Small Sample Bias in GMM Estimation of Covariance Structures

Joseph G. Altonji, Lewis M. Segal

NBER Technical Working Paper No. 156
Issued in June 1994
NBER Program(s):   LS

We examine the small sample properties of the GMM estimator for models of covariance structures, where the technique is often referred to as the optimal minimum distance (OMD) estimator. We present a variety of Monte Carlo experiments based on simulated data and on the data used by Abowd and Card (1987, 1990) in an examination of the covariance structure of hours and earnings changes. Our main finding is that OMD is seriously biased in small samples for many distributions and in relatively large samples for poorly behaved distributions. The bias is almost always downward in absolute value. It arises because sampling errors in the second moments are correlated with sampling errors in the weighting matrix used by OMD. Furthermore, OMD usually has a larger root mean square error and median absolute error than equally weighted minimum distance (EWMD). We also propose and investigate an alternative estimator, which we call independently weighted optimal minimum distance (IWOMD). IWOMD is a split sample estimator using separate groups of observations to estimate the moments and the weights. IWOMD has identical large sample properties to the OMD estimator but is unbiased regardless of sample size. However, the Monte Carlo evidence indicates that IWOMD is usually dominated by EWMD.

download in pdf format
   (1407 K)

email paper

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/t0156

Published: Altonji, Joseph G. and Lewis M. Segal. "Small-Sample Bias In GMM Estimation Of Covariance Structures," Journal of Business and Economic Statistics, 1996, v14(3,Jul), 353-366.

Users who downloaded this paper also downloaded these:
Burnside and Eichenbaum t0155 Small Sample Properties of Generalized Method of Moments Based Wald Tests
Angrist and Krueger t0150 Split Sample Instrumental Variables
Hulten and Isaksson w13469 Why Development Levels Differ: The Sources of Differential Economic Growth in a Panel of High and Low Income Countries
Tornell w6084 Rational Atrophy: The US Steel Industry
Christiano and Haan t0177 Small Sample Properties of GMM for Business Cycle Analysis
NBER Videos

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us