Nonstationary-volatility robust panel unit root tests and the great moderation

Abstract

This paper proposes a new testing approach for panel unit roots that is, unlike previously suggested tests, robust to nonstationarity in the volatility process of the innovations of the time series in the panel. 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.’ The panel test is based on Simes’ [Biometrika 1986, \An Improved Bonferroni Procedure for Multiple Tests of Signicance] 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, \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 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 suer from sometimes severe size distortions in the presence of nonstationary volatility, and that this defect can be remedied using the test proposed here. The new test is applied to test for a unit root in an OECD panel of gross domestic products, yielding inference robust to the ‘Great Moderation.’ We nd little evidence of trend stationarity.