Testing homogeneity in dynamic discrete games in finite samples

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 homogeneity 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 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).

Equilibrium multiplicity in dynamic games: Testing and estimation

“…In contrast to the asymptotic tests by Otsu et al (2016), Bugni et al (2021) propose an approximation to the exact randomization test (see chapter 15.2 of Lehmann and Romano, 2005) of the homogeneity hypothesis across markets and time periods 1 and H hom 0 , the sufficient statistic of the data d = (a t j , s t j ) j =1,...,M,t=1,...,T is given by…”

“…However, since is usually difficult to enumerate, this test is practically infeasible. To address this practical issue, Bugni et al (2021) propose an MCMC-based approximation for φ rd (d). In particular, they construct an iterative C The Author(s) 2022.…”

“…We describe the asymptotic tests by Otsu et al (2016) that examine homogeneity of the distribution of state variables, where asymptotics may refer to the number of time periods or the number of markets getting large. We also discuss recent advances on homogeneity or multiplicity testing, such as an approximately exact test by Bugni et al (2021) and rank test based on serial correlations due to multiplicity by de Paula and Tang (2021). Second, Section 4 discusses robust inference methods under equilibrium multiplicity.…”