Third party originators and mortgage prepayment risk: An agency problem?

Journal of Real Estate Research, The, 1999 by LaCour-Little, Michael, Chun, Georgory H

Methodology

Prepayment research using loan level data is typically based on techniques of survival analysis, which originated in biological studies of mortality and has also found frequent application in industrial engineering failure time studies. Loans "die" prior to scheduled maturity from either default or prepayment. Kalbfleisch and Prentice (1980) and Cox and Oakes (1985) provide classic statistical treatments of the topic; Allison (1995) may be consulted for many practical examples using a wide range of examples, drawn from both medicine and sociology; Kiefer (1988) provides an economics literature review of duration modeling.16 Data censoring is the principal econometric problem encountered, since loans that have not prepaid as of the end of the study period have their prepayment time censored; that is, we cannot observe the time-to-prepayment for loans that have not yet prepaid. Techniques to accommodate data censoring are needed, with the proportional and non-proportional hazard partial likelihood approaches most popular.

Proportional hazards models were developed by Cox (1972), hence, the frequent reference in the literature to Cox regression, which really refers both to the model and the estimation method. In its simplest form, without time-dependent covariates, the model for prepayment is:

Since the dollar savings on refinancing depend both on rate reduction and loan amount, original loan balance (ORIBAL) is included as an explanatory variable. We expect larger loans to be more likely to prepay, given the same refinancing incentive. The variable MONTH measures loan age and a squared version (MONTHSQ) is also included, to capture possible non-linearity in the effect of time on refinancing probability. The borrower's incentive to refinance (a rough proxy for the value of the borrower's call option) is measured as the spread between contract rate and the tenyear constant maturity Treasury rate (INCENTIVE). To compute refinancing incentive, we considered using matched maturity mortgage rates, such as the FHLMC's survey report of fifteen- and thirty-year mortgage rates. But to choose any particular rate is, in effect, to assume that borrowers only refinance into the same product. This is clearly an unrealistic assumption because, for example, when rates drop a borrower might elect to shift to a fifteen-year term to pay off their mortgage more quickly, while leaving monthly payment costs relatively unchanged. Likewise, when the slope of yield curve increases, a borrower might choose to refinance into an adjustable rate product even if the spread between note rate and current market rate for the same product is minimal. In contrast, the ten-year Treasury rate provides a general proxy for the level of interest rates. As a proxy for unmeasured borrower characteristics that may affect prepayment risk, we also include the variable INCOME, representing borrower annual income at time of loan origination. Finally, we include the variable THIRDPTY, an indicator variable set equal to one, if a mortgage broker or other third party originated the loan, and zero otherwise.