This article tests the main unemployment paradigms for the unemployment rates of the states of the United States and the European Union-15 countries over the past three decades. For that purpose, we employ a state-of-the-art panel stationarity test, which allows for an unknown number of endogenous structural breaks as well as for cross-sectional correlation. Overall, our analysis renders clear-cut evidence in favor of regime-wise stationarity in U.S. state unemployment, while hysteresis in European unemployment. Interestingly, the timing of the breaks broadly coincides with major macroeconomic shocks mainly associated with the oil crises of the 1970s and marked changes in interest rates in the 1980s and early 1990s. Based on our results, we draw some policy prescriptions that point to the need for greater flexibility in the European labor markets. (JEL C23, E24).