Optimal Privacy with Coarse Labels in Screening Markets

Abstract

We study the implications of fundamental information frictions for optimal information design in settings with screening. We introduce a regulator who observes imperfect information about a buyer's private valuation for quality based on a group-level characteristic, and can commit to provide a (possibly garbled) signal of these characteristics to a monopoly seller. In a setting with binary types and groups, we fully characterize optimal signals and derive their welfare properties. In contrast to much of the recent literature studying information design in markets, we find that aggregate surplus is often not maximized at full information; partial disclosure is optimal when group-level statistics suffer from sufficiently large Type I errors. In this way, our results provide a robust rationale for privacy protection that applies even when consumers and producers are treated symmetrically. Our main analysis focuses on information design in the classic setting of Mussa and Rosen (1978), but we show that the same economics apply in a broad array of classic information economics settings and to settings with many types. Our results can be interpreted through the lens of restrictions imposed on the observables on which monopolists may discriminate to aid their screening.

Keywords: Information Design, Bayesian Persuasion, Constraint Information Design, Price Discrimination, Nonlinear Pricing, Private Information

JEL Classification: D42, D83, L12