FHA Has Achieved Its Home Mortgage Capital Reserve Target, Technical Appendix

Congress asked GAO to estimate the value of FHA's Mutual Mortgage Insurance Fund, a capital reserve which backs most of FHA's single- family mortgages. This technical appendix presents estimates of the claim and non-claim termination propensities of single-family FHA mortgages. Competing risks continuous time hazard models are estimated on random samples of FHA mortgages originated between 1975 and 1993. Quarterly termination probabilities are estimated as a function of a variety of time- varying independent variables, and unobserved heterogeneity is controlled for with the Heckman-Singer non-parametric maximum- likelihood technique. The predicted signs are found on the usual suspects - equity, measured at the state level, lowers claims, while low relative interest rates foster prepayment. Substantial heterogeneity is found among individual borrowers, with 6% of borrowers estimated to have extremely low termination probabilities. Finally, the regressions provide evidence of adverse selection at time of prepayment. Borrowers who pass up profitable refinancing opportunities experience elevated claim rates in future quarters.