There is a great deal of discussion concerning the practice of conducting fair lending analyses of non-HMDA reportable lending using proxy methods. Recall that when analyzing such data, there is no information pertaining to the race, ethnicity, or gender of the applicant.

Instead, we use a proxy, a variable that is correlated with, but not equal to, the actual race. We therefore end up with the probability of target group (protected class) and control group (non-protected class) assignment instead of actual data.

## A Little Background

We have written previously on this subject and have a white paper available, which provides additional detail. Without getting too much “into the weeds” (although perhaps we will do that in the future), the use of a proxy leads to estimation bias. For example, in wage regressions economists sometimes use age as a proxy for experience.

Suppose we estimate this model and obtain a coefficient of $1. This tells us that an additional year of ‘age’ increases hourly wage by $1. However, the true effect of ‘experience’ on wages is larger than this since some workers experience periods of unemployment. The problem is that an additional year of age is not equivalent to an additional year of experience for all people. Likewise, when we use BISG proxies for race, we can only imperfectly estimate the true impact of race. The better the proxy (i.e., the closer to the true race), the better the estimate.

It is important to note that we never observe the **actual **target and control group distinction. Instead, we observe probabilities based on factors including last name and racial composition of the area in which the customer lives. Therefore, the variable in the model used to designate target or control group status is based on probabilities and does not represent the actual race of each customer; some customers will be correctly assigned but many will not be.

Perhaps one of the most difficult issues with regard to the use of proxies in fair lending is remediation. If we do not know with certainty an applicant’s correct group assignment, but there are fair lending concerns and we are contemplating restitution, how would funds be distributed?

## Let’s Look At An Example

For simplicity, suppose there are 500 customers divided into 5 equal groups with target and control group distributions as follows:

- Group A – 100 with 95% probability (95 target group and 5 control group)
- Group B – 100 with 80% probability (80 target group and 20 control group)
- Group C – 100 with 65% probability (65 target group and 35 control group)
- Group D – 100 with 35% probability (35 target group and 65 control group)
- Group E – 100 with 20% probability (20 target group and 80 control group)

So overall, there are 295 target group customers and 205 control group customers. The target group represents the affected customers and suppose that a $1,000 restitution is due. We do not know the correct group designation (target or control) for the individual customers, only the probabilities.

The question then becomes, how do we reimburse customers who may have been damaged? We do not know the *actual* race/ethnicity of the customers with certainty, so all that we can attempt to do is disburse funds as accurately as possible. So again, what is the best way to do this? Below, we consider two possible scenarios.

### The First Possibility

The first possibility would be to distribute funds to *all* 500 customers *weighted* by the probability of target group assignment. For example, customers in group A have a 95% probability of being in the target group and thus eligible for restitution. Therefore, all customers in group A would receive $950.

This is calculated by the probability multiplied by the dollar amount (.95 * $1,000 = $950). In this group, 95 true target group customers get almost the full payment amount, but 5 non-target group customers also receive nearly the full payment amount.

Applying this same method to group B, 80 true target group customers receive $800, but 20 non-target group customers also receive $800. If we work through the calculations for all five groups, the result is a total restitution amount paid by the institution of $295,000 (95*$950 + 80*$800 + 65*$650 + 35*$350 + 20*$200 = $212,750) with 72% of the total funds going to the target group and 28% going to the control group.

### The Second Possibility

The second possibility would be an “all or nothing” approach, which would use a cutoff to pay 100% of the restitution amount to each customer with the probability of target group assignment at or above the cutoff. Let’s assume we choose a 65% probability of target group assignment as the cutoff which means the chances are 2-1 that the person is a target group customer. Every customer in groups A, B, and C would be paid $1,000, and customers in groups D and E are paid nothing.

Under this scenario, target group customers would receive $240,000 (240*$1,000) and non-target group customers would receive $60,000 (60*$1,000). The total payout of $300,000 is slightly higher than under the first alternative, and there is a higher percentage of total funds going to target group customers; 80% versus 72% in the first scenario. However, 55 target group customers receive *nothing,* and 60 non-target group customers receive a large windfall.

### What’s The Best Choice?

In comparing the two approaches, we see in the first alternative a *lower* portion of the funds are paid to *affected* (target group) customers; BUT every affected customer receives something. Under the second alternative, a *higher* portion of funds go to affected customers BUT a significant number receive nothing.

Which approach is better? As shown, it is a tradeoff and likely situation-dependent as to which may be the better alternative. In both cases, some affected customers receive less than they deserve and unaffected customers receive monies they do not deserve. Provided the universe of applicants is small enough, best practices may be to try to verify group assignment through other means to ensure the most accurate and fair allocation of funds.

It is important to understand that the accuracy of the allocation of funds as measured by the portion of restitution going to potentially damaged customers is highly dependent on the composition of the sample. For example, in our hypothetical scenario, 60% of the sample were protected class applicants based on the proxies and 40% were non-protected.

If the same probabilities were reversed, resulting in a sample composition of 40% protected class as opposed to 60%, applying the same calculations would result in a much lower proportion of affected customers receiving restitution. In fact, there are scenarios in which protected class customers could receive *less than 50%* of restitution amounts.

## In Conclusion

In summary, if an institution faces a situation in which restitution is being considered, the method used should be chosen carefully and based on the situation and the data. If there are means outside of proxy methods by which accurate target and control group designations can be obtained or confirmed, this would result in more equitable restitution. Even if information was *not available for all applicants,* as shown above, any enhancement could significantly affect the accuracy and fairness of the distribution as opposed to relying on proxy methods alone.

**How to cite this blog post (APA Style):**

Premier Insights. (2017, October 12). BISG Proxies In Fair Lending Analysis and Fund Disbursement For Remediation [Blog post]. Retrieved from https://www.premierinsights.com/blog/the-use-of-bisg-proxies-in-fair-lending-analysis-and-fund-disbursement-for-remediation