 

metropolitan areas without identifying which area.11 

	 The ACS Chicago metropolitan area has boundaries that include five AHS metropolitan 

areas, including Gary, IN. In addition, the AHS separately identifies data that fall into 

one of four metropolitan areas included in the greater Chicago area, without specifying 

which metropolitan area. 

	 The ACS metropolitan area includes two or more AHS areas in the following nine cases: 

Boston (3), Bridgeport-Stamford (2), Dallas-Fort Worth (2), Los Angeles-Long Beach (2 

– the second being Santa Ana), Miami-Ft. Lauderdale (3), Pittsburg (2), St. Louis (3), San 

Francisco-Oakland (2), and Seattle-Tacoma (2). 

Appendix A lists all 118 ACS areas used in this analysis and the AHS metropolitan areas that are 

associated with them. 

Small Sample Sizes 

In the models developed in this research project, the author used AHS data only for constructing 

the dependent variables and used ACS data for all the independent variables.12 For many of the 

metropolitan areas, the AHS sample sizes are small, and therefore estimates based on these 

samples will be imprecise and granular. For example, if there are only 20 AHS sample cases in a 

metropolitan area, then all percentages will be multiples of 5. Normally, imprecision in 

estimating the dependent variable does not introduce bias into the coefficient estimates, but bias 

may result here because the independent variables are percentages and most of the observed 

percentages are zero or close to zero. Small sample sizes result in vectors of values for the 

dependent variables that appear to contain too many zeros. 

Table 3 calls attention to the fact that, except for having homeowners’ insurance, most of the 

AHS conditions occur infrequently; this is particularly true when a physical condition is 

combined with household need. A unit with a severe physical problem is a condition that 

occurred on average in only 1.6 percent of the units in the 118 metropolitan areas to be used in 

the regression for PCTSEVPROB.13 A unit with a severe physical problem and also occupied by 

a household with one or more needs occurs in only 0.5 percent of the units in the 118 

metropolitan areas to be used in the regression for PCTSEVPROBNEED. The coefficient of 

11 The AHS data on northern New Jersey (SMSA=9993) include some cases in the Trenton metropolitan area. The 

author elected to treat Trenton as a separate metropolitan area and to ignore the erroneous inclusion in the New York 

metropolitan area of any SMSA= 9993 cases that are in the Trenton metropolitan area. 12 AHS data were used for REGION for convenience; the AHS is not a necessary source for that information.
 13 The means reported in the table are unweighted means of the percentages observed in the different metropolitan
 

areas. 

10
 
Table 3: Sample Sizes and Descriptive Statistics for the AHS Condition Variables 

AHS CONDITION 

PCTSEVPROB

PCTSEVMODPROB

PCTNEEDHSHLD 

PCTSEVPROBNEED

PCTSEVMODPROBNEED

PCTOLDHSNEED

PCTMHNEED 

Sample size (N) 118 118 118 118 118 118 118 

Mean 0.016 0.055 0.324 0.005 0.020 0.052 0.0

Standard deviation 0.020 0.051 0.090 0.009 0.024 0.067 0.0

Coefficient of Variation 1.26 0.92 0.28 2.06 1.21 1.27 2

Maximum value 0.049 0.319 0.760 0.041 0.130 0.432 0.0

Minimum value 0.000 0.000 0.113 0.000 0.000 0.000 0.0

Range 0.049 0.319 0.647 0.041 0.130 0.432 0.0

11
 
 

 

 

variation and the range statistics indicate that, despite the low percentages, there is substantial 

variation in these conditions across metropolitan areas except for having homeowners’ 

insurance.14 

The author used the ordinary least squares (OLS) technique for the initial regression analysis; he 

eliminated some metropolitan areas from these regressions if it appeared that a zero-value for the 

dependent variable were the likely result of small samples.15 The models reported in this paper 

were estimated using fractional logit. The author chose not to eliminate metropolitan areas from 

the fractional logit analysis because he considered that technique less affected by false-zeros. 

Choice of Statistical Technique 

Linking the AHS and the ACS should be thought of as a statistical, rather than an econometric, 

problem. The national AHS can produce a mean value for each of the seven AHS-based 

condition variables identified in Section II, and users could apply this mean value to all 

metropolitan areas in the United States as a first approximation. The statistical problems are (1) 

to find covariates to include in a model that would produce better results (smaller variance) than 

using the mean value for all metropolitan areas, and (2) to choose an appropriate technique to 

estimate the relationship between the dependent and independent variables. Section IV deals 

with the selection of covariates. 

As noted in the discussion of small sample sizes, the author chose ordinary least squares for the 

initial analysis. The results were reported in the draft report of August 2009. While the Fstatistics and the R2

s were favorable for eight of the nine regressions, the OLS technique has 

certain limitations that render it inappropriate for this purpose.16 The two most serious limitations 

are: 

 OLS equations can produce predictions of less than 0 percent or more than 100 percent 

for specific metropolitan areas. While the estimated OLS equations did not result in 

predictions outside of the 0-100 range for the 118 areas used to estimate the equations, 

there was no guarantee that inadmissible predictions would not result if the equations 

were used to make predictions for other metropolitan areas. 

14 The coefficient of variation is the ratio of the standard deviation to the mean, and the range is the difference 

between the maximum and minimum values. 

