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Markov perfect industry dynamics with many firms

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  • Gabriel Y. Weintraub
  • C. Lanier Benkard
  • Benjamin Van Roy
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    Abstract

    We propose an approximation method for analyzing Ericson and Pakes (1995)-style dynamic models of imperfect competition. We develop a simple algorithm for computing an "oblivious equilibrium," in which each firm is assumed to make decisions based only on its own state and knowledge of the long run average industry state, but where firms ignore current information about competitors' states. We prove that, as the market becomes large, if the equilibrium distribution of firm states obeys a certain "lighttail" condition, then oblivious equilibria closely approximate Markov perfect equilibria. We develop bounds that can be computed to assess the accuracy of the approximation for any given applied problem. Through computational experiments, we find that the method often generates useful approximations for industries with hundreds of firms and in some cases even tens of firms.

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    Bibliographic Info

    Paper provided by Federal Reserve Bank of San Francisco in its series Working Paper Series with number 2005-23.

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    Date of creation: 2005
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    Handle: RePEc:fip:fedfwp:2005-23

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    Keywords: Competition ; Econometric models;

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    References

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    1. Ariel Pakes, 2000. "A Framework for Applied Dynamic Analysis in I.O," NBER Working Papers 8024, National Bureau of Economic Research, Inc.
    2. Melitz, Marc J, 2002. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," CEPR Discussion Papers 3381, C.E.P.R. Discussion Papers.
    3. By Kenneth L. Judd & Karl Schmedders & ┼×evin Yeltekin, 2012. "Optimal Rules For Patent Races," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 23-52, 02.
    4. C. Lanier Benkard, 2004. "A Dynamic Analysis of the Market for Wide-Bodied Commercial Aircraft," Review of Economic Studies, Wiley Blackwell, vol. 71, pages 581-611, 07.
    5. Shaked, Avner & Sutton, John, 1987. "Product Differentiation and Industrial Structure," Journal of Industrial Economics, Wiley Blackwell, vol. 36(2), pages 131-46, December.
    6. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    7. David Besanko & Ulrich Doraszelski, 2005. "Learning-by-Doing, Organizational Forgetting, and Industry Dynanmics," Computing in Economics and Finance 2005 236, Society for Computational Economics.
    8. Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Cowles Foundation Discussion Papers 937, Cowles Foundation for Research in Economics, Yale University.
    9. Novshek, William & Sonnenschein, Hugo, 1978. "Cournot and Walras equilibrium," Journal of Economic Theory, Elsevier, vol. 19(2), pages 223-266, December.
    10. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    11. Minjae Song, 2011. "A Dynamic Analysis Of Cooperative Research In The Semiconductor Industry," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(4), pages 1157-1177, November.
    12. Klette, Tor Jakob & Kortum, Samuel, 2002. "Innovating Firms and Aggregate Innovation," Memorandum 02/2002, Oslo University, Department of Economics.
    13. Drew Fudenberg & David K. Levine, 1986. "Limit Games and Limit Equilibria," Levine's Working Paper Archive 220, David K. Levine.
    14. repec:rus:hseeco:122439 is not listed on IDEAS
    15. Ulrich Doraszelski & Mark Satterthwaite, 2003. "Foundations of Markov-Perfect Industry Dynamics. Existence, Purification, and Multiplicity," Discussion Papers 1383, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    16. 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.
    17. Ronald L. Goettler & Christine A. Parlour, 2004. "Equilibrium in a Dynamic Limit Order Market," 2004 Meeting Papers 757, Society for Economic Dynamics.
    18. Gautam Gowrisankaran & Robert J. Town, 1997. "Dynamic Equilibrium in the Hospital Industry," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(1), pages 45-74, 03.
    19. Berry, Steven & Pakes, Ariel, 1993. "Some Applications and Limitations of Recent Advances in Empirical Industrial Organization: Merger Analysis," American Economic Review, American Economic Association, vol. 83(2), pages 247-52, May.
    20. Patricia Langohr, 2003. "Competitive Convergence and Divergence: Capability and Position Dynamics," Computing in Economics and Finance 2003 229, Society for Computational Economics.
    21. C. Lanier Benkard, 2004. "A Dynamic Analysis of the Market for Wide-Bodied Commercial Aircraft," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 581-611.
    22. de Roos, Nicolas, 2004. "A model of collusion timing," International Journal of Industrial Organization, Elsevier, vol. 22(3), pages 351-387, March.
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    Cited by:
    1. Xiao, Junji, 2008. "Markov Perfect Equilibrium in the US digital camera market," International Journal of Industrial Organization, Elsevier, vol. 26(5), pages 1233-1249, September.
    2. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2007. "Computational Methods for Oblivious Equilibrium," Research Papers 1969, Stanford University, Graduate School of Business.

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