The Quality of

America’s Assisted

Housing Stock:

Analysis of the 2011

and 2013 American

Housing Surveys

Multidisciplinary

Research Team

U.S. Department of Housing and Urban Development  |  Office of Policy Development and Research

The Quality of America’s Assisted Housing Stock:

Analysis of the 2011 and 2013 American Housing Surveys

Multidisciplinary Research Team

U.S. Department of Housing and Urban Development

Office of Policy Development and Research

March 2017

Submitted by:

Economic Systems Inc.

Falls Church, Virginia

Prepared by:

Sandra Newman, Ph.D.

C. Scott Holupka, Ph.D.

Johns Hopkins University

About MDRT

PD&R developed the Multidisciplinary Research Team (MDRT) vehicle to manage a team of

qualified researchers. Researchers are selected for their expertise to produce an array of high

quality, short-turnaround research. MDRT researchers use a variety of HUD and external data

sources to answer research questions relating to HUD’s priority policies and strategic goals.

Disclaimer

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.

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Contents

Executive Summary ........................................................................................................................ v

Introduction ..................................................................................................................................... 1

Literature Review............................................................................................................................ 3

Housing Quality Measurement and Data Collection Methods .................................................3

AHS Measurement of Housing Quality ...................................................................................4

Quality of Assisted Housing .....................................................................................................6

Research Approach ......................................................................................................................... 7

Data...........................................................................................................................................7

Samples.....................................................................................................................................8

Methods ....................................................................................................................................8

Results ........................................................................................................................................... 10

Housing Quality Indices .........................................................................................................12

Index Validity .........................................................................................................................21

Assisted Housing Quality .......................................................................................................25

Multivariate Analysis .............................................................................................................33

Discussion ..................................................................................................................................... 39

References ..................................................................................................................................... 43

Appendix A: Tables .................................................................................................................... A-1

Appendix B: Healthy Homes Module......................................................................................... B-1

Appendix C: Characteristics of Assisted Housing by Program Type ......................................... C-1

List of Tables

Table 1. 2011 AHS Housing Quality Measure, Mean Percent of All Housing ............................ 11

Table 2. Control Measures Included in Market Value (Hedonic) Models ................................... 12

Table 3. Market Value (Hedonic) Model Results, Housing Quality Measures ............................ 14

Table 4. Consumer Rating Model Results, Housing Quality Measures ....................................... 16

Table 5. Normative Standards Weighted and Unweighted Indices .............................................. 18

Table 6. Normative Standards Factor Analysis: Model Fit Test Results to Select Number of

Factors ........................................................................................................................................... 19

Table 7. Normative Standards Index: Factor Analysis Weights ................................................... 20

Table 8. Convergent Validity: Correlations Among Indices ........................................................ 22

Table 9. Convergent Validity: Correlations With AHS Measures Related to Housing Quality ... 22

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Table 10. Convergent Validity: Variation across the Distribution of Each Index ........................ 24

Table 11. Predictive Validity of Housing Quality Indices for Rents and Occupant Ratings

Using Multivariate Regression Analysis ...................................................................................... 25

Table 12. Prevalence Rates of 2011 Housing Problems by Assistance Status ............................. 27

Table 13a. Housing Quality Ratings of 2011 Assisted and Unassisted Housing Units,

Comparable Rents ......................................................................................................................... 28

Table 13b. Housing Quality Ratings of 2011 Assisted Housing and All Unassisted Housing Units . 28

Table 14. Housing Quality Ratings of 2011 Assisted Housing Units by Program Type .............. 29

Table 15. Housing Quality Ratings of 2011 Assisted Housing Units by Household Type .......... 29

Table 16. Housing Quality Ratings of 2011 Assisted Housing Households by Structure Type .. 30

Table 17. Housing Quality Ratings of 2011 Assisted Housing Units by Metropolitan Location  30

Table 18. Housing Quality Ratings of 2011 Assisted Housing Units by Census Region ............ 31

Table 19. Housing Quality Ratings of 2011 Assisted Housing Households by Household Size . 31

Table 20. Housing Quality Ratings of 2011 Assisted Housing Households by Race and

Ethnicity of Head .......................................................................................................................... 32

Table 21. Housing Quality Ratings of 2011 Assisted Housing Households by Household

Income Quartiles ........................................................................................................................... 32

Table 22. Housing Quality Ratings of 2011 Assisted Housing Households by Disabled

Household Member ....................................................................................................................... 33

Table 23. Multivariate Models Predicting Housing Quality ......................................................... 34

Table 24. Subgroup Regression Results on Consumer Rating Index ........................................... 35

Table 25. Persistence of Housing Quality Problems in Assisted Housing Units, 2011 and 2013 ... 38

Table 26. Comparison of Repair Reports on Assisted Housing and Comparable Unassisted

Housing ......................................................................................................................................... 39

Table A1. Selection of Analysis Sample: Units Excluded by Type or Category ....................... A-1

Table A2. Polychoric Correlation Matrix, Housing Quality Measures ...................................... A-2

Table A3. Distribution of Housing Quality Indices .................................................................... A-4

Table B1. Relationship between Indices and Healthy Homes Measures .................................... B-2

Table C1. Percent Distribution of Characteristics of Assisted Housing for Each Program Type . C-1

List of Figures

Figure 1. Distribution of Indices ................................................................................................... 21

Figure 2. Consumer Rating Index by Relative Cost ..................................................................... 37

iv

Executive Summary

The substantial literature on housing quality demonstrates both the importance and the

challenges of conceptualizing and measuring housing quality. The growing interest in “how

housing matters,” primarily in the low-rent unassisted housing stock, and the ongoing concerns

about housing quality standards in the assisted stock, make this an opportune time to revisit

housing quality.

In this paper, the research team reviews the relevant literature, develops alternative housing

quality indices, tests their validity, and applies them to both the assisted and comparable

unassisted housing stock. We focus on indicators of the physical integrity of housing systems

and exclude measures that are more likely to reflect residents’ housekeeping or behaviors.

Because no consensus exists about the features of the housing bundle that should be included in

the definition of a dwelling’s quality and how each should be weighted in determining overall

quality, we rely on three external criteria first suggested by research on the Experimental

Housing Allowance Program (Merrill, 1980): market value, consumer rating, and normative

standards. The market value criterion is the standard of choice for housing economists. The

consumer rating criterion identifies the dwelling features most associated with a resident’s

assessment of the dwelling as a good place to live regardless of the market price of these

features. This criterion is consistent with the renewed interest by economists in happiness and

subjective well-being. The normative standards criterion reflects community concerns and policy

decisions such as building codes. Our main data are the 2011 and 2013 national American

Housing Surveys (AHS). Both surveys provide augmented national samples and assisted housing

samples, with assisted housing identified by address matches to the U.S. Department of Housing

and Urban Development’s (HUD’s) administrative data, not respondent self-report.

Despite its intuitive appeal, the market value criterion for housing quality performs poorly and

we drop it from further analysis. We construct one consumer rating index using the results from

the multiple variable analysis as the weights. We also construct three indices using the normative standards criterion: a weighted index based on a previous analysis for HUD’s Office of Policy

Development and Research by Eggers and Moumen (2013b); an unweighted index; and an index

with weights derived from an analysis that examines which components of the index are most

closely associated with one another.

Consistent with much past AHS housing quality research, the prevalence rate of almost all

housing quality problems is very low, with most dwelling units having no problems. We also

find that the quality of assisted housing is comparable to the quality of unassisted housing.

Further, the incidence of housing problems persisting over 2 years, 2011 and 2013, is very low,

and repairs are made promptly.

Some heterogeneity in housing quality exists, however. Geographically, assisted housing quality

in central cities and in the Northeast region is considerably lower than in their counterpart

locations (that is, suburban or rural areas and the South, Midwest, and West regions).

Demographically, three household subgroups emerge as particularly likely to live in assisted

v

housing with lower-than-average housing quality: nonelderly disabled persons, non-White

persons, and large households. The analysis that simultaneously considers the strongest

predictors of assisted housing quality for each of these three groups generally corroborates these risk factors and adds further insights. For example, disabled persons enjoy better housing quality using a voucher compared with those living in multifamily housing. For large households, living

in the South and living in public housing are associated with considerably worse housing quality.

The analysis also provides hard evidence supporting the current 40th percentile of rents (that is, the point on the rent distribution where 40 percent of rents fall below this amount and 60 percent of rents are higher than this amount) definition of the Fair Market Rent (FMR). We find that the

FMR is set at a level that is roughly at the inflection point for maximizing assisted housing

quality as measured by our housing quality indices.

Overall, these positive findings demonstrate that the current inspection and quality control

systems appear to be achieving the goal of providing physically adequate housing to assisted

housing residents. They also lend support to two policy shifts—biennial inspections in the

voucher program and biennial and triennial inspections for standard and high performers,

respectively, in the public housing program—and to serious consideration of proposals to

streamline inspections to encourage participation in the voucher program by private owners of

rental properties.

Suggestions for future research include expanding the measures to include additional aspects of

the full housing bundle and comparing these results with housing inspection scores from HUD’s

administrative data—that is, the Public Housing Assessment System and Real Estate Assessment

Center housing inspection ratings for public housing and multifamily housing, respectively.

Additionally, a consideration of measures that are currently missing from the AHS, but should be

included in the future, is beyond the scope of the current effort but worth serious attention.

vi

Introduction

A key role of the U.S. Department of Housing and Urban Development (HUD) is designing,

implementing and monitoring most of the nation’s assisted housing programs. Central to this

responsibility is ensuring that the units receiving HUD assistance are physically adequate. This, in turn, verifies that recipient households live in decent and safe dwellings and reassures the public that tax dollars are not supporting deficient housing, or worse. To accomplish this objective, HUD

imposes a set of housing quality standards (HQS) that assisted units must meet, requires periodic

inspections to confirm that standards are being met, and, when necessary, issues citations of

violations that must be corrected within a specified time frame. 1 Although the broad outline of this assisted housing quality assurance system has remained essentially the same over several decades,

HUD has modified it from time to time in an effort to improve the efficiency of inspections and the effectiveness of achieving the statutory goals of decent and safe assisted housing units.

Several recent circumstances prompt a reexamination of assisted HQS. First, HUD’s  Strategic

Plan 2014–2018 calls for the development of a “uniform asset risk assessment management

model,” which requires systematic evidence on the most meaningful approaches to measuring the

quality of the assisted housing stock (HUD, 2014: 19). Second, the FY13 Senate Appropriation

Committee Report raises concerns about violations of HQS in housing units participating in the

Section 8 voucher program and “directs HUD to take meaningful and timely steps to strengthen

oversight and quality control” of the public housing agency (PHA) inspection process (U.S.

Senate, 2012: 92). An additional concern is that reports by HUD’s Office of the Inspector General

and the U.S. Government Accountability Office (GAO) note poor reliability of assisted housing

inspections using the HQS (GAO, 2000; HUD OIG, 2008). This conclusion is based on a

comparison of the PHA inspector scores with those collected by an independently trained rater.

This paper is designed to contribute to the reexamination of assisted housing  quality. We do so by developing composite measures of housing quality, or housing quality indices, testing their

validity, and then applying these indices to both the assisted and comparable unassisted housing

stock. Assisted housing refers to housing subsidized by the federal government to reduce monthly

rent and that is targeted on income-eligible households. Subsidies take two forms: demand side,

through a rent voucher provided to income-eligible households to use in the private rental market; and supply side, through either public housing developed and managed by local PHAs,

concessionary financing to private entities to develop or rehabilitate housing, or tax credits under the U.S. Department of the Treasury’s Low-Income Housing Tax Credit program. For simplicity in

the analysis, we will disaggregate assisted housing into three main programs: public housing;

privately owned, publicly subsidized housing (referred to by HUD as multifamily); and vouchers.

1 Inspection protocols and processes differ by program. Public housing and multifamily housing—for example, Section 8 new construction; Section 221(d)(3)—must meet property standards, while Section 8 vouchers must meet housing quality standards, or HQS. Inspectors employed by the local public housing agency conduct inspections on public housing and voucher housing, while inspectors contracted by the HUD regional offices inspect multifamily housing.

1

It is important to acknowledge at the outset that the concept of housing quality is not based on

definitive criteria and has no precise quantifiable definition of where “bad” ends and “good”

begins (Newman, 2008). As explained more fully below, because we lack a consensus definition

of housing quality, we construct measures that characterize the dwelling’s physical integrity (for example, holes in the floor) or housing systems (for example, heating system breakdown) and

exclude those that are more likely to reflect the resident’s housekeeping or behavior (for

example, leaving unsafe chemicals within a child’s reach). 2

We use rich data from the 2011 and 2013 American Housing Surveys (AHS) to describe the

quality of the assisted housing stock and to highlight geographic areas, types of households,

housing types, and housing assistance programs most likely to experience quality problems. The

AHS asks respondents about a wide range of conditions in their housing units. This allows us to

develop a composite measure or index of quality, thereby capturing the multiple dimensions of

housing quality. The 2011 and 2013 AHS samples have also been matched to administrative

records on assisted housing receipt, alleviating serious concerns about the validity of self-

reported housing assistance receipt.

We find that the quality of assisted housing is comparable to the quality of unassisted housing,

the incidences of persistent problems are very low, and requested repairs are made promptly.

Some heterogeneity in housing quality exists, however. Geographically, assisted housing quality

in central cities and in the Northeast region is lower than in their counterpart locations (that is, suburban or rural areas and South, Midwest, and West regions). Demographically, three

household subgroups emerge as particularly likely to live in assisted housing with lower than

average housing quality: nonelderly disabled persons, non-White persons, and large households.

Multivariate analysis of the strongest predictors of assisted housing quality for each of these

three groups generally corroborates these risk factors and adds further insights. For example,

disabled persons enjoy better housing quality using a voucher compared with those living in

multifamily housing. For large households, living in the South and living in public housing are

associated with considerably worse housing quality. The analysis also provides hard evidence

supporting HUD’s definition of the Fair Market Rent (FMR) as the 40th percentile of rents. We

find that the FMR is set at a level that is roughly at the inflection point for maximizing assisted housing quality as measured by our housing quality indices.

In the next section, we review the literature on housing quality, emphasizing past research on

assisted housing quality. The Literature Review section is followed by a discussion of our

research approach, including a description of the 2011 and 2013 AHS data, analysis samples,

methods, and alternative measures of housing quality, along with tests of their validity. We then

examine assisted housing quality from several perspectives including a comparison with

unassisted housing quality, an exploration of whether assisted housing quality varies depending

on the characteristics of the housing or the characteristics of the residents. We also explore how 2 Some features, such as mold, fall into a gray area.

2

well assisted housing quality aligns with the FMR, the persistence of assisted housing quality

problems, and the related issue of timeliness of repairs. In the final section, we summarize the

key results and discuss their implications for policy and for future research.

Literature Review

The substantial literature on housing quality spans nine decades and demonstrates both the

importance and the challenges of conceptualizing and measuring housing quality. We review

three relevant strands in past work: housing quality measurement and data collection methods;

the AHS measurement of housing quality; and the quality of assisted housing.

