The Bias of Bootstrapped Versus Conventional Standard Errors in the General Linear and SUR Models

Abstract

When estimating the seemingly unrelated regression (SUR) model in small samples, the bootstrap feasible generalized least-squares (FGLS) covariance estimator has been widely advocated as less biased than the conventional FGLS covariance estimator obtained by evaluating the asymptotic covariance matrix. Assuming multivariate normal errors and an unbiased estimator of the error covariance, Eaton proves that the conventional estimator is biased downward for a general SUR model. Ignoring terms O(T–2) for this model, we prove that the bootstrap estimator is also biased downward. However, from these results, the relative magnitude of these two biases is indeterminant in general. By ignoring terms O(T–2) for Zellner's two-equation, orthogonal regressor model with bivariate normal errors, we show that the bias of both estimators is downward and that the bootstrap estimator exhibits a smaller bias than the conventional estimator. Monte Carlo simulation results indicate that, in general, neither estimator uniformly dominates the other.