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Informational Content of Factor Structures in Simultaneous Binary Response Models

In: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications

Author

Listed:
  • Shakeeb Khan
  • Arnaud Maurel
  • Yichong Zhang
Abstract
We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a variety of settings in cross-sectional and panel data models, and in this chapter we formally quantify their identifying power in a bivariate system often employed in the treatment effects literature. Our main findings are that imposing a factor structure yields point-identification of parameters of interest, such as the coefficient associated with the endogenous regressor in the outcome equation, under weaker assumptions than usually required in these models. In particular, we show that a “non-standard” exclusion restriction that requires an explanatory variable in the outcome equation to be excluded from the treatment equation is no longer necessary for identification, even in cases where all of the regressors from the outcome equation are discrete. We also establish identification of the coefficient of the endogenous regressor in models with more general factor structures, in situations where one has access to at least two continuous measurements of the common factor.

Suggested Citation

  • 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.
    • Handle: RePEc:eme:aecozz:s0731-90532023000045b016
    DOI: 10.1108/S0731-90532023000045B016
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    Cited by:

    1. Benjamin Williams, 2018. "Identification of the Linear Factor Model," Working Papers 2018-002, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    2. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Dummy Endogenous Variables in Weakly Separable Multiple Index Models without Monotonicity," Boston College Working Papers in Economics 996, Boston College Department of Economics.
    3. Gu, Jiaying & Russell, Thomas M., 2023. "Partial identification in nonseparable binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 528-562.
    4. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Identification and Estimation of Weakly Separable Models Without Monotonicity," Papers 2003.04337, arXiv.org, revised Apr 2020.

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    More about this item

    Keywords

    Factor structures; discrete choice; causal effects; identification; binary dependent variable; endogeneity; C14; C31; C35;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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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