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Inference in ordered response games with complete information

Author

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  • 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 firm, or the daily number of flights on a city-pair offered by an airline. The model generalises single agent models such as ordered probit and logit to a simultaneous model of ordered response. We characterise identified sets for model parameters under mild shape restrictions on agents' payoff 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 behaviour. Using maximal inequalities for U-processes, we show that an asymptotically valid confidence set is attained by employing an easy to compute fixed 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 confidence 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.

Suggested Citation

  • Andres Aradillas-Lopez & Adam Rosen, 2013. "Inference in ordered response games with complete information," CeMMAP working papers CWP33/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:33/13
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    File URL: http://www.cemmap.ac.uk/wps/cwp331313.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random Coefficients in Static Games of Complete Information," Boston College Working Papers in Economics 835, Boston College Department of Economics.
    3. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    4. 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.
    5. 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.

    More about this item

    Keywords

    discrete games; ordered response; partial identification; conditional moment inequalities;

    JEL classification:

    • 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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