IDEAS home Printed from https://ideas.repec.org/p/mtl/montec/10-2019.html
   My bibliography  Save this paper

Imposing Equilibrium Restrictions in the Estimation of Dynamic Discrete Games

Author

Listed:
  • Victor Aguirregabiria

    (University of Toronto, CEPR)

  • Mathieu Marcoux

    (Université de Montréal, CIREQ)

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 10-2019, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  • Handle: RePEc:mtl:montec:10-2019
    as

    Download full text from publisher

    File URL: http://www.cireqmontreal.com/wp-content/uploads/cahiers/10-2019-cah.pdf
    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. Victor Aguirregabiria & Arvind Magesan, 2020. "Identification and Estimation of Dynamic Games When Players’ Beliefs Are Not in Equilibrium," Review of Economic Studies, Oxford University Press, vol. 87(2), pages 582-625.
    3. Otto Toivanen & Michael Waterson, 2005. "Market Structure and Entry: Where's the Beef?," RAND Journal of Economics, The RAND Corporation, vol. 36(3), pages 680-699, Autumn.
    4. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    5. 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.
    6. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July.
    7. 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.
    8. Tomlin, Ben, 2014. "Exchange rate fluctuations, plant turnover and productivity," International Journal of Industrial Organization, Elsevier, vol. 35(C), pages 12-28.
    9. 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.
    10. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 497-529.
    11. Adam Copeland & Cyril Monnet, 2009. "The Welfare Effects of Incentive Schemes," Review of Economic Studies, Oxford University Press, vol. 76(1), pages 93-113.
    12. 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.
    13. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    14. 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.
    15. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    16. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    17. 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.
    18. Paul B. Ellickson & Sanjog Misra, 2008. "Supermarket Pricing Strategies," Marketing Science, INFORMS, vol. 27(5), pages 811-828, 09-10.
    19. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    20. 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.
    21. Federico A. Bugni & Jackson Bunting, 2018. "On the iterated estimation of dynamic discrete choice games," Papers 1802.06665, arXiv.org, revised May 2020.
    22. 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.
    23. Han, Lu & Hong, Seung-Hyun, 2011. "Testing Cost Inefficiency Under Free Entry in the Real Estate Brokerage Industry," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 564-578.
    24. 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.
    25. 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(4), pages 1261-1290, November.
    26. 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).
    27. Liu, Xiaodong & Zhou, Jiannan, 2017. "A social interaction model with ordered choices," Economics Letters, Elsevier, vol. 161(C), pages 86-89.
    28. Kano, Kazuko, 2013. "Menu costs and dynamic duopoly," International Journal of Industrial Organization, Elsevier, vol. 31(1), pages 102-118.
    29. Ling Huang & Martin D. Smith, 2014. "The Dynamic Efficiency Costs of Common-Pool Resource Exploitation," American Economic Review, American Economic Association, vol. 104(12), pages 4071-4103, December.
    30. Federico A. Bugni & Takuya Ura, 2019. "Inference in dynamic discrete choice problems under local misspecification," Quantitative Economics, Econometric Society, vol. 10(1), pages 67-103, January.
    31. Michael Egesdal & Zhenyu Lai & Che‐Lin Su, 2015. "Estimating dynamic discrete‐choice games of incomplete information," Quantitative Economics, Econometric Society, vol. 6(3), pages 567-597, November.
    32. Martin Pesendorfer & Philipp Schmidt-Dengler, 2010. "Sequential Estimation of Dynamic Discrete Games: A Comment," Econometrica, Econometric Society, vol. 78(2), pages 833-842, March.
    33. Philip G. Gayle & Xin Xie, 2018. "Entry Deterrence And Strategic Alliances," Economic Inquiry, Western Economic Association International, vol. 56(3), pages 1898-1924, July.
    34. 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.
    35. 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.
    36. 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.
    37. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    38. Che-Lin Su, 2014. "Estimating discrete-choice games of incomplete information: Simple static examples," Quantitative Marketing and Economics (QME), Springer, vol. 12(2), pages 167-207, June.
    39. Jiawei Chen & Susanna Esteban & Matthew Shum, 2013. "When Do Secondary Markets Harm Firms?," American Economic Review, American Economic Association, vol. 103(7), pages 2911-2934, December.
    40. 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.
    41. Guillaume R. Fréchette & Alessandro Lizzeri & Tobias Salz, 2019. "Frictions in a Competitive, Regulated Market: Evidence from Taxis," American Economic Review, American Economic Association, vol. 109(8), pages 2954-2992, August.
    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. Taisuke Otsu & Martin Pesendorfer, 2021. "Equilibrium multiplicity in dynamic games: testing and estimation," STICERD - Econometrics Paper Series 618, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. 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.
    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. Victor Aguirregabiria & Allan Collard-Wexler & Stephen P. Ryan, 2021. "Dynamic Games in Empirical Industrial Organization," NBER Working Papers 29291, National Bureau of Economic Research, Inc.
    5. 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.
    6. Victor Aguirregabiria & Victor Aguirregabiria & Aviv Nevo & Aviv Nevo, 2010. "Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games," Working Papers tecipa-419, University of Toronto, Department of Economics.
    7. 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.
    8. Paul B. Ellickson & Sanjog Misra, 2011. "Structural Workshop Paper --Estimating Discrete Games," Marketing Science, INFORMS, vol. 30(6), pages 997-1010, November.
    9. 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.
    10. Raphael Corbi & Fabio Miessi Sanches, 2022. "Church Competition, Religious Subsidies and the Rise of Evangelicalism: a Dynamic Structural Analysis," Working Papers, Department of Economics 2022_09, University of São Paulo (FEA-USP).
    11. Joao Macieira, 2010. "Oblivious Equilibrium in Dynamic Discrete Games," 2010 Meeting Papers 680, Society for Economic Dynamics.
    12. 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.
    13. 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.
    14. 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.
    15. Jason R. Blevins & Minhae Kim, 2021. "Nested Pseudo Likelihood Estimation of Continuous-Time Dynamic Discrete Games," Papers 2108.02182, arXiv.org.
    16. Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    17. Wang, Jin, 2021. "Do birds of a feather flock together? Platform’s quality screening and end-users’ choices theory and empirical study of online trading platforms," International Journal of Industrial Organization, Elsevier, vol. 75(C).
    18. Che-Lin Su, 2014. "Estimating discrete-choice games of incomplete information: Simple static examples," Quantitative Marketing and Economics (QME), Springer, vol. 12(2), pages 167-207, June.
    19. Carlos Daniel Santos, 2009. "Recovering the Sunk Costs of R&D: the Moulds Industry Case," CEP Discussion Papers dp0958, Centre for Economic Performance, LSE.
    20. Hu Yingyao & Shum Matthew & Tan Wei & Xiao Ruli, 2017. "A Simple Estimator for Dynamic Models with Serially Correlated Unobservables," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-16, January.

    More about this item

    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:montec:10-2019. 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/cdmtlca.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/cdmtlca.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.