We investigate hysteresis and persistence behaviour in the course of unemployment in EU countries and US states by means of first and second generation panel unit root tests. While the former tests assume independent cross sections, the latter control for dependencies. The first generation tests indicate, that unemployment is persistent, but nevertheless stationary. Second generation tests reveal mixed results, but the evidence for stationarity is much stronger for the US. Hysteresis in EU unemployment is attributed to the idiosyncratic, but not to the common component. In contrast, idiosyncratic components are stationary in the US. If hysteresis behaviour is also relevant here, it is more likely to arise in the common component. These findings might reflect a lower degree of migration of the unemployed in the EU from starving into prosperous regions, possibly because of language barriers or national labour market regulations.