Implications of Stratified Sampling for Fair Lending Binary Logit Models

We examine the effect of sample design on estimation and inference for disparate treatment in binary logistic models used to assess for fair lending. Our Monte Carlo experiments provide information on how sample design affects efficiency (in terms of mean squared error) of estimation of the disparate treatment parameter and power of a test for statistical insignificance of this parameter. The sample design requires two decision levels: first, the degree of stratification of the loan applicants (Level I Decision) and secondly, given a Level I Decision, how to allocate the sample across strata (Level II Decision). We examine four Level I stratification strategies: no stratification (simple random sampling), exogenously stratifying loan cases by race, endogenously stratifying cases by loan outcome (denied or approved), and stratifying exogenously by race and endogenously by outcome. Then, we consider five Level II methods: proportional, balanced, and three designs based on applied studies. Our results strongly support the use of stratifying by both race and loan outcome coupled with a balanced sample design when interest is in estimation of, or testing for statistical significance of, the disparate treatment parameter.