We use Bayesian techniques to estimate bivariate VAR models for Swedish unemployment 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 likelihood 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.