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.