IDEAS home Printed from https://ideas.repec.org/p/mtl/montde/2019-08.html
   My bibliography  Save this paper

Imposing equilibrium restrictions in the estimation of dynamic discrete games

Author

Listed:
  • Victor Aguirregabiria

    (University of Toronto)

  • Mathieu Marcoux

    (Université de Montréal)

Abstract

Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions – MPEC, NFXP, NPL, and variations – have different merits and limitations. MPEC guarantees local convergence, but requires the computation of high-dimensional Jacobians. The NPL algorithm avoids the computation of these matrices, but – in games – may fail to converge to the consistent NPL estimator. We study the asymptotic properties of the NPL algorithm treating the iterative procedure as performed in finite samples. We find that there are always samples for which the algorithm fails to converge, and this introduces a selection bias. We also propose a spectral algorithm to compute the NPL estimator. This algorithm satisfies local convergence and avoids the computation of Jacobian matrices. We present simulation evidence illustrating our theoretical results and the good properties of the spectral algorithm.

Suggested Citation

  • Victor Aguirregabiria & Mathieu Marcoux, 2019. "Imposing equilibrium restrictions in the estimation of dynamic discrete games," Cahiers de recherche 2019-08, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2019-08
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/1866/22366
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Sequential Estimation of Structural Models With a Fixed Point Constraint," Econometrica, Econometric Society, vol. 80(5), pages 2303-2319, September.
    3. Alessandro Pinto & Gerald C. Nelson, 2009. "Land Use Change with Spatially Explicit Data: A Dynamic Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 43(2), pages 209-229, June.
    4. Ravi Varadhan & Christophe Roland, 2008. "Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 335-353, June.
    5. Victor Aguirregabiria & Cesar Alonso-Borrego, 2014. "Labor Contracts And Flexibility: Evidence From A Labor Market Reform In Spain," Economic Inquiry, Western Economic Association International, vol. 52(2), pages 930-957, April.
    6. Haizhen Lin, 2015. "Quality Choice And Market Structure: A Dynamic Analysis Of Nursing Home Oligopolies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1261-1290, November.
    7. Kano, Kazuko, 2013. "Menu costs and dynamic duopoly," International Journal of Industrial Organization, Elsevier, vol. 31(1), pages 102-118.
    8. Adam Dearing & Jason R. Blevins, 2019. "Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games," Papers 1912.10488, arXiv.org, revised Feb 2021.
    9. Panle Jia Barwick & Parag A. Pathak, 2015. "The costs of free entry: an empirical study of real estate agents in Greater Boston," RAND Journal of Economics, RAND Corporation, vol. 46(1), pages 103-145, March.
    10. Fedor Iskhakov & Jinhyuk Lee & John Rust & Bertel Schjerning & Kyoungwon Seo, 2016. "Comment on “Constrained Optimization Approaches to Estimation of Structural Models”," Econometrica, Econometric Society, vol. 84, pages 365-370, January.
    11. Aguirregabiria, Victor & Ho, Chun-Yu, 2012. "A dynamic oligopoly game of the US airline industry: Estimation and policy experiments," Journal of Econometrics, Elsevier, vol. 168(1), pages 156-173.
    12. Zhongjian Lin & Haiqing Xu, 2017. "Estimation of social‐influence‐dependent peer pressure in a large network game," Econometrics Journal, Royal Economic Society, vol. 20(3), pages 86-102, October.
    13. Andrew Sweeting, 2013. "Dynamic Product Positioning in Differentiated Product Markets: The Effect of Fees for Musical Performance Rights on the Commercial Radio Industry," Econometrica, Econometric Society, vol. 81(5), pages 1763-1803, September.
    14. Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
    15. Liu, Xiaodong & Zhou, Jiannan, 2017. "A social interaction model with ordered choices," Economics Letters, Elsevier, vol. 161(C), pages 86-89.
    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. Adam Dearing & Jason R. Blevins, 2019. "Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games," Papers 1912.10488, arXiv.org, revised Feb 2021.
    2. Victor Aguirregabiria & Allan Collard-Wexler & Stephen P. Ryan, 2021. "Dynamic Games in Empirical Industrial Organization," Papers 2109.01725, arXiv.org, revised Sep 2021.
    3. Jason R. Blevins & Minhae Kim, 2021. "Nested Pseudo Likelihood Estimation of Continuous-Time Dynamic Discrete Games," Papers 2108.02182, arXiv.org.

