Dynamic Bargaining between Hospitals and Insurers (Job Market Paper)

Abstract

This paper introduces the Nash-in-Kalai model, a new bargaining framework designed to tractably capture forward-looking dynamics in markets with staggered contracting. The Nash-in-Kalai model aligns with the usual Nash-in-Nash model in many leading static cases, but uniquely controls state space growth in dynamic settings. I use novel data on hospital–insurer contracts in West Virginia, which are typically trade secrets. Typical contract durations ranged from three years to a decade or longer. I use this data to provide the first estimated structural model of vertical market bargaining with staggered contracts. I find that negotiators were substantially forward-looking: I reject the null hypothesis of myopia and estimate an annual discounting rate of β = 0.899. I quantify a new counterfactual effect of a proposed government-driven reform on private payment dynamics. I find that the reform would increase private spending after nine years by $4.98 billion, while a myopic model lacking forward-looking responses would overestimate the effect by $2.35 billion and miss short-term dynamics, including the possibility of payments decreasing.