We analyse a simplified New-Keynesian model with an unobserved aggregate costpush shock in which firms and the central bank have different information about the shock. We consider a linear policy rule where a pure inflation targeting central bank decides how much to react to the shock given its information. In this framework we show that monetary policy performs both an allocational and an informational role, the latter due to firms extracting information on the aggregate shock from the monetary policy tool. When the informational role is present, optimal monetary policy is more cautious, that is, it responds less to the shock than the perfect information benchmark. A more cautious reaction to the shock implies that firms make more effective use of their private information and the endogenous information coming from the aggregate price in order to make inferences about the shock.