Unobserved Heterogeneity in Models of Competing Mortgage Termination

Abstract

This paper extends unobserved heterogeneity to the multinomial logit model (MNL) framework in the context of mortgages terminated by refinance, move, or default. It tests for the importance of unobserved heterogeneity when borrower characteristics such as income, age and credit score are included to capture lender-observed heterogeneity. It does this by comparing the proportional hazard model (PHM) to MNL with and without mass-point estimates of unobserved heterogeneous groups of borrowers.

The mass point mixed hazard model (MMH) yields larger and more significant coefficients for several important variables in the move model, whereas the MNL model without unobserved heterogeneity performs well with the refinance estimates. The MMH clearly dominates the alternative models in-sample and out-of-sample. However, it is sometimes difficult to obtain convergence for the models estimated jointly with mass points.

Keywords: Mortgage termination risks, Cox Proportional Hazard Model (CPH), Multinomial Logit Model (MNL), Out-of-sample prediction; Unobserved heterogeneity

JEL Classification: G21, C25, C41, C52, D12