Principled Frequentist Estimation of Racial Disparity in Credit Approval under Unobserved Race

TL;DR

This paper introduces a new frequentist method using OLS and MLE for estimating racial disparities in credit approval when race data is unobserved, improving accuracy over existing heuristics and Bayesian approaches.

Contribution

It develops a frequentist estimation approach under exogeneity assumptions, incorporating surname-only proxies and income stratification for better disparity measurement.

Findings

Reduces RMSE in disparity estimates by 79.7% in simulations.

Outperforms existing heuristic and Bayesian methods in accuracy.

Validated on 2023 Los Angeles HMDA data.

Abstract

Estimating racial disparities in loan-approval probabilities when race is unobserved is routinely required for fair lending compliance. In such cases, race probabilities-typically from Bayesian Improved Surname Geocoding (BISG)-stand in for true race. Prior work shows that common heuristic approaches, including the Threshold and Weighting estimators, are inconsistent under valid identification assumptions, compromising internal validity. A recent Bayesian approach demonstrates consistency under assumptions reasonable in many fair lending contexts. This approach hinges on the insight that identification requires the race predictors to be exogenous with respect to loan approval, essentially an instrumental-variables design. We present a frequentist counterpart to this solution via Ordinary Least Squares (OLS) and Maximum Likelihood Estimation (MLE) under a similar exogeneity assumption. To satisfy these assumptions in practice, we introduce (i) a surname-only proxy analogous to BISG and (ii) an income-stratified prior for race probabilities. Monte Carlo simulations and an application to 2023 Los Angeles HMDA data confirm superior performance: this method reduces RMSE in the LA Black/White adverse-impact ratio by 79.7% (from 10.639pp to 2.158pp) compared to a Weighting estimator with the standard prior.