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Random coefficients in static games of complete information

Author

Listed:
  • Fabian Dunker

    (Institute for Fiscal Studies)

  • Stefan Hoderlein

    () (Institute for Fiscal Studies and Boston College)

  • Hiroaki Kaido

    () (Institute for Fiscal Studies and Boston University)

Abstract

Individual players in a simultaneous equation binary choice model act differently in different environments in ways that are frequently not captured by observables and a simple additive random error. This paper proposes a random coefficient specification to capture this type of heterogeneity in behaviour, and discusses nonparametric identification and estimation of the distribution of random coefficients. We establish nonparametric point identification of the joint distribution of all random coefficients, except those on the interaction effects, provided the players behave competitively in all markets. Moreover, we establish set identification of the density of the coefficients on the interaction effects, and provide additional conditions that allow to point identify this density. Since our identification strategy is constructive throughout, it allows us to construct sample counterpart estimators. We analyse their asymptotic behaviour, and illustrate their finite sample behaviour in a numerical study. Finally, we discuss several extensions, like the semiparametric case, or correlated random coefficients.

Suggested Citation

  • 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.
  • Handle: RePEc:ifs:cemmap:12/13
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    File URL: http://www.cemmap.ac.uk/wps/cwp121313.pdf
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    References listed on IDEAS

    as
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    4. Kline, Brendan, 2015. "Identification of complete information games," Journal of Econometrics, Elsevier, vol. 189(1), pages 117-131.
    5. Eric Gautier & Erwann Le Pennec, 2011. "Adaptive Estimation in the Nonparametric Random Coefficients Binary Choice Model by Needlet Thresholding," Working Papers 2011-20, Center for Research in Economics and Statistics.
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    Citations

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    Cited by:

    1. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2014. "Nonparametric identification of endogenous and heterogeneous aggregate demand models: complements, bundles and the market level," CeMMAP working papers CWP23/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Fabian Dunker & Konstantin Eckle & Katharina Proksch & Johannes Schmidt-Hieber, 2017. "Tests for qualitative features in the random coefficients model," Papers 1704.01066, arXiv.org, revised Mar 2018.
    3. Breunig, Christoph & Hoderlein, Stefan, 2018. "Specification Testing in Random Coefficient Models," Rationality and Competition Discussion Paper Series 77, CRC TRR 190 Rationality and Competition.
    4. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    5. 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.
    6. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2017. "Nonparametric identification of random coefficients in endogenous and heterogeneous aggregate demand models," CeMMAP working papers CWP11/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    Games; heterogeneity; nonparametric identification; random coefficients; inverse problems;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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