In this paper, we analyse whether two key macroeconomic relationships in Australia-Okun's law and the Phillips curve-have been stable over time. This is done by estimating hybrid time-varying parameter Bayesian VAR models using quarterly data from 1978 to 2024. Model comparison based on marginal likelihoods indicates that Okun's law has been stable, whereas the Phillips curve has not. Using the preferred specification of the BVAR for the unemployment rate and inflation, we also calculate trend values for both variables. The model's trend unemployment rate at the end of the sample is approximately 5%; estimated trend inflation at the same point in time is close to the Reserve Bank of Australia's inflation target.