15 For each variable, the author estimated the ratio of the number of units in all 118 metropolitan areas with the 

specified characteristic to the number of occupied units in all metropolitan areas. The author then estimated the 

number of sample cases required to produce a probability equal to or less than 50 percent that no cases with the 

required characteristic would be obtained if the actual probability were equal to the computed ratio. If r is the ratio 

and n is the number of sample cases, the author found the minimum n that satisfied the following equation: 0.5 > (1-

r)n

. Then, for the model involving that dependent variable, the author eliminated all metropolitan areas where the 

observed percentage was 0 percent and the sample size was less than n. The rationale for using this procedure is that 

data from a metropolitan area should be used only if there is at least a 50-percent chance of finding the specified 

condition in the metropolitan area. 

16 The F-test statistic determines whether the set of independent variables contributes statistically to the prediction of 

the dependent variable, and the R2

 statistic measures the extent to which the regressions provide better predictions of 

the independent variables than the mean calculated over the areas included in the model. 

12
 
 

 

 

 The large variation in sample sizes across the 118 metropolitan areas insured that errors 

in measuring a particular dependent variable would vary substantially across the 

metropolitan areas. This leads to a statistical problem called heteroskedasticity that 

produces inefficient, albeit unbiased, estimates.17 An estimate is considered inefficient if 

it results in larger-than-necessary prediction errors. 

At the suggestion of Dr. Lee, we chose to use fractional logit, a technique designed to estimate 

proportions.18 

IV.Covariates for Modeling 

The author included three types of covariates in models tested in Section V: ACS 

approximations of the AHS condition, covariates to distinguish among metropolitan areas on 

non-housing factors, and covariates related to local housing markets and economic conditions. 

ACS Approximations of the AHS Condition 

For most of the nine conditions described in Section II, approximations can be created using 

published ACS data. The starting point for each model is the ACS approximation. The 

bracketed numbers beginning with “B” are the ACS table numbers where information can be 

found.19 

As the ACS approximation of PCTSEVPROB, the author defined: 

ACSPCTPROB = count of units without complete kitchen facilities [B25052] plus count 

of units without complete plumbing facilities [B25048])/count of occupied units 

[B25002] 

This variable created from the ACS does include units with many conditions that would 

be considered severe physical problems by the AHS. However, it will double count units 

that lack both complete kitchen facilities and complete plumbing facilities and will fail to 

count units with other physical deficiencies that the AHS considers severe. 

The author will also use ACSPCTPROB as the best ACS approximation for 

PCTSEVMODPROB. 

17 Dr. Lee pointed out that the OLS results were also inefficient because they failed to take into account the 

correlation among the error terms in the nine regressions. A statistical technique called seemingly unrelated 

regressions (SUR) could eliminate this source of inefficiency but the underlying inefficiency resulting from 

heteroskedasticity would remain. 

18 “Econometric Methods for Fractional Response Variables with an Application to 401(k) Plan Participation Rates” 

(with J.M. Wooldridge), Journal of Applied Econometrics 11, 619-632, November-December 1996. 

19 Those familiar with small area estimation will note that some of these ACS proxy variables are very similar to the 

small area estimates produced by “synthetic estimation.” Synthetic estimation involves using known relationships 

among variables at a higher level of geography to estimate variables for small areas by applying those relationships 

to data available at the small level. 

13
 
As the ACS approximation of PCTNEEDHSHLD, the author defined: 

ACSPCTNEED = (ACSNEED + ACSOTHNEED)/count of occupied housing units 

[B25002] where 

ACSNEED = count of households with incomes below the poverty level plus 

count of households with incomes above the poverty level who are classified as 

“other families” plus the count of households with incomes above the poverty 

level who are married couple households with householders 65 years or older plus 

the count of households with incomes above the poverty level who are nonfamily 

households with householders of either sex 65 years or older [all in B17017] 

ACSOTHNEED = ((count of occupied units [B25002] – ACSNEED) * (entered 

in 2000 or later [from B05005]/total population [from B03001]) 

As the ACS approximation of PCTSEVPROBNEED, the author defined: 

ACSPCTPROBNEED = ACSPCTPROB* ACSPCTNEED 

The author will also use ACSPCTPROBNEED as the best ACS approximation for 

PCTSEVMODPROBNEED. 

As the ACS approximation of PCTOLDHSNEED, the author defined: 

ACSOLDHSNEED = ACSPCTNEED* (count of units built prior to 1940 

[B25034]/total[B25034]) 

As the ACS approximation of PCTMHNEED, the author defined: 

ACSPCTMHNEED = ACSPCTNEED* (count of mobile homes[B25024]/total[B25024]) 

There are no ACS approximations for PCTOWNINS and PCTRENTINS. Table 4 presents the 

correlations between the AHS condition variables and these ACS approximations. The ACS 

approximation to physical problems does not correlate well with either severe or severe plus 

moderate as measured in the AHS. The variables derived from the AHS and ACS using age of 

housing have a correlation of 0.75. 

