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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(01), pages 8-46, February.
  • Handle: RePEc:cup:etheor:v:27:y:2011:i:01:p:8-46_00
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    6. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355, June.
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    8. Fosgerau, Mogens, 2006. "Investigating the distribution of the value of travel time savings," Transportation Research Part B: Methodological, Elsevier, pages 688-707.
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    Cited by:

    1. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2014.
    2. 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.
    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, pages 253-281.
    4. Subhayu Bandyopadhyay & Howard J. Wall, 2010. "Immigration and Outsourcing: A General-Equilibrium Analysis," Review of Development Economics, Wiley Blackwell, pages 433-446.
    5. Xiaohong Chen & Demian Pouzo, 2014. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Papers 1411.1144, arXiv.org, revised Mar 2015.
    6. Kyoo il Kim, 2006. "Higher Order Bias Correcting Moment Equation for M-Estimation and its Higher Order Efficiency," Working Papers 17-2006, Singapore Management University, School of Economics.
    7. Martins-Filho, Carlos & Yao, Feng, 2012. "Kernel-based estimation of semiparametric regression in triangular systems," Economics Letters, Elsevier, pages 24-27.
    8. Xiaohong Chen & Yin Jia Qiu, 2016. "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: a Gentle Guide," Cowles Foundation Discussion Papers 2032, Cowles Foundation for Research in Economics, Yale University.
    9. Delgado, Michael S. & Parmeter, Christopher F., 2014. "A simple estimator for partial linear regression with endogenous nonparametric variables," Economics Letters, Elsevier, pages 100-103.
    10. 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.
    11. Griffith, Rachel & Lee, Sokbae & Straathof, Bas, 2017. "Recombinant innovation and the boundaries of the firm," International Journal of Industrial Organization, Elsevier, pages 34-56.
    12. Arthur Lewbel, 2010. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, pages 67-80.
    13. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Labor Economics Working Papers 22452, East Asian Bureau of Economic Research.
    14. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897RR, Cowles Foundation for Research in Economics, Yale University, revised Nov 2014.
    15. Arthur Lewbel, 2010. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, pages 67-80.

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