We estimate an insurer-specific preference function which rationalizes hospital referrals for privately insured births in California. The function is additively separable in: a hospital price paid by the insurer, the distance traveled, and plan- and severity-specific hospital fixed effects (capturing hospital quality). We use an inequality estimator that allows for errors in price and detailed hospital-severity interactions and obtain markedly different results than those from a logit. The estimates indicate that insurers with more capitated physicians are more responsive to price. Capitated plans send patients further to utilize similar quality, lower-priced hospitals; but the cost-quality trade-off does not vary with capitation rates.

Commercial health insurers in California use provider capitation payments to different extents. These are similar to arrangements introduced by the recent health reforms to give physicians incentives to control costs. In a previous paper we showed that patients whose insurers used capitation incentives traveled further to access lower-priced, similar-quality hospitals than other same-severity patients. This paper predicts the implied effects of a move to widespread capitation. We show that, if the introduction of capitation prompted low-capitation insurers to act like high-capitation insurers, this would generate a 4-5 percent cost saving with some reduction in patient convenience but no reduction in quality.

We evaluate the consequences of narrow hospital networks in commercial health care markets. We develop a bargaining solution, "Nash- in-Nash with Threat of Replacement," that captures insurers' incentives to exclude, and combine it with California data and estimates from Ho and Lee (2017) to simulate equilibrium outcomes under social, consumer, and insurer- optimal networks. Private incentives to exclude generally exceed social incentives, as the insurer benefits from substantially lower negotiated hospital rates. Regulation prohibiting exclusion increases prices and premiums and lowers consumer welfare without significantly affecting social surplus. However, regulation may prevent harm to consumers living close to excluded hospitals.

This paper provides conditions under which the inequality constraints generated by either single agent optimizing behavior or the best response condition of multiple agent problems can be used as a basis for estimation and inference. An application illustrates how the use of these inequality constraints can simplify the analysis of complex behavioral models.