14
 
 

 

 

 

 

Table 4: Correlations among AHS Condition Variables and their ACS 

Approximations PCTSEVPROB

PCTSEVMODPROB

PCTNEEDHSHLD 

PCTSEVPROBNEED

PCTSEVMODPROBNEED

PCTOLDHSNEED

PCTMHNEED 

ACSPCTPROB 0.0849 0.2284 

ACSPCTNEED 0.2749 

ACSPCTPROBNEED -0.0156 0.2682 

ACSOLDHSNEED 0.7516 

ACSPCTMHNEED 0.3924 

Covariates to Distinguish among Metropolitan Areas on Non-Housing 

Factors 

Regional differences: 

Three dichotomous variables with SOUTH as the exclude region: 

NORTHEAST 

MIDWEST 

WEST 

Size differences: 

LNPOP = natural log of total population [B01003] 

Racial and ethnic differences: 

PCTBLACK = Black or African American alone (Hispanic plus nonHispanic)/total 

[B03002] 

PCTHISP = Hispanic or Latino/total [B03002] 

Age and growth history: 

OLDMETRO = (count of units built prior to 1940 [B25034]/total [B25034]) 

15
 
FASTMETRO = (count of units built 1990 or later [B25034]/total [B25034]) 

Relative income: 

RELINC = median household income [B19013]/$50,740 (U.S. median household 

income) 

Education level of workforce: 

EDUC = count of persons with associate’s degree or higher (males + females)/total 

[B15002] 

Covariates Related to Local Housing Markets and Economic Conditions 

Vacancy rate: 

VACRATE = vacant units/all housing units [B25002] 

Homeownership rate: 

HORATE = owner-occupied / total [B25003] 

Cost of housing – 3 possibilities: 

RELRENT = median gross rent [B25064]/$789 (U.S. median gross rent) 

RELVALUE = median value [B25077]/$194,300 (U.S. median value) 

OVERCROWD = count of units (owner + renter) with 1.01 or more occupants per 

room/total [B25014] 

The author used only RELRENT and OVERCROWD in the models. 

Type of housing structures: 

UNITS2TO4 = (count of units in structures with 2 to 4 units/total [B25024]) 

UNITS50 = (count of units in structures with 50 or more units/total [B25024]) 

Appendix B provides the correlation matrix for the independent variables. 

16
 
 

 

 

V. Statistical Models 

This section reports regression models that use the covariates from Section IV to estimate the 

nine AHS-based condition measures identified in Section II. Our evaluation of the model 

focuses on two statistics: 

	 A Chi-squared test which determines whether the set of independent variables contributes 

statistically to the prediction of the dependent variables, and 

	 the R2

 statistic which measures the extent to which the regressions provide better 

predictions of the independent variables than the mean calculated over the areas included 

in the model. 

In general, R2

 is not used to assess logit-type models; however, this statistic is appropriate in the 

context of this research project because the alternative to using a prediction from the fractional 

logit equation would be to use the mean of the dependent variable. After assessing these 

statistics, the author will examine the coefficients of the dependent variables primarily to 

determine whether there are any unwarranted relationships, but also out of curiosity. 

Table 5 presents the Chi-squared and the R2

 statistics for the nine models. 

 Table 5: Chi-squared and R2

 Statistics 

Chi-squared R2 

PCTSEVPROB Not significant 0.118 

PCTSEVMODPROB Not significant 0.297 

PCTNEEDHSHLD Significant at 0.01 0.258 

PCTSEVPROBNEED Not significant 0.163 

PCTSEVMODPROBNEED Not significant 0.283 

PCTOLDHSNEED Not significant 0.685 

PCTMHNEED Not significant 0.533 

PCTRENTINS Significant at 0.01 0.339 

PCTOWNINS Not significant 0.298 

In only two regressions is the relationship between the set of independent variables and the 

dependent variable considered statistically significant; these are the equations for the percentage 

of households in need (PCTNEEDHSLD) and the percentage of renters with insurance 

(PCTRENTINS). This is a very disappointing result. As noted earlier, eight of the nine OLS 

regressions were considered statistically significant. The added restriction that the predictions 

have to fall in the 0 to 100 range resulted in 6 of the 8 no longer being significant. 

R2 measures how much improvement the predictions of an equation make compared to the use of 

the sample mean. The R2

 statistics indicate that using the predictions from the fractional logit 

equations would eliminate 25.8 percent of the error resulting from using the mean estimate for 

PCTNEEDSHLD and 33.9 percent of the error from using the mean estimate for PCTRENTINS. 

In other words, the mean estimate, across the 118 metropolitan areas, of the percentage of 

households with one or more types of need (PCTNEEDHSHLD) is 32 percent (0.324). R2 

compares two alternatives: (1) the author could use the mean value of 32 percent for every 

17
 
 

 

metropolitan area, or (2) the author could use the value derived from the equation for 

PCTNEEDHSHLD. The R2

 for PCTNEEDHSHLD (0.258) means that the squared error from 

option (2) is 25.8 percent less than the squared error from option (1). The equation for 

PCTNEEDHSHLD furnishes a somewhat better estimate than just choosing the mean. These 

reductions in errors apply only to estimates for the 118 areas over which the equations were 

estimated. 

While the equations for households in units built before 1940 who are in need 

(PCTOLDHSNEED) and for households in mobile homes who are in need (PCTMHNEED) are 

not statistically significant, the estimates from these equations would eliminate 68.5 percent and 

53.3 percent, respectively, of the error resulting from using the mean estimates of these variables. 

The R2

s for five of the nine fractional logit equations are better than the R2s from the OLS 

regressions even though the OLS technique maximizes the R2, whereas the maximum likelihood 

techniques used in logit does not attempt to maximize R2

. 

Table 6 contains the full regression models for the two statistically significant equations. 

(Appendix C contains the full regression models for the other seven AHS condition variables. ) 

The author has shaded cells where the coefficient is statistically significant at the 10-percent 

level. There are only a few variables that are statistically significant even at the liberal 10-

percent level. This is certainly the result of statistically significant relationships among the 

covariates. Appendix B displays a number of high one-on-one correlations, and the possibility 

exists that there are many high multiple correlations as well. 

