IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/21331.html
   My bibliography  Save this paper

Generalized Maximum Entropy estimation of discrete sequential move games of perfect information

Author

Listed:
  • Wang, Yafeng
  • Graham, Brett

Abstract

We propose a data-constrained generalized maximum entropy (GME) estimator for discrete sequential move games of perfect information which can be easily implemented on optimization software with high-level 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) mixed-integer 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.

Suggested Citation

  • Wang, Yafeng & Graham, Brett, 2009. "Generalized Maximum Entropy estimation of discrete sequential move games of perfect information," MPRA Paper 21331, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:21331
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/21331/1/MPRA_paper_21331.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/70222/1/MPRA_paper_70222.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    2. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    3. Golan, Amos & Karp, Larry S & Perloff, Jeffrey M, 2000. "Estimating Coke's and Pepsi's Price and Advertising Strategies," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 398-409, October.
    4. Che‐Lin Su & Kenneth L. Judd, 2012. "Constrained Optimization Approaches to Estimation of Structural Models," Econometrica, Econometric Society, vol. 80(5), pages 2213-2230, September.
    5. Philip A. Haile & Ali Hortaçsu & Grigory Kosenok, 2008. "On the Empirical Content of Quantal Response Equilibrium," American Economic Review, American Economic Association, vol. 98(1), pages 180-200, March.
    6. 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.
    7. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    8. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, September.
    9. Timothy F. Bresnahan & Peter C. Reiss, 1990. "Entry in Monopoly Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(4), pages 531-553.
    10. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    11. R. Carter Hill & Randall C. Campbell, 2001. "Maximum Entropy Estimation in Economic Models with Linear Inequality Restrictions," Departmental Working Papers 2001-11, Department of Economics, Louisiana State University.
    12. Jouneau-Sion, Frederic & Torres, Olivier, 2006. "MMC techniques for limited dependent variables models: Implementation by the branch-and-bound algorithm," Journal of Econometrics, Elsevier, vol. 133(2), pages 479-512, August.
    13. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
    14. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    15. Horowitz, J. L., 1995. "Bootstrap Methods In Econometrics: Theory And Numerical Performance," SFB 373 Discussion Papers 1995,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    16. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    17. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
    18. Horowitz, J.L., 1995. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Working Papers 95-10, University of Iowa, Department of Economics.
    19. J.J. Heckman & E.E. Leamer (ed.), 2001. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 5, number 5.
    20. Shiko Maruyama, 2009. "Estimating Sequential-move Games by a Recursive Conditioning Simulator," Discussion Papers 2009-01, School of Economics, The University of New South Wales.
    21. Michael J. Mazzeo, 2002. "Product Choice and Oligopoly Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 33(2), pages 221-242, Summer.
    22. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
    23. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228, Elsevier.
    24. Golan, Amos & Judge, George & Perloff, Jeffrey, 1997. "Estimation and inference with censored and ordered multinomial response data," Journal of Econometrics, Elsevier, vol. 79(1), pages 23-51, July.
    25. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(1), pages 105-121, February.
    26. Philipp Schmidt-Dengler, 2006. "The Timing of New Technology Adoption: The Case of MRI," 2006 Meeting Papers 3, Society for Economic Dynamics.
    27. Donald W. K. Andrews & Patrik Guggenberger, 2009. "Hybrid and Size-Corrected Subsampling Methods," Econometrica, Econometric Society, vol. 77(3), pages 721-762, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Yafeng & Graham, Brett, 2010. "Simulation Based Estimation of Discrete Sequential Move Games of Perfect Information," MPRA Paper 23153, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yafeng Wang & Brett Graham, 2013. "Generalized Maximum Entropy Estimation of Discrete Sequential Move Games of Perfect Information," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    2. Wang, Yafeng & Graham, Brett, 2010. "Simulation Based Estimation of Discrete Sequential Move Games of Perfect Information," MPRA Paper 23153, University Library of Munich, Germany.
    3. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.
    4. Paul B. Ellickson & Sanjog Misra, 2011. "Structural Workshop Paper --Estimating Discrete Games," Marketing Science, INFORMS, vol. 30(6), pages 997-1010, November.
    5. Shiko Maruyama, 2009. "Estimating Sequential-move Games by a Recursive Conditioning Simulator," Discussion Papers 2009-01, School of Economics, The University of New South Wales.
    6. A. Orhun, 2013. "Spatial differentiation in the supermarket industry: The role of common information," Quantitative Marketing and Economics (QME), Springer, vol. 11(1), pages 3-37, March.
    7. Aguirregabiria, Victor & Nevo, Aviv, 2010. "Recent developments in empirical IO: dynamic demand and dynamic games," MPRA Paper 27814, University Library of Munich, Germany.
    8. Paul L. E. Grieco, 2014. "Discrete games with flexible information structures: an application to local grocery markets," RAND Journal of Economics, RAND Corporation, vol. 45(2), pages 303-340, June.
    9. Luo, Yao & Xiao, Ping & Xiao, Ruli, 2022. "Identification of dynamic games with unobserved heterogeneity and multiple equilibria," Journal of Econometrics, Elsevier, vol. 226(2), pages 343-367.
    10. Liu, Nianqing & Vuong, Quang & Xu, Haiqing, 2017. "Rationalization and identification of binary games with correlated types," Journal of Econometrics, Elsevier, vol. 201(2), pages 249-268.
    11. Paul Ellickson & Sanjog Misra, 2012. "Enriching interactions: Incorporating outcome data into static discrete games," Quantitative Marketing and Economics (QME), Springer, vol. 10(1), pages 1-26, March.
    12. Maruyama, Shiko, 2014. "Estimation of finite sequential games," Journal of Econometrics, Elsevier, vol. 178(2), pages 716-726.
    13. Andrew Sweeting, 2009. "The strategic timing incentives of commercial radio stations: An empirical analysis using multiple equilibria," RAND Journal of Economics, RAND Corporation, vol. 40(4), pages 710-742, December.
    14. Larry G. Epstein & Hiroaki Kaido & Kyoungwon Seo, 2016. "Robust Confidence Regions for Incomplete Models," Econometrica, Econometric Society, vol. 84, pages 1799-1838, September.
    15. Daniel Ackerberg, 2009. "A new use of importance sampling to reduce computational burden in simulation estimation," Quantitative Marketing and Economics (QME), Springer, vol. 7(4), pages 343-376, December.
    16. Liu, An-Hsiang & Siebert, Ralph B., 2022. "The competitive effects of declining entry costs over time: Evidence from the static random access memory market," International Journal of Industrial Organization, Elsevier, vol. 80(C).
    17. Davis, Peter, 2006. "Estimation of quantity games in the presence of indivisibilities and heterogeneous firms," Journal of Econometrics, Elsevier, vol. 134(1), pages 187-214, September.
    18. Kline, Brendan, 2015. "Identification of complete information games," Journal of Econometrics, Elsevier, vol. 189(1), pages 117-131.
    19. Gallant, A. Ronald & Hong, Han & Khwaja, Ahmed, 2018. "A Bayesian approach to estimation of dynamic models with small and large number of heterogeneous players and latent serially correlated states," Journal of Econometrics, Elsevier, vol. 203(1), pages 19-32.
    20. Nianqing Liu & Haiqing Xu, "undated". "Semiparametric Analysis of Binary Games of Incomplete Information," Department of Economics Working Papers 130911, The University of Texas at Austin, Department of Economics, revised Nov 2012.

    More about this item

    Keywords

    Game-Theoretic Econometric Models; Sequential-Move Game; Generalized Maximum Entropy; Mixed-Integer Nonlinear Programming;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:21331. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.