On the power of GLS-type unit root tests

Elliott, Rothenberg and Stock (1996), (ERS), present a 'GLS' variant of the Dickey-Fuller (DF) unit root test. Their statistic is approximately point- optimal invariant at a chosen local alternative, and usually displays bette r finite sample power than the DF test. Following the usual efficiency moti ve for GLS estimation, the higher finite sample power of the ERS test has o ften been attributed to the greater accuracy of the estimate of the series' nonstochastic component under stationary alternatives close to the null. T his paper shows that the CLS estimates of the non-stochastic component are not, in general, more accurate. The power gain arises from the fact that th e GLS statistic's null distribution has a greater positive shift relative t o the DF test, than its distribution under relevant alternatives, and this persists even when the GLS estimates of the non-stochastics have higher var iance than the OLS estimates.