Testing homogeneity in dynamic discrete games in finite samples

The literature on dynamic discrete games often assumes that the conditional choice probabilities and the state transition probabilities are homogeneous across markets and over time. We refer to this as the homogeneity assumption in dynamic discrete games. This homogeneity assumption enables empirical studies to estimate the games structural parameters by pooling data from multiple markets and from many time periods. In this paper, we propose a hypothesis test to evaluate whether the homogeneity assumption holds in the data. Our hypothesis is the result of an approximate randomization test, implemented via a Markov chain Monte Carlo (MCMC) algorithm. We show that our hypothesis test becomes valid as the (user-defined) number of MCMC draws diverges, for any fixed number of markets, time-periods, and players. We apply our test to the empirical study of the U.S. Portland cement industry in Ryan (2012).