Small Sample Bias in GMM Estimation of Covariance Structures

51 Pages Posted: 24 Jul 2000 Last revised: 7 Jun 2023

See all articles by Joseph G. Altonji

Joseph G. Altonji

Yale University - Economic Growth Center; National Bureau of Economic Research (NBER); Yale University - Cowles Foundation

Lewis M. Segal

Federal Reserve Bank of Chicago

Date Written: June 1994

Abstract

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.

Suggested Citation

Altonji, Joseph G. and Segal, Lewis M., Small Sample Bias in GMM Estimation of Covariance Structures (June 1994). NBER Working Paper No. t0156, Available at SSRN: https://ssrn.com/abstract=225115

Joseph G. Altonji (Contact Author)

Yale University - Economic Growth Center ( email )

Box 208269
New Haven, CT 06520-8269
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Lewis M. Segal

Federal Reserve Bank of Chicago

230 South LaSalle Street
Economic Research 11th Floor
Chicago, IL 60604
United States

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