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Semiparametric Estimators for Limited Dependent Variable (LDV) Models with Endogenous Regressors

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  • Myoung-Jae Lee

Abstract

This article reviews semiparametric estimators for limited dependent variable (LDV) models with endogenous regressors, where nonlinearity and nonseparability pose difficulties. We first introduce six main approaches in the linear equation system literature to handle endogenous regressors with linear projections: (i) ‘substitution’ replacing the endogenous regressors with their projected versions on the system exogenous regressors x, (ii) instrumental variable estimator (IVE) based on E{(error) × x} = 0, (iii) ‘model-projection’ turning the original model into a model in terms of only x-projected variables, (iv) ‘system reduced form (RF)’ finding RF parameters first and then the structural form (SF) parameters, (v) ‘artificial instrumental regressor’ using instruments as artificial regressors with zero coefficients, and (vi) ‘control function’ adding an extra term as a regressor to control for the endogeneity source. We then check if these approaches are applicable to LDV models using conditional mean/quantiles instead of linear projection. The six approaches provide a convenient forum on which semiparametric estimators in the literature can be categorized, although there are a few exceptions. The pros and cons of the approaches are discussed, and a small-scale simulation study is provided for some reviewed estimators.

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  • Myoung-Jae Lee, 2012. "Semiparametric Estimators for Limited Dependent Variable (LDV) Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 31(2), pages 171-214.
    • Handle: RePEc:taf:emetrv:v:31:y:2012:i:2:p:171-214
    DOI: 10.1080/07474938.2011.607101
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    Cited by:

    1. Goeun Lee & Myoung-jae Lee, 2023. "Regression Discontinuity for Binary Response and Local Maximum Likelihood Estimator to Extrapolate Treatment," Evaluation Review, , vol. 47(2), pages 182-208, April.
    2. Lee, M-J & Kim, Y-S, 2011. "Effects of Informal Family Care on Formal Health Care: Zero-Inflated Endogenous Count for Censored Response," Health, Econometrics and Data Group (HEDG) Working Papers 11/10, HEDG, c/o Department of Economics, University of York.
    3. Angelov, Nikolay & Johansson, Per & Lee, Myoung-jae, 2017. "The effect of fertility timing on labor market work duration," Working Paper Series 2017:13, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    4. Changhui Kang & Myoung-jae Lee, 2014. "Estimation of Binary Response Models With Endogenous Regressors," Pacific Economic Review, Wiley Blackwell, vol. 19(4), pages 502-530, October.
    5. Myoung‐jae Lee, 2021. "Instrument residual estimator for any response variable with endogenous binary treatment," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 612-635, July.
    6. Young-Min Ju & Myoung-Jae Lee, 2017. "Control Function Approach for Partly Ordered Endogenous Treatments: Military Rank Premium in Wage," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(6), pages 1176-1194, December.

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