The lack of statistically significant parameter estimates is not a concern because, as noted at the 

beginning of Section IV, this is not an econometric analysis in which we are trying to uncover 

causal relationships among the variables. Our goal is more modest. We are looking for a set of 

covariates that as a group help predict the AHS condition measures. The Chi-squared and R2 

analyses in Table 5 are the essential tests for this objective. 

The ACSPCTNEED variable was marginally significant in the equation for PCTNEEDHSHLD. 

PCTBLACK, UNITS2TO4, and the intercept were significant in this equation. LNPOP, 

OLDMETRO, VACRATE, and UNITS2TO4 were significant in the equation for 

PCTRENTINS. The PCTRENTINS equation did not have an equivalent ACS variable. 

Table 7 contains predicted values for PCTNEEDHSHLD and PCTRENTINS for 27 metropolitan 

areas—11 areas from the sample used to estimate the equations and 16 areas not in the sample.20 

The predictions, as required by the logit specification, all fall in the 0 to 100 percent range. The 

predictions vary significantly from the mean value from the sample. For PCTNEEDHSHLD, the 

predictions range from 71.5 percent to 153.4 percent of the mean; for PCTRENTINS, the 

predictions range from 1.9 percent to 201.4 percent of the mean. In the sample, there was much 

greater variability in PCTNEEDHSHLD than in PCTRENTINS; the coefficients of variation 

were 0.28 and 0.64, respectively. Reliance on the equation rather than the mean would produce 

significantly different expectations for many of these metropolitan areas. 

20 The program used to estimate the fractional logit regressions (STATA©) does not provide confidence intervals for 

predictions for fractional logit. 

18
 
Table 6: Regression Results 

PCTNEEDHSHLD PCTRENT

Coefficient Standard 

Error 

T-test Probability > 

|t| 

Coefficient Standard 

Error 

T

ACSPCTNEED 3.0128 1.6971 1.78 0.076 NORTHEAST 0.0639 0.1775 0.36 0.719 -0.2758 0.4042 MIDWEST -0.1148 0.1378 -0.83 0.405 -0.1560 0.2757 WEST -0.1764 0.1127 -1.57 0.117 0.0868 0.2610 LNPOP 0.0562 0.0348 1.61 0.107 0.1584 0.0817 PCTBLACK -0.8717 0.4151 -2.1 0.036 -0.6482 0.9652 PCTHISP -0.4448 0.4112 -1.08 0.279 -0.8293 0.7454 OLDMETRO -0.7677 1.0343 -0.74 0.458 3.5568 1.8691 FASTMETRO 0.1031 0.6313 0.16 0.87 1.3440 1.4251 RELINC 0.2743 0.5741 0.48 0.633 0.8901 1.1945 EDUC -0.6056 0.6755 -0.9 0.37 -3.3987 2.1668 VACRATE 0.8298 1.7600 0.47 0.637 -9.1562 4.9741 HORATE 0.5513 0.9017 0.61 0.541 -0.9178 2.3051 UNITS2TO4 2.1679 1.1043 1.96 0.05 -8.4372 2.6428 RELRENT -0.2974 0.4094 -0.73 0.468 -0.7329 0.9511 UNITS50 0.3274 3.0113 0.11 0.913 -7.8873 6.9356 Intercept -2.9493 1.2721 -2.32 0.02 -0.3938 2.0909 

19
 
 

 

Table 7: Predicted Values of PCTNEEDHSHLD and PCTRENTINS 

Metropolitan Area PCTNEEDHSHLD PCTRENTINS 

In sample Prediction 

Ratio to 

mean Prediction 

Ratio to 

mean 

Atlantic City, NJ 0.375 115.6% 0.098 40.5% 

Beaumont-Port Arthur, TX 0.343 105.8% 0.253 104.0% 

Charleston-North Charleston, SC 0.308 95.2% 0.170 69.8% 

Corpus Christi, TX 0.339 104.7% 0.111 45.7% 

Los Angeles-Long Beach-Santa Ana, CA 0.286 88.2% 0.205 84.2% 

Memphis, TN-MS-AR 0.304 93.7% 0.225 92.5% 

Miami-Fort Lauderdale-Pompano Beach, 

FL 0.384 118.4% 0.082 33.7% 

New Orleans-Metairie-Kenner, LA 0.350 108.2% 0.097 39.7% 

Oklahoma City, OK 0.351 108.3% 0.284 116.7% 

San Francisco-Oakland-Fremont, CA 0.259 80.0% 0.226 92.8% 

Washington-Arlington-Alexandria, DC-VAMD-WV 0.258 79.5% 0.318 131.0% 

Not in sample 

Anchorage, AK 0.282 87.1% 0.104 43.0% 

Cedar Rapids, IA 0.273 84.3% 0.489 201.4% 

Deltona-Daytona Beach-Ormond Beach, 

FL 0.400 123.3% 0.142 58.3% 

Fairbanks, AK 0.232 71.5% 0.114 46.9% 

Fargo, ND-MN 0.249 76.8% 0.341 140.2% 

Gulfport-Biloxi, MS 0.358 110.5% 0.137 56.4% 

Iowa City, IA 0.250 77.3% 0.263 108.1% 

Key West, FL Micro Area 0.380 117.4% 0.005 1.9% 

Naples-Marco Island, FL 0.497 153.4% 0.015 6.3% 

Portland-Vancouver-Beaverton, OR-WA 0.272 83.9% 0.453 186.3% 

Port St. Lucie, FL 0.412 127.2% 0.091 37.4% 

Savannah, GA 0.299 92.4% 0.189 78.0% 

Sioux Falls, SD 0.263 81.0% 0.392 161.1% 

Springfield, MO 0.329 101.5% 0.384 158.2% 

Virginia Beach-Norfolk-Newport News, VANC 0.290 89.5% 0.298 122.6% 

Wilmington, NC 0.375 115.7% 0.095 39.1% 

Sample Mean (unweighted) 0.324 0.243 

Minimum 0.232 71.5% 0.005 1.9% 

Maximum 0.497 153.4% 0.489 201.4% 

20
 
VI. Conclusions 

As proposed, this research was exploratory. The results are only mildly encouraging. Of the 

nine equations estimated, only two were statistically meaningful using the Chi-squared test. 

