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Testing for Equilibrium Multiplicity in Dynamic Markov Games

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  • Otsu, Taisuke
  • Pesendorfer, Martin
  • Takahashi, Yuya

Abstract

This paper proposes several statistical tests for finite state Markov games to examine the null hypothesis that the data are generated from a single equilibrium. We formulate tests of (i) the conditional choice probabilities, (ii) the steady-state distribution of states and (iii) the conditional distribution of states conditional on an initial state. In a Monte Carlo study we find that the chi-squared test of the steady-state distribution performs well and has high power even with a small number of markets and time periods. We apply the chi-squared test to the empirical application of Ryan (2012) that analyzes dynamics of the U.S. Portland Cement industry and test if his assumption of single equilibrium is supported by the data.

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Paper provided by Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich in its series Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems with number 423.

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Date of creation: Apr 2013
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Handle: RePEc:trf:wpaper:423

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Keywords: Dynamic Markov Game; Multiplicity of Equilibria; Testing;

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  1. Peter Arcidiacono & Robert A. Miller, 2011. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 79(6), pages 1823-1867, November.
  2. Aureo de Paula & Xun Tang, 2010. "Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information," PIER Working Paper Archive 10-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  3. Mireia Jofre-Bonet & Martin Pesendorfer, 2001. "Estimation of a Dynamic Auction Game," NBER Working Papers 8626, National Bureau of Economic Research, Inc.
  4. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  5. Timothy Dunne & Shawn D. Klimek & Mark J. Roberts & Daniel Yi Xu, 2009. "Entry, exit and the determinants of market structure," Working Paper 0907, Federal Reserve Bank of Cleveland.
  6. J. Levin & P. Bajari, 2004. "Estimating Dynamic Models of Imperfect Competition," 2004 Meeting Papers 579, Society for Economic Dynamics.
  7. Paul Ellickson & Beresteanu Arie, 2005. "The Dynamics of Retail Oligopolies," 2005 Meeting Papers 829, Society for Economic Dynamics.
  8. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, 01.
  9. Junichi Suzuki, 2010. "Land Use Regulation as a Barrier to Entry: Evidence from the Texas Lodging Industry," Working Papers tecipa-400, University of Toronto, Department of Economics.
  10. Peter Arcidiacono & Patrick J. Bayer & Jason R. Blevins & Paul Ellickson, 2010. "Estimation of Dynamic Discrete Choice Models in Continuous Time," Working Papers 10-49, Duke University, Department of Economics.
  11. Naoaki Minamihashi, 2012. "Natural Monopoly and Distorted Competition: Evidence from Unbundling Fiber-Optic Networks," Working Papers 12-26, Bank of Canada.
  12. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
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