TY - JOUR
AU - Altonji, Joseph G
AU - Segal, Lewis M
TI - Small Sample Bias in GMM Estimation of Covariance Structures
JF - National Bureau of Economic Research Technical Working Paper Series
VL - No. 156
PY - 1994
Y2 - June 1994
DO - 10.3386/t0156
UR - http://www.nber.org/papers/t0156
L1 - http://www.nber.org/papers/t0156.pdf
N1 - Author contact info:
Joseph G. Altonji
Department of Economics
Yale University
Box 208264
New Haven, CT 06520-8264
Tel: 203/432-6285
Fax: 203/432-5591
E-Mail: joseph.altonji@yale.edu
AB - 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.
ER -