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This paper studies the impact of the volatility of monetary policy using a structural vector auroregression (SVAR) model enriched along two dimensions. First, it allows for time‐varying variance of monetary policy shocks via a stochastic volatility specification. Second, it allows a dynamic interaction between the level of the endogenous variables in the VAR and the time‐varying volatility. The analysis establishes that the nominal interest rate, output growth, and inflation fall in reaction to an increase in the volatility of monetary policy. The analysis also develops a dynamic stochastic general equilibrium model enriched with stochastic volatility to monetary policy that generates similar responses and provides a theoretical underpinning of these findings.