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ADAPTIVE GMM SHRINKAGE ESTIMATION WITH CONSISTENT MOMENT SELECTION

Published online by Cambridge University Press:  25 February 2013

Zhipeng Liao
Zhipeng Liao*
Affiliation:
University of California, Los Angeles
*
*Address correspondence to Zhipeng Liao, Department of Economics, UC Los Angeles, 8279 Bunche Hall, Mail Stop: 147703, Los Angeles, CA 90095; e-mail: zhipeng.liao@econ.ucla.edu.
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Abstract

This paper proposes a generalized method of moments (GMM) shrinkage method to efficiently estimate the unknown parameters θo identified by some moment restrictions, when there is another set of possibly misspecified moment conditions. We show that our method enjoys oracle-like properties; i.e., it consistently selects the correct moment conditions in the second set and at the same time, its estimator is as efficient as the GMM estimator based on all correct moment conditions. For empirical implementation, we provide a simple data-driven procedure for selecting the tuning parameters of the penalty function. We also establish oracle properties of the GMM shrinkage method in the practically important scenario where the moment conditions in the first set fail to strongly identify θo. The simulation results show that the method works well in terms of correct moment selection and the finite sample properties of its estimators. As an empirical illustration, we apply our method to estimate the life-cycle labor supply equation studied in MaCurdy (1981, Journal of Political Economy 89(6), 1059–1085) and Altonji (1986, Journal of Political Economy 94(3), 176–215). Our empirical findings support the validity of the instrumental variables used in both papers and confirm that wage is an endogenous variable in the labor supply equation.

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 5 , October 2013 , pp. 857 - 904
Copyright
Copyright © Cambridge University Press 2013 

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Footnotes

The author is deeply indebted to Peter Phillips and Xiaohong Chen for guidance, inspiration, and encouragement. He is also grateful to Donald Andrews for valuable suggestion. The author benefited from insightful comments made by the co-editor, two anonymous referees, Joseph Altonji, Xu Cheng, Jinyong Hahn, Yuichi Kitamura, Oliver Linton, Xiaoxia Shi, Edward Vytlacil, and Bin Wang. Financial support from a Carl Arvid Anderson Prize of the Cowles Foundation is acknowledged.

References

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