Pooling data across markets in dynamic Markov games

This paper proposes several statistical tests for finite state Markov games to examine whether data from distinct markets can be pooled. We formulate homogeneity tests of (i) the conditional choice and state transition probabilities, (ii) the steady-state distribution, and (iii) the conditional state distribution given an initial state. The null hypotheses of these homogeneity tests are necessary conditions (or maintained assumptions) for poolability of the data. Thus rejections of these null imply that the data cannot be pooled across markets. Acceptances of these null are considered as supporting evidences for the maintained assumptions of estimation using pooled data. In a Monte Carlo study we find that the test based on the steady-state distribution performs well and has high powereven with small numbers of markets and time periods. We apply the tests to the empirical study of Ryan (2012) that analyzes dynamics of the U.S. Portland Cement industry and assess if the data across markets can be pooled.