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Article Excerpt
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. 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. Because refinancing and mobility behavior influences the market value of mortgages, our findings point out the importance of incorporating those unobserved factors into the current risk-based mortgage pricing. Nonetheless, space cannot account for all unobservable variables or model misspecifications, and our quest for creating a more complete picture of what drives the borrowers' decisions should continue.
In the following section we provide a brief review of the related mortgage termination studies. The third section provides a theoretical model that explicitly incorporates the individual unobservable transaction costs and their impact on termination behavior. The fourth section develops the empirical implementation. The fifth and sixth sections describe the data and provide the empirical results, and the final section concludes.
Literature Background
Kau and Keenan (1995) and Capone (2001) provide comprehensive reviews of the mortgage termination literature. One of the most important messages of this literature is that 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). To reconcile this discrepancy, we address the unobservable variables problem through modeling their spatial distribution. Pavlov (2001) first suggested this idea by dividing the Los Angeles metropolitan area into 22 exogenously determined neighborhoods and allowing the model parameters to vary across those neighborhoods.
Our first point of departure is that we incorporate the spatial distribution of the observations into the hazard model through the 3SMLE approach of Deng and Quigley (2002). They show that such an approach provides for substantial efficiency gains and is better able to handle complex covariance structures.
Furthermore, we model the spatial distribution of the observations nonparametrically using the SVC method. As Pavlov (2000) shows, this approach substantially improves the estimation both in terms of out-of-sample errors and in terms of neighborhood definition. Because our goal is to model the unobservable borrower characteristics, nonparametric definition of the neighborhoods is particularly important for the economic conclusions of the model.
This approach can be viewed as an extension of McMillen (1992) and Pinkse and Slade (1998) who allow for spatially correlated residuals within limited dependent variable models such as probit and logit. Our contribution to this literature is twofold. First, we incorporate spatially correlated residuals into a proportional hazard model. Second, we investigate the spatial heterogeneity of mortgage terminations.
Mortgage Termination and Transaction Costs
Following Pavlov (2001), we employ the following three-state variable framework: r = instantaneous riskless rate of interest, H = value of the mortgaged property and G = monetary equivalent gain from moving.
The dynamics of the riskless rate and home values are assumed to follow generalized stochastic processes that are potentially correlated. Following Clapp et al. (2001) and Pavlov (2001) we model the optimal and actual bundle of housing services as stochastic variables affecting the mortgage termination choices. The urban economics literature suggests that both the optimal housing consumption bundle, [h.sub.d], and the actual bundle of housing services provided, [h.sub.s], change over time. Turnbull (1995) suggests that housing consumption changes if income, prices or transportation costs change. Thus, we assume that the optimal housing consumption bundle, [h.sub.d], follows a stochastic process that is derived from a process describing individual circumstances. (1)
We denote the gap between the optimal and the actual bundles of housing services by g(t) = [h.sub.d](t) - [h.sub.s](t). This gap captures the desire to move and can be positive or negative. The larger, in absolute value, the difference between the optimal and the actual housing services, the more likely the benefit of moving will exceed the costs. The monetary equivalent gain from moving, G(t),...
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