his paper investigates the empirical relevance of both the hysteresis and the natural rate hypothesis on unemployment in three major economies, namely the UK, the US and Japan, by estimating the degree of dependence in the unemployment series. Both univariate and multivariate long memory methods are used. The results vary depending on whether the former or the latter approach is followed. Specifically, when taking a univariate approach, the unit root null cannot be rejected in case of the UK and Japanese unemployment series, and some degree of mean reversion (d < 1) is found in the case of the US unemployment rate. When applying multivariate methods instead, higher orders of integration are still found for the UK and Japanese series, but the natural rate hypothesis cannot be rejected in the case of the US.