Do Lenders Still Discriminate? A Robust Approach for Assessing Differences in Menus

Abstract

We use a new methodology to assess mortgage pricing discrimination by race. We make four main contributions. First, we show that existing estimates of mortgage pricing differences by race can be confounded by a "menu problem," which is the problem associated with evaluating equality in opportunity under multi-dimensional pricing. Though under-appreciated, the menu problem is broadly relevant in economic assessments of differences in opportunity given data on outcomes. Second, we provide a general methodology for resolving this menu problem based on relatively weak economic assumptions. More specifically, we use pairwise dominance relationships in mortgage pricing supplemented by restrictions on the range of plausible menus to define (1) a test statistic for equality in menus and (2) a difference in menus (DIM) metric for assessing whether one group of borrowers would prefer to switch to another group's menus. Our metrics are robust to arbitrary heterogeneity in borrower preferences across racial groups over the menu items, are sharp in terms of identification, and can be efficiently computed using methods from Optimal Transport. Third, to conduct statistical inference we devise a new procedure for hypothesis testing in the value of Optimal Transport problems based on directional differentiation. Fourth, we use our methodology to estimate mortgage pricing differentials by race on a new data set linking 2018--2019 Home Mortgage Disclosure Act (HMDA) data to Optimal Blue rate locks. We find robust evidence for mortgage pricing differentials by race, particularly among Conforming mortgage borrowers who are relatively creditworthy.

Keywords: Mortgage Discrimination, Fair Lending, Red-lining, Points, Interest Rate, Optimal Transport, Directional Differentiation, Menu Problem

JEL Classification: G21, G28, R51, C12, C44