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Information structure and statistical information in discrete response models

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  • Shakeeb Khan
  • Denis Nekipelov

Abstract

Strategic interaction parameters characterize the impact of actions of one economic agent on the payoff of another economic agent, and are of great interest in both theoretical and empirical work. In this paper, by considering econometric models involving simultaneous discrete systems of equations, we study how the information available to economic agents regarding other economic agents can influence whether or not these strategic information parameters can be inferred from the observed actions. We consider two extreme cases: the complete information case where the information sets of participating economic agents coincide and the incomplete information case where each agent's payoffs are privately observable. We find that in models with complete information, the strategic interaction parameters are more difficult to recover than they are in incomplete information models. We show this by exploring the Fisher information (from standard statistics literature) for the strategic interaction parameters in each of these models. Our findings are that in complete information models, the statistical (Fisher) information for the interaction parameters is zero, implying the difficulty in recovering them from data. In contrast, for incomplete information models, the Fisher information for the interaction parameters is positive, indicating that not only can these parameters be relatively easy to recover from data, but standard inference can be conducted on them. This finding is illustrated in two cases: treatment effect models (expressed as a triangular system of equations) and static game models.

Suggested Citation

  • Shakeeb Khan & Denis Nekipelov, 2018. "Information structure and statistical information in discrete response models," Quantitative Economics, Econometric Society, vol. 9(2), pages 995-1017, July.
  • Handle: RePEc:wly:quante:v:9:y:2018:i:2:p:995-1017
    DOI: 10.3982/QE288
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    Cited by:

    1. Lewbel, Arthur & Tang, Xun, 2015. "Identification and estimation of games with incomplete information using excluded regressors," Journal of Econometrics, Elsevier, vol. 189(1), pages 229-244.
    2. Shakeeb Khan & Arnaud Maurel & Yichong Zhang, 2019. "Informational Content of Factor Structures in Simultaneous Binary Response Models," Boston College Working Papers in Economics 985, Boston College Department of Economics.
    3. Kanaya, Shin & Taylor, Luke, 2020. "Type I and Type II Error Probabilities in the Courtroom," MPRA Paper 100217, University Library of Munich, Germany.
    4. Shakeeb Khan & Denis Nekipelov, 2013. "On Uniform Inference in Nonlinear Models with Endogeneity," Working Papers 13-16, Duke University, Department of Economics.
    5. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    6. Tadao Hoshino, 2020. "A Pairwise Strategic Network Formation Model with Group Heterogeneity: With an Application to International Travel," Papers 2012.14886, arXiv.org, revised Feb 2021.

    More about this item

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • 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
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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