However, the R2

s for these two equations indicate that using the predicted values may be a 

worthwhile improvement over assuming that all metropolitan areas have the same values, that is, 

using the sample mean. Out-of-sample predictions using these two equations suggest that 

conditions may vary substantially across metropolitan areas. 

Equations with better statistical properties might result from using household-level data rather 

than metropolitan-level data. This would involve using microdata from the AHS to estimate the 

equations and microdata from the ACS public use files to use the equations for predictive 

purposes. Microdata analysis would require substantially more effort and would be technically 

more difficult. For example, using individual observations within metropolitan areas would 

have called for random effects modeling. Nevertheless, if the AHS is a unique source of 

information important in preparing for or responding to disasters, the effort and difficulty in 

small area estimation might be well worthwhile. 

“If” is the key question. This research encountered an unexpected difficulty in identifying 

information unique to the AHS that would be obviously useful. The next major disaster may 

very well indicate what AHS information is crucial. Unfortunately, if such an event were to 

occur, there may not be time to carry out the desired microdata analysis. If so, the techniques 

explored in this paper might be a valuable second-best approach. 

21
 
22
 
 

Appendix A: ACS and AHS Metropolitan Areas 

ACS METRO AREA 

(combined metropolitan areas in bold) 

AHS occupied unit cases

Codes (SMSA) for corresponding 

AHS metropolitan areas 

1 Akron, OH Metro Area 41 80 

2 Albany-Schenectady-Troy, NY Metro Area 59 160 

3 Albuquerque, NM Metro Area 64 200 

4 Allentown-Bethlehem-Easton, PA-NJ Metro Area 57 240 

5 Appleton, WI Metro Area 24 460 

6 Atlanta-Sandy Springs-Marietta, GA Metro Area 268 520 

7 Atlantic City, NJ Metro Area 9 560 

8 Augusta-Richmond County, GA-SC Metro Area 28 600 

9 Austin-Round Rock, TX Metro Area 90 640 

10 Bakersfield, CA Metro Area 47 680 

11 Baltimore-Towson, MD Metro Area 225 720 

12 Baton Rouge, LA Metro Area 46 760 

13 Beaumont-Port Arthur, TX Metro Area 15 840 

14 Birmingham-Hoover, AL Metro Area 83 1100 

15 Boston-Cambridge-Quincy, MA-NH Metro Area 362 1120, 4160, 7090 

16 Boulder, CO Metro Area 28 1125 

17 Bridgeport-Stamford-Norwalk, CT Metro Area 69 1160, 8040 

18 Canton-Massillon, OH Metro Area 28 1320 

19 Cape Coral-Fort Myers, FL Metro Area 11 2700 

20 Charleston-North Charleston, SC Metro Area 39 1440 

21 Chattanooga, TN-GA Metro Area 42 1560 

22 Chicago-Naperville-Joliet, IL-IN-WI Metro Area 1046 1600, 2960,620,3965,9991 

23 Cincinnati-Middletown, OH-KY-IN Metro Area 120 1640 

24 Cleveland-Elyria-Mentor, OH Metro Area 204 1680 

25 Colorado Springs, CO Metro Area 44 1720 

26 Columbia, SC Metro Area 51 1760 

27 Columbus, OH Metro Area 152 1840 

28 Corpus Christi, TX Metro Area 38 1880 

29 Dallas-Fort Worth-Arlington, TX Metro Area 467 1920, 2800 

30 Davenport-Moline-Rock Island, IA-IL Metro Area 35 1960 

31 Denver-Aurora, CO Metro Area 91 2080 

32 Des Moines-West Des Moines, IA Metro Area 28 2120 

33 Detroit-Warren-Livonia, MI Metro Area 585 2160 

34 Duluth, MN-WI Metro Area 21 2240 

35 El Paso, TX Metro Area 79 2320 

36 Erie, PA Metro Area 13 2360 

37 Eugene-Springfield, OR Metro Area 26 2400 

A-1 
ACS METRO AREA 

(combined metropolitan areas in bold) 

