Bootstrap Methods for Covariance Structures

The optimal minimum distance (OMD) estimator for models of covariance structures is asymptotically efficient but has much worse finite-sample properties than does the equally-weighted minimum distance (EWMD) estimator. This paper shows how the bootstrap can be used to improve the finite-sample performance of the OMD estimator. The theory underlying the bootstrap's ability to reduce the bias of estimators and errors in the coverage probabilities of confidence intervals is summarized. The results of numerical experiments and an empirical example show that the bootstrap often essentially eliminates the bias of the OMD estimator. The finite-sample estimation efficiency of the bias-corrected OMD estimator often exceeds that of the EWMD estimator. Moreover, the true coverage probabilities of confidence intervals based on the OMD estimator with bootstrap critical values are very close to the nominal coverage probabilities. I thank Joseph Altonji for attracting my attention to the problem addressed in this paper and for making his data available. Gene Savin provided comments on an earlier draft. This research was supported in part by NSF grant SBR9307677.