When there are more moment conditions than observations, the usual GMM weighting matrix is singular. We show that using the generalized inverse is not a good idea. With continuous updating, the criterion function equals one for every parameter value.

The KPSS unit root test with lags is asymptotically valid and the fixed-b asymptotic distribution predicts its critical values well. A small positive number of lags improves the size of the test, without much loss in power.

This paper extends previous results on the equality of OLS and GLS. We give conditions under which GLS based on two different variance matrices gives the same estimate, and also conditions under which GLS equals a GMM estimator.