AHS occupied unit cases

Codes (SMSA) for corresponding 

AHS metropolitan areas 

38 Evansville, IN-KY Metro Area 13 2440 

39 Flint, MI Metro Area 36 2640 

40 Fort Wayne, IN Metro Area 26 2760 

41 Fresno, CA Metro Area 60 2840 

42 Grand Rapids-Wyoming, MI Metro Area 68 3000 

43 Greensboro-High Point, NC Metro Area 69 3120 

44 Greenville-Spartanburg-Anderson, SC CSA 46 3160 

45 

Hartford-West Hartford-East Hartford, CT Metro 

Area 

18 3280 

46 Honolulu, HI Metro Area 75 3320 

47 Houston-Sugar Land-Baytown, TX Metro Area 344 3360 

48 Indianapolis-Carmel, IN Metro Area 120 3480 

49 Jackson, MS Metro Area 22 3560 

50 Jacksonville, FL Metro Area 102 3600 

51 

Johnson City- Kingsport-Bristol (Tri-Cities) TNVA Combined Metro Area 

20 3660 

52 Kansas City, MO-KS Metro Area 174 3760 

53 Knoxville, TN Metro Area 49 3840 

54 Lakeland, FL Metro Area 14 3980 

55 Lancaster, PA Metro Area 23 4000 

56 Lansing-East Lansing, MI Metro Area 21 4040 

57 Las Vegas-Paradise, NV Metro Area 122 4120 

58 Lexington-Fayette, KY Metro Area 49 4280 

59 

Little Rock-North Little Rock-Conway, AR Metro 

Area 

46 4400 

60 

Los Angeles-Long Beach-Santa Ana, CA Metro 

Area 

1271 4480, 360 

61 Madison, WI Metro Area 31 4720 

62 McAllen-Edinburg-Mission, TX Metro Area 43 4880 

63 Memphis, TN-MS-AR Metro Area 88 4920 

64 

Miami-Fort Lauderdale-Pompano Beach, FL Metro 

Area 

534 5000, 2680, 8960 

65 Milwaukee-Waukesha-West Allis, WI Metro Area 164 5080 

66 

Minneapolis-St. Paul-Bloomington, MN-WI Metro 

Area 

277 5120 

67 Mobile, AL Metro Area 30 5160 

68 Modesto, CA Metro Area 29 5170 

69 Montgomery, AL Metro Area 24 5240 

70 

Nashville-Davidson--Murfreesboro--Franklin, TN 

Metro Area 

86 5360 

A-2 
 

 

ACS METRO AREA 

(combined metropolitan areas in bold) 

AHS occupied unit cases

Codes (SMSA) for corresponding 

AHS metropolitan areas 

71 New Haven-Milford, CT Metro Area 54 5480 

72 New Orleans-Metairie-Kenner, LA Metro Area 95 5560 

73 

New York-Northern New Jersey-Long Island, NYNJ-PA Metro Area 

2483 5600, 5380,875,3640,5015,5190, 

5640,9992,9993 

74 Oklahoma City, OK Metro Area 122 5880 

75 Omaha-Council Bluffs, NE-IA Metro Area 56 5920 

76 Orlando-Deltona-Daytona Beach, FL CSA 151 5960, 2020 

77 Oxnard-Thousand Oaks-Ventura, CA Metro Area 68 6000 

78 Palm Bay-Melbourne-Titusville, FL Metro Area 26 4900 

79 Pensacola-Ferry Pass-Brent, FL Metro Area 17 6080 

80 Peoria, IL Metro Area 32 6120 

81 

Philadelphia-Camden-Wilmington, PA-NJ-DE-MD 

Metro Area 

631 6160 

82 Phoenix-Mesa-Scottsdale, AZ Metro Area 331 6200 

83 Pittsburgh, PA Metro Area 224 6280, 845 

84 

Providence-New Bedford-Fall River, RI-MA Metro 

Area 

73 6480 

85 Raleigh-Durham-Cary, NC CSA 85 6640 

86 Riverside-San Bernardino-Ontario, CA Metro Area 190 6780 

87 Rochester, NY Metro Area 85 6840 

88 Rockford, IL Metro Area 15 6880 

89 

Sacramento--Arden-Arcade--Roseville, CA Metro 

Area 

156 6920 

90 Salinas, CA Metro Area 18 7120 

91 Salt Lake City, UT Metro Area 130 7160 

92 San Antonio, TX Metro Area 155 7240 

93 San Diego-Carlsbad-San Marcos, CA Metro Area 309 7320 

94 San Francisco-Oakland-Fremont, CA Metro Area 481 7360, 5775 

95 San Jose-Sunnyvale-Santa Clara, CA Metro Area 171 7400 

96 

Santa Barbara-Santa Maria-Goleta, CA Metro 

Area 

22 7480 

97 Santa Rosa-Petaluma, CA Metro Area 31 7500 

98 Sarasota-Bradenton-Venice, FL Metro Area 25 7510 

99 Scranton--Wilkes-Barre, PA Metro Area 52 7560 

100 Seattle-Tacoma-Bellevue, WA Metro Area 294 7600, 8200 

101 Shreveport-Bossier City, LA Metro Area 28 7680 

102 Spokane, WA Metro Area 29 7840 

103 Springfield, MA Metro Area 70 8000 

104 St. Louis, MO-IL Metro Area 226 7040, 2285, 275 

A-3 
ACS METRO AREA 

(combined metropolitan areas in bold) 

AHS occupied unit cases

Codes (SMSA) for corresponding 

AHS metropolitan areas 

105 Stockton, CA Metro Area 43 8120 

106 Syracuse, NY Metro Area 40 8160 

107 Tampa-St. Petersburg-Clearwater, FL Metro Area 225 8280 

108 Toledo, OH Metro Area 69 8400 

109 Trenton-Ewing, NJ Metro Area 18 8480 

110 Tucson, AZ Metro Area 77 8520 

111 Tulsa, OK Metro Area 59 8560 

112 Utica-Rome, NY Metro Area 12 8680 

113 Vallejo-Fairfield, CA Metro Area 29 8720 

114 

Washington-Arlington-Alexandria, DC-VA-MD-WV 

Metro Area 

406 8840 

115 Waterbury, CT Metropolitan NECTA 14 8880 

116 Wichita, KS Metro Area 49 9040 

117 Worcester, MA Metro Area 31 9240 

118 

Youngstown-Warren-Boardman, OH-PA Metro 

Area 

43 9320 

A-4 
Appendix B: Correlation Matrix for Independent Variables 

B-1 

ACSPCTPROB 

ACSPCTNEED 

ACSPCTPROBNEED 

ACSOLDHSNEED

ACSPCTMHNEED

NORTHEAST 

MIDWEST

WEST

LNPOP

ACSPCTPROB 1.0000 ACSPCTNEED 0.0385 1.0000 ACSPCTPROBNEED 0.9804 0.2148 1.0000 ACSOLDHSNEED -0.1826 -0.0728 -0.1980 1.0000 

