The problematic asymptotic distribution of SOLS arises due to the presence of long-run correlation between the cointegrating equation errors and regressor innovations and
, and cross-correlation between the cointegrating equation errors and the regressors
. In the special case where the
are strictly exogenous regressors so that
and
, the bias, asymmetry, and dependence on non-scalar nuisance parameters vanish, and the SOLS estimator has a fully efficient asymptotic Gaussian mixture distribution which permits standard Wald testing using conventional limiting
-distributions.