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Moment Estimation of the Probit Model with an Endogenous Continuous Regressor

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  • Daiji Kawaguchi
  • Yukitoshi Matsushita
  • Hisahiro Naito

Abstract

We propose a generalized method of moments (GMM) estimator with optimal instruments for a probit model that includes a continuous endogenous regressor. This GMM estimator incorporates the probit error and the heteroscedasticity of the error term in the first-stage equation in order to construct the optimal instruments. The estimator estimates the structural equation and the first-stage equation jointly and, based on this joint moment condition, is efficient within the class of GMM estimators. To estimate the heteroscedasticity of the error term of the first-stage equation, we use the k-nearest neighbour (k-nn) non-parametric estimation procedure. Our Monte Carlo simulation shows that in the presence of heteroscedasticity and endogeneity, our GMM estimator outperforms the two-stage conditional maximum likelihood estimator. Our results suggest that in the presence of heteroscedasticity in the first-stage equation, the proposed GMM estimator with optimal instruments is a useful option for researchers.
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Suggested Citation

  • Daiji Kawaguchi & Yukitoshi Matsushita & Hisahiro Naito, 2017. "Moment Estimation of the Probit Model with an Endogenous Continuous Regressor," The Japanese Economic Review, Japanese Economic Association, vol. 68(1), pages 48-62, March.
    • Handle: RePEc:bla:jecrev:v:68:y:2017:i:1:p:48-62
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    File URL: http://hdl.handle.net/10.1111/jere.12091
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    References listed on IDEAS

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    1. Lucchetti, Riccardo, 2002. "Inconsistency of naive GMM estimation for QR models with endogenous regressors," Economics Letters, Elsevier, vol. 75(2), pages 179-185, April.
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    7. Daiji Kawaguchi & Yukitoshi Matsushita & Hisahiro Naito, 2017. "Moment Estimation of the Probit Model with an Endogenous Continuous Regressor," The Japanese Economic Review, Japanese Economic Association, vol. 68(1), pages 48-62, March.
    8. Grogger, Jeffrey, 1990. "A simple test for exogeneity in probit, logit, and poisson regression models," Economics Letters, Elsevier, vol. 33(4), pages 329-332, August.
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    Cited by:

    1. Daiji Kawaguchi & Yukitoshi Matsushita & Hisahiro Naito, 2017. "Moment Estimation of the Probit Model with an Endogenous Continuous Regressor," The Japanese Economic Review, Japanese Economic Association, vol. 68(1), pages 48-62, March.
    2. David T. Frazier & Eric Renault & Lina Zhang & Xueyan Zhao, 2020. "Weak Identification in Discrete Choice Models," Papers 2011.06753, arXiv.org, revised Jan 2021.

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