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Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling

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  • Liangjun Su
  • Irina Murtazashvili
  • Aman Ullah

Abstract

We consider the local linear generalized method of moment (GMM) estimation of functional coefficient models with a mix of discrete and continuous data and in the presence of endogenous regressors. We establish the asymptotic normality of the estimator and derive the optimal instrumental variable that minimizes the asymptotic variance-covariance matrix among the class of all local linear GMM estimators. Data-dependent bandwidth sequences are also allowed for. We propose a nonparametric test for the constancy of the functional coefficients, study its asymptotic properties under the null hypothesis as well as a sequence of local alternatives and global alternatives, and propose a bootstrap version for it. Simulations are conducted to evaluate both the estimator and test. Applications to the 1985 Australian Longitudinal Survey data indicate a clear rejection of the null hypothesis of the constant rate of return to education, and that the returns to education obtained in earlier studies tend to be overestimated for all the work experience.

Suggested Citation

  • Liangjun Su & Irina Murtazashvili & Aman Ullah, 2013. "Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(2), pages 184-207, April.
    • Handle: RePEc:taf:jnlbes:v:31:y:2013:i:2:p:184-207
    DOI: 10.1080/07350015.2012.754314
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    Citations

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    Cited by:

    1. Tae‐Hwy Lee & Shahnaz Parsaeian & Aman Ullah, 2022. "Forecasting Under Structural Breaks Using Improved Weighted Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(6), pages 1485-1501, December.
    2. Huang, Bai & Lee, Tae-Hwy & Ullah, Aman, 2020. "Combined estimation of semiparametric panel data models," Econometrics and Statistics, Elsevier, vol. 15(C), pages 30-45.
    3. Shengjie Hong & Yu-Chin Hsu & Yuanyuan Wan, 2023. "Subvector inference for Varying Coefficient Models with Partial Identification," Working Papers tecipa-756, University of Toronto, Department of Economics.
    4. Irina Murtazashvili & Di Liu & Artem Prokhorov, 2015. "Two‐sample nonparametric estimation of intergenerational income mobility in the United States and Sweden," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 48(5), pages 1733-1761, December.
    5. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    6. Susan Athey & Julie Tibshirani & Stefan Wager, 2016. "Generalized Random Forests," Papers 1610.01271, arXiv.org, revised Apr 2018.
    7. Zhang, Hong-Fan, 2021. "Iterative GMM for partially linear single-index models with partly endogenous regressors," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    8. Samuele CENTORRINO & Jeffrey S. RACINE, 2017. "Semiparametric Varying Coefficient Models with Endogenous Covariates," Annals of Economics and Statistics, GENES, issue 128, pages 261-295.
    9. Tadao Hoshino, 2018. "Semiparametric Spatial Autoregressive Models With Endogenous Regressors: With an Application to Crime Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 160-172, January.
    10. Feng Yao & Junsen Zhang, 2015. "Efficient kernel-based semiparametric IV estimation with an application to resolving a puzzle on the estimates of the return to schooling," Empirical Economics, Springer, vol. 48(1), pages 253-281, February.
    11. Pan Zhao & Yifan Cui, 2023. "A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning," Papers 2310.09545, arXiv.org.
    12. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    13. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    14. Su, Liangjun & Hoshino, Tadao, 2016. "Sieve instrumental variable quantile regression estimation of functional coefficient models," Journal of Econometrics, Elsevier, vol. 191(1), pages 231-254.
    15. Cai, Zongwu & Fang, Ying & Lin, Ming & Su, Jia, 2018. "Inferences for a Partially Varying Coefficient Model With Endogenous Regressors," IRTG 1792 Discussion Papers 2018-047, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. Yan Li & Liangjun Su & Yuewu Xu, 2015. "A Combined Approach to the Inference of Conditional Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 203-220, April.
    17. Stefan Sperlich, 2014. "On the choice of regularization parameters in specification testing: a critical discussion," Empirical Economics, Springer, vol. 47(2), pages 427-450, September.

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