Housing Quality Measurement and Data Col ection Methods

The American Public Health Association provided some of the earliest contributions to the

housing quality literature. Its  Basic Principles of Healthful Housing (APHA, 1938) highlighted the connection between housing conditions and health, while  An Appraisal Method for

Measuring the Quality of Housing (APHA, 1945) recommended that data be collected through a field survey of many individual features of each dwelling unit, with penalty scores for each

feature that falls below an established standard. The sum of all scores represents the quality of

the dwelling. This methodology is roughly similar to that used for physical inspections of

assisted housing under HUD’s Uniform Physical Condition Standards (UPCS). 3

Another important early contribution was the U.S. Census Bureau’s methodological study of

housing quality measurement (Census Bureau, 1967). 4 The historical context of this landmark report is worth reviewing. For decades, the decennial census included interviewer observations

of housing features. In 1940, housing condition was measured by a dwelling’s “state of repair,”

with trained enumerators rating the structure as either needing “major” repairs or not. In 1950,

this approach was replaced by another dichotomous classification of structures as either

“dilapidated” or “not dilapidated.” This dichotomy was refined in 1960 by further classifying

those structures designated as “not dilapidated” as either “sound” or “deteriorating.” Following

the 1960 census, the Census Bureau launched a detailed and thorough evaluation of its approach

to measuring housing conditions that resulted in the 1967 publication. Its unambiguous

conclusion was that housing conditions collected through interviewer observations are unreliable

and, therefore, inaccurate. As a result, subsequent decennial censuses that relied on interviewers to administer the survey dropped the interviewer observations of housing unit condition. The

AHS followed suit in 1997. 5

3 UPCS currently exists for public housing and for multifamily housing. A version for the voucher program, UPCS-V, is under development and will replace the current HQS system (Arcara, 2016).

4 This discussion draws on Newman (2008).

5 AHS began interviewing returning households by phone, when possible, in 1997. In 2011, a phone-first policy was instituted for both new and returning households (Vandenbroucke, 2016).

3

Alongside concerns in the literature about the best way to collect data on housing quality is the

issue of the best way to measure housing quality. Curiously, much more attention has been paid

to developing a summary measure than to identifying the individual housing features that should

comprise the summary measure. The pioneering work of Kain and Quigley (1970) established

the feasibility of using housing-unit-level measures of quality as predictors of house prices and

rents, also known as hedonic models. The coefficients in these models can be viewed as weights

in a hedonic price index. Kain and Quigley’s work led to a burgeoning of hedonic modeling over

the ensuing decades (Coulson and Li, 2013; Kriström, 2008; Merrill, 1980; Thibodeau, 1995).

Three features of Kain and Quigley’s approach are particularly relevant to this current paper.

First, they apply factor analysis to reduce the 39 separate measures of housing quality in their St.

Louis survey data to a manageable number. Second, they find that the 7 survey measures

pertaining to the quality of the individual dwelling unit interior formed a single index or factor. 6

And third, in multivariate hedonic regressions, the dwelling unit quality factor has a statistically significant effect on rent. Consistent with most of the literature in this area, the authors do not take on the question of how best to conceptualize housing quality and, instead, assume that this

concept is captured by their 39 variables pertaining to “the physical or visual quality of the

bundle of residential services” (Kain and Quigley, 1970: 534).

AHS Measurement of Housing Quality

The AHS is the most comprehensive data source on the U.S. housing stock. 7 Policymakers, practitioners, and researchers seeking answers to questions about the conditions, costs, and

various other attributes of the nation’s housing rely on it. It is also relied on as a source of

housing questions for those developing their own surveys. A prominent example is the Moving

to Opportunity for Fair Housing Demonstration (Shroder, 2001). Of particular interest to many

users is the AHS composite measure of housing inadequacy available on the public use database,

a variable labeled ZADEQ. The measure combines multiple items on housing conditions into an

index, setting numerical thresholds for the presence or absence of physical deficiencies in the

dwelling to distinguish among “adequate,” “moderately inadequate,” and “severely inadequate”

units. 8 Both the AHS and data users refer to this composite as the AHS “housing quality”

measure. 9 Numerous published articles include the AHS measure in their analyses (Carter, 2011; Friedman and Rosenbaum, 2004; Khadduri, 2007; Ross et al., 2012). It plays a prominent role in

HUD’s  Worst Case Housing Needs reports (for example, HUD, 2011b) and is also included in

6 Their survey included many other items focusing on the condition of adjacent structures, parcels and block faces, along with the structure’s exterior condition.

7 The initial part of this discussion draws from Newman and Garboden (2013).

8 The number of items varies from one AHS to another. Eggers and Moumen (2013a) indicate it is 14 items, Newman and Garboden (2013) indicate it is 15 items, and we count 20 items in the 2011 AHS.

9 The AHS codebook notes: “This three-scale index, in which one is adequate and three is severely inadequate, is a summary measure of housing quality.” The composite measure is also listed in the AHS documentation under the category “Unit Quality” (HUD, 2011a).

4

the frequently cited Joint Center for Housing Studies’  The State of the Nation’s Housing reports (for example, JCHS, 2010) and U.S. Millennial Housing Commission Report (2002). However,

not until the last few years was the AHS quality measure subjected to careful examination.

Eggers and Moumen’s (2013a) analysis of the 2005, 2007, and 2009 AHS data implicitly raises

some concerns about whether the ZADEQ measure accurately reflects the quality of the housing

stock. The measure produces a very low incidence of severe inadequacy (2 percent); only two

items—sharing a bathroom and heating problems—account for most of the cases considered

severely inadequate, and these problems generally do not persist over a 2-year period. The

authors are particularly troubled by the lack of persistence in the shared bathroom item,

investigate it in greater detail, and conclude that this item is likely to have been measured

incorrectly. More generally, they conclude that the AHS quality measure may provide a

reasonable cross-sectional estimate of the most severely inadequate units, but provides little

information on the roughly 91 percent of units considered adequate. 10

In a second paper (2013b), Eggers and Moumen propose an alternative to ZADEQ that is designed

to provide more information about gradations within the adequate housing stock. A major

motivation is their particular interest in being able to study filtering, which requires a measure to reveal increases in deficiencies or inadequacies over time as a unit deteriorates and is presumably filtered down from higher income to lower income residents. They develop an alternative measure,

the poor quality index (PQI) that is a numeric scale of housing defects that draws on additional

measures in the AHS (for example, assessments of the structure’s exterior), as well as those

included in ZADEQ. Lacking a reliable source on how to weight each item in the index, they

assign weights based on a combination of ZADEQ’s definitions and their own judgment. The PQI

appears to achieve the goals of its creators. By contrast to ZADEQ, which estimates that a large

majority of units had no problems, 47 percent of units had at least one PQI inadequacy. 11 The stability of the classification of the unit also differs for the two indices (Eggers and Moumen,

2013b: 9). According to ZADEQ, 95 percent of units designated as adequate in one survey remain

adequate 2 years later, while roughly 30 to 35 percent of units categorized as moderately or

severely inadequate in one survey remained inadequate in the subsequent survey. Using the PQI, a

smaller share, 63 percent of units, remained adequate from one survey to the next, and a greater

share of inadequate units, roughly 60 percent, retained that designation over 2 years.

Emrath and Taylor (2012) examine the AHS ZADEQ index using a hedonic model. Because of

the multicollinearity among the individual measures that comprise ZADEQ, the authors test each

ZADEQ item separately, along with other features of the dwelling (for example, number of

rooms, geographic region, and square footage). They report that none of the ZADEQ items reach

statistical significance and, in some cases, have an unexpected sign. A major policy concern of

10 Authors’ estimate based on the 2011 AHS.

11 The PQI rate is based on the 1993 AHS. Unfortunately, the two Eggers and Moumen reports (2013a; 2013b) rely on different AHS years, so it is impossible to make direct comparisons between ZADEQ and PQI results.

5

the authors is that the very small rate of housing units meeting the definition of physically

inadequate using ZADEQ leads to the conclusion that the nation’s housing stock has no serious

housing problems. They challenge this conclusion by identifying measures in the AHS, many of

which are not included in ZADEQ, that have a strong effect on rents and prices. These items are

similar to those included in Eggers and Moumen’s (2013b) PQI. It is likely that Emrath and

Taylor’s ZADEQ results occur because of the very low variance of each individual item. This

was part of Kain and Quigley’s (1970) motivation for using factor analysis, which produced a

single dwelling unit quality factor. 12

A fourth recent paper assesses the reliability, consistency, and validity of the AHS ZADEQ

index (Newman and Garboden, 2013). Like Eggers and Moumen (2013a; 2013b) and Emrath

and Taylor (2012), the authors conclude that the index identifies only a very small share of units with multiple inadequacies and provides little information about variations among units

classified as adequate. They also find that the items included in the index do not appear to be

tapping the same underlying construct of housing quality. However, the two subindices within

ZADEQ, moderate inadequacy and severe inadequacy, are strong and statistically significant

predictors of residents’ housing satisfaction.

Quality of Assisted Housing

The research literature on the physical quality of the assisted housing stock is sparse, at least in part, because the AHS, the main data source on housing, typically relies on respondent self-reports of the receipt of housing assistance, which are known to be unreliable (Shroder, 2002).

The present paper can utilize the 2011 and 2013 AHS data, because the identification of assisted

housing receipt, by program type, relies on administrative records, not self-reports. Validation of assisted housing receipt was previously done in the 1989 AHS. One paper used these validated

data and a version of ZADEQ to study the assisted housing profiles of households with children

(Newman and Schnare, 1993). The authors report that 15 percent of public housing units

occupied by households with children had either a moderate or severe defect, compared with

5 percent of multifamily housing and 12 percent of voucher units. The average number of

defects, however, was generally similar across the programs.

A more recent study examined the quality of housing in the voucher program (Buron et al.,

2000). Data on voucher housing come from the 2000 Customer Satisfaction Survey (CSA). The

authors developed two measures of housing quality, one relying on all quality-related items in

the CSA and another using CSA items that align with those in the AHS. The CSA-based measure

was used to explore voucher housing quality, and the CSA-AHS measure was used to compare

housing quality in the voucher program with housing quality in a matched comparison sample of

unassisted renters. The CSA-based summary measure combined items into four categories:

12 Merrill (1980) used a somewhat similar approach in her hedonic modeling using data from the Experimental Housing Allowance Program demand data.

6

severely inadequate quality, moderately inadequate quality, adequate quality, and high quality.

Based on voucher respondent reports to the CSA, 41 percent of voucher housing was considered

high quality, 33 percent adequate quality, and 23 percent severely inadequate. The rate of severe

inadequacy is higher than the 12- to 21-percent range in Gray et al. (2008), HUD’s report on the

first-year results of the CSA, which relied on similar though not identical quality measures. The

analysis of voucher and comparable nonvoucher housing quality was based on a statistical match

between the households in the CSA’s voucher sample and households in the AHS. They use two

different measures of housing quality, one a simple count of problems aggregated into four

categories (0, 1–2, 3–4, 5+ problems) and another indicating whether at least one problem was

reported for each of five housing dimensions (for example, kitchen and bathrooms; electrical).

Both measures yield the similar finding of lower-quality housing of voucher users than housing

occupied by unassisted renters. For example, 59 percent of voucher renters reported no housing

problems, compared with 66 percent of unassisted renters. The authors caution that differences

between the CSA and AHS may account for some or most of these disparities.

Research Approach

Data

Our main sources of data are the 2011 and 2013 AHS. The AHS—begun in 1973, sponsored by

HUD, and conducted by the Census Bureau—is the primary source of data on housing in the

U.S. The national AHS sample typically includes about 60,000 nationally representative

residential dwellings. The 2011 and 2013 surveys differ in using larger samples. In 2011, to

reduce costs and improve the precision of national estimates, more than 115,000 units from the

29 metropolitan area samples were merged with the national AHS into a single “combined

national sample” of more than 186,000 housing units (Census Bureau, 2015). The 2013 national

AHS includes 84,355 units, a smaller sample size than in 2011 because it does not combine

national and metropolitan area samples except for the “big 5” metropolitan areas—Chicago,

Detroit, New York City, Northern New Jersey, and Philadelphia—that have historically been

included in the AHS national samples.

Another unique feature of the 2011 and 2013 data is that addresses of assisted housing are

identified based on matching sample addresses to HUD administrative data on HUD assisted

housing programs. 13 This greatly reduces the reliability and validity problems of self-reported receipt of housing assistance. In addition, an oversample of roughly 5,000 assisted housing units

was added to the national AHS beginning in 2011. Oversampling ensures adequate representation

13 The match to HUD data excludes housing units assisted by state and local programs and the federal Low-Income Housing Tax Credit (LIHTC) program, which is under the auspices of the Department of the Treasury. However, because a sizable share of LIHTC units also receives HUD subsidies, such as vouchers, these units are included in the HUD administrative files. O’Regan and Horn (2012) estimate that 46 percent of LIHTC households receive some form of rental assistance, Buron et al. (2000) puts the estimate at 37 percent, and GAO’s (1997) estimate is 39

percent.

7

of individuals (in this case, assisted housing units) that do not occur frequently in the population.

The 2011 AHS sample includes 9,721 assisted housing units and the 2013 sample includes 6,922

assisted housing units. 14

Samples

Our first analytic step is to develop indices that are designed to tap the concept of housing

quality. We base this analysis on the unassisted stock of rental housing, excluding all units

designated by the administrative address match as part of the assisted housing stock. Because we

will ultimately apply the quality indices to the assisted stock, we limit the unassisted cases to

units in a single-family or multifamily property and exclude unassisted cases that are rare or

nonexistent in the assisted stock (for example, manufactured housing; reduced rents because of

relationship between renter and landlord). We also exclude vacant or vacation units and units

where no interview was conducted. Table A1 highlights these selection criteria. After excluding these cases, the 2011 analysis sample for index development is 40,830 unassisted housing units.

We develop the housing quality indices using the 2011 AHS to take advantage of its much larger

sample size than the 2013 AHS. 15 We base the indices on 33 AHS items on housing conditions.

Two-thirds of these items have no missing data, and only 1 percent of observations are missing

on 25 percent of the items. Because such low rates are very unlikely to affect the estimates, we

make no adjustments for missing data. Diagnostics on the full analysis sample revealed virtually

no missing data or outlier values, and the AHS staff assigned reasonable top codes to continuous

measures. 16 Top coding may be used to prevent a small number of very high values from distorting analysis.

Methods

Because the concept of housing quality is not based on explicit criteria, the large number of

housing quality indices that have been developed with the AHS yield dramatically different

prevalence rates (Newman and Schnare, 1988). The core challenge is well known: a housing unit

is a bundle of attributes that extend beyond the dwelling itself, and it is unclear which of these attributes should be included in the definition of the dwelling’s quality and how each should be

weighted in determining overall quality (Merrill, 1980; Aaron, 1972).

