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Informational content of special regressors in heteroskedastic binary response models

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  • Chen, Songnian
  • Khan, Shakeeb
  • Tang, Xun

Abstract

We quantify the informational content of special regressors in heteroskedastic binary response models with median-independent or conditionally symmetric errors. Based on Lewbel (1998), a special regressor is additively separable in the latent payoff and conditionally independent from the error term. We find that with median-independent errors a special regressor does not increase the identifying power by a criterion in Manski (1988) or lead to positive Fisher information for the coefficients, even though it does help recover the average structural function. With conditionally symmetric errors, a special regressor improves the identifying power, and the information for coefficients is positive under mild conditions. We propose two estimators for binary response models with conditionally symmetric errors and special regressors.

Suggested Citation

  • Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2016. "Informational content of special regressors in heteroskedastic binary response models," Journal of Econometrics, Elsevier, vol. 193(1), pages 162-182.
    • Handle: RePEc:eee:econom:v:193:y:2016:i:1:p:162-182
    DOI: 10.1016/j.jeconom.2015.12.018
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    2. Bo E Honoré & Áureo de Paula, 2021. "Identification in simple binary outcome panel data models," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 78-93.
    3. Nail Kashaev, 2018. "Identification and estimation of multinomial choice models with latent special covariates," Papers 1811.05555, arXiv.org, revised Mar 2022.
    4. Merlo, Antonio & Tang, Xun, 2019. "New results on the identification of stochastic bargaining models," Journal of Econometrics, Elsevier, vol. 209(1), pages 79-93.
    5. Wan, Yuanyuan & Xu, Haiqing, 2015. "Inference in semiparametric binary response models with interval data," Journal of Econometrics, Elsevier, vol. 184(2), pages 347-360.
    6. 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.
    7. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Identification and Estimation of Weakly Separable Models Without Monotonicity," Papers 2003.04337, arXiv.org, revised Apr 2020.
    8. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    9. Songnian Chen & Shakeeb Khan & Xun Tang, 2018. "Exclusion Restrictions in Dynamic Binary Choice Panel Data Models," Boston College Working Papers in Economics 947, Boston College Department of Economics.

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    More about this item

    Keywords

    Binary response; Heteroskedasticity; Identification; Information; Median independence; Conditional symmetry;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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