Select the Valid and Relevant Moments: An Information-Based LASSO for GMM with Many Moments

80 Pages Posted: 22 Oct 2013

See all articles by Xu Cheng

Xu Cheng

University of Pennsylvania - Department of Economics

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics

Multiple version iconThere are 3 versions of this paper

Date Written: October 21, 2013

Abstract

This paper studies the selection of valid and relevant moments for the generalized method of moments (GMM) estimation. For applications with many candidate moments, our asymptotic analysis accommodates a diverging number of moments as the sample size increases. The proposed procedure achieves three objectives in one-step: (i) the valid and relevant moments are distinguished from the invalid or irrelevant ones; (ii) all desired moments are selected in one step instead of in a stepwise manner; (iii) the parameters of interest are automatically estimated with all selected moments as opposed to a post-selection estimation. The new method performs moment selection and efficient estimation simultaneously via an information-based adaptive GMM shrinkage estimation, where an appropriate penalty is attached to the standard GMM criterion to link moment selection to shrinkage estimation. The penalty is designed to signal both moment validity and relevance for consistent moment selection. We develop asymptotic results for the high-dimensional GMM shrinkage estimator, allowing for non-smooth sample moments and weakly dependent observations. For practical implementation, this one-step procedure is computationally attractive.

Keywords: Adaptive Penalty, GMM, Many Moments, Moment Selection, Oracle Properties, Shrinkage Estimation

JEL Classification: C12, C13, C36

Suggested Citation

Cheng, Xu and Liao, Zhipeng, Select the Valid and Relevant Moments: An Information-Based LASSO for GMM with Many Moments (October 21, 2013). PIER Working Paper No. 13-062, Available at SSRN: https://ssrn.com/abstract=2343130 or http://dx.doi.org/10.2139/ssrn.2343130

Xu Cheng (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

HOME PAGE: http://www.sas.upenn.edu/~xucheng/

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics ( email )

8283 Bunche Hall
Los Angeles, CA 90095-1477
United States

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