Fairness Testing for Algorithmic Pricing

2026-05-12

AI Summary

This study addresses the failure of existing algorithmic pricing fairness audits in deterministic systems, where the misuse of classical standard errors renders them incapable of detecting proxy discrimination. The authors reconstruct the statistical inference framework for regression-based audits, revealing for the first time a structural bias in conventional standard error estimates. They derive asymptotically valid variance and covariance estimators tailored to deterministic algorithms for both OLS and GLM models, thereby establishing a statistically sound theory for fairness testing. Empirical analysis of 34 auto insurers in Illinois demonstrates that the corrected method identifies significant discrimination across all firms, with 16 exceeding a substantive fairness threshold—while traditional methods entirely fail to detect any such disparities.

Abstract

Algorithmic systems now set prices across auto insurance, credit, and lending markets, and regulators increasingly require firms to demonstrate that these systems do not discriminate against protected groups. The standard audit regresses pricing output on a protected attribute and legitimate rating factors, then tests the resulting coefficient using ordinary least squares standard errors. We show that this approach is structurally invalid. Pricing algorithms are usually deterministic, so residuals reflect approximation error rather than sampling variability, rendering classical standard errors invalid in both direction and magnitude. We derive correct asymptotic variance estimators for OLS and GLM audit regressions and the correct cross-covariance formula for proxy discrimination testing. Applied to quoted premiums from 34 Illinois auto insurers, every insurer fails the conditional demographic parity test, with minority zip codes paying $34-$158 more per year than comparable-risk white zip codes. The standard proxy discrimination formula flags zero insurers. However, our corrected formula identifies all 34 as statistically significant, of which 16 exceed the substantive threshold. Our framework provides statistically valid audit tools for any deterministic algorithmic system subject to regression-based fairness testing.

Problem

• fairness testing
• algorithmic pricing
• proxy discrimination
• deterministic algorithms
• regression-based auditing

Innovation

• fairness testing
• algorithmic pricing
• proxy discrimination
• asymptotic variance estimation
• deterministic algorithms