Adverse Selection Without Single Crossing

Abstract

The single crossing assumption simplifies the analysis of screening models as local incentive compatibility becomes sufficient for global incentive compatibility. If single crossing is violated, global incentive compatibility constraints have to be taken into account. This paper studies monotone solutions in a model where single crossing is violated.

It is shown that local and non-local incentive constraints distort the solution in opposite directions. Therefore, the optimal decision might involve distortions above as well as below the first best decision. Furthermore, the well known “no distortion at the top” property does not necessarily hold. It is shown that the decision can even be distorted above first best for all types. Sufficient conditions for existence, monotonicity and continuity of the solution and an algorithm to obtain such a solution are derived.

Keywords: selection, single crossing, Spence-Mirrlees condition, global incentive compatibility

JEL Classification: D82, D86, L11