Forward detrending for heteroskedasticity-robust panel unit root testing

The variances of most economic time series display marked fluctuations over time. Panel unit root tests of the so-called first and second generation are not robust in such cases. In response to this problem, a few heteroskedasticity-robust panel unit root tests have been proposed. An important limitation of these tests is, however, that they become invalid if the data are trending. As a prominent means of drift adjustment under the panel unit root hypothesis, the (unweighted) forward detrending scheme of Breitung suffers from nuisance parameters if the data feature time-varying variances. In this article, we propose a weighted forward-detrending scheme. Unlike its unweighted counterpart, the new detrending scheme restores the pivotalness of the heteroskedasticity-robust panel unit root tests suggested by Demetrescu and Hanck and Herwartz et al. when applied to trending panels with heteroskedastic variances. As an empirical illustration, we provide evidence in favor of non-stationarity of health care expenditures as shares of GDP in a panel of OECD economies.