ACSPCTMHNEED 0.2104 0.5509 0.3137 -0.4643 1.0000 

NORTHEAST -0.0790 -0.1078 -0.0950 0.7105 -0.3030 1.0000 

MIDWEST -0.2947 -0.0197 -0.2935 0.3327 -0.2856 -0.2595 1.0000 

WEST 0.1612 -0.4400 0.0743 -0.3523 -0.1413 -0.2535 -0.3038 1.0000 

LNPOP -0.1601 -0.1814 -0.1929 -0.0875 -0.2560 -0.0306 -0.0775 0.0761 1.0000 PCTBLACK -0.0077 0.3613 0.0578 -0.2080 0.2880 -0.1404 -0.0965 -0.3995 0.0904 PCTHISP 0.3273 -0.1549 0.3156 -0.3932 0.0234 -0.1549 -0.3198 0.4417 0.1782 

OLDMETRO -0.1769 -0.1363 -0.2029 0.9964 -0.4877 0.7184 0.3278 -0.3306 -0.0712 

FASTMETRO 0.0179 0.2346 0.0698 -0.7618 0.4914 -0.5525 -0.2029 0.1280 0.0775 

RELINC -0.2025 -0.5451 -0.3092 0.0752 -0.5767 0.1860 -0.0877 0.3439 0.3915 

EDUC -0.1011 -0.3114 -0.1846 0.1339 -0.4377 0.1285 -0.0084 0.1448 0.3364 

VACRATE 0.0814 0.4432 0.1613 -0.2938 0.5374 -0.1545 -0.1103 -0.2718 -0.0906 HORATE -0.2542 0.2494 -0.1993 0.1456 0.2363 0.0266 0.3885 -0.5605 -0.2545 UNITS2TO4 0.0060 -0.1630 -0.0205 0.7055 -0.3768 0.7401 -0.0666 -0.1387 -0.0010 

UNITS50 0.0655 -0.2941 0.0027 0.0272 -0.4296 0.1304 -0.1063 0.1815 0.5038 

RELRENT -0.0077 -0.4463 -0.0967 -0.2264 -0.3156 0.0544 -0.3737 0.5177 0.3771 

RELVALUE 0.0311 -0.5016 -0.0680 -0.1236 -0.3557 0.0228 -0.2956 0.6625 0.2914 

OVERCROWD 0.3269 -0.1470 0.3187 -0.3854 0.0329 -0.2072 -0.2968 0.5396 0.1637 
OLDMETRO

FASTMETRO 

RELINC 

EDUC 

VACRATE 

HORATE

UNITS2TO4

UNITS50

RELRENT

ACSPCTPROB ACSPCTNEED ACSPCTPROBNEED ACSOLDHSNEED ACSPCTMHNEED NORTHEAST MIDWEST WEST LNPOP PCTBLACK PCTHISP OLDMETRO 1.0000 FASTMETRO -0.7713 1.0000 RELINC 0.1092 -0.1714 1.0000 

