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A note on GMM estimation of probit models with endogenous regressors

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  • Joachim Wilde

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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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Suggested Citation

  • 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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    References listed on IDEAS

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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. Lucchetti, Riccardo, 2002. "Inconsistency of naive GMM estimation for QR models with endogenous regressors," Economics Letters, Elsevier, vol. 75(2), pages 179-185, April.
    3. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 655-679.
    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. 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.
    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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    Citations

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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. 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.
    3. repec:eee:riibaf:v:42:y:2017:i:c:p:442-453 is not listed on IDEAS
    4. Austin Nichols, 2011. "Causal inference for binary regression with observational data," CHI11 Stata Conference 6, Stata Users Group.
    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

    More about this item

    Keywords

    Generalized method of moments; Probit model; Endogenous regressor;

    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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