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A Method for Implementing Counterfactual Experiments in Models with Multiple Equilibria


  • Victor Aguirregabiria


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 election 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.

Suggested Citation

  • Victor Aguirregabiria, 2009. "A Method for Implementing Counterfactual Experiments in Models with Multiple Equilibria," Working Papers tecipa-381, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-381

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    References listed on IDEAS

    1. 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, June.
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    7. Andrew Sweeting, 2007. "Dynamic Product Repositioning in Differentiated Product Markets: The Case of Format Switching in the Commercial Radio Industry," NBER Working Papers 13522, National Bureau of Economic Research, Inc.
    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.
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    12. Aguirregabiria, Victor, 2004. "Pseudo maximum likelihood estimation of structural models involving fixed-point problems," Economics Letters, Elsevier, vol. 84(3), pages 335-340, September.
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    Cited by:

    1. 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.
    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. Naoaki Minamihashi, 2012. "Natural Monopoly and Distorted Competition: Evidence from Unbundling Fiber-Optic Networks," Staff Working Papers 12-26, Bank of Canada.
    4. Joao Macieira, 2010. "Oblivious Equilibrium in Dynamic Discrete Games," 2010 Meeting Papers 680, Society for Economic Dynamics.
    5. 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.
    6. Victor Aguirregabiria & Gustavo Vicentini, 2006. "Dynamic Spatial Competition Between Multi-Store Firms," Working Papers tecipa-253, University of Toronto, Department of Economics.
    7. Jean-Pierre Dubé & Xueming Luo & Zheng Fang, 2015. "Self-Signaling and Prosocial Behavior: a Cause Marketing Mobile Field Experiment," NBER Working Papers 21475, National Bureau of Economic Research, Inc.
    8. 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.

    More about this item


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

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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