Spatial Heterogeneity in Mortgage Terminations by Refinance, Sale and Default

By Deng, Yongheng; Pavlov, Andrey D. et al. | Real Estate Economics, Winter 2005 | Go to article overview
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Spatial Heterogeneity in Mortgage Terminations by Refinance, Sale and Default


Deng, Yongheng, Pavlov, Andrey D., Yang, Lihong, Real Estate Economics


This article investigates the impact of spatially correlated unobservable variables on the refinancing, selling and default decisions of mortgage borrowers. Virtually the entire mortgage literature acknowledges that borrower-specific characteristics, such as culture, education or access to information, play an important role in mortgage termination decisions. While we do not observe these variables directly, we note that borrowers of similar background tend to cluster together in neighborhoods. We estimate a competing risks hazard model with random effects using a three-stage maximum likelihood estimation approach. We utilize the space-varying coefficient method to modify the covariance structure according to the spatial distribution of the observations. Beyond a significant improvement of the model performance, this yields a number of insightful implications for mortgage termination behavior. For instance, borrowers of the affluent "West Side" of Los Angeles County both refinance and move at a higher rate than predicted by the standard maximum likelihood estimation method. At the same time, borrowers from some lower-valued neighborhoods tend to stay longer than expected with their mortgages and properties.

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The mortgage-backed securities market has recently become the largest capital market for investors in the United States. Not surprisingly, a large volume of literature studies mortgage borrowers' prepayment and default behavior and its impact on the pricing of mortgage-backed securities. However, due to errors in variables or limited availability of borrower characteristics, most empirical studies find a substantial discrepancy between the theoretically derived optimal behavior and the observed decisions; see, for example, Deng, Quigley and Van Order (1996) and Stanton (1996). This article attempts to reconcile the theoretical option-based models of mortgage terminations with the empirical experience of mortgage terminations by refinancing, sale and default.

From a theoretical perspective, we explicitly model the borrower's costs associated with mortgage terminations and recognize that those costs vary across individuals and termination causes. Consistent with this approach, we empirically separate the three major causes of mortgage termination: refinancing, selling of the property and default. Furthermore, because borrowers of similar characteristics (education, income, culture and ethnic background, etc.) tend to cluster together in neighborhoods, many of the omitted variables and measurement errors are spatially correlated. Recognizing this spatial correlation we empirically model the variability of the mortgage termination costs through the use of the physical location of the properties. This approach gives raise to a competing risks hazard framework with spatially correlated errors.

Consistent with the above implication, we estimate the refinancing, selling and default probabilities using an innovative three-stage maximum likelihood estimation (3SMLE) approach for a competing risks hazard model with random effect proposed by Deng and Quigley (2002). In the first stage, we estimate a competing risks model of refinance, sale and default in a conventional maximum likelihood estimation approach and collect the residuals of the estimation for each individual loan. In the second stage, we estimate the neighborhood spatial heterogeneous functions using the residuals from the first-stage estimation following the space-varying coefficients method (SVC) of Pavlov (2000). In the third stage, we reestimate the competing risks hazard model of refinance, sale and default by accounting for the consistent estimation of neighborhood spatial heterogeneous error distributions. The 3SMLE approach allows us to account for unobserved neighborhood spatial heterogeneity using geocoded micro loan data and hence provides more efficient estimates.

Beyond providing a significantly better fit to the data, the proposed methodology allows us to make a number of insightful observations about the mortgage termination behavior of borrowers from different neighborhoods.

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