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Inference in Ordered Response Games with Complete Information

Author

Listed:
  • Andres Aradillas-Lopez

    (Institute for Fiscal Studies and University of Wisconsin)

  • Adam Rosen

    (Institute for Fiscal Studies and Duke University)

Abstract
We study econometric models of complete information games with ordered action spaces, such as the number of store fronts operated in a market by a rm, or the daily number of flights on a city-pair off ered by an airline. The model generalizes single agent models such as ordered probit and logit to a simultaneous equations model of ordered response, allowing for multiple equilibria and set identi cation. We characterize identif ed sets for model parameters under mild shape restrictions on agents' payo functions. We then propose a novel inference method for a parametric version of our model based on a test statistic that embeds conditional moment inequalities implied by equilibrium behavior. Using maximal inequalities for U-processes, we show that an asymptotically valid con dence set is attained by employing an easy to compute fi xed critical value, namely the appropriate quantile of a chi-square random variable. We apply our method to study capacity decisions measured as the number of stores operated by Lowe's and Home Depot in geographic markets. We demonstrate how our con dence sets for model parameters can be used to perform inference on other quantities of economic interest, such as the probability that any given outcome is an equilibrium and the propensity with which any particular outcome is selected when it is one of multiple equilibria, and we perform a counterfactual analysis of store con gurations under both collusive and monopolistic regimes.

Suggested Citation

  • Andres Aradillas-Lopez & Adam Rosen, 2014. "Inference in Ordered Response Games with Complete Information," CeMMAP working papers CWP36/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:36/14
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    References listed on IDEAS

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    Cited by:

    1. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    2. Ho, Kate & Rosen, Adam M., 2015. "Partial Identification in Applied Research: Benefits and Challenges," CEPR Discussion Papers 10883, C.E.P.R. Discussion Papers.
    3. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    4. Gualdani, Cristina, 2018. "An Econometric Model of Network Formation with an Application to Board Interlocks between Firms," TSE Working Papers 17-898, Toulouse School of Economics (TSE), revised Jul 2019.
    5. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers CWP63/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    7. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random coefficients in static games of complete information," CeMMAP working papers CWP12/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Navarro, Salvador & Takahashi, Yuya, 2012. "A Semiparametric Test of Agent's Information Sets for Games of Incomplete Information," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 432, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    9. Eleni Aristodemou & Adam M. Rosen, 2022. "A discrete choice model for partially ordered alternatives," Quantitative Economics, Econometric Society, vol. 13(3), pages 863-906, July.
    10. Tatiana Komarova & William Matcham, 2022. "Multivariate ordered discrete response models," Papers 2205.05779, arXiv.org, revised Mar 2023.
    11. Emerson Melo, 2022. "On the uniqueness of quantal response equilibria and its application to network games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 681-725, October.
    12. Eleni Aristodemou, 2021. "A discrete choice model for partially ordered alternatives," CeMMAP working papers CWP35/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Jeremy Fox & Natalia Lazzati, 2013. "Identification of discrete choice models for bundles and binary games," CeMMAP working papers CWP04/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Koh, Paul S., 2023. "Stable outcomes and information in games: An empirical framework," Journal of Econometrics, Elsevier, vol. 237(1).

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    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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