Microdata Methods and Practice

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Working papers

GMM with many weak moment conditions

Authors: Whitney Newey and Frank Windmeijer
Publication type: cemmap Working Papers, CWP18/05
Now published in: Econometrica [ Details]
ISSN: 1753-9196
Publication date: December 2005
Pages: 51 pp.

Using many moment conditions can improve efficiency but makes the usual GMM inferences inaccurate. Two step GMM is biased. Generalized empirical likelihood (GEL) has smaller bias but the usual standard errors are too small. In this paper we use alternative asymptotics, based on many weak moment conditions, that addresses this problem. This asymptotics leads to improved approximations in overidentified models where the variance of the derivative of the moment conditions is large relative to the squared expected value of the moment conditions and identification is not too weak. We obtain an asymptotic variance for GEL that is larger than the usual one and give a "sandwich" estimator of it. In Monte Carlo examples we find that this variance estimator leads to a better Gaussian approximation to t-ratios in a range of cases. We also show that Kleibergen (2005) K statistic is valid under these asymptotics. We also compare these results with a jackknife GMM estimator, finding that GEL is asymptotically more efficient under many weak moments.

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Keywords: GMM, Continuous Updating, Many Moments, Variance Adjustment

JEL classification: C12, C13, C23