Large Matching Markets as Two‐Sided Demand Systems

This paper studies two‐sided matching markets with non‐transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed‐point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.     

Guaranteed renewability uniquely prevents adverse selection in individual health insurance

New models of multi-period insurance show that health insurance buyers can be protected against changes in premiums from health shocks associated with chronic conditions by the addition of “guaranteed renewability” provisions. These models assume that a buyer’s risk level in every time period is observed by all insurers. They also require a premium sequence that is “front-loaded,” which may be costly to buyers if capital markets are imperfect. We relax the common knowledge feature of the model by assuming that a person’s risk in any time period is known only by that individual and the current insurer. One might suspect that a premium sequence with higher later period premiums would be incentive compatible because low risks will have less desirable offerings from alternative insurers. However, we show that generally, only the original premium schedule is incentive compatible, and attempts to alter front-loading will not be an equilibrium.