Empirical Analysis of Delinquency and Foreclosure Determinants
In this section we investigate to what extent a logit regression model can explain the high levels of delinquencies and foreclosures for the vintage 2006 mortgage loans in our database. The regression coefficients are assumed to be constant over time, which allows us to interpret the time variation in the regression error term. All results in this section will be based on a random sample of one million firstlien subprime mortgage loans, originated between 2001 and 2006.
3.1 Empirical Model Specification
We run the following logit regression
where the event is either delinquency or foreclosure of a subprime mortgage loan after a given number of months; $(x) = 1/(1 + exp(—x)) is the logit function; X is the vector of explanatory variables, including a constant; and 3 is the vector of regression coefficients. We will report the following statistics for each explanatory variable i:
contribution06i = $(ß'X + ßi(XÖ6i — Xi)) — $(ß'X) (4)
« marginali x deviation06i (5)
where X is the vector with mean values, ui is the standard deviation of the ith variable, and X06i is the mean value of the ith variable for vintage 2006 loans. We define deviation01 and contribution01 for vintage 2001 loans in a similar fashion. Equation (5) emerges from a firstorder Taylor approximation with the derivative of the logit function with respect to the ith variable approximated by marginal,,.10 The marginal statistic measures the effect of a onestandarddeviation increase in a variable (from its mean) on the probability of an event. The deviation statistic measures the number of standard deviations that the mean value of a variable in 2006/2001 was different from the mean value measured over the entire sample. The contribution statistic measures the deviation of the (average) event probability in 2006/2001 from the (average) event probability over the entire sample that can be explained by a particular variable.
For any subgroup of loans, such as a particular vintage, we can determine the predicted probability of an event by computing:
where the superscript j refers to the loan number and L is the total number of loans in the subgroup. 3.2 Variable Definitions
Table 2 provides the definitions of the dependent and independent (explanatory) variables used in the empirical analysis. We use either the delinquency or the foreclosure dummy variable as the dependent variable. We define a loan to be delinquent if payments on the loan are 60 or more days late, the loan is in foreclosure, or the associated house is real estate owned by a lender. We define a loan to be in foreclosure if the reported status is in foreclosure or real estate owned by a lender. Once a foreclosure procedure for a loan is finalized and/or the loan balance becomes zero, we drop this loan from our analysis. In Subsection
10Technically, we first change units by multiplying by at in Equation (2) and diving by at in Equation (3).
6.3 we show that our main results are robust to incorporating loan terminations.
The borrower and loan characteristics we use in the analysis are: the FICO credit score, the combined loantovalue ratio, the value of the debttoincome ratio (when provided), a dummy variable indicating whether the debttoincome ratio was missing, a dummy variable indicating whether the loan was a cashout refinancing, a dummy variable indicating whether the borrower was an investor (as opposed to an owneroccupier), a dummy variable indicating whether full documentation was provided, a dummy variable indicating whether there is a prepayment penalty on a loan, the (initial) mortgage rate, and the margin for adjustablerate and hybrid loans.11
In addition, we construct a variable that measures house price appreciation from the time of origination until the time we evaluate whether the loan is delinquent or in foreclosure. To this end we use metropolitan statistical area (MSA) level house price indexes from the Office of Federal Housing Enterprise Oversight (OFHEO) and match loans with MSAs by using the zip code provided by LoanPerformance.
We also considered the change in the unemployment rate from the period of origination until the period of loan performance evaluation, which we could only measure accurately at the statelevel for the entire sample. It turned out that the unemployment variable mainly picked up the time trend in the delinquency or foreclosure rate. The relationship between the (trending) unemployment rate and the (trending) loan performance, however, is spurious. When vintage dummy variables are included in the regression, the unemployment rate becomes insignificant, both statistically and economically. We therefore decided to omit the change in the unemployment rate as an explanatory variable.
In Table 2 we report the expected sign for the regression coefficient on each of the explanatory variables in parentheses.
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