In the absence of consensus responses to these questions, the next best option is to rely on an

external criterion, as suggested by Merrill (1980). We examine three alternatives: market value,

consumer rating, and normative standards. We test the market value criterion with a hedonic

approach. As described earlier, it assumes that the unit’s rent is correlated with the quantity and quality of housing such that higher rents reflect better quality. The consumer rating criterion

14 Based on sample design appendices to 2011 and 2013 AHS documentation.

15 We did not combine the 2011 and 2013 AHS samples because the 2013 AHS includes a subsample of units from the 2011 AHS. Because two waves of data are not available for every unit, combining the 2011 and 2013 AHS

samples would overweight the importance of housing units included in both AHS samples.

16 These measures include breakdowns in heating, toilets, or sewage; blown fuses; and rent.

8

identifies the dwelling features that are most closely associated with the resident’s assessment of the dwelling as a good place to live regardless of what the market price of these features might

be. This criterion broadens the concept of housing quality beyond specific housing features to the welfare of residents as they themselves report it (Goodman, 1978). It is consistent with the

renewed interest by economists in happiness and subjective well-being as a measure of the utility

an individual derives from goods and services (Dolan, Peasgood, and White, 2008). 17 The normative standards criterion is designed to reflect community concerns and policy decisions

about housing quality, such as state building codes and assisted housing physical inspection

standards. We test three versions of a normative standards index: a weighted index, an

unweighted index, and a factor analysis index. This analytic strategy allows us to systematically

examine housing quality from three different perspectives, driven by the empirical evidence. It

contrasts with ad hoc approaches, such as assigning weights to individual housing quality items

based on intuition or setting a priori thresholds on the number of breakdowns in key housing

systems, such as heating and plumbing, which distinguish severe housing quality problems from

moderate problems.

Although the AHS contains a rich array of measures plausibly associated with housing quality,

some measures are not repeated from one wave to the next, and not all questions are asked of all

housing types (that is, single-family or multifamily). Because our analysis includes a longitudinal component in which we assess whether housing inadequacies persist over the 2-year period from

the 2011 survey to the 2013 survey, we only incorporate measures included in both surveys. 18

We also limit the analysis to measures collected from all rental units, including single-family

properties and the housing units in multifamily buildings that are most relevant to our focus on

the assisted housing stock. Using this sample of rental housing units, we construct housing

quality indices using the consumer rating and normative standards perspectives, as described in

more detail below. Because the market value index does not perform well, we exclude it from

further analysis. We construct one consumer rating index and three indices using the normative

standards criterion. In general, the indices are calculated by assigning a weight to each housing

quality measure and then adding up the weighted scores of all quality measures identified for

each housing unit. For the consumer rating index, we apply the coefficients from regression

models used to predict house rating as weights. We treat each of the three normative standards

indices differently. We assign weights to one index based on a previous analysis by Eggers and

Moumen (2013b), assign the same weight of 1 to all individual items in a second index, which is

equivalent to an unweighted index, and use the results of a factor analysis to assign weights to a third normative standards index.

17 The market value model and the consumer rating model are also associated with other elements of the housing bundle that extend beyond the dwelling itself, such as neighborhood features. Therefore, we also control for neighborhood in these models.

18 See Appendix B on the Healthy Homes module in the 2011 AHS.

9

We assess the validity of the four well-performing indices we construct by establishing whether

the indices are strongly related to each other and to other measures that we can reasonably expect would be associated with housing quality, by studying their “convergent validity” and their

“predictive validity” (Carmines and Zeller, 1979). Because each index is designed to tap the

concept of housing quality, the indices should be strongly related to each other and to other

measures that we can reasonably expect would be associated with housing quality. Further, if

each index is effective at tapping housing quality, then it should predict quality-related

outcomes. We estimate convergent validity by examining the correlations, both among the four

indices and between each index and other attributes with which the index should be correlated,

such as rent and building age. We estimate predictive validity by testing multivariate models of

the predictive power and significance of the indices in predicting such outcomes as rent and the

resident’s housing satisfaction as measured by rating the house as a place to live on a 10-point

scale.

Results

Table 1 lists the AHS housing quality measures in this analysis and their mean values. 19

Consistent with much past AHS housing quality research, the prevalence rates of almost all

problems are very low. Most (55 percent) dwellings have no problems, and fewer than 5 percent

of units account for more than 75 percent of problems. 20

19 This table includes a few measures (for example, mold; broken steps) that we look at descriptively but do not include in any of the indices, because they do not meet all criteria.

20 Because the AHS included no reports of “number of times completely without running water,” we dropped this item from all subsequent analyses.

10

Table 1. 2011 AHS Housing Quality Measure, Mean Percent of All Housing

Mean

Mean Times

Prevalence Rate

for Counts

1.

Not all rooms have plugs

1

2.

# times blown fuses last 3 months

9

0.23

3.

Exposed wiring

2

4.

Unit does not have electricity

.03

5.

Unvented room heaters

1

6.

No heating equipment

1

7.

Use stove/oven for heat

0.1

8.

# heating breakdowns last winter

3

0.08

9.

Unit cold 24+ hours last winter

10

10.

Cold due to utility interruption last winter

1

11.

Cold due to inadequate heating capacity last winter

2

12.

Cold due to inadequate insulation last winter

2

13.

Cold due to other reason last winter

2

14.

Roof leak last 12 months

5

15.

Leak in wall/closet last 12 months

3

16.

Leak in basement last 12 months

1

17.

Leak other source last 12 months

1

18.

Leaking pipes last 12 months

5

19.

Leaking plumbing fixture last 12 months

2

20.

Leak unknown source last 12 months

4

21.

Crack in wall

7

22.

Holes in floor

1

23.

Peeling paint

3

24.

Signs of rodents last 12 months

3

25.

Signs of rats last 12 months

1

26.

Signs of mice last 12 months

9

27.

Signs of cockroaches last 12 months

5

28.

Incomplete plumbing

0.3

29.

# times toilet broke 6+ hours last 3 months

2

0.05

30.

Share plumbing facility

2

31.

Incomplete kitchen

4

32.

# times no water last 3 months

—

32.

# sewage disposal breakdowns last 3 months

1

0.03

33.

No working elevator

5

34.

Any mold

5

35.

Broken stairs

1

36.

Broken steps

1

Notes:

1. N = 40,830 unassisted rental units from 2011 AHS, excludes manufactured housing and units where a relationship exists between renter and landlord. See text and table A-1 for more details.

2. Weighted data.

3. “Mean times for counts” = average for entire sample, not just those reporting the problem.

4. “# times no water last 3 months” never reported.

5. Items 34, 35, and 36 from Healthy Homes module.

6. AHS = American Housing Survey.

11

Housing Quality Indices

Market Value Index

We estimate the market value index with a hedonic approach. Following standards established in

highly regarded housing economics research (Coulson and Li, 2013; Kriström, 2008; Thibodeau,

1995), we specify the dependent variable as the natural log of rent and add a granular level of

controls for multiple features of the housing unit (for example, size; amenities) and geographic

location (for example, region; city; suburb; rural). Because of the established importance of

neighborhood quality in market values, we include the respondent’s rating of the neighborhood, the only proxy measure available in the 2011 AHS, and include HUD’s FMR for the metropolitan area

as a gauge of the local housing market. Although our main interest is in the contribution of housing quality to market value, this effect could depend on the quality of the neighborhood, for example, or whether the unit is located in a central city, suburb, or rural area (often referred to as

“urbanicity”). Therefore, excluding these additional measures from the model could provide

misleading results. The full list of controls (or covariates) is shown in table 2.

Table 2. Control Measures Included in Market Value (Hedonic) Models

Systems

Unit

Room air conditioner

Single-family

Central air conditioner

Single-family attached

Dishwasher

Multifamily < 3 units

Garbage disposal

Multifamily 3–4 units

Clothes dryer

Multifamily 5–9 units

Washing machine

Multifamily 10–19 units

Electric heat

Multifamily 20+ units

Gas heat

Oil heat

Utility costs

Electric in rent

Physical

Gas in rent

# Baths

Oil in rent

# Bedrooms

Other fuel in rent

Basement

# Floors to unit

Neighborhood/location

Den/library/TV room

Neighborhood rating

Dining room

Region/metropolitan area

Family room

HUD Fair Market Rent

Working fireplace

Garage or carport

Other

# half bathrooms

Connected public sewer

Laundry/utility room

Use well water

Porch/deck/balcony/patio

# months live in unit

# Rooms

Building age

Building age-squared

Building age-cubed

# Floors in building

Other fuel in rent

Notes:

1. Control measures from 2011 American Housing Survey.

2. Models also include the 33 individual housing quality measures, see text for details.

3. # baths topcoded at 3.

4. # bedrooms and # floors topcoded at 4.

12

Because the 33 housing quality items in the analysis are often closely related to each other

(statistically referred to as “multicollinearity”), the best method to assess the contribution of

housing quality reflected in these individual quality items to rent is to combine them in a

composite measure. Unfortunately, this defeats our purpose of developing a weight for each

quality item to represent its individual contribution to rent. This leaves two alternative

approaches, neither of which is ideal. The first option is to examine each of the 33 quality items separately. Although this approach provides a weight for each individual quality measure, it runs

the risk of bias from omitting the other quality items. The second option is to include all 33 items in a single model. Although this approach also provides weights for individual quality items, it is less than ideal because of the substantial correlation among the 33 quality items. Recognizing

that neither approach is ideal from a methodological standpoint, we test both.

To estimate the effect of each individual measure of housing quality on market value, we tested

33 hedonic models, one for each housing quality measure. The results are shown in table 3.

Excluding any measure of housing quality, the other predictor variables account for 36 to 42

percent of the variance (that is, the  R2). This estimate remains unchanged after each individual housing quality measure is added, indicating virtually no contribution to the explanatory power

of the model. Of the 33 dwelling quality items, 12 reach statistical significance at least at the .10

level, but 7 of these coefficients have an unexpected sign. That 85 percent of a large number of

items purporting to represent some aspect of dwelling quality either do not reach statistical

significance or, in 7 cases, operate in the opposite direction of expectations, raises serious

questions about the usefulness of the market value approach in this context. Further, the large

number of multiple comparisons required to operationalize the market value approach runs the

risk of generating some statistically significant estimates purely by chance. Therefore, we adjust the threshold required for statistical significance using the Bonferroni correction. 21 After the correction, four measures remain statistically significant: seeing roaches daily; incomplete

plumbing; no working elevator; and number of fuses blown. The first three are plausible and

have reasonable interpretations. Incomplete plumbing has, by far, the most sizable effect,

reducing the average monthly gross rent of about $1,000 by $263. 22 The absence of an elevator reduces the rent by $81, and the persistent presence of roaches by $45. Blown fuses have a

positive sign, indicating that the rent is higher in dwellings with more blown fuses. It is difficult to interpret this odd relationship. However, despite the statistical significance of this item, it increases the rent by only about $9. 23

21 The Bonferroni correction is used to reduce the likelihood of reporting a false positive (for example, reporting a random difference as real). The correction divides the original significance level by the number of variables examined (here .10/33 = .003) so that the likelihood of reporting a false positive stays at .10 across the entire set of comparisons.

22 Dollar interpretations based on: Exp(B)*mean - mean = difference in price. Thus, for incomplete plumbing, where B = -.295: exp (-.295) = .745; times $1,028.8 = $765.974, which is subtracted from the mean rent of $1,028.80, yielding $-262.826.

23 One reviewer suggested that blown fuses may interact with historic buildings in high-cost urban areas.

13

Table 3. Market Value (Hedonic) Model Results, Housing Quality Measures

Separate

Combined

Coef.

p-value

Coef.

p-value

Not all rooms have plugs

– .043

.049

*

– .042

.060

+

# times blown fuses last 3 months

.009

.000

***

.010

.000

***

Exposed wiring

.008

.586

.001

.985

Unit does not have electricity

.332

.171

—

Unvented room heaters

– .063

.038

*

– .068

.029

*

No heating equipment

.011

.740

—

Use stove/oven for heat

– .072

.283

– .044

.521

# heating breakdowns last winter

.002

.624

.001

.815

Unit cold 24+ hours last winter

.011

.153

.005

.741

Cold due to utility interruption last winter

.028

.253

.015

.584

Cold due to inadequate heating capacity last winter

.018

.285

.016

.424

Cold due to inadequate insulation last winter

.028

.093

+

.016

.417

Cold due to other reason last winter

– .008

.648

– .013

.550

Roof leak last 12 months

.025

.018

*

.024

.024

*

Leak in wall/closet last 12 months

.025

.058

+

.019

.178

Leak in basement last 12 months

.040

.034

*

.034

.079

+

Leak other source last 12 months

.018

.383

.013

.524

Leaking pipes last 12 months

.014

.171

.013

.230

Leaking plumbing fixture last 12 months

.006

.685

.009

.516

Leak unknown source last 12 months

– .003

.806

– .006

.631

Crack in wall

– .008

.400

– .010

.320

Holes in floor

– .018

.367

– .011

.594

Peeling paint

– .022

.103

– .032

.028

*

Signs of rodents last 12 months

– .021

.155

– .025

.158

Signs of rats last 12 months

.023

.242

.038

.079

+

Signs of mice last 12 months

– .007

.422

– .001

.856

Signs of cockroaches last 12 months

– .045

.000

***

– .049

.000

***

Incomplete plumbing

– .295

.000

***

– .242

.000

***

# times toilet broke 6+ hours last 3 months

– .004

.450

– .006

.247

Share plumbing facility

– .040

.026

*

– .039

.033

*

Incomplete kitchen

– .011

.288

– .007

.537

# sewage disposal breakdowns last 3 months

.016

.049

*

.014

.039

*

No working elevator

– .081

.000

***

– .073

.000

***

Notes:

1. Separate = Results from 33 ordinary least squares (OLS) regressions on log rent with individual housing quality measures.

2. Combined = Results from single OLS regression on log rent with all housing quality measures in model.

3. See table 2 for other measures included in models.

4. “—” = dropped from combined analysis because perfectly correlated with other measures.

5. N = 36,833.

6.  p- values: + < .10, * < .05, ** < .01, *** < .001.

To test the effects of all 33 quality measures together, we estimated a hedonic model that included all 33 items simultaneously. These results are also shown in table 3.  There is remarkable consistency between the two sets of analyses. Of the 12 statistically significant measures identified in the separate analyses, 10 are also statistically significant in the combined model. The same

measures also emerge from both analyses as the strongest and most statistically significant: the

number blown fuses, signs of cockroaches, incomplete plumbing, and no working elevator. Several

of the unexpected results in the individual item models are also replicated in the simultaneous

model, such as the positive sign on blown fuses, leaking roofs, and leaking basements, indicating

that these problems increase the rent instead of decreasing the rent, as anticipated.

14

These hedonic results contrast with those of Kain and Quigley (1970) and Merrill (1980). The

difference is that we are interested in the effect of each individual measure of housing quality on rent and, therefore, we test each measure separately. Kain and Quigley and Merrill combine

measures of housing quality into a composite indicator or factor. 24 Our empirical results indicate that, despite a very large sample, 85 percent of the AHS measures are not statistically significant, and the rarity of each individual quality problem provides too little variance to make a

meaningful contribution to market values. Therefore, despite the appeal of the external criterion

of market value for assessing the relative importance of individual housing quality features, this approach is not feasible. Although estimating the relative contribution of a composite indicator to market value is feasible, it does not achieve the objective of identifying the most important

individual measures of housing quality.

