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. Nonstationary 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 existing tests, robust to such volatility processes. The panel test is based on Simes’ (Biometrika 73:751–754, 1986) classical multiple test, which combines evidence from time series unit root tests of the series in the panel. As time series tests, we employ the recent proposals of Cavaliere and Taylor (J Time Ser Anal 29:300–330, 2008b). The panel test is robust to general patterns of cross-sectional dependence and yet is straightforward to implement, only requiring valid p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document} values of time series tests, and no resampling. Simulations show other panel unit root tests to suffer from sometimes severe size distortions under nonstationary volatility and that this can be remedied using the test proposed here. We use the methods 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.