Date of Award
Doctor of Philosophy (PhD)
CARES Act, forbearance, mortgage termination, payment behavior, the Dirichlet distribution, unobserved heterogeneity
This dissertation is comprised of three essays on residential mortgage payment behavior. The first chapter analyzes the simultaneous mortgage-termination risks of 90-day delinquency and prepayment, the second and third chapters study borrower mortgage payment and exiting behavior in the CARES Act Mortgage Forbearance program.
Ding, Tian, Yu, and Guo (2012) analyze transformations of the binomial logit duration model for which the results are an exact binomial logit duration model when the transformation parameter equals one and an interval censored proportional hazard model as the transformation parameter limits to zero. In the first chapter, which is co-authored with Ran An and Jan Ondrich, we incorporate one of the Ding et al. transformations into a model with more than one mortgage-termination risk. In this case the resulting model is multinomial logit when the transformation parameter equals one. The resulting model as the transformation parameter approaches zero is not an interval censored competing risk proportional hazard model (see An and Qi 2012). However, it may approximate one and is in any case a valid statistical model. We analyze the simultaneous mortgage-termination risks of 90-day delinquency and prepayment for single-family 30-year fixed-rate mortgages securitized by Fannie Mae using the Fannie Mae public use data. We show that the transformation can control for over-dispersion in the data and that transformed models perform better than the corresponding models without the transformation.
The second chapter uses borrower mortgage payment behavior in the CARES Act Mortgage Forbearance program to predict the mode of exit from the program. The CARES Act permits borrowers to postpone mortgage payments without penalty. In the empirical work, this chapter extends the beta-logistic model in Heckman and Willis (1977) to the Dirichlet nested logit model, which allows the state dependence of choices to vary across different nests. The results show that the beta distribution of probabilities of choices within the nest and between nests are both J shaped, which indicates that the payment behavior probability of relatively few borrowers is near the average. Moreover, borrowers who make curtailment payments are more likely to exit forbearance with prepayment or reinstatement. In comparison, borrowers who frequently forbear payments are more likely to leave with payment deferral or trial/modification.
The models in the second chapter estimate the effect of payment behavior in the CARES Act forbearance program as the program continues through time. For a given exit time, the likelihoods contained information on only those mortgages that failed at that exit time. Results were presented for three exit times: 6, 12, and 18 months. A two-step estimation technique was used and standard errors were corrected in the second step. The first improvement in the final chapter incorporates information on all mortgages that survive until a given time into the likelihood functions. I show that the estimation can be accomplished in a single step. The accuracy of the two-step estimation and single-step estimation results are compared. The second improvement in the final chapter is to construct a single model, estimated in a single step, that uses information for all of the first six months. The accuracy rate of the estimation for this new model is substantially higher than the accuracy rate of the estimation for the model with a single survival time of six months. Future work is to extend the estimation to cover the entire length of the program.
Lin, Wenzhen No Middle Name, "Three Essays on Residential Mortgage Payment Behavior" (2023). Dissertations - ALL. 1706.