Consumer Rating Index

To assess the contribution of each housing quality measure to the household’s preferences, we rely on the AHS question asking the respondent to provide a house rating. The specific item asks: “On

a scale of 1 to 10, how would you rate your unit as a place to live?” Although the original coding designates 10 as best and one as worst, we reverse these codes for consistency with the normative

standards indices we discuss later. Thus, a higher value indicates lower housing quality.

We test the consumer rating model using ordered logistic regression, because the house rating is an ordinal scale with only 10 points. As a result, the estimated contribution of each of the quality

measures, or parameter estimates, is expressed as odds ratios: how much a unit changes in the

housing quality item changes the house rating. As with the market value criterion, we test consumer rating two ways: individual quality items separately, and all quality items combined. Because the

results are similar, we present the results from the separate quality measure tests for simplicity. 25

The results are shown in table 4. In contrast to the market value analysis, each quality measure is shown to contribute to the consumer’s rating. Virtually all of the odds ratios are greater than one, indicating that the presence of the condition worsens the rating, as hypothesized. 26 The five measures that make the largest contribution to house rating are: holes in the floor; peeling

paint; cracks in the walls; presence of rodents; 27 and cold due to inadequate insulation. For example, the presence of holes in the floor makes it 3.5 times more likely that the consumer’s

house rating is poorer. Peeling paint makes a poorer score 3.3 times more likely, and rodents

24 Creating a composite indicator also addresses the multicollinearity among the individual quality items, as does testing these items one at a time.

25 In the model including all quality measures simultaneously, the odds ratios tend to be roughly 25 percent lower because of multicollinearity, and some nearly perfectly collinear measures do not reach statistical significance (for example, exposed wiring; reasons for cold unit; sewage disposal breakdown).

26 One exception is the use of an oven for heat, which affects a very small proportion of rental units (see table 1).

27 The item on rodents is asked because some respondents cannot be certain whether they are seeing mice or rats.

These three items are very highly correlated, as shown in table 13. Arguably, all three items are substantively important, because they overlap.

15

make this 2.7 times more likely. 28 It is worth noting that these items do not overlap at all with the few statistically significant and qualitatively important measures that emerge from the

market value model. The consumer rating model also attains good explanatory power, the large

majority of the quality items are highly statistically significant, and they operate in the

expected direction. We use the odds ratio for each quality measure as a weight to create a

housing quality index based on the consumer rating criterion.

Table 4. Consumer Rating Model Results, Housing Quality Measures

Odds Ratio

p-value

Not all rooms have plugs

1.973

.000

***

# times blown fuses last 3 months

1.175

.000

***

Exposed wiring

1.363

.000

***

Unit does not have electricity

1.770

.573

Unvented room heaters

1.075

.588

No heating equipment

1.261

.106

Use stove/oven for heat

0.725

.269

# heating breakdowns last winter

1.225

.000

***

Unit cold 24+ hours last winter

2.017

.000

***

Cold due to utility interruption last winter

1.731

.000

***

Cold due to inadequate heating capacity last winter

2.212

.000

***

Cold due to inadequate insulation last winter

2.656

.000

***

Cold due to other reason last winter

1.531

.000

***

Roof leak last 12 months

1.987

.000

***

Leak in wall/closet last 12 months

1.801

.000

***

Leak in basement last 12 months

1.921

.000

***

Leak other source last 12 months

1.541

.000

***

Leaking pipes last 12 months

1.678

.000

***

Leaking plumbing fixture last 12 months

1.904

.000

***

Leak unknown source last 12 months

1.482

.000

***

Crack in wall

2.708

.000

***

Holes in floor

3.509

.000

***

Peeling paint

3.253

.000

***

Signs of rodents last 12 months

2.657

.000

***

Signs of rats last 12 months

2.127

.000

***

Signs of mice last 12 months

1.626

.000

***

Signs of cockroaches last 12 months

2.052

.000

***

Incomplete plumbing

1.430

.197

# times toilet broke 6+ hours last 3 months

1.275

.000

***

Share plumbing facility

1.111

.172

Incomplete kitchen

1.208

.000

***

# sewage disposal breakdowns last 3 months

1.243

.000

***

No working elevator

1.262

.002

**

Notes:

1. Results from 33 separate ordinal logistic regressions on subjective housing rating (reverse coded so high score =

poorer quality). See table 2 for other measures included in model.

2. N = 36,833.

3.  p- values: + < .10, * < .05, ** < .01, *** < .001.

4. Odds ratio =  eβ where “β” is the coefficient from the logistic model.

28 The odds ratios apply identically across the house rating distribution (that is, across the 1–10 rating). Thus, there are equal odds of a higher score if the original score is 2 versus an original score of 8, for example.

16

Normative Standards Index

We test three versions of a normative standards index: a weighted index, an unweighted index,

and a factor analysis index. Each of these indices is based on the same array of housing quality

measures included in the market value and consumer rating models.

Weighted Index.   Because no consensus criteria exist for assigning weights to individual housing conditions presumably associated with housing quality, we adopt the weights assigned by Eggers

and Moumen (2013b), which are based on a combination of the AHS ZADEQ housing quality

measure and the authors’ judgment. 29 For example, Eggers and Moumen assign their highest weight, 10, to each deficiency classified by ZADEQ as a severe inadequacy (that is, incomplete

plumbing, incomplete kitchen, lacking electricity, lacking heating equipment, using a stove or

oven for heat). Conversely, Eggers and Moumen assign their lowest weight, 2, to deficiencies

that ZADEQ includes in its “moderately inadequate” category. The second column in table 5

lists the Eggers and Moumen weights for the items included in the present analysis.

To address items that measure how many times a particular problem arises (for example, number

of heating system breakdowns), we compute the total weight by multiplying the number of times

the problem occurred by the Eggers and Moumen weight. We also standardize the weights to

account for minimal missing data and multiply the result by 100, which produces an index value

that ranges from 0 to 100. 30

Unweighted Index.   The unweighted index directly acknowledges the absence of consensus criteria for assigning weights. Each item in this index has the identical weight of 1, as shown in the third column of table 5. As in the weighted index, we standardize for nominal missing data and multiply the result by 100.

Factor Analysis Index.   Our third methodology for creating a normative standards index is factor analysis. This method provides a more systematic approach for weighting each of the 33

measures purported to reflect housing quality than the relatively ad hoc approach of the weighted

and unweighted indices. Factor analysis examines the correlations among measures to determine

the amount of common variance among them. 31 The analysis produces factor “loadings,” which indicate how much variance is shared among the observed measures and the unobserved

construct (in the present case, housing quality). The loadings or scores can be used as weights to create the factor analysis index.

29 We exclude measures that do not meet our criteria noted earlier. Therefore, our measures do not entirely overlap with those of Eggers and Moumen’s PQI.

30 Imagine, for instance, that all of the housing measures are equally weighted with a score of 1 and that we are comparing two housing units, one with responses on all 33 housing quality measures and the other with responses to only 30 measures. Each household reports having two problems, so each has an initial index score of 2. For the first unit, we adjust this score by dividing it by the number of observed problems (that is, 2/33). For the second unit, this same procedure reflects that fewer questions were answered (that is, 2/30). The weighted index is computed using this procedure but adjusting the weights to account for the different values assigned by Eggers and Moumen.

31 As Newman and Garboden (2013) expressed it, how well the measures “hang together.”

17

Table 5. Normative Standards Weighted and Unweighted Indices

Weighted

Unweighted

Not all rooms have plugs

3

1

# times blown fuses last 3 months

1

1

Exposed wiring

4

1

Unit does not have electricity

10

1

Unvented room heaters

4

1

No heating equipment

10

1

Use stove/oven for heat

10

1

# heating breakdowns last winter

2

1

Unit cold 24+ hours last winter

4

1

Cold due to utility interruption last winter

2

1

Cold due to inadequate heating capacity last winter

2

1

Cold due to inadequate insulation last winter

2

1

Cold due to other reason last winter

2

1

Roof leak last 12 months

2

1

Leak in wall/closet last 12 months

2

1

Leak in basement last 12 months

2

1

Leak other source last 12 months

2

1

Leaking pipes last 12 months

2

1

Leaking plumbing fixture last 12 months

2

1

Leak unknown source last 12 months

2

1

Crack in wall

2

1

Holes in floor

2

1

Peeling paint

2

1

Signs of rodents last 12 months

1

1

Signs of rats last 12 months

2

1

Signs of mice last 12 months

1

1

Signs of cockroaches last 12 months

3

1

Incomplete plumbing

10

1

# times toilet broke 6+ hours last 3 months

2

1

Share plumbing facility

2

1

Incomplete kitchen

10

1

# sewage disposal breakdowns last 3 months

2

1

No working elevator

4

1

Notes:

1. Weighted index values based on Eggers & Moumen (2013b), see text for details.

2. For continuous variables = # times * weight value.

3. Both weighted and unweighted scores are summed, divided by the total possible score and multiplied by 100 to create the final index.

Because many of the AHS quality measures are dichotomous, based on “yes or no” questions

(for example, is there a leak in the roof? has the resident seen rodents?), we use a polychoric

correlation matrix. 32,33 The results are shown in table A2. One challenge in estimating a polychoric factor analysis is that the standard approaches for selecting the number of factors

(that is, examining the scree plot or comparing chi-square values) are either inappropriate or

32  Polychoric correlation is a technique for estimating the correlation between two theorized normally distributed continuous latent variables from two observed ordinal variables.

33 We used Mplus to estimate the polychoric matrix.

18

unavailable. However, Preacher et al. (2013) recommend that when the goal is to identify the

number of factors that most accurately summarize the underlying structure of the data, the best

approach is to select the smallest number of factors for which the root mean square error of

approximation (RMSEA) is below .05.

Table 6 shows the RMSEA values for one-, two-, three-, and four-factor models. The table shows the lower and upper bound values at the 90 percent confidence interval, along with the

average RMSEA scores. Preacher et al. advise that one can select the number of factors when

either the average RMSEA score falls below .05, or the lower bound of the RMSEA score falls

below this threshold. Fortunately, both the average and lower bound of the RMSEA scores are

below .05. The results support the use of a one-dimensional index for measuring housing quality

and provide weights for an index based on the factor scores.

Table 6. Normative Standards Factor Analysis: Model Fit Test Results to Select Number of

Factors

Number of Factors Tested

1

2

3

4

RMSEA

.026

.019

.013

.010

90% CI lower bound

.026

.018

.013

.010

90% CI upper bound

.027

.019

.014

.011

Notes:

1. Factor analyses estimated in Mplus using polychoric correlations.

2. RMSEA = root mean square error of approximation.

3. CI = confidence interval.

4. Lower and upper bounds based on 90 percent confidence interval for RMSEA, see text for details.

5. Preacher et al. (2013) recommend selecting the smallest number of factors with RMSEA < .05.

Table 7 shows the factor loadings from the single-factor model. Factor models assign one variable to be the reference variable, which in this case is whether all rooms in the dwelling have electric receptacles. This reference variable is automatically assigned a factor score of 1. The

highest factor loadings occur for presence of rodents, number of times the dwelling was cold for

24 hours or longer, presence of mice, holes in the floor, peeling paint, and cracks in the walls.

Examples of items with the lowest factor loadings are using the oven for heat, lacking heating

equipment, number of toilet breakdowns lasting 6 hours or longer, and incomplete plumbing and

sharing plumbing facilities. 34 There is notable overlap between the measures with the highest and lowest weights in the factor analysis normative standards model and the consumer rating model.

34 All of these problems are reported by no more than 2 to 3 percent of units, and incomplete plumbing and using stove for heat are reported by less than 1 percent of units.

19

Table 7. Normative Standards Index: Factor Analysis Weights

Factor Analysis Weight

Not all rooms have plugs

1.000

# times blown fuses last 3 months

0.921

Exposed wiring

1.465

Unit does not have electricity

1.649

Unvented room heaters

0.968

No heating equipment

– 1.435

Use stove/oven for heat

– 1.497

# heating breakdowns last winter

0.747

Unit cold 24+ hours last winter

3.340

Cold due to utility interruption last winter

2.593

Cold due to inadequate heating capacity last winter

2.626

Cold due to inadequate insulation last winter

—

Cold due to other reason last winter

2.184

Roof leak last 12 months

2.019

Leak in wall/closet last 12 months

1.920

Leak in basement last 12 months

1.755

Leak other source last 12 months

1.454

Leaking pipes last 12 months

1.812

Leaking plumbing fixture last 12 months

1.787

Leak unknown source last 12 months

1.263

Crack in wall

2.667

Holes in floor

2.702

Peeling paint

2.685

Signs of rodents last 12 months

3.629

Signs of rats last 12 months

2.441

Signs of mice last 12 months

2.783

Signs of cockroaches last 12 months

2.071

Incomplete plumbing

1.629

# times toilet broke 6+ hours last 3 months

0.717

Share plumbing facility

0.270

Incomplete kitchen

0.707

# sewage disposal breakdowns last 3 months

0.207

No working elevator

0.482

Notes: 1. Factor analysis estimated in Mplus using polychoric correlations.

2. “—” = dropped from factor analysis because perfectly correlated with other measures.

A few key features of the foregoing discussion of index creation are worth summarizing at this

point. First, despite its intuitive appeal, we are forced to drop the hedonic index reflecting the market value criterion because of its poor performance. In addition, the scores on the four

housing quality indices that perform well are highly skewed. This is vividly demonstrated in

figure 1 and can also be seen in table A3, which shows the distribution of each of the four housing quality indices. Most housing units have none of the 33 housing quality problems

included in this analysis, with only a small fraction experiencing one or more problems. 35

35 It is important to note that some of the rarest housing conditions among the 33 measures, such as incomplete plumbing, are also a priori, serious problems and certainly related to housing quality. The only index that accounts for this a priori acknowledgment is the weighted index. However, the high correlation between this index and each of the other three indices in this analysis should allay concerns about this issue.

20

Figure 1. Distribution of Indices

60

50

40

units

30

nt of rcePe 20

10

0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18

Weighted

Unweighted

House rating

Factor analysis

Notes:

1. For weighted index 11 = 10 to 15, 12 = 15 to 20, 13 = 20 to 30, and 14 = 30+.

2. For consumer rating, normative standards unweighted, and factor analysis indices: 16 = 15 to 20; 17 = 20 to 30; and 18 = 30+.

Index Validity

Convergent Validity

Analytical techniques to check for convergent validity revealed that several indices point to the

same findings, suggesting that they are likely to be measuring the same underlying phenomenon

or construct.

Table 8 shows the correlations among the four indices. All of the correlations exceed 0.80. The

strongest correlations are among the normative standards factor analysis index, consumer rating

index, and normative standards unweighted index, which range between 0.94 and 0.97.

Relatively speaking, the weighted index is less strongly correlated with the others, with a range

of 0.81 to 0.88. Nonetheless, these are still very high correlations.

