Whitney Newey () (Institute for Fiscal Studies and Massachusetts Institute of Technology) Frank Windmeijer () (Institute for Fiscal Studies and University of Bristol)
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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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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number
CWP18/05.
Length: 51 pp. Date of creation: Dec 2005 Date of revision: Handle: RePEc:ifs:cemmap:18/05
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Find related papers by JEL classification: C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data
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