Housing Affordability and Child Well-Being

Abstract

We test three hypotheses about the role of housing affordability in child cognitive achievement, behavior, and health. Using longitudinal data from the Panel Study of Income Dynamics, we apply both propensity-score matching and instrumental-variable modeling as identification strategies and test the sensitivity of results to omitted variable bias. The analysis reveals an inverted-U-shaped relation between the fraction of income devoted to housing and cognitive achievement. The inflection point at approximately 30% supports the long-standing rule-of-thumb definition of affordable housing. There is no evidence of affordability effects on behavior or health.

Keywords::

• housing affordability
• child well-being
• low-income

Acknowledgments

The authors gratefully acknowledge financial support from the MacArthur Foundation; insightful comments from Steve Raudenbush, Tama Leventhal, and Peter Zorn; participants in the Homer Hoyt Institute; Greg Duncan, Warren Lambert, Liz Stuart, Mujde Erten, Joe Terza, Amy Davidoff, and Dan Naiman; programming assistance by David Kantor and Marcella Sapun; and research assistance by Nina Castells and Amy Robie.

Notes

^1. Authors' calculations based on the 2010 American Community Survey's 1 - year sample (U.S. Bureau of the Census, 2012).

^2. The main analysis results are provided in tables. All other analyses and results discussed are documented in a technical appendix available from the authors.

^3. This hypothesis addresses a major criticism of the housing-cost-burden measure, namely, that it does not account for differences in housing quality (Belsky, Goodman, & Drew, 2005; Bogdon & Can, 1997; Goodman, 2001; Hulchanski, 1995).

^4. This hypothesis may also be extended to the social environment associated with more-affordable versus less-affordable locations. In this case, a mechanism such as collective socialization or contagion (e.g., Jencks & Mayer, 1990) would result in beneficial effects for poor children. Although this hypothesis has never been tested, qualitative research on children living in poor, inner-city neighborhoods compared with more affluent, suburban neighborhoods suggests that children benefit more from the institutional resources available in the suburban settings than from social interaction with more affluent neighbors (Keels, 2008).

^5. This represents 84% of families interviewed in 1997 and 74% of families eligible for the 1997 wave.

^6. Children were ages 0–12 in the 1997 CDS and 5–17 in the 2002 CDS. Thus, the period of observation for the oldest child in this analysis is 1986–2001, with outcomes measured in 2002.

^7. Data are interpolated linearly between decennial years, and state estimates are used as proxies for nonmetropolitan areas.

^8. Only a minority of households migrate from one housing market to another. In 2010, for example, roughly 20% of the population made intermetropolitan moves in the prior year (U.S. Bureau of the Census, 2010b). Excluding intermetro movers results in the loss of only 26% of cases. Intermetro movers have higher incomes, more education, and lower average housing-cost burdens than do nonmovers and intrametro movers, supporting concerns about self-selection effects that could bias results if these cases were included in the analysis.

^9. Chow test results are available in a technical appendix available from the authors. Because the PSID-CDS is nationally representative, some fraction of the children in this sample lived in assisted housing. We examined whether relationships differed when the assisted housing subgroup was excluded using a special version of the PSID in which PSID addresses between 1968 and 1995 have been matched to assisted-housing addresses (see Newman & Schnare, 1997, for a description of the PSID-Assisted Housing Database). The fraction of cases with at least 1 year of assisted-housing receipt is 11.4%. Results do not differ substantively when we exclude these cases.

^10. Raudenbush, Jean, and Art (2011), for example, compute propensity scores on a measure of school mobility that, while bounded, is essentially continuous.

^11. The number of propensity strata required to obtain balance (i.e., absence of a statistically significant relationship between each covariate and housing-cost burden controlling for propensity stratum) is determined in an iterative process, varying the number of strata until the best balance is obtained on all covariates. The cognitive-outcomes sample required 19 strata to obtain balance on all covariates, and the behavior and health sample required 15 strata.

^12. We thank one of the reviewers for highlighting this double robustness.

^13. While some argue that linearity restrictions are not necessarily a major concern with IV models (e.g., Angrist & Pischke, 2009), others, such as Leamer (1983), come to the opposite conclusion. Recent work by Mogstad and Wiswall (2010) and Løken, Mogstad, and Wiswall (2012), for instance, demonstrates that IV and fixed-effect models are sensitive to functional form assumptions. It is also possible to estimate nonlinear IV models such as ours using extensions of the standard two-stage predictor substitution (2SPS) method because the model is linear in the parameters, although this would require finding additional instruments for the power terms. However, Terza et al. (2008) find that the 2SRI method is consistently superior to the 2SPS in estimating nonlinear IV models, and this is therefore the approach we have chosen.

^14. The BPI is skewed because most children have few, if any, problems. However, logging the BPI has no effect on results. For ease of interpretation, we present the OLS estimates of the untransformed BPI.

^15. Models estimated using an ordered logit instead of OLS produced similar results (see technical appendix available from authors). We present OLS estimates for ease of interpretation.

^16. Roughly 96% of caregivers rated the child's health as “excellent,” “very good,” or “good.” Therefore, reverse causality (poor health affecting family income and housing cost) is unlikely.

