GMM with many weak moment conditions

Whitney Newey and Frank Windmeijer

No CWP18/05, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: 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.

Keywords: GMM; Continuous Updating; Many Moments; Variance Adjustment (search for similar items in EconPapers)
JEL-codes: C12 C13 C23 (search for similar items in EconPapers)
Pages: 51 pp.
Date: 2005-12-06
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (20)

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