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

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We use a new methodology to assess mortgage pricing discrimination faced by minority borrowers. When getting a mortgage, borrowers can choose to avoid closing costs and pay a high interest rate or contribute to closing costs to get a lower rate. While data on both dimensions of mortgage pricing are by now often available, intuitively attractive metrics of lender pricing discrimination currently used by the literature can lead to false positives (seeing discrimination where none exists), false negatives (not seeing discrimination where it does exist), and sometimes contradictory results depending on which methodology is used. This "menu problem" stems from potential heterogeneity in preferences across racial groups and is broadly relevant whenever agents make multi-dimensional trade-offs, but is generally underappreciated. To address this problem, we define (1) a new, robust test statistic for equality in menus and (2) a difference in menus (DIM) metric for assessing whether one group of consumers would prefer to switch to another group's menus, both based on pairwise dominance relationships in the data. We show how these metrics can be computed using methods from optimal transport and devise a new procedure for hypothesis testing in this class of problems based on directional differentiation. We implement our metrics on a new data set matching 2018--2019 Home Mortgage Disclosure Act (HMDA) data to Optimal Blue rate locks. We find robust evidence that Black and Hispanic borrowers were offered menus that, in terms of rates and points by lenders, were worse than the menus offered to non-Hispanic white borrowers for conforming mortgages. Furthermore, the differences we detect are not explained by loan originator compensation and were particularly concentrated among more creditworthy borrowers.

Last updated on 11/27/2020