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A note on GMM estimation of probit models with endogenous regressors

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  • Joachim Wilde

Abstract

Dagenais (1999) and Lucchetti (2002) have demonstrated that the naive GMM estimator of Grogger (1990) for the probit model with an endogenous regressor is not consistent. This paper completes their discussion by explaining the reason for the inconsistency and presenting a natural solution. Furthermore, the resulting GMM estimator is analyzed in a Monte-Carlo simulation and compared with alternative estimators.
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  • Joachim Wilde, 2008. "A note on GMM estimation of probit models with endogenous regressors," Statistical Papers, Springer, vol. 49(3), pages 471-484, July.
    • Handle: RePEc:spr:stpapr:v:49:y:2008:i:3:p:471-484
    DOI: 10.1007/s00362-006-0027-2
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    1. Avery, Robert B & Hansen, Lars Peter & Hotz, V Joseph, 1983. "Multiperiod Probit Models and Orthogonality Condition Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(1), pages 21-35, February.
    2. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    3. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
    4. Lucchetti, Riccardo, 2002. "Inconsistency of naive GMM estimation for QR models with endogenous regressors," Economics Letters, Elsevier, vol. 75(2), pages 179-185, April.
    5. 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.
    6. Daiji Kawaguchi & Hisahiro Naito, 2005. "The efficient moment estimation of the probit model with an endogenous continuous regressor," Hi-Stat Discussion Paper Series d05-106, Institute of Economic Research, Hitotsubashi University.
    7. 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.
    8. Dagenais, Marcel G., 1999. "Inconsistency of a proposed nonlinear instrumental variables estimator for probit and logit models with endogenous regressors," Economics Letters, Elsevier, vol. 63(1), pages 19-21, April.
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    Cited by:

    1. Francesca Modena & Fabio Sabatini, 2012. "I would if I could: precarious employment and childbearing intentions in Italy," Review of Economics of the Household, Springer, vol. 10(1), pages 77-97, March.
    2. Jean-Marie Dufour & Joachim Wilde, 2018. "Weak identification in probit models with endogenous covariates," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 611-631, October.
    3. Francesca Modena & Concetta Rondinelli & Fabio Sabatini, 2014. "Economic Insecurity and Fertility Intentions: The Case of Italy," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(S1), pages 233-255, May.
    4. Mili, Mehdi & Sahut, Jean-Michel & Trimeche, Hatem & Teulon, Frédéric, 2017. "Determinants of the capital adequacy ratio of foreign banks’ subsidiaries: The role of interbank market and regulation," Research in International Business and Finance, Elsevier, vol. 42(C), pages 442-453.
    5. Qian Chen & David Giles, 2012. "Finite-sample properties of the maximum likelihood estimator for the binary logit model with random covariates," Statistical Papers, Springer, vol. 53(2), pages 409-426, May.
    6. repec:gig:joupla:v:6:y:2014:i:3:p:129-158 is not listed on IDEAS
    7. Tinaikar, Surjit & Xu, Bo, 2023. "Does competition exacerbate investment inefficiencies? Evidence from Japanese firms," International Review of Economics & Finance, Elsevier, vol. 87(C), pages 35-53.
    8. Austin Nichols, 2011. "Causal inference for binary regression with observational data," CHI11 Stata Conference 6, Stata Users Group.
    9. Daniela Benavente, 2010. "Constraining and supporting effects of the multilateral trading system on U.S. unilateralism," IHEID Working Papers 09-2010, Economics Section, The Graduate Institute of International Studies.

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    More about this item

    Keywords

    Generalized method of moments; Probit model; Endogenous regressor;
    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
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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