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

Abstract

This paper extends empirical dynamic bargaining models to accommodate the possibility of nontransferable utility. I leverage the Kalai proportional bargaining solution, which coincides with Nash bargaining under transferable utility, but is the only solution satisfying independence of irrelevant alternatives that is identified under nontransferable utility given unobserved information sets. In recursive problems, Kalai proportional bargaining enables a finite dependence-type cancellation of future states. For multilateral games, I propose the Nash-in-Kalai model, which aligns with Nash-in-Nash under transferable utility, but which enables valid general method of moments estimation even when agreements have foreseeable and nontransferable contracting externalities on future states. I apply this model to hospital-insurer contract panel data from West Virginia, where agreements had nontransferable contracting externalities on future deals reached during their tenure. Negotiators were substantially forward-looking, with an estimated annual discounting rate of 0.899.