We construct a quantitative equilibrium model with firms setting prices in a staggered fashion and use it to ask whether monetary shocks can generate business cycle fluctuations. These fluctuations include persistent movements in output along with the other defining features of business cycles, like volatile investment and smooth consumption. We assume that prices are exogenously sticky for a short time. Persistent output fluctuations require endogenous price stickiness in the sense that firms choose not to change prices much when they can do so. We find that for a wide range of parameter values, the amount of endogenous stickiness is small. Thus, we find that in a standard quantitative model, staggered price‐setting, alone, does not generate business cycle fluctuations.