This paper analyses the implications of heteroscedasticity for optimal macroeconomic policy and welfare. We find that changes in the variance structure driven by exogenous processes like generalized autoregressive conditional heteroscedasticity (GARCH) affect welfare but not the optimal feedback rule. However, changes in the variance structure driven by state-dependent processes affect both. We also derive certainty-equivalent transformations of state-dependent volatility models that allow standard quadratic dynamic programming algorithms to be employed to study optimal policy. These results are illustrated numerically using a reduced-form model of the US economy in which changes in volatility are driven by a GARCH process and the rate of inflation.