Bounds for the Covariance Matrices of Zellner's Estimator in the SUR Model and the 2SAE in a Heteroscedastic Model

Abstract

This article gives a bound for the covariance matrix of Zellner's estimator with the unrestricted sample covariance matrix in the two equations seemingly unrelated regression (SUR) model, and a bound for the covariance matrix of the two-stage Aitken estimator (2SAE) in a heteroscedastic model with two distinct variances. Some efficiencies of these estimators relative to the ordinary least squares estimator (OLSE) are also considered.

Key Words:

• Seemingly unrelated regression
• Zellner estimator
• Two-stage Aitken estimator
• Heteroscedastic model
• Covariance matrix