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Relaxing Conditional Independence in an Endogenous Binary Response Model

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  • Alyssa Carlson

    (Department of Economics, University of Missouri-Columbia)

Abstract

For binary response models, the literature primarily addresses endogeneity by a control function approach assuming conditional independence (CF-CI). However, as the literature also notes, CF-CI implies conditions like homoskedasticity (of the latent error with respect to the instruments) that fail in many empirical settings. I propose an alternative approach that allows for heteroskedasticity, achieving identification with a conditional mean restriction. These identification results apply to a latent Gaussian error term with flexibly parametrized heteroskedasticity. I propose a two-step conditional maximum likelihood estimator and derive its asymptotic distribution. In simulations, the new estimator outperforms others when CF-CI fails and is fairly robust to distributional misspecification. An empirical illustration studies married women's labor force participation.

Suggested Citation

  • Alyssa Carlson, 2020. "Relaxing Conditional Independence in an Endogenous Binary Response Model," Working Papers 2008, Department of Economics, University of Missouri.
  • Handle: RePEc:umc:wpaper:2008
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    References listed on IDEAS

    as
    1. Krief, Jerome M., 2014. "An Integrated Kernel-Weighted Smoothed Maximum Score Estimator For The Partially Linear Binary Response Model," Econometric Theory, Cambridge University Press, vol. 30(3), pages 647-675, June.
    2. Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.
    3. Khan, Shakeeb, 2013. "Distribution free estimation of heteroskedastic binary response models using Probit/Logit criterion functions," Journal of Econometrics, Elsevier, vol. 172(1), pages 168-182.
    4. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    5. Alyssa Carlson, 2019. "Parametric Identification of Multiplicative Exponential Heteroscedasticity," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(3), pages 686-696, June.
    6. Edward Vytlacil, 2006. "A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(4), pages 515-518, August.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Binary choice model; Endogenous regressors; Control function; Heteroskedasticity;
    All these keywords.

    JEL classification:

    • 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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