Central bank announcements simultaneously convey information about monetary policy and the central bank's assessment of the economic outlook. This paper disentangles these two components and studies their effect on the economy using a structural vector autoregression estimated on both US and euro area data. It relies on the information inherent in high-frequency comovement of interest rates and stock prices around policy announcements: a surprise policy tightening raises interest rates and reduces stock prices, while the complementary positive central bank information shock raises both. These two shocks have intuitive and very different effects on the economy. Ignoring the central bank information shocks biases the inference on monetary policy non-neutrality. We make this point formally and offer an interpretation of the central bank information shock using a New Keynesian macroeconomic model with financial frictions.