A simple modification to improve the finite sample properties of Ng and Perron's unit root tests

The tests introduced by Ng and Perron [Ng, S., Perron, P., 20011. “Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power,” Econometrica 69, 1519-1554] have the drawback that for non-local alternatives the power can be very small. The aim of this note is to point out an easy solution to this power reversal problem, which in addition leads to tests having an exact size even closer, in most cases, to nominal size. It involves using OLS instead of GLS detrended data when constructing the modified information criterion.