21

Table 8. Convergent Validity: Correlations Among Indices

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

Consumer rating

1

Weighted

.877

1

(.000)

Unweighted

.937

.871

1

(.000)

(.000)

Factor analysis

.967

.815

.949

1

(.000)

(.000)

(.000)

Notes:

1. Weighted data.

2. Correlation ( p- value) two-tailed significance.

Table 9 provides the correlations between each of the four housing quality indices and other AHS measures that are plausibly associated with housing quality. In addition to rent (both actual

and logged), house rating, and building age, we also test the relationship of each index to

ZADEQ, the housing quality measure included in the AHS data set. Although the house rating

measure is the basis for the consumer rating index, it is distinct from the index. The index

assigns weights to each of the 33 quality measures based on the respondent’s rating of the

dwelling, while the housing rating measure is the respondent’s rating, from 1 to 10, of the

dwelling as a good place to live, without any direct reference to the 33 quality measures.

Table 9. Convergent Validity: Correlations With AHS Measures Related to Housing

Quality

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

Rent

– .017

– .025

– .021

– .022

(.000)

(.000)

(.000)

(.000)

Log rent

– .015

– .028

– .023

– .019

(.000)

(.000)

(.000)

(.000)

House rating

– .341

– .302

– .342

– .338

(.000)

(.000)

(.000)

(.000)

Building age

.214

.205

.235

.223

(.000)

(.000)

(.000)

(.000)

ZADEQ

.419

.585

.436

.375

(.000)

(.000)

(.000)

(.000)

Notes:

1. Weighted data.

2. Correlation ( p- value) two-tailed significance.

3. ZADEQ is measure of housing unit quality computed in the American Housing Survey (AHS).

22

All of the correlations are statistically significant and all operate in the expected direction. Each of the indices is correlated with ZADEQ and, in fact, these correlations are the highest in the

table. On the other hand, the range of these correlations also indicates that our four indices and ZADEQ differ from each other. It is no surprise that the consumer rating index correlates highly

with the house rating outcome (measured ordinally, with values ranging from 1 to 10). What is

worthy of note is that the correlations of the house rating outcome with the factor analysis index and with the unweighted normative standards index are nearly as high. This suggests that all

three indices are likely to be measuring the same underlying phenomenon or construct.

Correlations assume a linear relationship between two measures. But it is also possible that one

or more indices have a nonlinear relationship with one or more of the outcomes. We test for

nonlinearities by focusing on three outcomes: rent, building age, and house rating. We divide the

distribution of index scores for each of the four housing quality indices into five categories,

ranging from zero (best quality) to 90+ percent (worst quality). 36 We then calculate the mean value for each of the three outcomes for each of the five categories of each housing index.

Table 10 summarizes the results. The patterns are generally linear, with adequate housing units (zero problems) consistently having the best scores on each of the quality indices and housing

units with greater age or the most problems having the worst scores. For building age and house

rating, the pattern is also monotonic across the middle of the distribution, consistent with a linear effect. But for rent, the distribution across the middle categories is relatively flat. This suggests that the effect of housing quality on rent is limited to housing units at the highest and lowest ends of the distributions for each of the housing quality indices. 37

36 Because there is no assumption of a linear relationship between rent and the categories of the index, we use rent in its unlogged form in this analysis.

37 The nonlinearity in the rent models helps explain why a market value index using the hedonic specification performs poorly.

23

Table 10. Convergent Validity: Variation across the Distribution of Each Index

Consumer Rating Index

0

1–30%

30–70%

70–90%

90+

p-value

Rent ($)

1,035

1,048

1,007

1,037

976

.000

Building age (years)

42.5

50.5

50.6

55.8

64.9

.000

House rating

8.12

7.96

7.50

6.94

5.68

.000

Normative Standards Indices:

Weighted

0

1–30%

30–70%

70–90%

90+

p-value

Rent ($)

1,035

1,009

1,061

1,002

943

.000

Building age (years)

42.5

47.8

54.3

54.1

64.1

.000

House rating

8.12

7.76

7.45

7.03

5.95

.000

Unweighted

0

1–30%

30–70%

70–90%

90+

p-value

Rent ($)

1,035

1,026

1,029

1,029

989

.016

Building age (years)

42.3

48.9

53.6

56.3

63.5

.000

House rating

8.12

7.77

7.40

7.09

5.96

.000

Factor Analysis

0

1–30%

30–70%

70–90%

90+

p-value

Rent ($)

1,037

1,044

1,006

1,033

968

.000

Building age (years)

42.5

49.0

51.9

56.1

65.6

.000

House rating

8.12

7.89

7.49

6.92

5.73

.000

Notes:

1. Weighted data.

2. Unequal intervals reflect skewed distributions of each index as shown in table A3.

Predictive Validity

Table 11 summarizes the results from testing the predictive power of each of the four indices on two outcomes: house rating and rent. The house rating equation uses an ordered logistic

specification, and the rent equation is estimated using an ordinary least squares (OLS) hedonic

specification. The strongest results are for the consumer rating index. Poorer housing quality,

indicated by higher scores on each of the indices, is associated with a higher, and therefore,

worse house rating even after controlling for household and geographic location characteristics.

The coefficient on each index is also strongly statistically significant ( p < .001) relative to house rating. These coefficients suggest that a one-standard-deviation increase in each of the four

indices produces nearly a 20 percent reduction (improvement) in house rating. The predictive

validity using rent as the outcome is somewhat weaker. Although the coefficient on each housing

quality index is negative, supporting the expectation that more housing problems are associated

with lower rent, none of the index coefficients is statistically significant at the .05 level, and the consumer rating index does not reach significance at the more liberal .10 level. The somewhat

flat relationship between the housing quality measures and rent in the middle part of each

distribution shown earlier in table 10 probably contributes to the relatively small size and more modest statistical significance of the effect of each index on rent. Further, the hedonic models

explain only about one-third of the variance in housing cost ( R2 ranges from .357 to .358), less 24

than half the total variance explained in, for example, the Kain and Quigley (1970) models

( R2 ~.72). 38 Because Kain and Quigley studied only a single housing market, St. Louis, they are better able to control for features of the market plausibly associated with rents. By contrast, our analysis is based on a national sample comprising widely varying housing markets. Although we

apply controls for attributes associated with housing markets, specifically geographic location,

urbanicity, and FMR, these controls are relatively coarse.

Table 11. Predictive Validity of Housing Quality Indices for Rents and Occupant Ratings

Using Multivariate Regression Analysis

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

Log rent

– 1.518

– 2.505

– 1.550

– 2.376

(.157)

(.086)

(.097)

(.055)

House rating

.848

.831

.874

.830

(.000)

(.000)

(.000)

(.000)

Notes:

1. Top number shown is regression coefficient (for rent) or odds ratio (for house rating). Bottom number is  p- value.

2. Log rent uses ordinary least squares, house rating uses ordinal logistic regression.

3. Log rent models also control for log household income, household head’s age, race and ethnicity, air conditioning, washer and dryer, type of heat, fireplace, garage, laundry room, porch, number of rooms, pay for utilities, number of months in unit, age of building, area Fair Market Rent, number of bedrooms, number of bathrooms, geographic location (region and central city, suburban, or rural).

4. House rating models also control for log household income, household head’s age, gender, race and ethnicity, geographic location (region and central city, suburban, or rural).

Assisted Housing Quality

We rely on the 2011 AHS to assess the physical quality of assisted housing in two ways. First,

we examine differences between the assisted and unassisted housing stock for each of the 33

individual housing quality measures that comprise the four housing quality indices. 39 We also include 3 additional measures from the 2011 AHS Healthy Homes module in this analysis. We

then compare differences in index ratings of assisted housing by program type, structure type,

geography, and household characteristics. Because most of these analyses are based on the large

sample sizes available in the AHS, measures of statistical significance are not very useful to

gauge substantive importance. Therefore, we rely heavily on the size of the effect, measured by a

statistical test known as Cohen’s  d. 40

38 Many other hedonic analyses are similarly based on one or only a few housing markets.

39 We apply the same exclusion criteria to the unassisted stock used earlier to develop the housing quality indices.

40 Cohen’s  d is the difference in means between two groups divided by the standard deviation for the pooled sample of the two groups.

25

Assisted and Unassisted Housing Quality

Based on the 36 individual housing quality measures in the 2011 AHS, the quality of assisted

housing is comparable to the quality of unassisted housing. This conclusion is based on a

comparison of prevalence rates and applies whether we limit the unassisted stock to units with

rents at or below the FMR, to all unassisted rental units, or to housing units emerging from

matching the assisted and unassisted units using propensity score matching (PM), a statistical

procedure. 41 Table 12,  which displays these prevalence rates, shows the comparisons to low-rent units in the first set of columns, followed by comparisons to the entire rental stock in the

remaining columns. Even for the most highly significant measures, such as those pertaining to

heating, roof leaks, rodents and mice, broken toilet, and nonworking elevator, Cohen’s  d  never achieves 0.2, which defines the threshold for a small effect.

In light of the absence of large differences in individual items that constitute the housing indices, coupled with the predominance of “no problems” in both the assisted and unassisted stock, it is,

therefore, not surprising that whether a housing unit is assisted or not is only weakly associated with its rating on the housing quality indices. As shown in tables 13a and 13b, the effect sizes fall below the level required for even a small effect whether the comparison is to units with

comparable rents or all comparable rental units, respectively.

41 In supplementary analysis, we used PM in two ways: (1) to match assisted housing units to unassisted housing units that are comparable based on a range of housing characteristics; and (2) to match assisted housing households to comparable low-income households not receiving housing assistance based on multiple household characteristics.

Both of these PM samples produced similar results to those reported here, with not even small effect size.

26

Table 12. Prevalence Rates of 2011 Housing Problems by Assistance Status

Rentals ≤ FMR

All Rentals

Assisted

Unassisted

Cohen’s

Assisted

Unassisted

Housing

Housing

d

Housing

Housing

1.

Not all rooms have plugs

1.3

1.1

+

1.3

0.9

**

2.

Ever blown fuses

8.6

8.9

8.6

9.3

+

# times blown fuses

22.1

22.3

22.1

23.3

3.

Exposed wiring

2.8

2.3

*

2.8

2.2

**

4.

Unit does not have electricity

0.00

0.02

0.00

0.03

5.

Unvented room heaters

0.3

1.3

***

.091

0.3

1.0

***

6.

No heating equipment

0.2

1.0

***

.094

0.2

0.7

***

7.

Use stove or oven for heat

0.1

0.2

0.1

0.1

8.

Ever heating breakdowns

4.6

3.4

***

.060

4.6

3.1

***

# times heating broke down

11.3

9.4

+

11.3

8.1

***

9.

Unit cold 24+ hours last winter

17.5

12.3

***

.100

17.5

11.3

***

10.  Cold: utility interruption

1.2

1.1

1.2

1.0

11.  Cold: inadequate heating

3.0

2.2

**

3.0

1.9

***

12.  Cold: inadequate insulation

2.3

1.8

*

2.3

1.7

***

13.  Cold: other reason

2.3

1.8

*

2.3

1.5

***

14.  Roof leak last 12 months

3.2

5.3

***

.098

3.2

4.9

***

15.  Leak in wall/closet

3.4

3.0

+

3.4

2.9

*

16.  Leak in basement

1.3

1.2

1.3

1.4

17.  Leak other source

1.4

1.3

1.4

1.3

18.  Leaking pipes

5.4

5.2

5.4

4.9

19.  Leaking plumbing fixture

2.4

2.4

2.4

2.4

20.  Leak unknown source

5.0

3.7

***

.069

3.6

5.0

***

21.  Cracks in walls

7.5

7.7

7.5

6.9

22.  Holes in floor

2.1

1.6

*

2.1

1.4

***

23.  Peeling paint

3.9

3.7

3.9

3.1

***

24.  Signs of rodents

5.3

4.0

***

.066

5.3

3.1

***

25.  Signs of rats last

1.1

1.3

1.1

1.2

26.  Signs of mice last

12.8

10.2

***

.087

12.8

9.0

***

27.  Signs of cockroaches

5.8

6.3

5.8

4.5

***

28.  Incomplete plumbing

0.2

0.5

**

0.2

0.3

29.  Toilet ever broke

3.3

2.5

***

.048

3.3

2.3

***

# times toilet broke

6.7

4.9

**

6.7

5.0

**

30.  Share plumbing facility

2.3

1.7

**

2.3

1.6

***

31.  Incomplete kitchen

4.8

4.3

4.8

4.0

**

32.  Ever sewage breakdown

1.5

1.5

1.5

1.3

# sewage breakdowns

3.8

3.2

3.8

3.0

33.  No working elevator

6.1

4.7

***

.066

6.1

5.0

***

34.  Any mold

8.0

8.5

8.0

7.9

35.  Broken stairs

0.6

0.8

0.6

0.8

36.  Broken steps

0.9

1.2

0.9

1.3

+

Notes:

1. Assisted housing N = 8,472; All rentals unassisted housing N = 40,830; Rentals ≤ FMR unassisted housing N = 24,190.

2. Weighted data.

3. Average for counts (“#”) = average for entire sample, not just those reporting the problem.

4.  p- values: + < .10, * < .05, ** < .01, *** < .001.

5. Cohen’s  d computed for all effects significant at .001 or less. Values < 0.2 indicate virtually no difference.

6. FMR = Fair Market Rent.

27

Table 13a. Housing Quality Ratings of 2011 Assisted and Unassisted Housing Units,

Comparable Rents

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

Assisted housing

2.49

1.94

3.51

2.24

Unassisted housing

2.22

1.78

3.14

1.95

p- value

.000

.000

.000

.000

Cohen’s  d

.069

.054

.075

.069

Notes:

1. Assisted housing N = 8,472; Unassisted housing N = 24,190.

2. Weighted data.

3. Comparable unassisted housing = rents at or below HUD’s Fair Market Rent.

4. Cohen’s  d computed for all effects significant at .001 or less. Values < 0.2 indicate virtually no difference.

Table 13b. Housing Quality Ratings of 2011 Assisted Housing and All Unassisted Housing

Units

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

Assisted housing

2.49

1.94

3.51

2.24

Unassisted housing

2.03

1.62

2.88

1.77

p- value

.000

.000

.000

.000

Cohen’s  d

.119

.109

.136

.141

Notes:

1. Assisted housing N = 8,472; Unassisted housing N = 40,830.

2. Weighted data.

3. Cohen’s  d computed for all effects significant at .001 or less. Values < 0.2 indicate virtually no difference.

Subgroup Variation in Assisted Housing Quality

Despite the lack of notable differences in the housing quality of the assisted and unassisted

housing, there still may be sizable variations in quality within the assisted housing stock.

Table C1 displays selected characteristics of assisted housing by program type. Even a cursory glance demonstrates considerable variation in some basic features of assisted housing including

its geographic location, racial and ethnic composition, and household size, among others.

Unsurprisingly, we find differences in housing quality ratings for assisted housing that pertain to both the assisted stock’s housing-related attributes and the characteristics of households residing in assisted housing.

28

Housing Characteristics.  Differences of housing quality by program type are shown in table 14.

