GMM with many weak moment conditions

By Whitney K. Newey, F. Windmeijer. 2005

73 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3394a5c16af43c8992a32829073e1a185cb198ca

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Statistics and Probability

Citations in the corpus

Estimation With Many Instrumental Variables (2006, background): “It is well known that this will hold with additional tail conditions on the remainder in the stochastic expansions of Theorem 3; see Rothenberg (1984). To do this is beyond the scope of this article.”
GMM for Panel Count Data Models (2006, methodology): “ Newey and Windmeijer (2005) derive the asymptotic distribution of the CUE under”
On the Failure of the Bootstrap for Matching Estimators (2006, result): “Finally, our results cast doubts on the validity of the standard bootstrap for other estimators that are asymptotically normal but not asymptotically linear (see, e.g., Newey and Windmeijer, 2005).”
Empirical Likelihood Methods in Econometrics: Theory and Practice (2006, methodology): “(iv) and the minimax estimator by Kitamura and Otsu (2005) (ˆ ld) with c = 0.1 and 0.2.”
The validity of instruments revisited (2012, methodology): “A similar argument is used (when only the degrees of freedom converge to infinity and concentration parameter is constant) in proof of Theorem 4 in Newey and Windmeijer (2007).”