Government Subsidy in the U.S. Mortgage Market: A Structural Analysis with Bunching

Abstract

It is of vital importance to better understand the US housing market, a market where the global financial crisis was originated from. In this paper, we build an infinite-horizon continuous-time structural model to study the effects of the long-standing and widespread Government-Sponsored Enterprises’ (GSEs) mortgage default insurance subsidy on banks’ equilibrium lending behavior in the US. Despite the richness of the model, we obtain analytical solutions for the equilibrium loan size and interest rate. We then use truncated loan-level data to obtain the maximum likelihood estimate of the magnitude of the default insurance subsidy, despite the fact that the pre-subsidy data are unavailable. We do so by using a salient feature in the data that a large number of borrowers “bunch” at a loan size exactly equal to the subsidy eligibility cutoff. We find that the subsidy is about 25 basis points per dollar, reduces the equilibrium mortgage interest rate by the same amount (3.6% of the sample average), and increases the loan size by $15,026 (10.4% of the sample average). To the best of our knowledge, this is the first paper to estimate the size of the GSE subsidy using a structural approach with loan-level data. The estimation of this crucial parameter, along with our modeling framework, would allow future work to conduct welfare assessment and evaluation of the housing finance system in the US.