On the Power of GLS‐Type Unit Root Tests
指出ERS提出的GLS单位根检验比DF检验功效更高，并非因为GLS对非随机成分的估计更准确，而是因为其零分布相对于备择分布有更大的正向偏移。
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 better finite sample power than the DF test. Following the usual efficiency motive for GLS estimation, the higher finite sample power of the ERS test has often been attributed to the greater accuracy of the estimate of the series’ non‐stochastic component under stationary alternatives close to the null. This paper shows that the GLS estimates of the non‐stochastic component are not, in general, more accurate. The power gain arises from the fact that the GLS statistic's null distribution has a greater positive shift relative to the DF test, than its distribution under relevant alternatives, and this persists even when the GLS estimates of the non stochastics have higher variance than the OLS estimates.