Subsidized Housing and Residential Trajectories: An Application of Matched Sequence Analysis

Abstract

Scholars have long debated the relative merits of site-based, subsidized housing owned and operated by a public entity or by the private sector. This is the first study to classify long-term residential trajectories of nationally representative low-income households in the United States by their initial assisted housing status. We employ a matched sequence analysis of neighborhood poverty and racial trajectories of low-income households in the Panel Study of Income Dynamics who formed during 1988–1992. Among households carefully matched by their demographic and economic attributes, we find that those first forming households in public housing spend much longer durations over the subsequent 20 years in poorer, minority dominant neighborhoods than similar households first forming in market-rate housing do. In contrast, forming a household in private site-based subsidized housing is associated with superior neighborhood socioeconomic (but not desegregated racial composition) trajectories compared with starting in market-rate housing. Implications for housing policy are discussed.

Keywords:

• Sequence analysis
• longitudinal studies
• neighborhood poverty
• contextual mobility
• assisted housing
• public housing

Acknowledgments

The authors gratefully acknowledge the research assistance of Katrina Rinehart and Sylvia Tatman-Burruss. The collection of the Panel Study on Income Dynamics used in this study was partly supported by the National Institutes of Health under Grant R01 HD069609 and the National Science Foundation under Award 1,157,698. Special thanks to the Wayne State University School of Social Work for purchasing the National Neighborhood Change Database.

Notes

1. This article does not address populations that are homeless or in other institutional settings, although they are important for housing policy because of data limitations.

2. PSID changed from an annual to a biennial survey in 1997 and added several additional waves of households (Hispanics, immigrants) over time to remain more representative.

3. Our initial sample comprises 55% non-Hispanic Whites, 36% non-Hispanic African Americans, 5% Hispanics, and 4% others. Note that these are the race of the household head, that is self-reported by respondents. For example, some individuals from the Latino sample belong to non-Hispanic Whites. This is either because their household heads (e.g., husbands) are actually non-Hispanics Whites or due to reporting error.

4. In our data, less than 3% of the sequences (n = 8, with five in treatment and three in control) contain 1-year data because of attrition in the PSID, which are weighted to compensate for attrition. These are still informative about variation of initial neighborhood conditions. There is no set minimum length in the sequence literature, but sequence length is important for cluster quality and still under active study (Dlouhy & Biemann, 2015; Studer & Ritschard, 2016). In response to a query by an anonymous reviewer, we verified that the cluster solution was not adversely affected by including single-element sequences.

5. On average, sample attrition amounts to 1–3% in every wave, and is generally applied to the entire PSID sample. About 12% of our sample belongs to the Latino sample that was added between 1990 and 1995 and discontinued after 1995. In addition, the original core sample was reduced from nearly 8,500 households in 1996 to approximately 6,168 in 1997, causing a shrinkage of our sample by about 15%.

6. On December 27, 2000, the White House Office of Management Budget introduced the CBSA, which incorporated both metropolitan statistical areas and micropolitan statistical areas, the latter having an urban cluster under 50,000 but at least 10,000 persons. We did not drop observations from micropolitan areas, because this is a small portion of the sample. However, we did drop observations from Broomfield County, Colorado, because it was created from parts of Adams, Boulder, Jefferson, and Weld on November 15, 2001, and this made it challenging to calculate the county median family income for each decade (U.S. Census Bureau, 2014).

7. Constructed by GeoLytics and the Urban Institute, the NCDB contains data from the decennial census from 1970 to 2010 (for some 2010 variables, data are from American Community Survey 2006–2010 5-year estimates). We used data normalized to the 2010 tract boundaries to mitigate potential problems associated with tract boundary changes across census years

8. We attempted our analyses using deciles and results were quite consistent. However, deciles introduced an even larger number of permutations that were difficult to interpret in sequence plots. Results using deciles are available upon request.

9. PSID became biennial from 1997. We assumed that if a household in a given PSID year appears to be in the same geocode as in the previous PSID year, it has not made actual moves between two years.

10. Because clustering uses sample size as an input, we used the PSID family weight for the first year of the observation as the weighting variable to ensure that cluster membership reflected the sampling design of the PSID.

