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Information Structure and Statistical Information in Discrete Response Models

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  • Shakeeb Khan
  • Denis Nekipelov

Abstract

Discrete response models are of high interest in economics and econometrics as they encompass treatment effects, social interaction and peer effect models, and discrete games. We study the impact of the structure of information sets of economic agents on the Fisher information of (strategic) interaction parameters in such models. While in complete information models the information sets of participating economic agents coincide, in incomplete information models each agent has a type, which we model as a payoff shock, that is not observed by other agents. We allow for the presence of a payoff component that is common knowledge to economic agents but is not observed by the econometrician (representing unobserved heterogeneity) and have the agents' payoffs in the incomplete information model approach their payoff in the complete information model as the heterogeneity term approaches 0. We find that in the complete information models, there is zero Fisher information for interaction parameters, implying that estimation and inference become nonstandard. In contrast, positive Fisher information can be attained in the incomplete information models with any non-zero variance of player types, and for those we can also find the semiparametric efficiency bound with unknown distribution of unobserved heterogeneity. The contrast in Fisher information is illustrated in two important cases: treatment effect models, which we model as a triangular system of equations, and static game models. In static game models we show this result is not due to equilibrium refinement with an increase in incomplete information, as our model has a fixed equilibrium selection mechanism. We find that the key factor in these models is the relative tail behavior of the unobserved component in the economic agents' payoffs and that of the observable covariates.

Suggested Citation

  • Shakeeb Khan & Denis Nekipelov, 2011. "Information Structure and Statistical Information in Discrete Response Models," Working Papers 11-19, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:11-19
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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. 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.
    3. 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.
    4. Hoshino, Tadao & Yanagi, Takahide, 2023. "Treatment effect models with strategic interaction in treatment decisions," Journal of Econometrics, Elsevier, vol. 236(2).
    5. Shakeeb Khan & Arnaud Maurel & Yichong Zhang, 2023. "Informational Content of Factor Structures in Simultaneous Binary Response Models," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 385-410, Emerald Group Publishing Limited.
    6. Kanaya, Shin & Taylor, Luke, 2020. "Type I and Type II Error Probabilities in the Courtroom," MPRA Paper 100217, University Library of Munich, Germany.
    7. Khan, Shakeeb & Nekipelov, Denis, 2024. "On uniform inference in nonlinear models with endogeneity," Journal of Econometrics, Elsevier, vol. 240(2).
    8. Shakeeb Khan & Denis Nekipelov, 2013. "On Uniform Inference in Nonlinear Models with Endogeneity," Working Papers 13-16, Duke University, Department of Economics.
    9. Arthur Lewbel, 2012. "An Overview of the Special Regressor Method," Boston College Working Papers in Economics 810, Boston College Department of Economics.
    10. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.

    More about this item

    Keywords

    endogeneity; semiparametric efficiency; optimal convergence rate; strategic response;
    All these keywords.

    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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