Heteroskedasticity Robust Panel Unit Root Testing Under Variance Breaks in Pooled Regressions

Abstract

Noting that many economic variables display occasional shifts in their second order moments, we investigate the performance of homogenous panel unit root tests in the presence of permanent volatility shifts. It is shown that in this case the test statistic proposed by Herwartz and Siedenburg (2008) is asymptotically standard Gaussian. By means of a simulation study we illustrate the performance of first and second generation panel unit root tests and undertake a more detailed comparison of the test in Herwartz and Siedenburg (2008) and its heteroskedasticity consistent Cauchy counterpart introduced in Demetrescu and Hanck (2012a). As an empirical illustration, we reassess evidence on the Fisher hypothesis with data from nine countries over the period 1961Q2-2011Q2. Empirical evidence supports panel stationarity of the real interest rate for the entire subperiod. With regard to the most recent two decades the test results cast doubts on market integration, since the real interest rate is diagnosed nonstationary. pt

Heteroskedasticity-Robust Unit Root Testing for Trending Panels

“…These studies find that the (augmented) Dickey-Fuller (Dickey and Fuller, 1979) tests have seriously distorted empirical sizesand, hence, provide deceptive inference-if volatility varies over time. The same problem carries over to panel unit root tests (PURTs), as shown in Demetrescu and Hanck (2012a,b) and Herwartz et al (2016). In particular, widely applied PURTs such as those suggested in Levin et al (2002) and Breitung and Das (2005) are no longer pivotal if the homoskedasticity assumption is violated (Herwartz et al, 2016).…”

“…Recently, Herwartz et al (2016) show that time-varying volatility does not affect the pivotalness of t HS .…”

“…To formalize cross-sectional dependence and heteroskedasticity, we adopt the following assumptions about the vector of error terms e t as in Herwartz et al (2016) with strengthened moment conditions:…”

“…Namely, available detrending schemes introduce nuisance parameters that affect the limiting distribution of the tests under variance breaks (Herwartz et al, 2016;Westerlund, 2014). This problem significantly limits the applicability of the tests as many macroeconomic time series exhibit trending behavior.…”

“…As the sign function of Cauchy instrumenting reduces the lagged level series to -1 and 1-irrespective of the underlying time varying volatility-these tests are argued to be robust to heteroskedasticity. Herwartz et al (2016) show that the non-Cauchy version of the test in Demetrescu and Hanck (2012a), which was initially proposed in Herwartz and Siedenburg (2008), is robust to volatility shifts. Another heteroskedasticity-robust PURT has been suggested by Westerlund (2014).…”