A powerful wild bootstrap diagnosis of panel unit roots under linear trends and time-varying volatility

Abstract

Noting that standard panel unit root tests (PURTs) are not reliable in the presence of time varying volatility, recent papers have suggested a few heteroskedasticity–robust PURTs. These tests do not remain pivotal, however, if they are applied on detrended data. Building on recent asymptotic results for bootstrap approximations (Smeekes and Urbain in A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing, 2014), we provide simulation evidence that recursive detrending followed by a wild bootstrap correction leads to very good size precision for a variety of PURTs designed for testing against panel stationarity formalized with a cross sectionally homogenous autoregressive parameter. With respect to power, the bootstrap variant of the original nonrobust test of Levin et al. (J Econom 108(1):1–24, 2002) turns out to be the most effective among alternative tests. At the implementation side, performing the wild bootstrap correction using the so-called Rademacher distribution is found to be the most effective for both size and power properties of panel unit root inference by means of wild bootstrap based critical values. The empirical illustration shows that GDP per capita is best characterized as a unit root process.