02286cam a22002417 4500001000600000003000500006005001700011008004100028100002300069245012600092260006600218490005100284500001500335520130400350530006101654538007201715538003601787700002001823710004201843830008601885856003701971856003602008t0156NBER20191018170305.0191018s1994 mau||||fs|||| 000 0 eng d1 aAltonji, Joseph G.10aSmall Sample Bias in GMM Estimation of Covariance Structuresh[electronic resource] /cJoseph G. Altonji, Lewis M. Segal. aCambridge, Mass.bNational Bureau of Economic Researchc1994.1 aNBER technical working paper seriesvno. t0156 aJune 1994.3 aWe 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.1 aSegal, Lewis M.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0156.4 uhttp://www.nber.org/papers/t015641uhttp://dx.doi.org/10.3386/t0156