Wang, Yafeng and Graham, Brett (2009): Generalized Maximum Entropy estimation of discrete sequential move games of perfect information.

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Abstract
We propose a dataconstrained generalized maximum entropy (GME) estimator for discrete sequential move games of perfect information which can be easily implemented on optimization software with highlevel interfaces such as GAMS. Unlike most other work on the estimation of complete information games, the method we proposed is data constrained and does not require simulation and normal distribution of random preference shocks. We formulate the GME estimation as a (convex) mixedinteger nonlinear optimization problem (MINLP) which is well developed over the last few years. The model is identified with only weak scale and location normalizations, monte carlo evidence demonstrates that the estimator can perform well in moderately size samples. As an application, we study the social security acceptance decisions in dual career households.
Item Type:  MPRA Paper 

Original Title:  Generalized Maximum Entropy estimation of discrete sequential move games of perfect information 
Language:  English 
Keywords:  GameTheoretic Econometric Models, SequentialMove Game, Generalized Maximum Entropy, MixedInteger Nonlinear Programming 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  21331 
Depositing User:  Yafeng Wang 
Date Deposited:  12. Mar 2010 00:41 
Last Modified:  30. Dec 2015 23:56 
References:  Aguirregabiria, V. and P. Mira (2007). "Sequential Estimation of Dynamic Discrete Games." Econometrica 75 : 153. Andrews, D. W. K. and P. Guggenberger (2009). "Hybrid and SizeCorrected Subsampling Methods." Econometrica 77 (3): 721762. De Angelis, D. and P. Hall, et al. (1993). "Analytical and Bootstrap Approximations to Estimator Distributions in L1 Regression." Journal of the American Statistical Association 88 : 13101316. Bajari, P. and H. Hong, et al. (2009). "Estimating Static Models of Strategic Interactions." forthcoming Journal of Business and Economic Statistics. Bajari, P. Han Hong, and Stephen Ryan (2009). "Identification and Estimation of a Discrete Game of Complete Information." forthcoming Econometrica. Berry, Steven T. (1992). "Estimation of a Model of Entry in the Airline Industry." Econometrica 60 (4): 889917. Pierre Bonami, Mustafa Kilinc and Jeff Linderoth (2009). "Algorithms and Software for Convex Mixed Integer Nonlinear Programs." Technical Report. Bresnahan, T. F. and P. C. Reiss (1990). "Entry in Monopoly Markets." Review of Economic Studies 57 : 531553. Bresnahan, T. F. and P. C. Reiss (1991). "Empirical models of Discrete Games." Journal of Econometrics 48 : 5781. Brooke, A., D. Kendrick, A. Meeraus, and R. Raman (2008). GAMS  A User's Guide, Washington, DC: GAMS Development Corporation. Online at: http://www.gams.com/dd/docs/bigdocs/GAMSUsersGuide.pdf. Campbell, R. C. and R. C. Hill (2001). "Maximum Entropy Estimation in Economic Models with Linear Inequality Restrictions." Working Paper. Chen and Mangasarian (1996). "A class of smoothing functions for nonlinear and mixed complementarity problems." Computational Optimization and Applications 5 (2): 97  138. Golan, A., George Judge, and J. Miller (1996). Maximum Entropy Econometrics: Robust Estimation with Limited Data. New York: John Wiley & Sons. Golan, A. and G. Judge, et al. (1997). "Estimation and Inference with Censored and Ordered Multinomial Response Data." Journal of Econometrics 79 (1): 2351. Golan, A. and L. S. Karp, et al. (1998). "Estimating a Mixed Strategy: United and American Airlines." Working Paper. Golan, A. and L. S. Karp, et al. (2000). "Estimating Coke's and Pepsi's Price and Advertising Strategies." Journal of Business