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Additive Nonparametric Regression in the Presence of Endogenous Regressors

Author

Listed:
  • Ozabaci, Deniz

    (University of Connecticut)

  • Henderson, Daniel J.

    (University of Alabama)

  • Su, Liangjun

    (Singapore Management University)

Abstract

In this paper we consider nonparametric estimation of a structural equation model under full additivity constraint. We propose estimators for both the conditional mean and gradient which are consistent, asymptotically normal, oracle efficient and free from the curse of dimensionality. Monte Carlo simulations support the asymptotic developments. We employ a partially linear extension of our model to study the relationship between child care and cognitive outcomes. Some of our (average) results are consistent with the literature (e.g., negative returns to child care when mothers have higher levels of education). However, as our estimators allow for heterogeneity both across and within groups, we are able to contradict many findings in the literature (e.g., we do not find any significant differences in returns between boys and girls or for formal versus informal child care).

Suggested Citation

  • Ozabaci, Deniz & Henderson, Daniel J. & Su, Liangjun, 2014. "Additive Nonparametric Regression in the Presence of Endogenous Regressors," IZA Discussion Papers 8144, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp8144
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    Citations

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    Cited by:

    1. Xin Geng & Carlos Martins-Filho & Feng Yao, 2015. "Estimation of a Partially Linear Regression in Triangular Systems," Working Papers 15-46, Department of Economics, West Virginia University.
    2. Hao Dong & Taisuke Otsu & Luke Taylor, 2022. "Nonparametric estimation of additive models with errors-in-variables," Econometric Reviews, Taylor & Francis Journals, vol. 41(10), pages 1164-1204, November.
    3. Teresa D. Harrison & Daniel J. Henderson & Deniz Ozabaci & Christopher A. Laincz, 2023. "Does one size fit all in the non‐profit donation production function?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(2), pages 373-402, April.
    4. Centorrino Samuele & Feve Frederique & Florens Jean-Pierre, 2017. "Additive Nonparametric Instrumental Regressions: A Guide to Implementation," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-25, January.
    5. Regmi, Krishna & J. Henderson, Daniel, 2019. "Labor demand shocks at birth and cognitive achievement during childhood," Economics of Education Review, Elsevier, vol. 73(C).
    6. Daniel J. Henderson & Anne-Charlotte Souto, 2018. "An Introduction to Nonparametric Regression for Labor Economists," Journal of Labor Research, Springer, vol. 39(4), pages 355-382, December.
    7. Qingliang Fan & Zijian Guo & Ziwei Mei & Cun-Hui Zhang, 2023. "Uniform Inference for Nonlinear Endogenous Treatment Effects with High-Dimensional Covariates," Papers 2310.08063, arXiv.org, revised Oct 2023.
    8. Chi‐Yang Chu & Mingming Jiang, 2021. "Financial depth, income inequality, and economic transition," Southern Economic Journal, John Wiley & Sons, vol. 88(1), pages 199-244, July.
    9. Kourtellos, Andros & Stengos, Thanasis & Sun, Yiguo, 2022. "Endogeneity In Semiparametric Threshold Regression," Econometric Theory, Cambridge University Press, vol. 38(3), pages 562-595, June.
    10. Regmi, Krishna & Henderson, Daniel J., 2019. "Labor Demand Shocks at Birth and Cognitive Achievement during Childhood," IZA Discussion Papers 12521, Institute of Labor Economics (IZA).
    11. Mustafa Koroglu, 2019. "Growth and Debt: An Endogenous Smooth Coefficient Approach," JRFM, MDPI, vol. 12(1), pages 1-22, February.
    12. Kumbhakar, Subal C. & Li, Mingyang & Lien, Gudbrand, 2023. "Do subsidies matter in productivity and profitability changes?," Economic Modelling, Elsevier, vol. 123(C).

    More about this item

    Keywords

    child care; structural equation; additive regression; endogeneity; generated regressors; oracle estimation; nonparametric regression; test scores;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth

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