The Effect of Variable Correlation on the Efficiency of Seemingly Unrelated Regression in a Two-Equation Model

Abstract

The efficiency gain of seemingly unrelated regression (SUR) relative to OLS is a decreasing function of correlation of variables across equations. This article examines the efficiency gain for an individual coefficient in a two-equation model. It is seen that the effect of correlation among variables across the equations greatly depends on the multicollinearity already existing within an equation. In particular, the major factor determining the efficiency gain of SUR for the coefficient on an individual variable is not the correlation between that variable and those in the other equation. Rather, it is the correlation between the latter and the residuals obtained by regressing the variable in question on the remaining variables in its own equation.

Key Words:

• Seemingly unrelated regression: Efficiency
• Variable correlation
• Multicollinearity