11. Two conditions are necessary to obtain strong ignorability of any potential selection bias to treatment or confounding (Rosenbaum & Rubin, 1983). First, the treatment and comparison groups must have no significant difference in means on all variables that could have influenced treatment assignment. Second, the treatment and comparison groups must have common support in their distributions.

12. There were six households who resided in both public housing and private, site-based assisted housing during 1988–1992 and they were considered the public housing treatment group. Seventy-seven percent of the treatment group of private, site-based assisted housing started in developments with federal subsidies.

13. AHD provides the information of voucher receipts only starting from 1995, and formal HOPE IV projects have started after our 5-year window period of 1988–1992.

14. The sample size of those residing in public and private assisted housing at the time of household formation is quite small compared with the number of all low-income families. Hence, it is possible that the PSID sample is representative of general low-income households but may not be representative of assisted housing recipients.

15. The strata were automatically processed using the cem add-on package in Stata 12 (Iacus et al., 2012).

16. Austin (2011) notes that there is no consensus for setting a caliper, but recommends a caliper below 0.20 in nearest-neighbor matching. In its guidance of propensity score matching, STATA suggests to start at 0.03 and go up to 0.10 (StataCorp, 2015). To ensure the quality of matching based on the balance check and Kolmogorov–Smirnov test for quality of distribution of propensity score (see Appendix B), we used a caliper of 0.03 for our matching. As noted, this process dropped several treatment observations.

17. Of course, our research design focuses on two different site-based housing types at the time of household formation, not at any time in the life course. Whereas it would be ideal to have the information of the receipt of tenant-based subsidies among our sample households and model these recipients as a separate group, we do not have complete information over our sample period.

18. We conducted analysis in Stata using the SQ-Ados package (Brzinsky-Fay et al., 2006).

19. We use the PSID family weights (nonnormalized) for this inferential analysis before matching because normalized weights result in small cell sizes for the chi-square test. For the analyses using the matched samples, we use the propensity score weight generated from matching.

20. The numbers represent the sum of the mean percentage duration spent in neighborhoods with Quintile 1, Quintile 2, and Quintile 3 in terms of % poverty from Table 3: 1.98 + 2.35 + 2.51 = 6.8 (for Treatment I) versus 3.02 + 6.23 + 11.34 = 20.6 (for Comparison I).

21. The numbers represent the sum of percentages of households that belong to sequence patterns comprising Quintile 4 and Quintile 5 only from Table 4: 23% + 5% + 15% + 5% + 3% + 3% = 54% (for Treatment II) versus 40% + 7% + 9% + 4% + 4% + 4% = 70% (for Comparison II).

22. We find that whereas low-income households show a slightly higher probability of being clustered into neighborhood trajectories consisting of higher poverty states, the distribution of their neighborhood trajectories is quite even across different cluster memberships.

23. A chi-square test result is significant (=1,425.51, d.f. = 10, p < 2e-16) and the share of discrepancy measured by pseudo R² is significant (R² = 0.012, p < .001). The within-group similarity is also statistically significant (Levene = 222.60, p < .002).

24. A Fisher’s exact test robust to small cell sizes had almost identical p values in both cases.

25. A chi-square test result is significant (χ² = 1968.037, df = 10, p < 2e-16) and the share of discrepancy measured by pseudo R² is significant (R² = 0.027, p < .001). The within-group similarity is also statistically significant (Levene = 915.66, p = .001).

26. We started with the same pool of the public housing group (n = 43) and the private subsidized housing group (n = 54) that were cleaned up after the merging process and used for previous matching. For the propensity score matching of these households, we used the same matching criteria as shown in Table 2 and caliper = 0.03 for 2-to-1 nearest-neighbor matching with replacement. During the matching process, we lost three households in the treatment group because no households in the pool of the comparison group had a propensity score within the caliper width of 0.03 of these treated households’ propensity score and they were left unmatched (n = 40 for the public housing treatment group). They were matched with 44 households from the private subsidized housing comparison group.

27. We observed a similar distinction when we used employment rates and college-educated rates as our neighborhood indicators.