Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-13T02:32:44.005Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

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.)

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

REFERENCES

Altonji, J. (1986) Intertemporal substitution in labor supply: Evidence from micro data. Journal of Political Economy 94(3), 176–215.CrossRefGoogle Scholar
Andrews, D. (1999) Consistent moment selection procedures for generalized method of moments estimation. Econometrica 67(3), 543–563.CrossRefGoogle Scholar
Andrews, D., Cheng, X., & Guggenberger, P. (2011) Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests. Cowles Foundation Discussion Paper No.1813.CrossRefGoogle Scholar
Angrist, J. & Krueger, A. (1991) Does compulsory school attendance affect schooling and earnings. Quarterly Journal of Economics 106(4), 979–1014.CrossRefGoogle Scholar
Arellano, M. & Bover, O. (1995) Another look at the instrumental variable estimation of error-components models. Journal of Econometrics 68(1), 29–51.CrossRefGoogle Scholar
Belloni, A., Chen, D., Chernozhukov, V., & Hansen, C. (2012) Sparse models and methods for optimal instruments with an application to eminent domain. Econometrica 80(6), 2369–2431.Google Scholar
Blundell, R. & Bond, S. (1998) Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87(1), 115–143.CrossRefGoogle Scholar
Caner, M. (2009) Lasso-type GMM estimator. Econometric Theory 25(1), 270–290.CrossRefGoogle Scholar
Caner, M. & Zhang, H. (2012) Adaptive Elastic Net for Generalized Methods of Moments, Working paper, North Carolina State University.Google Scholar
Eichenbaum, M., Hansen, L., & Singleton, K. (1988) A time series analysis of representative agent models of consumption and leisure choice under uncertainty. Quarterly Journal of Economics 103(1), 51–78.CrossRefGoogle Scholar
Fan, J. & Li, R. (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96(456), 1348–1360.Google Scholar
Gautier, E. & Tsybakov (2011) High-dimensional Instrumental Variables Regression and Confidence Sets. Preprint, arXiv: 1105.2454v2, ENSAE Paris Tech.Google Scholar
Geyer, C. (1994) On the asymptotics of constrained M-estimation. Annals of Statistics 22(4), 1993–2010.CrossRefGoogle Scholar
Guggenberger, P. (2012) On the asymptotic size distortion of tests when instruments locally violate the exogeneity assumption. Econometric Theory 28, 387–421.CrossRefGoogle Scholar
Hahn, J. & Kuersteiner, G. (2002) Discontinuities of weak instrument limiting distributions. Economics Letters 75(3), 325–331.Google Scholar
Hong, H., Preston, B., & Shum, M. (2003) Generalized empirical likelihood-based model selection criteria for moment condition models. Econometric Theory 19(6), 923–943.CrossRefGoogle Scholar
Knight, K. (1999) Epi-convergence in Distribution and Stochastic Equisemicontinuity. Working paper, University of Toronto.Google Scholar
Knight, K. & Fu, W. (2000) Asymptotics for lasso-type estimators. Annals of Statistics 28(5), 1356–1378.Google Scholar
Leeb, H. & Pötscher, B.M. (2005) Model selection and inference: Facts and fiction. Econometric Theory 21(01), 21–59.CrossRefGoogle Scholar
Leeb, H. & Pötscher, B.M. (2008) Sparse estimators and the oracle property, or the return of the Hodges estimator. Journal of Econometrics 142(1), 201–211.CrossRefGoogle Scholar
MaCurdy, T. (1981) An empirical model of labor supply in a life-cycle setting. Journal of Political Economy 89(6), 1059–1085.CrossRefGoogle Scholar
Miguel, E., Satyanath, S., & Sergenti, E. (2004) Economic shocks and civil conflict: An instrumental variables approach. Journal of Political Economy 112(4), 725–753.CrossRefGoogle Scholar
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.CrossRefGoogle Scholar
Sargan, J. (1958) The estimation of economic relationships using instrumental variables. Econometrica, 26(3), 393–415.CrossRefGoogle Scholar
Schmidt, M. (2010) Graphical Model Structure Learning with L1-Regularization. Thesis, University of British Columbia.Google Scholar
Stock, J. & Wright, J. (2000) GMM with weak identification. Econometrica 68(5), 1055–1096.CrossRefGoogle Scholar
Zou, H. (2006) The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101(476), 1418–1429.CrossRefGoogle Scholar