When the central bank has information that can help the private sector predict the future better, should it communicate such information to the public? In a simple New Keynesian model, such Delphic forward guidance unambiguously reduces ex ante welfare by increasing the variability of inflation and the output gap. In other words, it cannot persuade private agents to change their actions in favor of the central bank. In more elaborate DSGE models, the welfare effect may be either positive or negative, depending on the type of shock as well as distortions and frictions. These results suggest that improving welfare by Delphic forward guidance may be particularly difficult under model uncertainty.