The Nash-in-Kalai Model for Estimation with Dynamic Bargaining and Nontransferable Utility

Abstract

This paper extends empirical models of dynamic bargaining to allow for the possibility of nontransferable utility. The model agrees with Nash bargaining when utility is transferable, but leverages the Kalai proportional bargaining solution to enable identification in the presence of uncertainty over nontransferable Pareto frontiers. The model extends the class of dynamic bargaining models for which there is a known valid general method of moments estimation strategy to include agreements that have foreseeable and nontransferable contracting externalities on the distribution of future states, and the model uniquely possesses a discrete-time representation even when bargaining is defined in continuous time. I estimate an empirical model in this class using novel hospital–insurer contract panel data from West Virginia, where agreements had nontransferable contracting externalities on other deals reached while the terms remained in place. I find that dynamic aspects of bargaining are important: the estimated annual discounting rate of 0.899 corresponds to a strong forward-looking response.