We use a Bayesian time-varying parameter structural VAR with stochastic volatility to investigate changes in both the reduced-form relationship between vacancies and the unemployment rate, and in their relationship conditional on permanent and transitory output shocks, in the post-WWII United States. Evidence points towards similarities and differences between the Great Recession and the Volcker disinflation, and wide-spread time variation along two key dimensions. First, the slope of the Beveridge curve exhibits a large extent of variation from the mid-1960s on. It is also notably pro-cyclical, whereby the gain is positively correlated with the transitory component of output. The evolution of the slope of the Beveridge curve during the Great Recession is very similar to its evolution during the Volcker recession in terms of both its magnitude and its time profile. Second, both the Great Inflation episode and the subsequent Volcker disinflation are characterized by a significantly larger negative correlation between the reduced-form innovations to vacancies and the unemployment rate than the rest of the sample period. Those years also exhibit a greater cross-spectral coherence between the two series at business-cycle frequencies. This suggests that they are driven by common shocks.