Nonstationary-Volatility Robust Panel Unit Root Tests and the Great Moderation

This paper argues that typical applications of panel unit root tests should take possible nonstationarity in the volatility process of the innovations of the panel time series into account. Nonstationarity volatility arises for instance when there are structural breaks in the innovation variances. A prominent example is the reduction in GDP growth variances enjoyed by many industrialized countries, known as the `Great Moderation.' It also proposes a new testing approach for panel unit roots that is, unlike many previously suggested tests, robust to such volatility processes. The panel test is based on Simes' [Biometrika 1986, "An Improved Bonferroni Procedure for Multiple Tests of Signi cance"] classical multiple test, which combines evidence from time series unit root tests of the series in the panel. As time series unit root tests, we employ recently proposed tests of Cavaliere and Taylor [Journal of Time Series Analysis 2008b, "Time-Transformed Unit Root Tests for Models with Non-Stationary Volatility"]. The panel test is robust to general patterns of cross-sectional dependence and yet is straightforward to implement, only requiring valid p-values of time series unit root tests, and no resampling. Monte Carlo experiments show that other panel unit root tests suffer from sometimes severe size distortions in the presence of nonstationary volatility, and that this defect can be remedied using the test proposed here. We use the methods developed here to test for unit roots in OECD panels of gross domestic products and inflation rates, yielding inference robust to the `Great Moderation.' We find little evidence of trend stationarity, and mixed evidence regarding inflation stationarity.