Testing homogeneity in dynamic discrete games in finite samples

TL;DR

This paper develops a hypothesis test to evaluate the validity of the homogeneity assumption in dynamic discrete games, using an MCMC-based randomization approach, with application to the U.S. cement industry.

Contribution

It introduces a novel hypothesis testing method for the homogeneity assumption in dynamic discrete games, applicable to finite samples and implemented via MCMC.

Findings

The test is valid as the number of MCMC draws increases.

Applied to the U.S. Portland cement industry data.

Provides a tool for empirical validation of homogeneity assumptions.

Abstract

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 assumption enables empirical studies to estimate the game's 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 test 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).