EDUC 0.1516 -0.0939 0.7353 1.0000 

VACRATE -0.3142 0.3637 -0.3892 -0.3586 1.0000 

HORATE 0.1307 0.0715 -0.2564 -0.1435 0.3359 1.0000 

UNITS2TO4 0.7237 -0.5815 0.1755 0.1123 -0.2018 -0.1987 1.0000 

UNITS50 0.0513 -0.2270 0.4930 0.4233 -0.1455 -0.4079 0.1914 1.0000 

RELRENT -0.1932 -0.0270 0.8131 0.4758 -0.0975 -0.4852 0.0918 0.5439 1.0000 

RELVALUE -0.0894 -0.1790 0.7680 0.4330 -0.3003 -0.6102 0.1289 0.5100 0.9173 

OVERCROWD -0.3714 0.1293 0.1267 -0.1993 -0.0777 -0.6225 -0.0527 0.2601 0.4418 

B-2 
Appendix C: Fractional Logit Estimates for the Other Dependent Variables 

PCTSEVPROB PCTSEVMOD

Coefficient Standard 

Error 

T-test Probability > 

|t| 

Coefficient Standard 

Error 

T

ACSPCTNEED ACSPCTPROB -5.2664 35.6593 -0.15 0.883 10.4478 26.3435 

NORTHEAST 0.4281 0.5417 0.79 0.429 -0.4338 0.3849 MIDWEST 0.5677 0.4539 1.25 0.211 -0.3751 0.2980 WEST 0.7082 0.3522 2.01 0.044 -0.2801 0.2614 LNPOP -0.0177 0.1241 -0.14 0.887 0.0334 0.0926 PCTBLACK 5.1903 1.4662 3.54 0 2.2785 0.7310 PCTHISP 2.5612 1.0983 2.33 0.02 0.4296 0.9169 OLDMETRO 2.8387 3.1496 0.9 0.367 0.2308 1.9978 FASTMETRO 1.4299 1.6027 0.89 0.372 -1.3200 1.4928 RELINC -2.2034 1.8627 -1.18 0.237 0.3813 1.5509 EDUC 3.5406 3.0584 1.16 0.247 -1.3407 2.7121 VACRATE -2.9247 5.8339 -0.5 0.616 -3.2564 3.6568 HORATE 0.6308 3.0541 0.21 0.836 0.5736 2.2759 UNITS2TO4 0.0168 4.1944 0 0.997 1.4681 2.7292 RELRENT 0.6795 1.4864 0.46 0.648 -1.0477 1.0508 UNITS50 1.2433 7.9552 0.16 0.876 10.9556 6.2848 Intercept -5.9021 2.9175 -2.02 0.043 -2.6052 2.3264 

C-1
 
PCTSEVPROBNEED PCTSEVMODPR

Coefficient Standard 

Error 

T-test Probability > 

|t| 

Coefficient Standard 

Error 

T

ACSPCTPROBNEED -65.8803 114.3013 -0.58 0.564 -7.9438 64.1697 NORTHEAST 0.9001 0.9318 0.97 0.334 -0.7667 0.5078 MIDWEST 1.0754 0.8667 1.24 0.215 -0.8555 0.4269 WEST -0.6787 0.8743 -0.78 0.438 -0.4610 0.3973 LNPOP -0.0265 0.1984 -0.13 0.894 0.0203 0.1214 PCTBLACK 4.0738 2.1168 1.92 0.054 1.7618 1.1591 PCTHISP 0.0839 1.9244 0.04 0.965 0.7265 1.2090 OLDMETRO 7.5726 4.0854 1.85 0.064 3.9475 2.8851 FASTMETRO 7.0776 2.3055 3.07 0.002 -1.0361 1.7367 RELINC -7.2507 2.9273 -2.48 0.013 -0.1288 2.3289 EDUC 7.6935 5.2743 1.46 0.145 -0.6612 3.3636 VACRATE -8.3265 7.4277 -1.12 0.262 -0.3342 4.6626 HORATE 6.1371 4.3357 1.42 0.157 0.8857 2.5708 UNITS2TO4 -0.2073 6.4485 -0.03 0.974 1.0894 3.9898 RELRENT 5.8123 2.2975 2.53 0.011 -0.9302 1.6668 UNITS50 22.7393 13.6065 1.67 0.095 14.0666 7.0925 Intercept -13.6801 4.4343 -3.09 0.002 -4.1594 2.6056 

C-2
 
PCTOLDHSNEED PCTMHNE

Coefficient Standard 

Error 

T-test Probability > 

|t| 

Coefficient Standard 

Error 

T

ACSPCTOLDHSNEED 22.4424 20.8664 1.08 0.282 ACSPCTMHNEED 41.8080 6.0764 NORTHEAST 1.0882 0.4738 2.3 0.022 0.6048 1.0390 MIDWEST 0.7693 0.3374 2.28 0.023 1.5797 0.8319 WEST 0.4765 0.3704 1.29 0.198 0.6787 0.5013 LNPOP -0.1104 0.0940 -1.17 0.241 0.7471 0.1879 PCTBLACK 0.7858 1.3037 0.6 0.547 -0.3954 2.2538 PCTHISP -0.3845 1.1304 -0.34 0.734 -2.0096 2.2808 OLDMETRO -7.8653 9.7669 -0.81 0.421 -17.1197 8.7563 FASTMETRO -3.9265 1.7599 -2.23 0.026 -5.9456 1.9658 RELINC 2.7880 1.5706 1.78 0.076 3.5614 2.3570 EDUC -0.0555 2.2861 -0.02 0.981 -14.0630 3.8358 VACRATE 6.5825 4.4638 1.47 0.14 -9.9068 10.4712 HORATE -2.0760 2.9284 -0.71 0.478 -5.6974 6.4108 UNITS2TO4 -0.5221 2.3317 -0.22 0.823 5.4033 11.6386 RELRENT -2.9447 1.2526 -2.35 0.019 0.8997 1.9428 UNITS50 -0.9985 10.3088 -0.1 0.923 -27.3179 16.6719 Intercept -0.6942 2.6467 -0.26 0.793 -8.1955 5.0650 

C-3
 
PCTOWNINS 

Coefficient Standard 

Error 

T-test Probability > 

|t| 

NORTHEAST 0.1614 0.6802 0.24 0.812 

MIDWEST 0.9892 0.5594 1.77 0.077 WEST 0.7828 0.3769 2.08 0.038 LNPOP -0.1438 0.1111 -1.29 0.195 PCTBLACK 0.6589 1.2659 0.52 0.603 PCTHISP -0.4942 0.8924 -0.55 0.58 OLDMETRO 4.5449 4.0289 1.13 0.259 FASTMETRO 5.4160 2.8111 1.93 0.054 RELINC -1.1439 2.0336 -0.56 0.574 EDUC -0.4740 4.0203 -0.12 0.906 VACRATE -11.2206 4.6812 -2.4 0.017 HORATE 1.2656 3.4849 0.36 0.716 UNITS2TO4 -1.3065 4.3789 -0.3 0.765 RELRENT 1.6425 1.5697 1.05 0.295 UNITS50 -7.0673 6.7807 -1.04 0.297 Intercept 3.0960 2.8048 1.1 0.27 

C-4