We study an economy with financial frictions in which a regulator designs a test that reveals outside information about a firm's quality to investors. The firm can also disclose verifiable inside information about its quality. We show that the regulator optimally aims for “public speech and private silence,” which is achieved with tests that give insiders an incentive to stay quiet. We fully characterize optimal tests by developing tools for Bayesian persuasion with incentive constraints, and use these results to derive novel guidance for the design of bank stress tests, as well as benchmarks for socially optimal corporate credit ratings.

Innovations in statistical technology in functions including credit‐screening have raised concerns about distributional impacts across categories such as race. Theoretically, distributional effects of better statistical technology can come from greater flexibility to uncover structural relationships or from triangulation of otherwise excluded characteristics. Using data on U.S. mortgages, we predict default using traditional and machine learning models. We find that Black and Hispanic borrowers are disproportionately less likely to gain from the introduction of machine learning. In a simple equilibrium credit market model, machine learning increases disparity in rates between and within groups, with these changes attributable primarily to greater flexibility.