Cholesky Decomposition of Variance-Covariance Matrix Effect on the Estimators of Seemingly Unrelated Regression Model

Abstract

Seemingly Unrelated Regression (SUR) model which takes cognizance of correlations and strength of
association between the error variables to yield more efficient estimates is a common tool in multi-equation
regression analysis. The use of Cholesky method to partition the variance-covariance matrix ? into lower and
upper triangular matrices to establish contemporaneous relationship among equations through their errors was
investigated in this paper. Literature on the efficiency of SUR and Ordinary Least Squares (OLS) estimators
assumed inconsequential the use of either upper or lower triangular matrices from a decomposed variancecovariance
matrix. This study investigated the sensitivity of the two triangular matrices on SUR and OLS
estimators. A Monte Carlo experiment was performed on a four-equation model with sample sizes n = 10, 30,
50, 100, 500 and 1000 and each replicated 10000 times. The Average Mean Square Error (AMSE) was used to
assess the performance of the estimators. It was observed that the upper triangular matrix had higher AMSE
values than the lower triangular matrix for SUR and OLS estimators. Also, the AMSE of SUR estimator was
lower than that of OLS estimator, irrespective of the triangular matrix used.