and Economic Statistics 18 (4): 398409. Golan, A. and J. M. Perloff, et al. (2000). "Estimating a Demand System with Nonnegativity Constraints: Mexican Meat Demand." Working Paper. Ignacio E. Grossmann (2002). "Review of Nonlinear MixedInteger and Disjunctive Programming Techniques." Optimization and Engineering (3): 227252. Hahn, J. (1995). "Bootstrapping Quantile Regression Estimators." Econometric Theory 11 (01): 105121. Haile, P., and A. Hortacsu, et al. (2003). "On the Empirical Content of Quantal Response Equilibrium." Working Paper. Horowitz, J. L. (1995). "Bootstrap Methods in Econometrics: Theory and Numerical Performance." Prepared for presentation to the Invited Symposium on Bootstrap Methods in Econometrics, 7th World Congress of the Econometric Society, Tokyo. Horowitz, J. L. (1998). "Bootstrap Methods for Median Regression Models." Econometrica 66 (6): 13271352. Horowitz, J. L. (2001). "The Bootstrap." In J. Heckman and E. Leamer (Ed.) Handbook of Econometrics, Vol.5, pp. 31593228, Elsevier Science, The Netherlands. Jaynes, E. T. (1957a). "Information Theory and Statistical Mechanics." Physics Reviews 106: 620630. Jaynes, E. T. (1957a). "Information Theory and Statistical Mechanics, II." Physics Reviews 108: 171190. Jaynes, E. T. (1984). "Prior Information and Ambiguity in Inverse Problems." In McLaughlin (Ed.) Inverse Problems, pp. 151166, SIAM Proceedings, American Mathematical Society, Providence, RI. JouneauSiona and Torrès. (2006). "MMC techniques for limited dependent variables models: Implementation by the branchandbound algorithm." Journal of Econometrics 133 : 479512. AradillasLopez (2007). "Pairwise Difference Estimation of Incomplete Information Games." Working Paper. AradillasLopez (2008). "Semiparametric Estimation of a Simultaneous Game with Incomplete Information." Working Paper. Maruyama, S. (2009). "Estimating Sequentialmove Games by a Recursive Conditioning Simulator." Working Paper. Mazzeo, Michael J. (2002). "Product Choice and Oligopoly Market Structure." Rand Journal of Economics 33 (2): 221242. Mittelhammer, R. C. and N. S. Cardell (1997). "The DataConstrained GME Estimator of the GLM: Asymptotic Theory and Inference." Working Paper. I. Nowak and S. Vigerske (2008), "LaGO  a (heuristic) Branch and Cut algorithm for nonconvex MINLPs." Central European Journal of Operations Research 16 (2): 127138. Nunez, G. (2009). "A Maximum Entropy Estimation of Armington Elasticities for Mexico." Working Paper. Martin J. Osborne and Ariel Rubinstein. (1994). A Coure in Game Theory. The MIT Press. R. Raman and I. E. Grossmann. (1991). "Relation between MILP modelling and logical inference for chemical process synthesis." Computers and Chemical Engineering 15. Klaus Ritzberger (2002). Foundations of NonCooperative Game Theory. Oxford University Press. Rust, J. (1987). "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher." Econometrica 55 (5): 9991033. SchmidtDengler, P. (2006). "The Timing of New Technology Adoption: The Case of MRI." Working Paper. Seim,. K. (2005). "An Empirical Model of Firm Entry with Endogenous ProductType Choices." Rand Journal of Economics 37 (3): 619640. Shannon, C.E. (1948). "A Mathematical Theory of Communication." Bell System Technical Journal 27: 379423. Su, C. and K. L. Judd (2008). "Constrained Optimization Approaches to Estimation of Structural Models." Working Paper. Tamer, E. (2003). "Coordination Games, Multiple Equilibria and the Timing of Radio Commercials." Working Paper. H.P. Williams. (1985). Model Building in Mathematical Programming. New York: John Wiley & Sons. Zeng and Lin (2008). "Efficient resampling methods for nonsmooth estimating functions." Biostatistics 9 (2): 355363. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/21331 