Heteroskedasticity-Robust Unit Root Testing for Trending Panels

Abstract

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Panel Unit-root Tests for Heteroskedastic Panels

“…1. Note that the assumption of finite eighth-order moments is required only for the test in Herwartz, Maxand, and Walle (2017). This assumption enables us to derive asymptotic properties of the test statistic from the theory of near-epoch dependent sequences.…”

“…Noting that existing heteroskedasticity-robust tests do not remain pivotal in cases where the data feature panel-specific linear trends, that is, when μ = 0 under H 0 and when δ = 0 under H 1 in (2), Herwartz, Maxand, and Walle (2017) propose a new test that allows trending panels to be heteroskedastic. Their test is a modified version of t HS that is adjusted for biases arising from heteroskedastic detrended data.…”

“…Their test is a modified version of t HS that is adjusted for biases arising from heteroskedastic detrended data. More precisely, the test statistic in Herwartz, Maxand, and Walle (2017) involves detrending the lagged level as in Chang (2002),…”

“…While these tests are heteroskedasticity robust in cases where the data feature an intercept term, they are not robust to volatility shifts if the series contain a linear trend. To our knowledge, the test in Herwartz, Maxand, and Walle (2017) is unique in avoiding complicated resampling techniques used to define PURTs in trending heteroskedastic panels. This is an important property because several macroeconomic time series, including gross domestic product, money supply, and commodity prices, contain a linear trend (Westerlund 2015).…”

“…Here we present the new command xtpurt, which implements the heteroskedasticityrobust PURTs suggested in Herwartz and Siedenburg (2008), Demetrescu and Hanck (2012a), and Herwartz, Maxand, and Walle (2017).…”