Two-Sided Matching in Physician-Insurer Networks: Evidence from Medicare Advantage

Many health insurance plans in the U.S. restrict enrollees to choose from a set of providers the insurer has contracted with. These provider networks are formed via bilateral bargaining between insurers and providers. Provider networks are an important tool for product differentiation and cost containment for insurers and also put real restrictions on consumers’ choice of providers. Surprisingly, in most health insurance markets provider networks are largely unregulated, in contrast to other plan characteristics like benefits or cost sharing. Quantifying the incentives of insurers and providers underlying the formation of the networks is crucial to understanding the tradeoffs (or complementarities) between plan quality and network quality.   

In this paper, I analyze matching between insurers offering Medicare Advantage Plans and physicians, using a unique data set consisting of all insurer-physician links in several counties. I estimate parameters of a two-sided, many-to-many matching model which describes formation of provider networks, using the Maximum Score estimator of Fox (2010). This method uses implications of a pairwise stability condition to estimate a joint surplus function which depends on insurer-physician links. The surplus function accounts for the role of physician and insurer characteristics in determining their match values, and also for interactions between physicians linked to the same insurer, whose services may be complements or substitutes.    

This paper augments the literature on hospital-provider networks. Clearly, both hospitals and physicians are important for how consumers choose and utilize their health insurance. The literature has shied away from including physicians in models of provider networks, in part because of the computational complexity of models of matching and bargaining with many agents. I circumvent this difficulty in two ways. First, the methods of Fox (2010) allow for tractable estimation of an object of interest, the joint surplus function, without having to solve a full game. Second, the restriction to insurers participating in Medicare Advantage reduces the number of agents and links involved. At the same time, since these insurers plus original Medicare are the only competitors for the relevant pool of patients, Medicare eligibles, a full market is captured.

The results indicate that insurers prefer on the margin to link with physicians who increase the specialty concentration of their network and whose offices are located near those of other physicians in the network. Furthermore, physicians are negatively affected by having a broader referral network, as defined by having a larger set of physicians with whom they have insurer links in common. These forces could lead to networks being undesirably narrow, excluding specialties, locations and specific physicians that would be valuable for some plan enrollees. Finally, compared with regional insurers, nationally active insurers have a larger number of exclusive links with physicians, and match with more physicians with U.S. medical degrees. If these characteristics proxy for quality, then this result suggests positive assortative matching, where high quality insurers benefit from linking with high quality physicians. In that case, regulations aimed at encouraging high plan quality would also tend to positively impact network quality.