Although housing quality index ratings are always worst for public housing and best for

multifamily housing, the effect size approaches but never reaches the 0.2 threshold for a small

effect. By contrast, sizable disparities in quality are evident among assisted housing for elderly, nonelderly disabled, and nonelderly families, as shown in table 15.42 Across all four housing quality indices, elderly housing has the best housing quality and housing in which a nonelderly

disabled person resides has the worst. Three of the four indices reach a medium effect size and

all are at least twice the criterion for a small effect size. Despite the relatively large variations in structure type by assisted housing program (see table C1), table 16 indicates that no notable disparities in assisted housing quality are associated with the type of structure.

Table 14. Housing Quality Ratings of 2011 Assisted Housing Units by Program Type

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

All assisted housing

2.49

1.94

3.51

2.24

Public housing

2.96

2.20

4.07

2.67

Multifamily

2.19

1.82

3.14

1.96

Voucher

2.48

1.91

3.50

2.23

p- value

.006

.000

.000

.000

Cohen’s  d

.182

.121

.186

.194

Notes:

1. All assisted housing N = 8,472; Public housing N = 2,007; Multifamily N = 3,848; Voucher N = 2,617.

2. Weighted data.

3. Cohen’s  d computed for all effects significant at .001 or less. Values < 0.2 indicate virtually no difference.

Table 15. Housing Quality Ratings of 2011 Assisted Housing Units by Household Type

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

Elderly

1.71

1.49

2.57

1.57

< 62 disabled

3.79

2.76

5.14

3.45

< 62 family

2.57

1.88

3.56

2.31

p- value

.000

.000

.000

.000

Cohen’s  d

.500

.409

.512

.514

Notes:

1. Weighted data.

2. Elderly N = 3,165; < 62 disabled N = 1,597; < 62 family N = 2,648.

3. Excludes 14 percent of assisted housing cases where head < 62, not disabled and no children.

4. Cohen’s  d compares highest/lowest categories; values < 0.2 indicate virtually no difference.

42 The AHS does not identify housing for the elderly, families, or young disabled. To construct these categories, we assume a household head 62 years of age or older is living in elderly housing, that families with children 18 or younger and without a disabled member are living in family housing, and that nonelderly persons younger than 62, even if they are living with family members, are in housing for the disabled. This is admittedly a very blunt approach but is the best that can be done with the AHS data.

29

Table 16. Housing Quality Ratings of 2011 Assisted Housing Households by Structure Type

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

All assisted housing

2.49

1.94

3.51

2.24

Single-family

2.64

1.75

3.56

2.42

Multifamily ≤ 4 units

2.41

2.08

3.47

2.14

Multifamily 5+ units

2.45

1.97

3.50

2.20

p- value

.306

.021

.909

.118

Cohen’s  d

.055

.111

.017

.076

Notes:

1. Weighted data.

2. Cohen’s  d computed for all effects significant at .001 or less. Values < 0.2 indicate virtually no difference.

Tables 17 and 18 indicate that geography matters for assisted housing quality. A central city location is associated with worse assisted housing quality compared with a suburban or rural

location. Because assisted housing quality in suburbs and rural areas is extremely close, the small effect size in three of the four indices is driven entirely by the disparity between assisted housing quality in central cities versus other locations. Nearly 56 percent of assisted housing is located in central cities, and 65 percent of public housing units are located in central cities (see ). Table 18

shows that assisted housing quality is worst in the Northeast, with the South, Midwest, and West

following in descending order. While these three latter regions differ somewhat from each other

in the housing quality index ratings, these differences are far smaller than those between the

Northeast and the three other regions. The disparities are large enough to approach a medium

effect size in three of the four indices. Here, too, a larger share of public housing is located in the Northeast compared with the fraction of multifamily and of voucher units in the Northeast (see

table C1).

Table 17. Housing Quality Ratings of 2011 Assisted Housing Units by Metropolitan

Location

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Weighted

All assisted housing

2.49

1.94

3.51

2.24

Central city

2.93

2.18

4.08

2.67

Suburb

1.93

1.65

2.82

1.69

Rural

1.95

1.64

2.76

1.73

p- value

.000

.000

.000

.000

Cohen’s  d

.237

.168

.253

.245

Notes:

1. Weighted data.

2. Cohen’s  d computed for all effects significant at .001 or less. Values < 0.2 indicate virtually no difference.

30

Table 18. Housing Quality Ratings of 2011 Assisted Housing Units by Census Region

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

All assisted housing

2.49

1.94

3.51

2.24

Northeast

3.55

2.68

4.86

3.27

Midwest

2.04

1.63

2.92

1.83

South

2.29

1.73

3.27

2.00

West

1.73

1.49

2.53

1.55

p- value

.000

.000

.000

.000

Cohen’s  d

.414

.366

.451

.446

Notes:

1. Weighted data.

2. Cohen’s  d computed for all effects significant at .001 or less. Values < 0.2 indicate virtually no difference.

Household Characteristics. The household characteristic with the greatest variation in assisted housing quality is household size. As shown in table 19, large households of six persons or more, which constitute roughly 15 percent of assisted housing households, have the worst quality

ratings on all four indices, one-person households enjoy the best quality ratings, and two- to five-person households fall between these two poles. The weighted and factor analysis normative

standards ratings also follow a roughly monotonic improvement from the largest households to

single-person households. By contrast, the consumer rating and unweighted normative standards

indices display a larger gap between two- to five-person households and the largest households.

For all indices except the weighted normative standards index, the effect size exceeds the

threshold for a medium effect; for the weighted index,  d exceeds the threshold for a small effect.

Public housing has a larger fraction of very large households compared with the other two

programs (see table C1).

Table 19. Housing Quality Ratings of 2011 Assisted Housing Households by Household Size

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

All assisted housing

2.49

1.94

3.51

2.24

1 person

1.85

1.62

2.78

1.66

2–5 persons

2.85

2.13

3.90

2.55

6+ persons

4.12

2.67

5.49

3.87

p- value

.000

.000

.000

.000

Cohen’s  d

.651

.383

.604

.683

Notes:

1. Weighted data.

2. Cohen’s d   compares highest/lowest categories; values < 0.2 indicate virtually no difference.

Race and ethnicity also appear to have some association with assisted housing quality, with

White households enjoying better housing quality, on average, than non-White households.

These results are shown in table 20.  This disparity generally reaches a small effect size and, thus, is considerably weaker than the relationship of housing quality and household size. Non-White

31

households include Black people, Hispanic people, and people of other races and ethnicities.

Initial analysis including each race and ethnicity separately demonstrated that the main disparity in housing quality is between White households and non-White households. Table 21 shows no association between household income, here measured in quartiles, and housing quality. 43 The presence of a household member who is disabled tends to be associated with worse housing

quality, as shown in table 22.  However, the effect approaches but does not quite achieve the standard for a small effect. This weak result most likely occurs because elderly households and

families without a disabled member are combined into the “not disabled” category, as can be

seen by comparing this table with table 15, which separates “elderly” and “family.”

Table 20. Housing Quality Ratings of 2011 Assisted Housing Households by Race and

Ethnicity of Head

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

All assisted housing

2.49

1.94

3.51

2.24

White

1.92

1.61

2.82

1.69

Non-White

2.78

2.11

3.86

2.52

p- value

.000

.000

.000

.000

Cohen’s  d

.210

.163

.209

.229

Notes:

1. Weighted data.

2. Cohen’s d   compares highest/lowest categories; values < 0.2 indicate virtually no difference.

3. Non-White includes all races and ethnicities other than White.

Table 21. Housing Quality Ratings of 2011 Assisted Housing Households by Household

Income Quartiles

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

All assisted housing

2.49

1.94

3.51

2.24

Lowest

2.52

2.00

3.55

2.22

> 25–50%

2.51

1.98

3.60

2.37

> 50–75%

2.36

1.80

3.40

2.14

Highest

2.57

1.97

3.48

2.23

p- value

.569

.308

.742

.432

Cohen’s  d

.050

.066

.040

.062

Notes:

1. Weighted data.

2. Lowest quartile = ≤ $7,200; 25–50% = >$7,200 to $11,475; 50–75% = >$11,475 to $21,142; Highest = >$21,142

(2011$)

3. Cohen’s d   compares highest/lowest categories; values < 0.2 indicate virtually no difference.

43 We use quartiles to divide the income distribution of the sample into four equally sized groups, each representing 25 percent of the sample. Thus, the lowest quartile includes the 25 percent of the sample with the lowest incomes.

32

Table 22. Housing Quality Ratings of 2011 Assisted Housing Households by Disabled

Household Member

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

All assisted housing

2.49

1.94

3.51

2.24

No disability

2.23

1.77

3.16

1.98

With disability

2.94

2.23

4.11

2.69

p- value

.000

.000

.000

.000

Cohen’s  d

.171

.152

.192

.195

Notes:

1. Weighted data.

2. Designation of disabled household member based on response to American Housing Survey variable HDSB

(household has a disabled person), which is a recoded variable that is computed based on responses to disability questions for individual household members.

3. Cohen’s  d computed for all effects significant at .001 or less. Values < 0.2 indicate virtually no difference.

Multivariate Analysis

Assisted and Unassisted Housing Quality

In an effort to look comprehensively at the contribution of the array of attributes discussed thus far to the quality of the assisted housing stock, we estimated two sets of multiple regression

models. In these models, the housing quality index ratings are the dependent variables, and

housing, geographic, and household characteristics are the independent or explanatory variables

(also referred to as covariates) that are plausibly related to housing quality. For simplicity of

presentation, we use two of the four housing quality indices, the consumer rating index and the

factor analysis normative standards index, as the dependent variables to be explained.

The first set of models is limited to the assisted housing sample, and we include assisted housing program type as one of the explanatory variables. 44 Our goal is to determine whether, once multiple attributes are accounted for, the type of assisted housing program or any of the other

explanatory variables makes a meaningful contribution to housing quality. The second set of

models broadens the sample to include both assisted and unassisted housing. We first test

whether knowing a unit is assisted or unassisted is associated with a substantial difference in

housing quality. In a second test, we distinguish assisted housing by program type to estimate

whether a particular program has a substantively important relationship with housing quality

even if assisted housing, as a whole, does not. We estimate the models twice—once OLS, the

most common approach for estimating multivariate models, and a second time using a different

estimation approach, Negative Binomial Modeling. This second technique is appropriate when

the data are heavily skewed and when the distributions have considerable dispersion. Both

44 Because program type is a categorical variable with three values—public housing, multifamily, and voucher—we use voucher as the excluded reference category.

33

conditions apply in the present case, casting doubt on the utility of the OLS estimates. More than half of the samples report no problems using either index, and the standard deviation is larger

than the mean. 45

Table 23 displays the results. The coefficients shown, betas for the OLS regression and odds ratios for the negative binomial models, can be interpreted as effect sizes. None of the odds

ratios, the more appropriate coefficients for this analysis, achieves the standard for a small effect, despite several being statistically significant (Chen, Cohen, and Chen, 2010). 46

Table 23. Multivariate Models Predicting Housing Quality

Ordinary Least

Negative Binomial

Squares

Beta

p

Odds Ratio

p

Assisted housing only

(1) Consumer rating index

Public housing

– .002

.952

Multifamily (vouchers excluded)

– .030

+

.987

(2) Factor analysis index

Public housing

– .002

.924

Multifamily (vouchers excluded)

– .032

*

.962

Assisted and unassisted (≤ FMR) housing

(1) Consumer rating index

Assisted housing

– .032

**

.925

*

(2) Factor analysis index

Assisted housing

– .023

***

.956

(3) Consumer rating index

Public housing

– .011

+

.869

*

Multifamily

– .028

***

.942

Voucher (unassisted excluded)

– .020

**

.934

+

(4) Factor analysis index

Public housing

– .006

.894

*

Multifamily

– .024

***

.966

Voucher (unassisted excluded)

– .013

*

.970

Notes:

1. Total unweighted N = 25,808.

2. Weighted data.

3.  p- values: *** < .001, ** < .01, *< .05, + < .10.

4. Covariates are census region, metropolitan location, head’s age, race, gender and marital status, number of persons in household, whether anyone in household disabled, income quartile and structure type.

5. Because negative binomial models cannot use decimals, dependent variables multiplied by 100 and rounded.

6. Beta coefficients can be interpreted like Cohen’s  d, with values < 0.2 indicating virtually no difference. Odds ratio > 1.4

if greater than 1 and < .710 if less than 1 considered the threshold for a small effect (equivalent to a Cohen’s  d of 0.2).

7. FMR = Fair Market Rent.

45 Both indices have dispersion ratios of approximately 1.8 or a standard deviation that is nearly twice as large as the mean.

46 Chen, Cohen, and Chen (2010) demonstrate that odds ratios above 1.4 or below 0.71 are the equivalent of a Cohen’s  d at 0.2, a small effect.

34

Assisted Housing Subgroups With the Most Housing Quality Problems

Three demographic subgroups that are particularly likely to have housing quality problems

emerge from the foregoing analysis: nonelderly disabled households, non-White households, and

large households. In an attempt to further elucidate the characteristics most closely associated

with the housing quality of these three subgroups, we estimated a multivariate regression model

for each subgroup in which the consumer rating housing quality index is the dependent variable

and selected housing, geographic, and household characteristics are the independent variables.

We again rely on negative binomial estimation because of the skew and dispersion in the

dependent variables. Because the sample sizes of these subgroups are much smaller than those

used in the previous analysis, we can rely on both the statistical significance and the effect size for interpretation.

Table 24 summarizes the results. Location in the Northeast region is statistically significant for all groups and produces a quality rating that is more than twice as bad as that for the West. For

nonelderly disabled persons, being part of a large household (six or more persons) is also

significant and associated with worse housing quality. Voucher receipt is associated with

housing quality about 50 percent better than those living in multifamily housing, and living in a

large household is associated with a housing quality rating that is about 50 percent worse than

smaller households.

Table 24. Subgroup Regression Results on Consumer Rating Index

< 62, Disabled

Non-White

Large households

Odds

p

Odds

p

Odds

p

Ratio

Ratio

Ratio

Public housing

1.255

.929

1.449

+

Voucher

.679

**

.875

+

.808

Central city

1.089

1.445

***

2.848

***

Northeast

2.049

***

2.323

***

2.173

**

Midwest

.882

1.350

**

.888

South

1.184

1.397

***

1.421

White

.900

2.053

**

Disabled

1.432

***

2.422

***

Large household

1.433

**

1.387

**

N

1,082

3,663

261

Notes:

1. Negative binomial regressions using weighted samples

2. Excluded categories: multifamily housing and western region. Central city, White, disabled, and large households are all dichotomous variables

3.  p- values: *** < .001, ** < .01, * < .05, + < .10.

4. Bold = Odds ratio > 1.4 if greater than 1 and < .710 if less than 1 considered the threshold for at least a small effect (equivalent to a Cohen’s  d of 0.2).

For non-White households, beyond living in the Northeast, both a central city location and

having a disabled household member is significantly associated with worse housing quality. In

both cases, the consumer housing quality rating is about 50 percent worse than the respective

excluded category (that is, non-central-city location and no disabled person in the household).

35

The large household model produces the largest number of covariates that are statistically

significant and substantively meaningful. Beyond living in the Northeast, the largest effect is

living in a central city, which is associated with a nearly three times worse housing quality rating than living in a suburban or rural area. The next largest effect is if a nonelderly disabled person is a member of the household, which is associated with more than two times worse housing quality.

