Stock market bubbles arise as a joint monetary and financial phenomenon. We assess the potential of monetary policy in mitigating the onset of bubbles by means of a Markov-switching Bayesian Vector Autoregression model estimated on US 1960–2019 data. Bubbles are detected and dated from the regime-specific interplay among asset prices, fundamental values, and monetary policy shocks. We rationalize the empirical evidence with an Overlapping Generations model, able to generate a bubbly scenario with shifts in monetary policy, and where agents form beliefs over transition dynamics. By matching the VAR impulse responses, we find that procyclicality and financial instability align with high equity premia and the presence of asset price bubbles. Monetary policy tightening, by increasing real rates, is ineffective in deflating bubble episodes.