GMM with Many Weak Moment Conditions
Author(s)Newey, Whitney K.; Windmeijer, Frank
Generalized Method of Moments With Many Weak Moment Conditions
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Using many moment conditions can improve efficiency but makes the usual generalized method of moments (GMM) inferences inaccurate. Two-step GMM is biased. Generalized empirical likelihood (GEL) has smaller bias, but the usual standard errors are too small in instrumental variable settings. In this paper we give a new variance estimator for GEL that addresses this problem. It is consistent under the usual asymptotics and, under many weak moment asymptotics, is larger than usual and is consistent. We also show that the Kleibergen (2005) Lagrange multiplier and conditional likelihood ratio statistics are valid under many weak moments. In addition, we introduce a jackknife GMM estimator, but find that GEL is asymptotically more efficient under many weak moments. In Monte Carlo examples we find that t-statistics based on the new variance estimator have nearly correct size in a wide range of cases.
DepartmentMassachusetts Institute of Technology. Department of Economics
Econometrica : journal of the Econometric Society
Newey, Whitney K., and Frank Windmeijer. “Generalized Method of Moments With Many Weak Moment Conditions.” Econometrica 77.3 (2009): 687-719.
Author's final manuscript
variance adjustment, many moments, continuous updating, GMM