Living in the South (compared with living in the West) and living in public housing (compared

with living in multifamily housing) each worsens the housing quality rating by about 50 percent.

Assisted Housing Quality and Fair Market Rents

One policy question is how well the housing quality rating for assisted housing aligns with the

FMR, now generally set at the 40th percentile of rents in each housing market (typically a

metropolitan area). One objective in setting the FMR at a particular point in the distribution of

rents is the household’s ability to find physically decent rental housing at or below the FMR

threshold. We explore this alignment by examining the relationship between the housing quality

rating and the relative housing cost of the assisted housing sample of households. The relative

housing cost is calculated by adding rent and utility costs and dividing by the FMR. We then

divide the housing cost scale into equal units (for example: 40 to 45 percent of the FMR, 45 to 50

percent of the FMR, and so on) so that the FMR (defined here as 100 percent of the FMR) sits in

the middle of the distribution and can be specifically designated.

Figure 2 graphically displays the results for the consumer rating housing quality index. 47 The most important result is that housing quality appears to be maximized roughly at the FMR, as

indicated by the vertical line. The graph also suggests that the worst housing quality occurs at

about the 24th percentile of rent (note the peak at approximately the 60th percentile; 60 x 40 =

24). In some cases, HUD approves payment standards up to 120 percent of the FMR, such as

when a disabled household member requires reasonable accommodations in the voucher

program. Figure 2 shows no appreciable difference in housing quality at 120 percent of the FMR.

The same analysis using the factor analysis normative standards index produces a very similar

pattern.

47 We topcoded consumer rating index scores at the 99th percentile to avoid problems with outliers. We also limit the housing cost scale to range from the 5th to the 95th percentile of cases, again to avoid outlier problems at both ends of the scale.

36

Figure 2. Consumer Rating Index by Relative Cost

3.0

2.5

x

inde 2.0

1.5

er rating 1.0

Consum 0.5

0.0

50%

75%

FMR

5%

0%

12

15

Housing cost as percent of FMR

Notes:

1. Housing cost = rent + utilities (obtained from HUD’s Housing Affordability Data System).

2. Housing cost relative to Fair Market Rent (FMR) = (Housing Cost / FMR) * 100.

3. The consumer rating index topcoded at the 99th percentile to avoid problems with outliers.

4. FMR scale excludes top and bottom 5 percent to avoid outliers at both ends of this distribution.

Persistence of Housing Quality Problems in Assisted Housing

Although housing quality problems are rare in assisted housing, one objective of the housing

inspection and resolution regulations is to identify and address these problems in a timely

manner. To shed some light on the timeliness of repairs and its opposite, the persistence of

problems, we examine changes in reports of a problem for each of the 33 individual items that

comprise the housing quality indices between the 2011 and 2013 AHS.  Table 25 displays the full pattern of changes over the 2-year period (problem reported in both years; reported in 2011, not

2013; not reported in 2011 but reported in 2013; and not reported in either year). The table

demonstrates, again, that the large majority of respondents report none of these problems in

either year (0,0 column). The smallest group in terms of prevalence is persistent problems; that is 1,1—a problem that is reported in both 2011 and 2013. These data suggest that the prevalence of

persistent problems, defined as housing quality problems that are reported to be present in both

years, is very low.

The 1,0 category (present in 2011, not present in 2013) addresses the timeliness of repairs. These rates, while relatively modest, are nonetheless considerably larger than those for persistent

problems (the 1,1 column). This suggests that problems are more likely to be addressed than to

persist over a 2-year period. The 0,1 category (not present in 2011, present in 2013) provides

further evidence of the low prevalence of these individual housing quality problems in assisted

housing.

37

Table 25. Persistence of Housing Quality Problems in Assisted Housing Units, 2011 and

2013

1,1

1,0

0,1

0,0

1.

Not all rooms have plugs

0.0

1.3

1.4

97.3

2.

Ever blown fuse

0.8

5.6

3.7

89.8

3.

Exposed wiring

0.0

2.6

2.0

95.4

5.

Unvented room heaters

0.1

0.2

0.1

99.6

6.

No heating equipment

0.2

0.0

0.0

99.8

7.

Use stove/oven for heat

0.1

0.0

0.1

99.8

8.

Ever heating breakdown

0.5

3.6

3.0

92.9

9.

Unit cold 24+ hours last winter

3.7

10.4

7.2

78.6

10.

Cold: utility interruption

0.1

1.2

1.0

97.7

11.

Cold: inadequate heating

0.6

2.4

1.2

95.7

12.

Cold: inadequate insulation

0.2

2.0

1.4

96.4

13.

Cold: other reason

0.1

2.2

1.6

96.0

14.

Roof leak last 12 months

0.5

2.8

2.3

94.4

15.

Leak in wall/closet

0.4

3.1

2.3

94.2

16.

Leak in basement

0.5

0.8

0.7

98.0

17.

Leak other source

0.1

1.3

0.7

97.9

18.

Leaking pipes

0.6

4.9

4.0

90.6

19.

Leaking plumbing fixture

0.1

2.2

3.2

94.5

20.

Leak unknown source

0.3

4.7

2.2

92.8

21.

Crack in wall

2.1

5.6

5.8

86.5

22.

Holes in floor

0.1

2.2

1.5

96.2

23.

Peeling paint

0.7

3.3

2.7

93.3

24.

Signs of rodents

1.0

4.7

2.8

91.4

25.

Signs of rats last

0.1

0.8

0.9

98.1

26.

Signs of mice last

4.8

8.7

5.3

81.2

27.

Signs of cockroaches

2.0

4.1

3.8

90.1

29.

Toilet ever broke

0.3

3.2

2.7

93.8

30.

Share plumbing facility

0.1

2.2

1.1

96.6

31.

Incomplete kitchen

0.2

4.6

3.8

91.3

32.

Ever sewage breakdown

0.1

1.4

1.4

97.2

33.

No working elevator

4.0

2.2

0.8

92.9

Notes:

1. Unweighted sample = 5,362 assisted housing cases in both 2011 and 2013 American Housing Survey (AHS) 2. Weighted data.

3. “1,1” = problem reported in 2011 and 2013 AHS.

4. “1,0” = problem reported in 2011 but not in 2013 AHS.

5. “0,1” = problem reported in 2013 but not in 2011 AHS.

6. “0,0” = problem not reported in 2011 or 2013 AHS.

7. “Unit does not have electricity” (4) and “Incomplete plumbing” (28) not shown because no problems reported in 2011 or 2013 for this sample.

Because a change in household or in the household respondent could affect housing quality

reporting, we conducted additional analysis (not shown) on the effect of household reporter

status on the change in the consumer rating index between 2011 and 2013. The change in the

index rating is small and is unaffected by the household reporter (< .1 of a standard deviation).

Promptness of Repairs in Assisted Housing

We can also gain insights into the timeliness of repairs from a set of questions asked in the 2011

AHS about the promptness and effectiveness of repairs to rental housing units and whether

38

owners were polite and considerate during the repair process. 48 We compared responses from assisted and comparable unassisted housing and find only weak effects. These results are

summarized in table 26. The large majority of residents in assisted and unassisted housing report that both major and minor repairs are started soon enough, solved quickly, and handled politely.

Table 26. Comparison of Repair Reports on Assisted Housing and Comparable Unassisted

Housing

Assisted

Unassisted

p-

Cohen’s

Housing

Housing

Value

d

Major repairs

Start repairs soon enough

77.8

79.6

.008

.043

Solve repairs quickly

82.0

83.8

.002

.049

Handled politely

90.5

92.2

.000

.061

Minor repairs

Start repairs soon enough

79.9

81.9

.001

.052

Solve repairs quickly

84.8

86.6

.001

.053

Handled politely

91.1

92.5

.002

.050

Notes:

1. Comparable unassisted housing based on rents at or below HUD’s Fair Market Rent.

2. Cohen’s  d computed for all effects significant at .001 or less. Values < 0.2 indicate virtually no difference.

This section on promptness, and the preceding one on persistence, lend support to the biennial

inspections in the voucher program and the biennial and triennial inspections for standard and

high performers, respectively, in the public housing program. 49

Discussion

The substantial literature on housing quality demonstrates both the importance and the

challenges of conceptualizing and measuring housing quality. The growing interest in how

housing matters—primarily in the low-rent unassisted housing stock—and the ongoing concerns

about housing quality standards in the assisted stock, make this an opportune time to revisit

housing quality.

In this paper, we review the relevant literature, develop alternative housing quality indices, test their validity, and apply them to both the assisted and comparable unassisted housing stock. We

focus on indicators of physical integrity of housing systems and exclude measures that are more

likely to reflect residents’ housekeeping or behaviors.

48 The questions, which are repeated for “major maintenance or repairs” and “minor maintenance or repairs” are: (1) Do they start quickly enough? (2) Do they solve the problem quickly once they start? (3) Are they polite and considerate of your home?

49 The one exception is the inspection of the unit when it changes hands from one household to another.

39

Because there is no consensus about the features of the housing bundle that should be included in

the definition of a dwelling’s quality and how each should be weighted in determining overall

quality, we rely on three external criteria first suggested by research on the Experimental

Housing Allowance Program (EHAP; Merrill, 1980): market value, consumer rating, and

normative standards. We test the market value criterion with a hedonic approach. The consumer

rating criterion identifies the dwelling features most associated with a resident’s assessment of

the dwelling as a good place to live regardless of what the market price of these features might

be. This criterion is consistent with the renewed interest by economists in happiness and

subjective well-being. The normative standards criterion reflects community concerns and policy

decisions such as building codes. Our main data are the 2011 and 2013 national AHS. Both

surveys provide augmented national samples and assisted housing samples, and assisted housing

is identified by address matches to HUD administrative data, not respondent self-report.

Despite its intuitive appeal, the market value criterion performs poorly. This likely occurs

because the national sample comprises widely varying housing markets, and our controls for

market attributes are relatively coarse. Another explanation is that the individual dwelling quality measures may not be the main drivers of rents, as suggested by Merrill (1980). Therefore, we

drop this market value criterion from further analysis. We construct one consumer rating index

and three indices using the normative standards criterion: a weighted index based on a previous

analysis for HUD’s Office of Policy Development and Research by Eggers and Moumen

(2013b); an unweighted index; and an index with weights derived from a factor analysis. For the

consumer rating index, we use the odds ratios from ordered logistic regressions as the weights.

Consistent with much past AHS housing quality research, the prevalence rate of almost all

problems is very low, with most dwelling units having no problems. There is notable overlap

between the measures that are the strongest predictors of the consumer ratings index and the

factor analysis normative standards index. These are presence of rodents, cold dwelling unit,

holes in the floor, peeling paint, and cracks in the walls. Both the convergent validity and

predictive validity of the four indices are strong.

Although the four indices we construct are similar to each other, the consumer ratings index and

the factor analysis normative standards index emerge as consistently the strongest. Thus, the

weighted index, which applied the weights developed by Eggers and Moumen (2013b), while

reasonable on its face, is not quite as good as these two other approaches. Our results also call

into question the applicability of hedonic models using individual measures of physical

inadequacies as predictors for rental properties, as is done in Emrath and Taylor (2012). Merrill

(1980) raised this same issue in her EHAP analysis.

We find that the quality of assisted housing is comparable to the quality of unassisted housing.

This conclusion applies whether we limit the unassisted stock to units with rents at or below the

FMR, to all unassisted rental units, or to housing units emerging from statistically matching the

assisted and unassisted units. Consistent with the sound quality of most of the assisted housing

stock is the very low incidence of housing problems persisting over 2 years, 2011 and 2013, and

the promptness of repairs.

40

The type of assisted housing program does not appear to have an appreciable effect on housing

quality. Although housing quality index ratings are always worst for public housing and best for

multifamily housing, the effect size falls below the threshold for a small effect. The quality of

assisted housing located in central cities and in the Northeast region is considerably lower than

counterpart locations (that is, suburban or rural areas; South, Midwest, and West regions). Large

households of six persons or more have the worst assisted housing quality while one-person

households enjoy the best quality ratings. This is consistent with our finding that elderly headed households enjoy better housing quality than families. But it is households that include a

disabled member that have much lower housing quality than either elderly households or

families without a disabled member. Non-White households also are more likely than White

households to live in lower-quality assisted housing. Thus, three household subgroups emerge as

particularly likely to live in assisted housing with lower than average housing quality: nonelderly disabled households, non-White households, and large households. More detailed analysis

revealed that disabled persons enjoy better housing quality using a voucher compared with living

in multifamily housing. For large households, living in the South and living in public housing are associated with considerably worse housing quality.

This research provides hard evidence supporting the current 40th percentile of rents definition of the FMR. We find that the FMR is set at a level that is roughly at the inflection point for

maximizing assisted housing quality as measured by our housing quality indices.

Overall, these positive findings demonstrating that the quality of the assisted housing stock

suggest that the current inspection and quality control systems appear to be achieving the goal of providing physically adequate housing to assisted housing residents. They also lend support to

the shift to biennial inspections in the voucher program and the biennial and triennial inspections for standard and high performers, respectively, in the public housing program. The lack of

persistent problems over a 2-year period and the promptness of repairs further suggest that

proposals to streamline inspections to encourage participation in the voucher program by private

owners of rental properties should be seriously considered. 50 The findings reported may also be useful to HUD as it finalizes plans for a demonstration program to test a new approach to

physical inspections including a single inspection protocol for public housing and voucher

units. 51

We view this research as one step along the path toward improving our understanding of housing

quality. One important enhancement of this work is expanding the measures to include additional

aspects of the full housing bundle, particularly neighborhood features. This could be done by

linking the AHS data via confidential geocodes to census tract data and an array of

administrative data at the neighborhood level. Another extension would be to compare these

results with housing inspection scores from HUD’s administrative data (that is, the Public

50 See H.R. 3700, Housing Opportunity Through Modernization Act.

51 See the joint Explanatory Statement accompanying the Consolidated Appropriations Act, 2016 (Pub. L. 114-113).

41

Housing Assessment System and Real Estate Assessment Center housing inspection ratings for

public housing and multifamily housing, respectively). At the more conceptual end of the

continuum, this report does not focus on what measures  should be included in a measure of

housing quality, only on how well the measures included in the AHS appear to be reliable and

valid and form a coherent index. A consideration of what measures currently missing from the

AHS should be included in the future is beyond the scope of the current effort but worth serious

attention.

42

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Housing Tax Credit Program by Looking at the Tenants?” New York: New York University,

Furman Center for Real Estate and Housing Policy.

Preacher, Kristopher, Guangjian Zhang, Cheongtag Kim, and Gerhard Mels. 2013. “Choosing an

Optimal Number of Factors in Exploratory Factor Analysis: A Model Selection Perspective,”

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Shroder, Mark. 2001. “Moving to Opportunity: An Experiment in Social and Geographic

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———. 2002. “Does Housing Assistance Perversely Affect Self-Sufficiency? Review Essay,”

Journal of Housing Economics 11 (4): 381–417.

