Asymptotic efficiency of the ordinary least-squares estimator for sur models with integrated regressors

For seemingly unrelated regression (SUR) models with integrated regressors, two sufficient conditions are identified, under which the ordinary least-squares estimator (OLSE) is asymptotically efficient. The first condition is that every pair of regressor processes are cointegrated in a specific way that one regressor is a linear combination of the other regressor up to a zero-mean stationary error and the second condition is that, for every pair of regressor processes, the pair of error processes deriving the regressor processes have zero long-run covariance.