We use Bayesian techniques to estimate bivariate VAR models for Swedish unem-ployment rate and inflation. Employing quarterly data from 1995Q1 to 2018Q3 and new tools for model selection, we compare models with time-varying parameters and/or stochastic volatility to specifications with constant parameters and/or covariance matrix. The evidence in favour of a stable dynamic relationship between the unemployment rate and inflation is mixed. Model selection based on marginal like-lihood calculations indicates that the relation is time varying, whereas the use of the deviance information criterion suggests that it is constant over time; we do, however, note consistent evidence in favour of stochastic volatility. An out-of-sample forecast exercise is also conducted, but similarly provides mixed evidence regarding which model to favour. Importantly though, even if time-varying parameters are allowed for, our results do not suggest that the Phillips curve has been flatter in more recent years. This finding thereby questions the explanation that a flatter Phillips curve is the cause of the low inflation that Sweden has experienced in recent year.