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Computing Markov perfect Nash equilibria: numerical implications of a dynamic differentiated product model

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  • Paul McGuire
  • Ariel Pakes

Abstract

This paper provides an algorithm for computing Markov Perfect Nash Equilibria (Maskin and Tirole, 1988a and b) for dynamic models that allow for heterogeneity among firms and idiosyncratic (or firm specific) sources of uncertainty. It has two purposes. To illustrate the ability of such models to reproduce important aspects of reality, and to provide a tool which can be used for both descriptive and policy analysis in a framework rich enough to capture many of the features of firm level data sets (thereby enabling it to be integrated with the empirical detail in those data sets). We illustrate by computing the policy functions, and simulating the industry structures, generated by a class of dynamic differentiated product models in which the idiosyncratic uncertainty is due to the random outcomes of each firm's research process (we also allow for an autonomous aggregate demand process). The illustration focuses on comparing the effects of different regulatory and institutional arrangements on market structure and on welfare for one particular set of parameter values. The simulation results are of independent interest and can be read without delving into the technical detail of the computational algorithm The last part of the paper begins with an explicit consideration of the computational burden of the algorithm, and then introduces approximation techniques designed to make computation easier. This section provides some analytic results which dramatically reduce the computational burden of computing equilibria for industries in which a large number of firms are typically active.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Paul McGuire & Ariel Pakes, 1992. "Computing Markov perfect Nash equilibria: numerical implications of a dynamic differentiated product model," Discussion Paper / Institute for Empirical Macroeconomics 58, Federal Reserve Bank of Minneapolis.
  • Handle: RePEc:fip:fedmem:58
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    References listed on IDEAS

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    1. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
    2. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
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    4. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    5. Steven J. Davis & John Haltiwanger, 1990. "Gross Job Creation and Destruction: Microeconomic Evidence and Macroeconomic Implications," NBER Chapters, in: NBER Macroeconomics Annual 1990, Volume 5, pages 123-186, National Bureau of Economic Research, Inc.
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    9. Ariel Pakes, 1991. "Dynamic Structural Models: Problems and Prospects. Mixed Continuous Discrete Controls and Market Interactions," Cowles Foundation Discussion Papers 984, Cowles Foundation for Research in Economics, Yale University.
    10. Lars Peter Hansen & Thomas J. Sargent, 1993. "Recursive linear models of dynamic economies," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
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