Seemingly Unrelated Regressions

Abstract Seemingly unrelated regression (SUR) is a widely used modeling approach introduced by Zellner for situations where several linear regression relationships are being investigated at the same time. Examples of the use of SUR in environmetrics include Boisvert et al., who considered separate equations for the effect of water contamination on both the purchase price and rental value of farmland, and Xu, who estimated separate equations for the impact of environmental legislation on the output of each of a number of industrial sectors. The key feature in these cases is that each of the linear equations, on its own, satisfies the classical conditions underpinning the linear regression model, and hence the ordinary least squares (OLS) estimator can be used to estimate each equation individually. However, if the error terms of the different equations are correlated across the equations, then joint estimation of the equations may be able to exploit this cross equation correlation to obtain more efficient estimates.