Simultaneous Estimation of Housing Demand and Mortgage Demand: An Extended Two-Stage Approach with Two Sequential Choices

Abstract:     
This paper establishes an econometric model for analyzing four inter-related decisions at the time of home purchase, including tenure choice, demand for housing services, choice of mortgage instrument, and decision on the amount of borrowed funds. The modeling approach employed by the study is a switching-simultaneous equation model. First, we model two sequential decisions of tenure choice and choice of mortgage type (between fixed-rate (FRM) and adjustable-rate (ARM) mortgages). Second, we specify the demand for housing services and the decision on loan-to-value (LTV) ratios as a regime-switching simultaneous model by controlling for the selectivity biases caused by the two choice factors. The empirical estimates from the model are based on two data sources: the American Housing Survey and a sample of Fannie Mae loan acquisition data. The Fannie Mae data are compiled through a synthetic matching sampling method. Our results indicate that the patterns of housing and mortgage demand are noticeably distinct between borrowers choosing ARMs versus borrowers choosing FRMs. For example, the LTV ratios significantly raise the levels of housing demand for FRM borrowers, but not for ARM borrowers, thus implying that the ARM contract tends to mitigate the effect of the wealth constraint in mortgage borrowing.

JEL Classification: R21, G21

working papers series