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

61 Pages Posted: 16 Aug 2021 Last revised: 18 Aug 2022

See all articles by David Hao Zhang

David Hao Zhang

Harvard University; Harvard University, Harvard Business School, Students

Paul Willen

Federal Reserve Bank of Boston - Research Department; National Bureau of Economic Research (NBER)

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Date Written: August 2021

Abstract

Motivated by the assessment of racial discrimination in mortgage pricing, we introduce a new methodology for comparing the menus of options borrowers face based on their choices. First, we show how standard regression-based approaches for assessing discrimination in the menus context can lead to misleading and contradictory results. Second, we propose a new methodology that is robust these problems based on relatively weak economic assumptions. More specifically, we use pairwise dominance relationships in choices 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 statistics are robust to arbitrary heterogeneity in borrower preferences across racial groups, are sharp in terms of identification, and can be efficiently computed using Optimal Transport methods. Third, we devise a new approach for inference on the value of Optimal Transport problems based on directional differentiation. Fourth, we use our methodology to estimate mortgage pricing differentials by race on a novel 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.

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Suggested Citation

Zhang, David Hao and Willen, Paul S., Do Lenders Still Discriminate? A Robust Approach for Assessing Differences in Menus (August 2021). NBER Working Paper No. w29142, Available at SSRN: https://ssrn.com/abstract=3905707

David Hao Zhang (Contact Author)

Harvard University ( email )

Cambridge, MA
United States

Harvard University, Harvard Business School, Students ( email )

Cambridge, MA
United States

Paul S. Willen

Federal Reserve Bank of Boston - Research Department ( email )

600 Atlantic Avenue
Boston, MA 02210
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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