In this paper we study 2-state Markov switching VAR models of monthly unemployment and inflation for three countries: Sweden, United Kingdom, and the United States. The primary purpose is to examine if periods of low inflation are associated with high or low unemployment volatility. We find that MS-VAR models seem to provide a better description of the data than single regime VARs and need fewer lags to account for serial correlation. To interpret the regimes the empirical results are compared with the predictions from a version of Rogoff's (1985) model of monetary policy. We find that both the theoretical and empirical results suggest that an increase in central bank conservativeness can be associated with either a higher or a lower variance in unemployment. In the U.S. case we find that the variance of unemployment is lower in the low inflation regime than in hte high inflation regime, while the Swedish and the U.K. cases suggest that unemployment variability is higher in the low inflation regime.