44

Thibodeau, Thomas. 1995. “House Price Indices from the 1984–1992 MSA American Housing

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45

Appendix A: Tables

Table A1. Selection of Analysis Sample: Units Excluded by Type or Category

2011 AHS

2013 AHS

Total units in sample

186,448

84,355

URE1, vacant or noninterviews

51,530

24,258

Occupied unit interviews

134,918

60,097

Occupied unit interviews:

Mobile home

4,736

2,282

Other type of housing unit

850

160

House/apartment/flat

129,332

57,655

House/apartment/flat:

Owner-occupied

78,291

34,004

Occupied without rent

1,739

809

Rental unit

49,302

22,842

Rental units:

Unassisted

40,830

16,602

Assisted

8,472

6,240

Notes:

1. URE = usual residence elsewhere (for example, vacation home).

2. AHS = American Housing Survey.

A-

1

Table A2. Polychoric Correlation Matrix, Housing Quality Measures

Plugs

Fuses

Wiring

No Elec  Unvented  No Heat

Oven

# Heat

Cold 24

Util

Cap

Insul

Other

Plugs

1.000

Fuses

0.061

1.000

Wiring

0.417

0.068

1.000

No elec

0.516  – 0.176

0.603

1.000

Unvented

0.118

0.030

0.115

– 0.766

1.

000

No heat

0.054

0.044

0.096

– 0.743

1.

000

Oven

0.095  – 0.093

0.266

– 0.

797

– 0.781

1.

000

# Heat

0.184

0.102

0.196

– 0.

828

0.047

1.

000

Cold 24+

0.180

0.105

0.167

0.262

0.117

0.

012

0.836

1.

000

Cold util

– 0.069

0.050  – 0.037

– 0.760

– 0.381

– 0.823

0.086

0.775

1.000

Cold cap

0.248

0.103

0.184

– 0.793

0.223

0.239

0.131

0.798

0.214  1.

000

Cold insul

0.147

0.092

0.161

0.133

0.205

0.032

0.266

0.785

0.214  0.643

1.

000

Cold other

0.128

0.062

0.181

– 0.783

0.096

– 0.213

0.169

0.792

0.172  0.228

0.306

1.000

Leak roof

0.142

0.083

0.118

– 0.849

0.040

– 0.

012

0.172

0.273

0.262

0.112  0.279

0.227

0.254

Leak wall

0.178

0.081

0.122

– 0.262

0.057  – 0.850

0.282

0.261

0.075  0.255

0.267

0.183

Leak base.

– 0.039

0.067

0.051

0.

268

– 0.150

– 0.383

.

0.133

0.175

0.132  0.100

0.189

0.014

Leak other

0.054

0.055

0.028

– 0.762

– 0.001

– 0.085

0.135

0.223

0.166

0.077  0.172

0.135

0.138

Leak pipe

0.107

0.078

0.142

– 0.837

0.085

– 0.067

0.173

0.293

0.261

0.100  0.294

0.295

0.146

Leak fix.

0.180

0.078

0.087

– 0.781

– 0.024

0.161  – 0.255

0.244

0.226

0.010  0.167

0.295

0.165

Leak unk

0.093

0.065

0.080

– 0.833

– 0.089

– 0.051  – 0.004

0.258

0.216

0.048  0.232

0.187

0.212

Crack

0.285

0.120

0.182

0.107

0.209

0.040  – 0.156

0.381

0.383

0.159  0.350

0.364

0.271

Hole

0.266

0.093

0.274

0.269

0.263

0.200

0.046

0.304

0.345  – 0.106  0.374

0.340

0.227

Paint

0.227

0.104

0.209

– 0.791

0.140

0.040

0.011

0.352

0.377

0.109  0.373

0.368

0.325

Rodents

0.183

0.090

0.206

0.122

0.191

0.170

0.232

0.357

0.367

0.128  0.385

0.265

0.368

Rats

0.071

0.054

0.229

– 0.760

0.267

0.202

0.263

0.229

0.306

0.073  0.300

0.231

0.238

Mice

0.114

0.090

0.110

0.298

0.182

0.027

0.135

0.329

0.305

0.123  0.326

0.267

0.216

Roaches

0.121

0.070

0.180

0.173

0.335

0.192

0.309

0.288

0.001  0.302

0.270

0.252

Inc. plumb

0.065  – 0.012

0.242

0.232

0.314

0.460

0.044

0.082  – 0.037  0.075  – 0.855

0.218

# Toilet

0.166

0.094

0.196

– 0.

792

0.035

0.175  – 0.846

0.246

0.254

0.001  0.278

0.265

0.192

Share bath

0.193  – 0.011

0.175

– 0.800

0.006

0.032  – 0.045  – 0.042

– 0.020  – 0.140  0.034

0.114  – 0.074

Inc. kitchen

0.116

0.016

0.094

– 0.114

– 0.054

0.074

0.150

0.005

0.023  – 0.042  0.140

0.060

0.052

# Sewer

0.080

0.093

0.136

– 0.790

0.241

0.135

0.317

0.252

0.037  0.193

0.264

0.137

Mold

0.149

0.051

0.195

0.244

– 0.030

0.000  – 0.13

2

0.305

0.414

0.165  0.208

0.235

0.203

Stair

0.285

0.066

0.201

0.088

– 0.109

0.129

0.231  – 0.299  0.090

0.096

0.197

A-

2

Table A2. Polychoric Correlation Matrix, Housing Quality Measures (continued)

Roof

Wall

Base

Lk: Oth

Pipe

Fixture

Lk: Unk

Crack

Hole

Paint

Rodents

Rats

Mice

Leak roof

1.000

Leak wall

0.351

1.

000

Leak base.

0.289

0.335

1.

000

Leak other

0.204

0.310

0.273

1.

000

Leak pipe

0.211

0.235

0.108

0.251

1.

000

Leak fix.

0.152

0.263

0.143

0.147

0.220

1.

000

Leak unk

0.099

0.192

0.095

0.246

– 0.021

– 0.061

1.

000

Crack

0.379

0.317

0.238

0.256

0.346

0.306

0.191

1.

000

Hole

0.316

0.236

0.239

0.185

0.336

0.287

0.155

0.677

1.

000

Paint

0.427

0.356

0.247

0.239

0.343

0.231

0.270

0.590

0.527

1.

000

Rodents

0.313

0.263

0.228

0.207

0.263

0.187

0.179

0.452

0.437

0.425

1.

000

Rats

0.218

0.210

0.012

0.233

0.218

0.253

0.080

0.369

0.382

0.303

0.681

1.

000

Mice

0.271

0.209

0.318

0.200

0.226

0.176

0.117

0.356

0.359

0.344

0.851

0.296

1.

000

Roaches

0.255

0.226

– 0.097

0.199

0.243

0.240

0.254

0.355

0.391

0.379

0.528

0.406

0.340

Inc. plumb

0.021

0.058

– 0.309

– 0.189

– 0.113

– 0.194

0.034

0.121

0.220

0.091

0.282

0.197

0.170

# Toilet

0.254

0.229

0.116

0.181

0.233

0.418

0.100

0.345

0.283

0.326

0.329

0.247

0.204

Share bath

0.010

– 0.013

– 0.050

0.139

0.019

0.015

– 0.175

0.054

0.002

0.098

0.057

0.065

0.025

Inc. kitchen

0.039

0.102

– 0.128

– 0.027

0.043

– 0.024

– 0.018

0.076

0.106

0.044

0.089

0.089

– 0.022

# Sewer

0.235

0.215

0.218

0.153

0.249

0.435

0.216

0.276

0.250

0.280

0.247

0.192

0.190

Mold

0.263

0.345

0.299

0.229

0.235

0.218

0.214

0.365

0.357

0.412

0.328

0.239

0.256

Stair

0.266

0.127

0.307

– 0.164

0.096

– 0.064

0.092

0.217

0.109

0.094

0.173

0.107

0.172

Roaches

Plumb

# Toilet

Bath

Kitchen

# Toilet

Mold

Stairs

Roaches

1.000

Inc. plumb

0.204

1.

000

# Toilet

0.315

– 0.131

1.

000

Share bath

– 0.005

0.221

0.034

1.

000

Inc. kitchen

0.114

0.437

0.112

0.002

1.

000

# Sewer

0.327

0.086

0.662

0.002

0.063

1.

000

Mold

0.322

0.001

0.225

– 0.154

0.058

0.200

1.

000

Stair

0.041

– 0.064

0.100

– 0.172

0.114

0.109

0.266

1.

000

A-

3

Table A3. Distribution of Housing Quality Indices

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

N

40,654

40,654

40,654

40,654

Mean

2.03

1.62

2.88

1.77

Median

0

0

0

0

Standard Deviation

3.80

2.88

4.58

3.30

Skewness

3.630

3.239

2.645

3.136

Kurtosis

20.669

17.317

10.077

13.876

Percentiles

10

0

0

0

0

20

0

0

0

0

30

0

0

0

0

40

0

0

0

0

50

0

0

0

0

60

1.330

1.124

2.941

.604

70

1.887

1.685

2.941

1.683

80

3.360

2.809

5.882

2.896

90

6.025

5.618

8.823

5.636

95

9.424

7.303

11.765

8.491

99

18.201

13.483

20.588

15.595

Notes:

1. Weighted data.

2. Skewness > 1 indicates non-normally distributed distribution.

3. Kurtosis > 3 indicates more cases than expected in the tail of the distribution.

A-

4

Appendix B: Healthy Homes Module

The 2011 American Housing Survey includes a topical module, Healthy Homes, designed to

collect information on hazards and safety features in a home. Most of the questions in this

module are not applicable to this study because they pertain either to a person’s health (for

example, does anyone in the household have asthma) or to a household’s behavior (for example,

are hazardous materials stored out of children’s reach), not housing quality  per se. We limit this discussion to the three questions that most likely pertain to housing unit quality: presence of

mold; broken steps; and missing railings on stairs.

Our analysis of these items strongly suggests that had we been able to include these three

measures in the analysis, results would not have been qualitatively different, as summarized in

tables A3 and B1. In particular:

1.  The polychoric correlation between presence of mold and several other items included in the

33 housing quality measures used in this paper’s analysis is ≥.30, reasonably large. These

items are: unit was cold for 24 hours or more; cracks in the walls; holes in the floor; presence

of rodents; and seeing roaches daily.

2.  Including the three Healthy Homes items along with the 33 individual quality measures in the

factor analysis still yields a single “housing quality” factor.

3.  The correlations between the presence of mold and each of the four housing quality indices

are 0.23 with the weighted index, 0.28 with the unweighted index, 0.28 to the factor analysis

index, and 0.28 with house rating.

The correlations are much smaller between each of the four indices and the steps and stairs

items, primarily because very few units report either of these problems. However, rental units

that report any of the three Healthy Homes problems have much higher scores on all four indices

than units that do not report these problems. The index scores are roughly twice as high for units with steps or stairs problems and more than three times higher for units with mold.

B-1

Table B1. Relationship between Indices and Healthy Homes Measures

Mold

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

No mold

1.800

1.476

2.593

1.565

With mold

6.502

4.490

8.406

5.717

p- value

(.000)

(.000)

(.000)

(.000)

Broken Steps

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

No mold

2.023

1.617

2.869

1.761

With mold

5.036

3.513

6.409

4.450

p- value

(.000)

(.000)

(.000)

(.000)

Broken Stair Rail

Consumer

Normative Standards Indices

Rating Index

Weighted

Unweighted

Factor Analysis

No mold

1.995

1.602

2.836

1.736

With mold

4.153

3.003

5.359

3.675

p- value

(.000)

(.000)

(.000)

(.000)

Notes:

1. Weighted data.

2. Mean value for each group.

B-2

Appendix C: Characteristics of Assisted Housing by Program Type

Table C1. Percent Distribution of Characteristics of Assisted Housing for Each Program

Type

Public Housing

Multifamily

Voucher

Total

Region

Northeast

34.0

28.0

27.7

29.0

Midwest

15.8

27.7

19.0

20.8

South

35.6

30.1

27.3

29.7

West

14.5

14.2

26.0

20.5

Metropolitan location

Central city

65.0

56.7

51.1

55.3

Suburban

16.6

27.0

34.0

28.7

Rural

18.2

16.4

14.9

15.9

Structure type

Single-family

23.7

8.8

30.2

23.0

Multifamily ≤ 4 units

27.9

13.6

22.8

21.2

Multifamily 5+ units

48.4

77.5

47.0

55.8

Household type

Elderly

21.8

45.7

23.5

29.4

< 62, disabled

20.7

15.2

21.5

19.6

< 62, family

41.9

27.8

39.0

36.4

< 62, no children

15.6

11.4

16.0

14.6

Race and ethnicity

White

28.9

37.0

33.8

33.7

Non-White

71.1

63.0

66.2

66.3

Household size

1 person

38.0

54.3

36.6

41.8

2–5 persons

55.8

42.9

58.2

53.5

6+ persons

6.2

2.8

5.3

4.7

Disabled household

member

Not disabled

67.0

58.9

64.8

63.6

Disabled

33.0

41.1

35.2

36.4

C-1

Document Outline

- Cover

- Title Page

- About MDRT

- Contents

- List of Tables

- List of Figures

- Executive Summary

- Introduction

- Literature Review

- Housing Quality Measurement and Data Collection Methods

- AHS Measurement of Housing Quality

- Quality of Assisted Housing

- Research Approach

- Data

- Samples

- Methods

- Results

- Housing Quality Indices

- Market Value Index

- Consumer Rating Index

- Normative Standards Index

- Index Validity

- Convergent Validity

- Predictive Validity

- Assisted Housing Quality

- Assisted and Unassisted Housing Quality

- Subgroup Variation in Assisted Housing Quality

- Multivariate Analysis

- Assisted and Unassisted Housing Quality

- Assisted Housing Subgroups With the Most Housing Quality Problems

- Assisted Housing Quality and Fair Market Rents

- Persistence of Housing Quality Problems in Assisted Housing

- Promptness of Repairs in Assisted Housing

- Discussion

- References

- Appendix A: Tables

- Appendix B: Healthy Homes Module

- Appendix C: Characteristics of Assisted Housing by Program Type

Table of Contents

Cover

Title Page

About MDRT

Contents

List of Tables

List of Figures

Executive Summary

Introduction

Literature Review

Housing Quality Measurement and Data Collection Methods

AHS Measurement of Housing Quality

Quality of Assisted Housing

Research Approach

Data

Samples

Methods

Results

Housing Quality Indices

Market Value Index

Consumer Rating Index

Normative Standards Index

Index Validity

Convergent Validity

Predictive Validity

Assisted Housing Quality

Assisted and Unassisted Housing Quality

Subgroup Variation in Assisted Housing Quality

Multivariate Analysis

Assisted and Unassisted Housing Quality

Assisted Housing Subgroups With the Most Housing Quality Problems

Assisted Housing Quality and Fair Market Rents

Persistence of Housing Quality Problems in Assisted Housing

Promptness of Repairs in Assisted Housing

Discussion

References

Appendix A: Tables

Appendix B: Healthy Homes Module

Appendix C: Characteristics of Assisted Housing by Program Type