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The heterogeneous spatial impact of foreclosures on nearby property values

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Abstract

Foreclosures have negative impacts not just on homeowners, but also on neighboring properties. Due to the heterogeneous characteristics of the housing market, different neighborhoods can be impacted differently by foreclosures. This study focuses on the varying impacts of foreclosures on nearby property values across space. These results can provide insightful directions for decision makers to identify places in greatest need. A semi-parametric approach is applied to allow estimates varying over space. In Chicago, property values most impacted by foreclosures are in the south where the vacancy rate and crime occurrences are high and incomes are low. The spatial variation in impacts is wider for homes priced at the 10th quantile than at the 90th quantile. Moreover, the impacts are generally larger for home prices at the 10th quantile than at the 90th quantile, but the differences are not uniform across space.

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Notes

  1. Challenges not only include limited grants for many qualified impacted areas, but also many practical perspectives need to be considered, such as occupancy status, property conditions, number of available real-estate-owned properties (REOs), and deadlines to locate the grants (Bak and Hewings 2017).

  2. According to the first quarter of 2013 RealtyTrac’s U.S. Foreclosure Market Report: https://chicagoagentmagazine.com/2013/04/12/q1-realtytrac-foreclosure-report-a-mixed-bag/.

  3. This also aligns with the choices in the literature (Immergluck and Smith 2006; Campbell et al. 2011; Anenberg and Kung 2014; Gerardi et al. 2015), where ring buffers with a radius ranging between 0 and 0.33 miles3 are used.

  4. It is also often referred to as “geographically weighted regression” (e.g., Fotheringham et al. 2015; Yu 2006) or “locally weighted regression” (Cleveland and Devlin 1988). We are aware of the correlation among estimates across the space and between different coefficients. However, we intent to focus on the spatial trend of the estimates, but less focus on specific estimates for a particular location.

  5. This adds some degree of parameterization.

  6. See Loader (1999) for details on the target selection approach and interpolation options. Estimation in this paper is fulfilled by using command “qregcpar” in McSpatial package (McMillen 2013a) in R, which uses an adaptive decision tree approach for selecting the target locations and the modified Shepard algorithm for bivariate interpolation.

  7. Since coefficients are estimated for different target locations, there could be more noise in the estimates for locations with few observations.

  8. It is worth noting that the quantiles are conditional on explanatory variables rather than unconditional quantiles. In other words, the quantile comparison is location based: The 10th quantile level for the housing price in a wealthy neighborhood is different than the 10th quantile level in a southern neighborhood. When different results at different quantiles are compared, they are the quantile levels in each geographic location but not the quantile levels from the whole sample (e.g., 10th vs. 90th quantile within the same rich neighborhood and 10th vs. 90th quantile at the same poor location).

  9. We choose this large window size rather than other smaller window sizes since the usage of small window size can generate observations with little variation. This causes the singular matrix problem in our analysis when solving quantile regression using “rq” command that is embedded in “quantreg” command.

  10. Foreclosed properties are likely to sell for less (Coulson and Zabel 2013), due to potential stigma effects or other unobserved factors related to foreclosed properties.

  11. The foreclosure risk score calculation also included the area price change and unemployment rate at the higher geographic level, such as the city or county. Thus, they do not account for any variation of foreclosure risk within the geographic scope of our study.

  12. An additional robustness check controlling for the spatial autocorrelation within census tract is added in “Appendix B”.

  13. Following Gerardi et al. (2015), we use a mix of both flow and stock measurement. “Active” foreclosures are the stock measurement of foreclosures (between filing and auction), while “Auctions in the past 0–12 months” is the flow measurement. Alternative ways to define the measurement of foreclosures (flow vs. stock measurement) are apparent in the literature. For an example of detailed stock foreclosure measurement, see Bak and Hewings (2013) where similar datasets are used as this paper (Sect. 3.1 and Fig. 6). Using the detailed stock measurement, they track the trend of foreclosure impacts by quarterly phases over a total of 3 years after the auction and more than 1 year before the auction (active inventory). But on average, the patterns and magnitude are very similar to ours in this paper: between negative 1 and 2% within 0.3 miles. Therefore, our flow definitions are valid in terms of not biasing the results compared to using the stock definition.

