Mortgage-backed securities market has recently become the largest capital market for investors in the U.S. 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 paper 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, since 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 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 re-estimate 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 a geo-coded 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. For instance, we find that borrowers from the affluent West Side of Los Angeles County tend to both refinance and move at a higher rate than predicted by standard maximum likelihood estimation. On the contrary, borrowers from some lower income neighborhoods tend to stay with their mortgages and homes longer than predicted by a standard model. Since refinancing and mobility behavior influences the market value of mortgages, our findings have direct implications for mortgage pricing and have the potential to improve the efficiency and fairness of the lending industry.
In Section 2, which follows, we provide a brief review of the related mortgage termination studies. Section 3 provides a theoretical model that explicitly incorporates the individual unobservable transaction costs and their impact on termination behavior. Section 4 develops the empirical implementation. Sections 5 and 6 describe the data and provide the empirical results and Section 7 concludes.
Download
Spatial Heterogeneity in Mortgage Terminations by Refinance, Sale and Default
