Joint Analysis of the Discount Factor and Payoff Parameters in Dynamic Discrete Choice Models

Abstract

Most empirical and theoretical econometric studies of dynamic discrete choice models assume the discount factor to be known. We show the knowledge of the discount factor is not necessary to identify parts, or all, of the payoff function. We show the discount factor can be generically identified jointly with the payoff parameters. It is known the payoff function cannot non-parametrically identified without any a priori restrictions. Our identification of the discount factor is robust to any normalization choice on the payoff parameters. In IO applications normalizations are usually made on switching costs, such as entry costs and scrap values. We also show that switching costs can be non-parametrically identified, in closed-form, independently of the discount factor and other parts of the payoff function. Our identification strategies are constructive. They lead to easy to compute estimands that are global solutions. We illustrate with a Monte Carlo study and the dataset from Ryan (2012).