We propose a new Bayesian heteroskedastic Markov-switching structural vector autoregression with data-driven time-varying identification. The model selects alternative exclusion restrictions over time and, as a condition for the search, allows to verify identification through heteroskedasticity within each regime. Based on four alternative monetary policy rules, we show that a monthly six-variable system supports time variation in US monetary policy shock identification. In the sample-dominating first regime, systematic monetary policy follows a Taylor rule extended by the term spread and is effective in curbing inflation. In the second regime, occurring after 2000 and gaining more persistence after the global financial and COVID crises, the Fed acts according to a money-augmented Taylor rule. This regime's unconventional monetary policy provides economic stimulus, features the liquidity effect, and is complemented by a pure term spread shock. Absent the specific monetary policy of the second regime, inflation would be over one percentage point higher on average after 2008.
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