This paper proposes a novel way of formulating priors for estimating economic models. System priors are priors about the model's features and behavior as a system, such as the sacrifice ratio or the maximum duration of response of inflation to a particular shock, for instance. System priors represent a very transparent and economically meaningful way of formulating priors about parameters, without the unintended consequences of independent priors about individual parameters. System priors may complement or also substitute for independent marginal priors. The new philosophy of formulating priors is motivated, explained and illustrated using a structural model for monetary policy.