  14. Kolmogorov–Smirnov test is used to test the equality of distributions of the estimates between different quantiles. Comparisons for all pairs (10th vs. 50th, 50th vs. 90th and 10th vs. 90th) reject the null hypothesis of the equality of distributions at 1% significant level. Test results are available upon request.

  15. Following Chasco and Gallo (2015), since it is better for visualizing prediction surfaces that are not distributed normally.

  16. However, this does not invalidate the usefulness of quantile estimates in some situations. Assuming two properties are similar in house characteristics and in the same neighborhood (conditional on observed explanatory variables) except for different price levels, it would not be difficult to inform policy makers that the lower-priced house belongs to the lower price quantile and vice versa. If the lower quantile estimates are larger than the higher quantile estimates (in absolute terms), then the lower-priced home is experiencing a larger price discount rate due to the nearby foreclosures.

  17. We also tested the differences between the 25th and 75th quantiles, and no significant difference is found between them. Moreover, all quantile regressions used demeaned variables at the census tract-year-quarter level in order to control for census tract-by-year-quarter fixed effect.

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Acknowledgements

The authors greatly acknowledge Illinois REALTORS for data provision; the interpretations presented in this paper are those of the authors. The authors would like to thank Daniel McMillen and two anonymous reviewers for the comments on earlier drafts of this paper. Contributions from participants in seminars at the Regional Economics Applications Laboratory (REAL) and the Department of Agricultural and Consumer Economics (ACE) at the University of Illinois at Urbana–Champaign are also gratefully acknowledged.

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Authors and Affiliations

  1. Freddie Mac, McLean, VA, USA

    Xian F. Bak

  2. Department of Agricultural and Consumer Economics and Regional Economics Applications Laboratory, University of Illinois, Champaign, IL, USA

    Geoffrey J. D. Hewings

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  1. Xian F. Bak
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Correspondence to Xian F. Bak.

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Appendices

Appendix A

From columns 2–4, estimates are presented, respectively, for the 10th, 50th, and 90th quantiles. At all three quantiles, similar results are presented as the OLS regression results. Column 5 compares the differences between the 10th and 90th quantiles,Footnote 17 and results are not significantly different from each other. This finding is different from Zhang and Leonard (2014), where foreclosure impacts are found greatest on homes at lower price quantiles (Table 5).

Table 5 OLS and quantile regression estimates
Full size table

Appendix B

In the base model, spatial fixed effects (census tract) are used to control for the spatial autocorrelation. However, there may exist spatial autocorrelation among housing prices at a local housing market within the census tract. To control for that, we use the spatial autoregressive model with autoregressive disturbances (SARAR) in addition to the census tract-by-year-quarter fixed effect in the base model (Walls et al. 2017). We estimate SARAR (1,1) model which contains both spatial lags of both the dependent variable and the disturbance term, and it is written as \( y = \lambda Wy + X\beta + u \) and \( u = \rho Wu + \epsilon \).

Due to computational inconvenience for a larger dataset, we break our data sample into two parts: the southern and northern parts of Chicago (divided by Interstate-55 exogenously). We test a distance less than 0.5 miles or 1 mile to define neighbors and use an inverse-distance spatial weighting matrix. Generalized spatial two-stage least squares (GS2SLS) estimator (Kelejian and Prucha 1998) is applied.

Results in table B1 compare the results with (SARAR) and without (OLS) controlling for the within-census tract fixed effects by the south and north parts, respectively. Given spatial fixed effects are used in all models, the results between the OLS models and SARAR models are largely consistent. Therefore, the spatial autocorrelation within census tracts is trivial and our base model results are robust (Table 6).

Table 6 Robustness check for spatial autocorrelation within census tracts
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Appendix C

See Table 7.

Table 7 OLS regression results: interactions with neighborhood characteristics variables
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Bak, X.F., Hewings, G.J.D. The heterogeneous spatial impact of foreclosures on nearby property values. Ann Reg Sci 62, 439–466 (2019). https://doi.org/10.1007/s00168-019-00903-4

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