On the equivalence of pooled and mixed estimation

The mixed estimator which uses sample moments from a cross-section as a stochastic restriction in a time series equation is shown to be identical to the efficient pooled estimator. It is also shown that Theil's compatibility test statistic is identical to the Wald test for the validity of pooling. As usual I have had much good advice from Noxy Dastoor, some of which I have ignored.