Constrained Efficient Equilibria in Selection Markets with Continuous Types

We prove the existence of the constrained efficient Miyazaki (1977)-Wilson (1977)-Spence (1978) equilibrium in competitive markets with adverse selection when the distribution of unobservable types is continuous. Our existence proof applies under extremely general assumptions about individual preferences. When we restrict preferences to have the widely-used-in-the-selection-markets-literature quasilinear form, we characterize the properties of this equilibrium by developing a simple and computationally efficient numerical method for constructing it. Applying this method, we show in a natural setting how one would compute the equilibrium allocation, potentially facilitating empirical work using the MWS equilibrium. We illustrate this empirical application in the context of policy interventions and show that the welfare implications of a coverage mandate critically hinge on whether the market implements a constrained efficient allocation like the MWS equilibrium or a constrained inefficient allocation like in Azevedo and Gottlieb (2017)