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Empirical Likelihood Estimation Of Conditional Moment Restriction Models With Unknown Functions

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  • Otsu, Taisuke

Abstract

This paper proposes an empirical likelihood-based estimation method for conditional moment restriction models with unknown functions, which include several semiparametric models. Our estimator is called the sieve conditional empirical likelihood (SCEL) estimator, which is based on the methods of conditional empirical likelihood and sieves. We derive (i) the consistency and a convergence rate of the SCEL estimator for the whole parameter, and (ii) the asymptotic normality and efficiency of the SCEL estimator for the parametric component. As an illustrating example, we consider a partially linear regression model with nonparametric endogeneity and heteroskedasticity.

Suggested Citation

  • Otsu, Taisuke, 2011. "Empirical Likelihood Estimation Of Conditional Moment Restriction Models With Unknown Functions," Econometric Theory, Cambridge University Press, vol. 27(1), pages 8-46, February.
    • Handle: RePEc:cup:etheor:v:27:y:2011:i:01:p:8-46_00
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    Citations

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    Cited by:

    1. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897, Cowles Foundation for Research in Economics, Yale University.
    2. Arthur Lewbel, 2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80.
    3. 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.
    4. Xiaohong Chen & Yin Jia Jeff Qiu, 2016. "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: A Gentle Guide," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 259-290, October.
    5. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    6. Martins-Filho, Carlos & Yao, Feng, 2012. "Kernel-based estimation of semiparametric regression in triangular systems," Economics Letters, Elsevier, vol. 115(1), pages 24-27.
    7. Chen, Xiaohong & Pouzo, Demian & Powell, James L., 2019. "Penalized sieve GEL for weighted average derivatives of nonparametric quantile IV regressions," Journal of Econometrics, Elsevier, vol. 213(1), pages 30-53.
    8. Xiaohong Chen & Demian Pouzo, 2014. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," CeMMAP working papers 38/14, Institute for Fiscal Studies.
    9. 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.
    10. Xiaolin Sun, 2022. "Estimation of Heterogeneous Treatment Effects Using a Conditional Moment Based Approach," Papers 2210.15829, arXiv.org, revised Dec 2022.
    11. Bertille Antoine & Xiaolin Sun, 2022. "Partially linear models with endogeneity: a conditional moment-based approach [Efficient estimation of models with conditional moment restrictions containing unknown functions]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 256-275.
    12. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Working Papers 19-2006, Singapore Management University, School of Economics.
    13. Delgado, Michael S. & Parmeter, Christopher F., 2014. "A simple estimator for partial linear regression with endogenous nonparametric variables," Economics Letters, Elsevier, vol. 124(1), pages 100-103.

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