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We study the implications of increased price flexibility on aggregate output volatility in a dynamic stochastic general equilibrium (DSGE) model. First, using a simplified version of the model, we show analytically that the results depend on the shocks driving the economy and the systematic response of monetary policy to inflation: More flexible prices amplify the effect of demand shocks on output if interest rates do not respond strongly to inflation, while higher flexibility amplifies the effect of supply shocks on output if interest rates are very responsive to inflation. Next, we estimate a medium-scale DSGE model using post-WWII U.S. data and Bayesian methods and, conditional on the estimates of structural parameters and shocks, ask: Would the U.S. economy have been more or less stable had prices been more flexible than historically? Our main finding is that increased price flexibility would have been destabilizing for output and employment.