One of us earlier this year proposed a statistical relationship essential to understanding the issue of disparate impact.

This is the relationship between each demographic group’s (1) ratio of credit approvals-credit declines, and (2) its default ratio. In the popularized data, we are always told of the inputs — approval and decline rates, but we are never told of the outcomes — default rates. With only half of the data, you can’t know what it means.

So one fundamental change would greatly enhance objectivity and clarity, while greatly reducing the uncertainty involved. We need to add to the analysis of Home Mortgage Disclosure Act mortgage origination data the actual default rates on mortgages, organized by the same demographic categories used in HMDA reporting.

Default data by HMDA category has not been readily available from typical mortgage servicing records. But now, thanks to the AEI Center on Housing Markets and Finance, we have a large sample of mortgage loans covering five years of experience to test the relationships, showing that the relevant data matching is indeed practicable and useful.

Applying the same credit standards to everybody in a non-discriminatory way, regardless of demographic group, is exactly what every lender should be doing and is what the law requires. What, however, if a lender applies exactly the same credit standards to all credit applicants, but this results in different groups having different credit approval-credit decline ratios? For example, suppose minority borrowers have lower approval rates than white borrowers, or in general, that any Group A has lower approval and higher decline rates than some Group B. Does that necessarily mean there was discrimination? No, it doesn’t. That is only half the relevant data. You cannot draw conclusions until you know what the matching loan default rates are.

In other words, we must take the default rates on the mortgages for each group and compare them to the approval-decline ratios. We also need to adjust the default rates for differences in ex-ante credit risk factors and make sure, of course, that the results are statistically significant.

If the risk-adjusted default rates for Group A are the same as for Group B, the approval-decline ratios were appropriate and fair, since they resulted in the same default outcome. Controlling and predicting defaults is the whole point of credit underwriting. If the defaults rates are equal, there is no disparate impact problem.

If the risk-adjusted default rates for Group A are higher than for Group B, then A has effectively been given easier credit than B, in spite of A’s lower approval and higher decline rates. Indeed, the origination process may have inadvertently operated in Group A’s favor. If its default rates are higher, there is no disparate impact problem for Group A.

Only if Group A’s risk-adjusted default rates are lower than Group B’s would there be evidence that A is experiencing an effectively higher credit standard, which suggests a problem.

Nobel laureate in economics Gary Becker stated the point succinctly two decades ago: “The theory of discrimination contains the paradox that the rate of default on loans approved for blacks and Hispanics by discriminatory banks should be lower, not higher, than those on mortgage loans to whites.”

If the default rates are the same or higher, in short, there is no problem — the issue arises only if they are lower.

What do the data say?

The AEI Center on Housing Markets and Finance compiled the records for and analyzed the performance of originations of FHA loans for the five years 2013 to 2017. This sample represents more than 2.7 million mortgage loans. It divides the borrowing population into two categories of white and minority (defined as black or Hispanic). The AEI Mortgage Risk Index of ex-ante credit risk is used to risk-adjust the default rates.

The empirical results are that credit approval rates for minorities were lower, but their default rates were significantly higher, as were their risk-adjusted default rates.

In 2017, for example, the FHA approval rates for minorities were about 69.6%, compared to 77.1% for whites, but 90 day or more default rates were 2.7% for minorities, compared to 1.6% for whites; risk-adjusted default rates were 2.5% compared to 1.6%, respectively. In 2013, the first year of the data, approval rates were 65.2% for minorities and 73.9% for whites, but default rates were 12.4% for minorities compared to 9.2% for whites, and risk-adjusted default rates were 11.5% compared to 9.2%, respectively.

This same pattern is true in all the intermediate years. The data is summarized in the charts below.

Thus there is no indication of a disparate impact issue in the aggregate because the relevant default rates for minorities are in all cases higher, showing no bias in the credit decisions. There would only be an issue if their default rates were lower.

We conclude that this mode of analysis shows the way to address the disparate impact question on an objective basis. The encouragement to use this analysis should be written into the disparate impact regulations of the Department of Housing and Urban Development, and it should be required as part of any government report on the issue.