Joint analysis of the discount factor and payoff parameters in dynamic discrete choice models

Abstract

Most empirical models of dynamic games assume the discount factor to be known and focus on the estimation of the payoff parameters. However, the discount factor can be identifed when the payoffs satisfy parametric or other nonparametric restrictions. We show when the payoffs take the popular linear-in-parameter specification, the joint identification of the discount factor and payoff parameters can be simplified to a one-dimensional model that is easy to analyze. We also show that switching costs (e.g. entry costs) that often feature in empirical work can be identifed in closed-form, independently of the discount factor and other specification of the payoff function. Our identification strategies are constructive. They lead to easy to compute estimands that are global solutions. Estimating the discount factor permits direct inference on borrowing rate. Our estimates of the switching costs can be used for specification testing. We illustrate with a Monte Carlo study and the dataset from Ryan (2012).