The Trouble with DTI as an Underwriting Variable

Richard Green:

The Trouble with DTI as an Underwriting Variable--and as an Overlay: Access to mortgage credit continues to be a problem. Laurie Goodman at the Urban Institute shows that, under normal circumstances (say those of the pre-2002 period), we would expect to see 1 million more mortgage originations per year in the market than we are seeing. I suspect an important reason for this is the primacy of Debt-to-Income (DTI) as an underwriting variable.

There are two issues here. First, while DTI is a predictor of mortgage default, it is a fairly weak predictor. The reason is that it tends to be measured badly, for a variety of reasons. ...

Let's get more specific. Below are result from a linear default probability regression model based on the performance of all fixed rate mortgages purchased by Freddie Mac in the first quarter of 2004. This is a good year to pick, because it is rich in high DTI loans, and because its loans went through a (ahem) difficult period. ...

The definition of default is over-90 days late. ... This is an estimation sample with 166,585 randomly chosen observations; I did not include 114,583 observations so I could do out of sample prediction (which will come later). The default rate for the estimation sample is 14.34 percent; for the hold out sample is 14.31 percent, so Stata's random number generator did its job properly. For those that care, the R^2 is .12.

Note that while DTI is significant, it is not particularly important as a predictor of default. ...

The Consumer Financial Protection Board has deemed mortgages with DTIs above 43 percent to not be "qualified." This means lenders making these loans do not have a safe-harbor for proving that the loans meet an ability to repay standard. Fannie and Freddie are for now exempt from this rule, but they have generally not been willing to originate loans with DTIs in excess of 45 percent. This basically means that no matter the loan-applicant's score arising from a regression model predicting default, if her DTI is above 45 percent, she will not get a loan.

This is not only analytically incoherent, it means that high quality borrowers are failing to get loans, and that the mix of loans being originated is worse in quality than it otherwise would be. That's because a well-specified regression will do a better job sorting borrowers more likely default than a heuristic such as a DTI limit.

To make the point, I run the following comparison using my holdout sample: the default rate observed if we use the DTI cut-off rule vs a rule that ranks borrowers based on default likelihood. If we used the DTI rule, we would have ... a default rate of 14.0 percent. If we use the regression based rule, and make loans to slightly more borrowers..., we get an observed default rate of 10.0 percent. One could obviously loosen up on the regression rule, give more borrowers access to credit, and still have better loan performance.

Let's do one more exercise, and impose the DTI rule on top of the regression rule I used above. The number of borrower getting loans drops to 73,133 (or about 20 percent), while the default rate drops by .7 percent relative to the model alone. That means an awful lot of borrowers are rejected in exchange for a modest improvement in default. ... In short, whether the goal is access to credit, or loan performance (or, ideally, both), regression based underwriting just works far better than DTI overlays.

(I am happy to send code and results to anyone interested.)