Central banks behave purposefully when they set monetary policy, basing their decisions upon the data that is available and upon their understanding of the economy. At the same time, policy decisions affect economic outcomes, and the likelihood of observing a given state of the world. This paper uses a DSGE model of the business cycle with nominal rigidities and habit formation to investigate how policy choices affect the policymakers' ability to learn the true structure of the economy. Central to our analysis is the fact that a central bank that wants to implement an optimal policy will need to learn about the structural equations that constrain its decisions, rather than simply about the system's reduced-form equilibrium relationships. Using the DSGE model we examine the probability with which an optimizing central bank will detect that it is using a mis-specified model. We derive conditions under which the true model can be learnt, and investigate how the random innovations and the choice of policy affect the speed at which learning is achieved. We show that it is possible for a non-optimizing policymaker - for example, a policymaker that sets policy using a forward-looking Taylor-type rule - to be able to learn about the economy more quickly than a central bank that attempts to stabilize the economy using an optimal policy. The very act of behaving optimally may in fact reduce the likelihood that equilibrium outcomes are observed that reveal the model mis-specification to the policymaker
