Small-Sample Bias in GMM Estimation of Covariance Structures

A Comparative Analysis of Different IV and GMM Estimators of Dynamic Panel Data Models

“…This is an important finding, as both of these are frequently used in practice. The bias was presumably a function of the excessive number of instruments (see, for example, Arellano & Bover, 1995;Altonji & Segal, 1996). Note, that although the results from the AM estimator are reported, this could easily be placed in the same bracket (heavy small sample bias and an excess of instruments).…”

Trends in the Transitory Variance of Male Earnings

“…Then the set of M equations in 2-23 constitutes an SUR system whose efficient estimation requires an initial consistent estimate of the covariance matrix of the ε im . However, following the findings and recommendations of Altonji and Segal (1996) on bias in estimating covariance structures of this type, we employ the identity matrix for the estimation. Hence we choose θ to minimize the sum of squared residuals: $$\underset{\mathrm{\theta }}{min}\sum _{i=1}^N\sum _{m=1}^M{[s_{im}-f(\mathrm{\theta },j,k)]}^2$$ or, equivalently, since f is not a function of i ,…”

Trends in the covariance structure of earnings in the U.S.: 1969–1987

“…Then the set of M equations in (B1) constitutes an SUR system whose efficient estimation requires an initial consistent estimate of the covariance matrix of the ε im . However, following the findings and recommendations of Altonji and Segal (1991) on bias in estimating covariance structures of this type, we employ the identity matrix for the estimation. 28 Hence we choose θ to minimize the sum of squared residuals: $$\underset{\mathrm{\theta }}{\text{Min}}\sum _{\mathrm{normali}=1}^{\mathrm{N}}\sum _{\mathrm{m}=1}^{\mathrm{normalM}}{[{\mathrm{normals}}_{\text{im}}-\mathrm{f}(\mathrm{\theta },\mathrm{j},\mathrm{k})]}^2$$ or, equivalently, since f is not a function of i,…”