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A Method for Implementing Counterfactual Experiments in Models with Multiple Equilibria

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  • Victor, Aguirregabiria

Abstract

This paper proposes a method for implementing counterfactual experiments in estimated models that have multiple equilibria. The method assumes that the researcher does not know the equilibrium selection mechanism and wants to impose minimum restrictions on it. Our key assumption is that the equilibrium selection function does not jump discontinuously between equilibria as we change marginally the structural parameters of the model. Under this assumption, we show that, although the equilibrium selection function is unknown, the researcher can obtain an approximation of this function in a neighborhood of the estimated values of the structural parameters. Under the additional assumption that the counterfactual equilibrium is stable, this approximation can be combined with iterations in the equilibrium mapping to obtain the exact counterfactual equilibrium. We illustrate the differences between our approach and other methods, such as the selection of a counterfactual equilibrium that is closer to the equilibrium in the data, and equilibrium mapping iterations using the equilibrium in the data as the initial value. We show that, in general, these alternative methods are not consistent with the assumption that the equilibrium selection mechanism is continuous with respect to the structural parameters.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 17805.

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Date of creation: 10 Oct 2009
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Handle: RePEc:pra:mprapa:17805

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Keywords: Structural models with multiple equilibria; Counterfactual experiments; Equilibrium selection.;

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  1. Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
  2. Stephen P. Ryan, 2012. "The Costs of Environmental Regulation in a Concentrated Industry," Econometrica, Econometric Society, vol. 80(3), pages 1019-1061, 05.
  3. 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.
  4. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, 06.
  5. Patrick Bajari & Han Hong & John Krainer & Denis Nekipelov, 2006. "Estimating Static Models of Strategic Interaction," NBER Working Papers 12013, National Bureau of Economic Research, Inc.
  6. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov-perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243.
  7. Victor Aguirregabiria, 2004. "Pseudo Maximum Likelihood Estimation of Structural Models Involving Fixed-Point Problems," Econometrics 0402003, EconWPA.
  8. Allan Collard-Wexler, 2006. "Demand Fluctuations and Plant Turnover in the Ready-Mix Concrete Industry," Working Papers 06-25, New York University, Leonard N. Stern School of Business, Department of Economics.
  9. Victor Aguirregabiria & Pedro Mira, 2004. "Sequential Estimation Of Dynamic Discrete Games," Working Papers wp2004_0413, CEMFI.
  10. J. Levin & P. Bajari, 2004. "Estimating Dynamic Models of Imperfect Competition," 2004 Meeting Papers 579, Society for Economic Dynamics.
  11. Brock, William A & Durlauf, Steven N, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 235-60, April.
  12. Martin Pesendorfer & Philipp Schmidt-Dengler, 2008. "Asymptotic Least Squares Estimators for Dynamic Games -super-1," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 901-928.
  13. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  14. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
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Cited by:
  1. Besanko, David & Doraszelski, Ulrich & Kryukov, Yaroslav, 2011. "The economics of predation: What drives pricing when there is learning-by-doing?," CEPR Discussion Papers 8708, C.E.P.R. Discussion Papers.
  2. Aguirregabiria, Victor & Ho, Chun-Yu, 2010. "A dynamic game of airline network competition: Hub-and-spoke networks and entry deterrence," International Journal of Industrial Organization, Elsevier, vol. 28(4), pages 377-382, July.
  3. Joao Macieira, 2010. "Oblivious Equilibrium in Dynamic Discrete Games," 2010 Meeting Papers 680, Society for Economic Dynamics.
  4. Naoaki Minamihashi, 2012. "Natural Monopoly and Distorted Competition: Evidence from Unbundling Fiber-Optic Networks," Working Papers 12-26, Bank of Canada.
  5. Victor Aguirregabiria & Victor Aguirregabiria & Aviv Nevo & Aviv Nevo, 2010. "Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games," Working Papers tecipa-419, University of Toronto, Department of Economics.
  6. Victor Aguirregabiria & Gustavo Vicentini, 2012. "Dynamic Spatial Competition Between Multi-Store Firms," Working Papers tecipa-457, University of Toronto, Department of Economics.
  7. Nathan Yang, 2011. "An Empirical Model of Industry Dynamics with Common Uncertainty and Learning from the Actions of Competitors," Working Papers 11-16, NET Institute.

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