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Efficient Kernel-Based Semiparametric IV Estimation with an Application to Resolving a Puzzle on the Estimates of the Return to Schooling

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  • Feng Yao

    (Department of Economics, West Virginia University)

  • Junsen Zhang

    (Department of Economics, The Chinese University of Hong Kong)

Abstract

An interesting puzzle in estimating the effect of education on labor market earnings (Card (2001)) is that the 2SLS estimate for the return to schooling typically exceeds the OLS estimate, but the 2SLS estimate is fairly imprecise. We provide a new explanation that it could be due to the restrictive linear functional form specification on the control variables and the reduced form. For the parameters of endogenous regressors, we propose two kernel-based semiparametric IV estimators that relax the tight functional form assumption on the control variables and the reduced form. They have explicit algebraic structures and are easily implemented without numerical optimizations. We show that they are consistent, asymptotically normally distributed, and reach the semiparametric efficiency bound. A Monte Carlo study demonstrates that our estimators perform well in finite samples. We apply the proposed estimators to estimate the return to schooling in Card (1995). We find that the semiparametric estimates of the return to schooling are much smaller and more precise than the 2SLS estimate, and the difference largely comes from the misspecification in the linear reduced form.

Suggested Citation

  • Feng Yao & Junsen Zhang, 2013. "Efficient Kernel-Based Semiparametric IV Estimation with an Application to Resolving a Puzzle on the Estimates of the Return to Schooling," Working Papers 13-01, Department of Economics, West Virginia University.
    • Handle: RePEc:wvu:wpaper:13-01
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    Cited by:

    1. Zhang, Hong-Fan, 2021. "Iterative GMM for partially linear single-index models with partly endogenous regressors," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).

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    More about this item

    Keywords

    Instrumental variables; semiparametric regression; efficient estimation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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