Dynamic Rational Inattention and the Phillips Curve

We develop a tractable and portable method for characterizing the solution to dynamic multivariate rational inattention models in linear quadratic Gaussian settings. We apply our framework to propose an attention driven theory of the Phillips curve, the slope of which is endogenous to how monetary policy is conducted. We show that the Phillips curve is flatter when the monetary policy is more hawkish: rationally inattentive firms find it optimal to ignore monetary policy shocks when the monetary authority commits to stabilize nominal variables. Moreover, we show that an unexpectedly more dovish monetary policy leads to a completely flat Phillips curve in the short-run and a steeper Phillips curve in the long-run.