^17. Missing data arises for various reasons such as the age thresholds for cognitive questions (6 or older for W–J broad reading) and limitations on distances that PSID-CDS interviewers were authorized to travel to interview respondents (Hofferth et al., 1997).

^18. We imputed utility costs for renters in years in which none or only a subset of utility costs were collected by the PSID. Respondents are asked how much rent they pay per month, not the monthly rent of the unit. This should avoid confusion for those receiving housing assistance where part of the monthly rent is covered by a government subsidy. (There are no instances of families that were “no cash renters” across childhood in this sample. Any year with zero rent is averaged into the rent calculation across childhood years; see technical appendix available from authors for details.) We also include the category “other lodging expenses,” a miscellany of expenses (e.g., special security fees in condos and co-ops) that are relatively rare and nominal.

^19. Previous research indicates that breastfeeding has positive effects on child development (Kramer, 2005; Lawrence, 2005; Perez-Escamilla, 2005; Woodward & Liberty, 2005). In the PSID-CDS, mother's cognitive ability is based on a passage comprehension test of the W–J Achievement Test–Revised during the 1997 CDS interview.

^20. Children eligible for subsidized lunches score between 0.69 and 0.76 standard deviations below ineligible children on a commonly used standardized achievement test (the National Assessment of Educational Progress; Pallas, 2010).

^21. Part I crimes included are murder, rape, robbery, assault, burglary, larceny, and motor vehicle theft (arson is excluded because it is not reported uniformly). Crime data cover the 1985–2002 period and are matched to the child's housing market.

^22. The six items in this scale are average January temperature, average days of sun in January, winter/summer low temperature gap, average July humidity, topographic variation, and water area in county (McGranahan, 1999).

^23. There are few missing data on the independent variables with the exception of a few locational features. We assign the mean when less than 1% of cases are missing. If these measures indicate a difference between Whites and Blacks, we assign the mean for each race instead of the full sample mean. If missing data exceed 1% of cases, we use regression model–based imputation.

^24. The propensity-score first-stage model also includes measures of the census geographic division and crowding in the home (persons per room).

^25. This description pertains to the full analysis sample of 813 children.

^26. About 35% of poor children live in the central cities or counties of their metro areas, which tend to have lower rents than do the rest of their metro areas that include more expensive, suburban jurisdictions.

^27. There is no obvious connection between the Stock–Yogo test results for the linear case (test statistics, corresponding asymptotics, and tables of critical values) and the nonlinear contexts for which 2SRI is appropriate (J. Terza, personal communication, February 19, 2013).

^28. The community-amenities hypothesis predicts better outcomes in higher-priced markets, and higher housing prices are correlated with higher housing-cost burdens. However, it is unclear how controls for locational features will affect the shape of the relationship between housing-cost burden and child outcomes. We therefore focus on the housing-cost-burden hypotheses, controlling for locational features.

^29. Although we tested all combinations of these three specifications, we display only the two that reveal the most distinct patterns. Assuming linear = a, quadratic = b, and cubic = c, if b is superior to a, and c is superior to b, then because a is nested in b, c must also be superior to a. Further, if b is not superior to a, but c is superior to b, then c must also be superior to a.

^30. It is inappropriate to look at the individual effects of polynomial variables. For linear models, the p-values from the Wald test are identical to the regression results. For quadratic models, the Wald test shows the likelihood that both the linear and quadratic terms are zero. For the cubic model, the Wald test shows the likelihood that the linear, quadratic, and cubic terms are zero.

^31. The inflection point in the propensity and IV models is 35% in both cases for W–J broad reading, and 26% and 27%, respectively, for W–J applied problems. The range of scores for W–J broad reading is approximately 50% larger than the range for the W–J applied problems (36–185 versus 43–150, respectively), and the distribution for broad reading is more skewed (skewness value of 0.81 versus 0.03, respectively). The more skewed distribution for broad reading may be pulling the inflection point upward compared with the more normal distribution for applied problems.

^32. Table 5 provides the results for housing-cost burden. Results for the mother's cognitive score appear in Table 4.

^33. At 51%, there is a decrement of about 1 test score point for the W–J broad reading test and 4 points for W–J applied problems test.

Additional information

Notes on contributors

Sandra J. Newman

Sandra J. Newman, Ph.D. is Professor of Policy Studies at Johns Hopkins University, where she also directs both the Center on Housing, Neighborhoods and Communities and the International Fellows in Urban Studies Program at the Hopkins Institute for Health and Social Policy. She holds joint appointments with the departments of Sociology and Health Policy and Management. Newman's interdisciplinary research focuses on the effects of housing and neighborhoods on children and families, and on the dynamics of neighborhood change. She co-directs the MacArthur Research Network on Housing and Families with Children.

C. Scott Holupka

C. Scott Holupka, Ph.D., is a Senior Research Associate at the Johns Hopkins University Institute for Health and Social Policy. His research focuses on housing, including special needs housing, as well as the dynamics of neighborhood change. He holds a Ph.D. in Sociology from Johns Hopkins.