Hostname: page-component-7dd5485656-wlg5v Total loading time: 0 Render date: 2025-10-31T03:37:35.817Z Has data issue: false hasContentIssue false
  • English
  • Français

EMPIRICAL LIKELIHOOD ESTIMATION OF CONDITIONAL MOMENT RESTRICTION MODELS WITH UNKNOWN FUNCTIONS

Published online by Cambridge University Press:  30 April 2010

Taisuke Otsu
Taisuke Otsu*
Affiliation:
Yale University
*
*Address correspondence to Taisuke Otsu, Department of Economics, Yale University, Box 208281, New Haven, CT 06520-8281, USA; e-mail: taisuke.otsu@yale.edu.
Get access Rights & Permissions [Opens in a new window]

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.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 1: SPECIAL ISSUE ON EMPIRICAL LIKELIHOOD AND RELATED METHODS , February 2011 , pp. 8 - 46
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Ai, C. & Chen, X. (1999) Efficient estimation of models with conditional moment restrictions containing unknown functions. Working paper, New York University.Google Scholar
Ai, C. & Chen, X. (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71, 1795–1843.CrossRefGoogle Scholar
Chen, X. (2007) Large sample sieve estimation of semi-nonparametric models. In Heckman, J.J. & Learner, E.E. (eds.), Handbook of Econometrics, pp. 5549–5632. Elsevier.CrossRefGoogle Scholar
Chen, X., Linton, O., & Van Keilegom, I. (2003) Estimation of semiparametric models when the criterion function is not smooth. Econometrica 71, 1591–1608.CrossRefGoogle Scholar
Chen, X. & Shen, X. (1998) Sieve extremum estimates for weakly dependent data. Econometrica 66, 289–314.CrossRefGoogle Scholar
Donald, S.G., Imbens, G.W., & Newey, W.K. (2003) Empirical likelihood estimation and consistent tests with conditional moment restrictions. Journal of Econometrics 117, 55–93.CrossRefGoogle Scholar
Fan, J. & Zhang, J. (2004) Sieve empirical likelihood ratio tests for nonparametric functions. Annals of Statistics 32, 1858–1907.CrossRefGoogle Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.CrossRefGoogle Scholar
Hjort, N.L., McKeague, I.W., & van Keilegom, I. (2009) Extending the scope of empirical likelihood. Annals of Statistics 37, 1079–1111.CrossRefGoogle Scholar
Kitamura, Y. (2003) A Likelihood-Based Approach to the Analysis of a Class of Nested and Non-Nested Models. Working paper, University of Pennsylvania.Google Scholar
Kitamura, Y., Tripathi, G., & Ahn, H. (2004) Empirical likelihood-based inference in conditional moment restriction models. Econometrica 72, 1667–1714.CrossRefGoogle Scholar
Newey, W.K. & Powell, J.L. (2003) Instrumental variable estimation of nonparametric models. Econometrica 71, 1565–1578.CrossRefGoogle Scholar
Newey, W.K. & Smith, R.J. (2004) Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 72, 219–256.CrossRefGoogle Scholar
Otsu, T. (2007) Penalized empirical likelihood estimation of semiparametric models. Journal of Multivariate Analysis 98, 1923–1954.CrossRefGoogle Scholar
Owen, A. (2001) Empirical Likelihood. Chapman & Hall/CRC.Google Scholar
Qin, J. & Lawless, J. (1994) Empirical likelihood for linear models. Annals of Statistics 22, 300–325.Google Scholar
Shen, X. (1997) On methods of sieves and penalization. Annals of Statistics 25, 2555–2591.CrossRefGoogle Scholar
Shen, X. & Wong, W.H. (1994) Convergence rate of sieve estimates. Annals of Statistics 22, 580–615.CrossRefGoogle Scholar
Smith, R.J. (1997) Alternative semi-parametric likelihood approaches to generalized method of moments estimation. Economic Journal 107, 503–519.CrossRefGoogle Scholar
Smith, R.J. (2007) Local GEL estimation with conditional moment restrictions. In Phillips, G.D.A. & Tzavalis, E. (eds.), The Refinement of Econometric Estimation and Test Procedures: Finite Sample and Asymptotic Analysis, pp. 100–122. Cambridge University Press.CrossRefGoogle Scholar
Van der Vaart, A. & Wellner, J. (1996) Weak Convergence and Empirical Process. Springer-Verlag.CrossRefGoogle Scholar
Zhang, J. & Gijbels, I. (2003) Sieve empirical likelihood and extensions of the generalized least squares. Scandinavian Journal of Statistics 30, 1–24.CrossRefGoogle Scholar
Zhang, J. & Liu, A. (2003) Local polynomial fitting based on empirical likelihood. Bernoulli 9, 579–605.CrossRefGoogle Scholar