This paper proposes the use of covariate unit root tests and the exploitation of the information on the cross-sectional dependence when the panel data null hypothesis of a unit root is rejected or when N is relatively small in order to help the interpretation of the test results.
In particular, it investigates the optimal point optimal covariate unit root test by Juhl and Xiao (2003), which is based on the theory by Hansen (1995) and Elliott and Jansson (2003). We first compare the asymptotic power function of the covariate test with those of panel unit root tests and show that the covariate unit root test can be potentially more powerful than panel unit root tests when the cross-sectional dimension is not so large. We also suggest several methods to choose appropriate covariates. The Monte Carlo simulations show that some of our methods work fairly well compared with the simple method of using only one covariate. Using our methods, we investigate the Prebish-Singer hypothesis for nine commodity prices and find that this hypothesis holds except for the price of petroleum. We also examine the PPP hypothesis employing eight real exchange rates of developed economies relative to the US dollar.