GMM with Many Weak Moment Conditions
Whitney K. Newey
Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)
University of Bristol - Department of Economics; University of Bristol - Leverhulme Centre for Market and Public Organisation (CMPO); Institute for Fiscal Studies (IFS) - Centre for Microdata Methods and Practice
CEMMAP Working Paper Series No. CWP18/05
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.
Number of Pages in PDF File: 51
Keywords: GMM, Continuous Updating, Many Moments, Variance
JEL Classification: C12, C13, C23working papers series
Date posted: December 20, 2005
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