Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T08:50:54.498Z Has data issue: false hasContentIssue false
  • English
  • Français

LOCAL IDENTIFICATION IN EMPIRICAL GAMES OF INCOMPLETE INFORMATION

Published online by Cambridge University Press:  17 March 2010

Jean-Pierre Florens  and
Erwann Sbaï
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies identification for a broad class of empirical games in a general functional setting. Global identification results are known for some specific models, e.g., in some standard auction models. We use functional formulations to obtain general criteria for local identification. These criteria can be applied to both parametric and nonparametric models, and also to models with asymmetry among players and affiliated private information. A benchmark model is developed where the structural parameters of interest are the distribution of private information and an additional dissociated parameter, such as a parameter of risk aversion. Criteria are derived for some standard auction models, games with exogenous variables, games with randomized strategies, such as mixed strategies, and games with strategic functions that cannot be derived analytically.

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1638 - 1662
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

We thank Peter Phillips for his comments, Olivier Scaillet and Christian Gourieroux for their comments on an early version of this paper, the co-editor, and two anonymous referees. Various versions have been presented to the World Congress of the Econometric Society, Seattle, 2000, the Young Econometricians Meeting, Marseilles, 2000, the New Zealand Econometric Study Group meeting, 2006, and seminars at the University of Toulouse, 2001, University of Mannheim, 2003, and University of Auckland, 2006.

References

REFERENCES

Armantier, O., Florens, J.-P., & Richard, J.-F. (2008) Approximation of Bayesian Nash equilibrium. Journal of Applied Econometrics 23, 965–981.10.1002/jae.1040CrossRefGoogle Scholar
Armantier, O. & Sbaï, E. (2006) Estimation and comparison of treasury auction formats when bidders are asymmetric. Journal of Applied Econometrics 21, 745–779.CrossRefGoogle Scholar
Athey, S. & Haile, P.A. (2002) Identification of standard auction models. Econometrica 70, 2107– 2140.CrossRefGoogle Scholar
Campo, S., Guerre, E., Perrigne, I., & Vuong, Q. (2002) Semiparametric Estimation of First-Price Auctions with Risk Averse Bidders. Working paper, Pennsylvania State University.Google Scholar
Carrasco, M., Florens, J.-P., & Renault, E. (2007) Linear inverse problems in structural econometrics. In Heckman, J.J. & Leamer, E.E. (eds.), Handbook of Econometrics, vol. 6, pp. 5633–5751. North-Holland.CrossRefGoogle Scholar
Chesher, A. (2003) Identification in nonseparable models. Econometrica 71, 1405–1441.10.1111/1468-0262.00454CrossRefGoogle Scholar
Donald, S.G. & Paarsch, H.J. (1996) Identification, estimation, and testing in parametric empirical models of auctions within the independent private values paradigm. Econometric Theory 12, 517–67.CrossRefGoogle Scholar
Fisher, F.M. (1959) Generalization of the rank and order conditions for identifiability. Econometrica 27, 531–547.CrossRefGoogle Scholar
Fisher, F.M. (1961) Identifiability criteria in nonlinear systems. Econometrica 29, 574–590.CrossRefGoogle Scholar
Fisher, F.M. (1966) The Identification Problem in Econometrics. McGraw-Hill.Google Scholar
Florens, J.-P. (2007) Regularized Non Parametric Estimation of Game Theoretic Models. Mimeo, University of Toulouse.Google Scholar
Florens, J.-P., Protopopescu, C., & Richard, J.-F. (2001) Identification and Estimation of a Class of Game Theoretic Models. Mimeo, University of Toulouse.Google Scholar
Guerre, E., Perrigne, I., & Vuong, Q. (2000) Optimal nonparametric estimation of first-price auctions, Econometrica 68, 525–574.CrossRefGoogle Scholar
Guerre, E., Perrigne, I., & Vuong, Q. (2009) Nonparametric identification of risk aversion in first-price auctions under exclusion restrictions. Econometrica 77, 1193–1227.Google Scholar
Koopmans, T.C., Rubin, H., & Leipnik, R.B. (1950) Measuring the equation systems of dynamic economics. In Koopmans, T.C. (ed.), Statistical Inference in Dynamic Economic Models, Cowles Commission Monograph 10, pp. 52–237. Wiley.Google Scholar
Laffont, J.-J. & Vuong, Q. (1996) Structural analysis of auction data. American Economic Review 86, 414–420.Google Scholar
Nashed, M.Z. (1971) Generalized inverses, normal solvability, and iteration for singular operator equations. In Rall, Louis B. (ed.), Nonlinear Functional Analysis and Applications, pp. 311–359. Academic Press.CrossRefGoogle Scholar
Paarsch, H.J. (1992) Deciding between the common and private value paradigms in empirical models of auctions. Journal of Econometrics 51, 191–215.CrossRefGoogle Scholar
Paarsch, H.J. & Hong, H. (2006) An Introduction to the Structural Econometrics of Auction Data. MIT Press.Google Scholar
Perrigne, I. & Vuong, Q. (2004) Econometrics of Incentive Regulation: Nonparametric Identification. Mimeo, Pennsylvania State University.Google Scholar
Rieder, H. (1994) Robust Asymptotic Statistics, Springer Series in Statistics. Springer-Verlag.CrossRefGoogle Scholar
Rothenberg, T.J. (1971) Identification in parametric models. Econometrica 39, 577–591.CrossRefGoogle Scholar
Sbaï, E. (2007) Applications of a Local Identification Procedure to Some Empirical Games. Mimeo, University of Auckland.Google Scholar
Serfling, R.J. (1980) Approximation Theorems of Mathematical Statistics, Wiley Series in Probability and Mathematical Statistics. Wiley.CrossRefGoogle Scholar
Wald, A. (1950) Note on the identification of economic relations. In Koopmans, T.C. (ed.), Statistical Inference in Dynamic Economic Models, Cowles Commission Monograph 10, pp.238–257. Wiley.Google Scholar
Wegge, L. (1965) Identifiability criteria for a system of equations as a whole. Australian Journal of Statistics 7, 67–77.CrossRefGoogle Scholar