GMM with Many Moment Conditions

Chirok Han and Peter Phillips

No 1515, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models covering moderate time spans and with correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A general framework for the GMM limit distribution theory is developed based on epiconvergence methods. Some illustrations are provided, including consistent GMM estimation of a panel model with time varying individual effects, consistent LIML estimation as a continuously updated GMM estimator, and consistent IV structural estimation using large numbers of weak or irrelevant instruments. Some simulations are reported.

Keywords: Epiconvergence; GMM; Irrelevant instruments; IV; Large numbers of instruments; LIML estimation; Panel models; Pseudo true value; Signal; Signal Variability; Weak instrumentation (search for similar items in EconPapers)
JEL-codes: C22 C23 (search for similar items in EconPapers)
Pages: 45 pages
Date: 2005-06
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: CFP 1165
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Published in Econometrica (January 2006), 74(1): 147-192

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Related works:
Journal Article: GMM with Many Moment Conditions (2006)
Working Paper: GMM with Many Moment Conditions (2004)
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