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Generalized Method of Moments and Empirical Likelihood

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  • Imbens, Guido W

Abstract

Generalized method of moments (GMM) estimation has become an important unifying framework for inference in econometrics in the last 20 years. It can be thought of as encompassing almost all of the common estimation methods, such as maximum likelihood, ordinary least squares, instrumental variables, and two-stage least squares, and nowadays is an important part of all advanced econometrics textbooks. The GMM approach links nicely to economic theory where orthogonality conditions that can serve as such moment functions often arise from optimizing behavior of agents. Much work has been done on these methods since the seminal article by Hansen, and much remains in progress. This article discusses some of the developments since Hansen's original work. In particular, it focuses on some of the recent work on empirical likelihood-type estimators, which circumvent the need for a first step in which the optimal weight matrix is estimated and have attractive information theoretic interpretations.

Suggested Citation

  • Imbens, Guido W, 2002. "Generalized Method of Moments and Empirical Likelihood," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 493-506, October.
  • Handle: RePEc:bes:jnlbes:v:20:y:2002:i:4:p:493-506
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    Cited by:

    1. Lee, Seojeong, 2016. "Asymptotic refinements of a misspecification-robust bootstrap for GEL estimators," Journal of Econometrics, Elsevier, vol. 192(1), pages 86-104.
    2. Fan, Yanqin & Gentry, Matthew & Li, Tong, 2011. "A new class of asymptotically efficient estimators for moment condition models," Journal of Econometrics, Elsevier, vol. 162(2), pages 268-277, June.
    3. Stefan Boes, 2010. "Count Data Models with Correlated Unobserved Heterogeneity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 382-402.
    4. Otsu, Taisuke, 2011. "Moderate deviations of generalized method of moments and empirical likelihood estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1203-1216, September.
    5. Demian Pouzo, 2014. "Bootstrap Consistency for Quadratic Forms of Sample Averages with Increasing Dimension," Papers 1411.2701, arXiv.org, revised Aug 2015.
    6. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, February.
    7. Jowaheer, Vandna & Sutradhar, Brajendra, 2009. "GMM versus GQL inferences for panel count data," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1928-1934, September.
    8. Doran, Howard E. & Schmidt, Peter, 2006. "GMM estimators with improved finite sample properties using principal components of the weighting matrix, with an application to the dynamic panel data model," Journal of Econometrics, Elsevier, vol. 133(1), pages 387-409, July.
    9. Li, Daoji & Pan, Jianxin, 2013. "Empirical likelihood for generalized linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 63-73.
    10. Roberto Baragona & Francesco Battaglia & Domenico Cucina, 2016. "Empirical Likelihood for Outlier Detection and Estimation in Autoregressive Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 315-336, May.
    11. Giuseppe Ragusa, 2011. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 406-456, August.
    12. Yuan, Ao & Xu, Jinfeng & Zheng, Gang, 2014. "On empirical likelihood statistical functions," Journal of Econometrics, Elsevier, vol. 178(P3), pages 613-623.
    13. Wang, Xuexin, 2016. "A New Class of Tests for Overidentifying Restrictions in Moment Condition Models," MPRA Paper 69004, University Library of Munich, Germany.
    14. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
    15. Zhiguo Xiao, 2011. "Efficient Estimation of Moment Condition Models with Heterogenous Populations," Annals of Economics and Finance, Society for AEF, vol. 12(1), pages 89-107, May.
    16. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    17. Stefan Boes, 2007. "Count Data Models with Unobserved Heterogeneity: An Empirical Likelihood Approach," SOI - Working Papers 0704, Socioeconomic Institute - University of Zurich.
    18. Kennedy, Edward H. & Joffe, Marshall M. & Small, Dylan S., 2015. "Optimal restricted estimation for more efficient longitudinal causal inference," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 185-191.

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