    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. Victor Aguirregabiria & Allan Collard-Wexler & Stephen P. Ryan, 2021. "Dynamic Games in Empirical Industrial Organization," Papers 2109.01725, arXiv.org, revised Sep 2021.
    2. Victor Aguirregabiria & Margaret Slade, 2017. "Empirical models of firms and industries," Canadian Journal of Economics, Canadian Economics Association, vol. 50(5), pages 1445-1488, December.
    3. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    4. Aguirregabiria, Victor & Nevo, Aviv, 2010. "Recent developments in empirical IO: dynamic demand and dynamic games," MPRA Paper 27814, University Library of Munich, Germany.
    5. Aguirregabiria, Victor & Gu, Jiaying & Luo, Yao, 2021. "Sufficient statistics for unobserved heterogeneity in structural dynamic logit models," Journal of Econometrics, Elsevier, vol. 223(2), pages 280-311.
    6. Yingyao Hu & Zhongjian Lin, 2018. "Misclassification and the hidden silent rivalry," CeMMAP working papers CWP12/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Chomsisengphet, Souphala & Kiefer, Hua & Liu, Xiaodong, 2018. "Spillover effects in home mortgage defaults: Identifying the power neighbor," Regional Science and Urban Economics, Elsevier, vol. 73(C), pages 68-82.
    8. Aguirregabiria, Victor, 2009. "Estimation of Dynamic Discrete Games Using the Nested Pseudo Likelihood Algorithm: Code and Application," MPRA Paper 17329, University Library of Munich, Germany.
    9. Anirban Mukherjee & Vrinda Kadiyali, 2018. "The Competitive Dynamics of New DVD Releases," Management Science, INFORMS, vol. 64(8), pages 3536-3553, August.
    10. Victor Aguirregabiria, 2006. "Another Look at the Identification of Dynamic Discrete Decision Processes: With an Application to Retirement Behavior," 2006 Meeting Papers 169, Society for Economic Dynamics.
    11. Tobias Salz & Emanuel Vespa, 2020. "Estimating dynamic games of oligopolistic competition: an experimental investigation," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 447-469, June.
    12. Joao Macieira, 2010. "Oblivious Equilibrium in Dynamic Discrete Games," 2010 Meeting Papers 680, Society for Economic Dynamics.
    13. Dubois, Pierre & Griffith, Rachel & O'Connell, Martin, 2014. "The Effects of Banning Advertising on Demand, Supply and Welfare: Structural Estimation on a Junk Food Market," CEPR Discussion Papers 9942, C.E.P.R. Discussion Papers.
    14. Maximilian Blesch & Philipp Eisenhauer, 2021. "Robust decision-making under risk and ambiguity," Papers 2104.12573, arXiv.org, revised Oct 2021.
    15. Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2014. "Testing Equilibrium Multiplicity in Dynamic Games," CEPR Discussion Papers 10111, C.E.P.R. Discussion Papers.
    16. Aguirregabiria, Victor & Ho, Chun-Yu, 2012. "A dynamic oligopoly game of the US airline industry: Estimation and policy experiments," Journal of Econometrics, Elsevier, vol. 168(1), pages 156-173.
    17. Aamir Rafique Hashmi & Johannes Van Biesebroeck, 2016. "The Relationship between Market Structure and Innovation in Industry Equilibrium: A Case Study of the Global Automobile Industry," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 192-208, March.
    18. Ji, Yongjie & Rabotyagov, Sergey & Kling, Catherine L., 2014. "Crop Choice and Rotational Effects: A Dynamic Model of Land Use in Iowa in Recent Years," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170366, Agricultural and Applied Economics Association.
    19. Ji, Yongjie & Rabotyagov, sergey & Valcu-Lisman, Adriana, 2015. "Estimating Adoption of Cover Crops Using Preferences Revealed by a Dynamic Crop Choice Model," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205799, Agricultural and Applied Economics Association.
    20. Li, Shengyu, 2018. "A structural model of productivity, uncertain demand, and export dynamics," Journal of International Economics, Elsevier, vol. 115(C), pages 1-15.

    More about this item

    Keywords

    Dynamic discrete game; Nested pseudo-likelihood; Fixed point algorithms; Convergence; Convergence selection bias;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:mtl:montde:2019-08. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/demtlca.html .

    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: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/demtlca.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.