How Low Can You Go? An Optimal Sampling Strategy for Fair Lending Exams

This study uses Monte Carlo simulation to examine the impact of nine sampling strategies on the finite sample performance of the maximum likelihood logit estimator. Empirical researchers face a tradeoff between the lower resource costs associated with smaller samples and the increased confidence in the results gained from larger samples. Choice of sampling strategy is one tool researchers can use to reduce costs yet still attain desired confidence levels. The nine sampling strategies examined in this study include simple random sampling and eight variations of stratified random sampling. Bias, mean-square-error, percentage of models that are feasibly estimated, and percentage of simulated estimates that differ statistically from the true population parameters are used as measures of finite sample performance. The results show stratified random sampling by action (loan approval/denial) and race of the applicant, with balanced strata sizes and a bias correction for choice-based sampling, outperforms each of the other sampling strategies with respect to the four performance measures. These findings, taken together with supporting evidence presented in Scheuren and Sangha (1998) and Giles and Courchane (2000) make a strong argument for implementing such a sampling strategy in future fair lending exams. The views expressed in this paper are those of the author alone, and do not necessarily reflect those of the Office of the Comptroller of the Currency or the Department of the Treasury. The author would like to thank Jeff Brown, Irene Fang, David Guilkey, Amber Jessup, Shanzi Ke, Dom Mancini, Todd Vermilyea, and Morey Rothberg for their insightful comments and editorial assistance. Please address correspondence to Jason Dietrich, Economist, Risk Analysis Division, Office of the Comptroller of the Currency, 250 E. Street, S.W., Washington, DC 20219 (phone: 202-874-5119; e-mail: [email protected]).