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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.

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Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-381.

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Length: 11 pages
Date of creation: 28 Oct 2009
Date of revision:
Handle: RePEc:tor:tecipa:tecipa-381
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  1. Victor Aguirregabiria, 2004. "Pseudo Maximum Likelihood Estimation of Structural Models Involving Fixed-Point Problems," Econometrics 0402003, EconWPA.
  2. 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.
  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 & Steve Berry, 2004. "Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Examples)," Harvard Institute of Economic Research Working Papers 2036, Harvard - Institute of Economic Research.
  5. Bajari, Patrick & Benkard, C. Lanier & Levin, Jonathan, 2007. "Estimating Dynamic Models of Imperfect Competition," Research Papers 1852r1, Stanford University, Graduate School of Business.
  6. 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.
  7. Juan Escobar & Ulrich Doraszelski, 2008. "A Theory of Regular Markov Perfect Equilibria\\in Dynamic Stochastic Games: Genericity, Stability, and Purification," 2008 Meeting Papers 453, Society for Economic Dynamics.
  8. Bajari, Patrick & Hong, Han & Krainer, John & Nekipelov, Denis, 2010. "Estimating Static Models of Strategic Interactions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 469-482.
  9. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  10. Victor Aguirregabiria & Pedro Mira, 2004. "Sequential Estimation of Dynamic Discrete Games," Industrial Organization 0406006, EconWPA.
  11. Brock,W.A. & Durlauf,S.N., 2000. "Discrete choice with social interactions," Working papers 7, Wisconsin Madison - Social Systems.
  12. 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.
  13. 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.
  14. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov-perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243.
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