Abstract
House price regression residuals often display spatial dependence but historically mortgage models, which employ house prices, assume independence and use only the own borrower/loan characteristics. This manuscript uses a spatial probit model to investigate spatial dependence among the disturbances and the effect of borrower/loan characteristics from nearby properties on own default propensity. We find that allowing spatial dependence in the disturbances greatly improve the predictive accuracy of a probit default model, and that spillovers from risky neighbor characteristics have statistically significant and material effects on own payment default propensity. In addition, measurement of spatial effects can improve policy analysis.
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Notes
The location related omitted variables may include property, neighborhood and borrower characteristics.
See Beron and Vijverberg (2004) as well as LeSage and Pace (2009) for other developments and motivations of spatial probit models.
The simultaneous autoregressive (SAR) specification \(\Omega _{SAR}=(I_{n}-\rho W)^{-2}\) is the most popular in spatial econometrics. The moving average (MA) specification \(\Omega _{MA}=(I_{n}+\rho W)^{2}\) appears less frequently.
For large n, the sampling variability of \(\bar d\) should be low since \({\rm{pdf}} (\varphi _{i})\) has a magnitude that is between 0 and 0.3989 (\({\rm{pdf}} (0)\)). Even when \({\rm{pdf}} (\varphi _{i})\) is not independent across i, the variability of \({\rm{pdf}} (\varphi _{i})\) is bounded and therefore its average (\(\bar d\)) should show low sampling variability. In which case, the distribution of the estimated direct, indirect, and total random effects will be dominated by the sampling variability associated with \(\tilde \beta \), \(\tilde \theta \), and \(\tilde \beta +\tilde \theta \). Also, this marginal analysis does not apply strictly to discrete explanatory variables. There are no fundamental computational barriers to obtaining more exact versions of these effects. However, the approximations in Eqs. 36–38 simplify interpretation.
There are some additional complications for interpretation that arise for models with spatially dependent disturbances and global spillovers that LeSage et al. (2011) examined in a study of business recovery in New Orleans after Katrina.
The average time lag between the transaction date and the filing date is 25 days, from the transactions with both transaction date and the filing date.
Results are about the same when 60+ days delinquency is reclassified as default.
As a robustness check, results are qualitatively similar for year 2007 to 2010.
This is indicated by the same property site address and tax billing address.
Sometimes dummy variables that cover only a small number of observations can pick up unobservables associated with these idiosyncratic observations. However, for these data the dummy variable that covered the fewest cases was the company owned dummy which nonetheless included 4.82 percentage of the 79,652 observations. Therefore, the dummy variables used in this analysis covered a substantial number of cases.
Note, the intercept in this regression and the following regressions would be associated with the base case of a non-fully documented fixed rate loan without a prepayment penalty or exotic features associated with the initial purchase of the property. Since \(y_{i}=1\) represents a default, smaller intercepts point to lower default rates for the base case.
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Acknowledgments
The authors would like to thank the helpful comments from Paulo Rodrigues, Peng Liu, and other participants in LSU seminar, KSU seminar, 2011 MIT-NUS-Maastricht real estate research symposium and 2012 FMA conference. We would like to thank the very helpful comments from John Clapp. The authors would like to acknowledge support for this research provided by the National Science Foundation (BCS-0136193, SES-0554937, and SES-0729264). The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the views of the National Science Foundation. In addition, Pace would like to acknowledge support from the BP-LSU Oil Spill grant. We appreciate the support from Blackbox Logic, LSU High Performance Computing Center, LSU and KSU Finance department. All errors are our own.
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Zhu, S., Pace, R.K. Modeling Spatially Interdependent Mortgage Decisions. J Real Estate Finan Econ 49, 598–620 (2014). https://doi.org/10.1007/s11146-013-9419-y
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DOI: https://doi.org/10.1007/s11146-013-9419-y