Read this first: what this can and can't show
The limits come before the results because they decide how the results can be read.
- Associations, not causes. A gap that remains after the controls is consistent with discrimination. It is also consistent with things the files don't record, or record with error. No number here proves that any lender discriminated, or that none did.
- The controls aren't neutral. Some recorded variables, like the lender's own "meets credit guidelines" judgment, were made by the people being studied. Controlling for them can hide part of a real gap. Leaving out true creditworthiness can make a gap look bigger than it is. The Econometrics tab shows how the answer moves with each choice.
- The outcome is a decision, not a repayment. "Approved" records what a lender decided in 1990, not whether the borrower would have repaid. A model trained on it learns to imitate those lenders.
- Small groups. There are Black or Hispanic applicants ( and ). Every estimate is shown with its 95% interval, and some of the intervals are wide.
- One place, one year. This is a textbook subset of the Boston Fed's study, and the study's data quality was itself debated (see Method). Nothing here describes any lender today. Version 2 of this project will use current public HMDA data for Virginia.
Approval rates by group
Share of applications approved (the lender's decision as recorded), with 95% intervals
Show as a table
What the audit found
The gap as controls are added
Difference in approval probability, white minus Black-or-Hispanic applicants, in percentage points, from the linear probability model (the table adds probit and logit marginal effects). All four rows use the same applications. Bars are 95% intervals (robust standard errors).
Show as a table, with Black and Hispanic applicants separately
Do debts count the same for everyone?
Average predicted approval from a probit with a white × obligations-ratio interaction, setting every applicant's obligations ratio to the value shown and the white indicator to 1 or 0 (other variables as recorded). Shaded bands are 95% intervals.
Show as a table
Problem set 6, reproduced
ECON 3720's starting models: approval on white, hrat, obrat,
loanprc, unem, male, married, dep and pubrec,
on the applications with no missing values. The estimates match the course's Stata output to every printed digit.
How much of the gap do the recorded variables account for?
Oaxaca-Blinder decomposition of the approval gap between white and Black-or-Hispanic applicants. "Explained" is the part predicted by differences in the recorded variables; "unexplained" is the rest, the part the same variables don't account for. It is not a measure of discrimination by itself.
Show as a table, with 95% bootstrap intervals
Which differences make up the explained part?
Each variable's contribution to the explained part (pooled reference, credit-history model), in percentage points, with 95% bootstrap intervals. Positive means the variable's group difference predicts a higher approval rate for white applicants.
Show as a table, with group means
A model that never sees race
Show every group, with AUC and accuracy
How to read the rates: the "truth" here is the lender's 1990 decision. TPR is the share of applicants the lenders approved whom the model also approves; FPR is the share the lenders denied whom the model approves. Equal TPRs is "equal opportunity"; equal TPRs and FPRs is "equalized odds"; equal approval rates is "demographic parity". Each one is measured against the 1990 decisions, which is the problem the label-bias section takes up.
Calibration: does the same score mean the same thing?
Observed approval rate against the model's average predicted probability, in fixed score bins, by group. Points on the diagonal are well calibrated. Bars are 95% intervals.
Show as a table
Proxies: how much race the other inputs carry
How well each set of variables predicts whether an applicant is Black or Hispanic (out-of-fold AUC; 0.5 is no better than a coin, 1.0 is perfect). Leaving race out of a model doesn't leave it out of the data.
Show as a table, both model types
The single strongest signals
Each variable alone (AUC distance from 0.5), with the group averages
Mitigation and what it costs
Ways to narrow the race-blind logistic model's approval gap, each approving the same total share of applicants as the lenders did. "Agreement" is the share of decisions that match the 1990 lenders'.
The frontier
Moving each group's approval rate step by step from one cutoff to equal approval rates: agreement with the 1990 decisions against the remaining gap