Optimal Panel Unit Root Testing with Covariates
Joakim Westerlund (Lund University)
This paper provides asymptotic optimality results for panel unit root tests with covariates by deriving the Gaussian power envelope. The results extend those of Moon et al. (2007), who consider the special case when no information on covariates is available. The main conclusion is that the use of covariates holds considerable promise in the panel data context, much more so than in the time series context. The biggest difference occurs in the empirically relevant case with incidental trends. Speci cally, while the power envelope without covariates is defined within N^{-1/4}T^{-1}-neighborhoods of unity, the envelope with covariates is in general defined within N^{-1/2}T^{-1}-neighborhoods. Therefore, the use of the covariates not only leads to increased power, but it can actually have an order effect on the shrinking neighborhoods around unity for which power is non-negligible. As a way to explore this increase in power in practice, a feasible point optimal unit root test is proposed, whose small-sample properties are investigated by means of Monte Carlo simulation.