This paper studies the implications for monetary policy of heterogeneous expectations in a New Keynesian model. The assumption of rational expec?tations is replaced with parsimonious forecasting models where agents select between predictors that are underparameterized. In a Misspecification Equilib?rium agents only select the best-performing statistical models. We demonstrate that, even when monetary policy rules satisfy the Taylor principle by adjusting nominal interest rates more than one for one with inflation, there may exist equilibria with Intrinsic Heterogeneity. Under certain conditions, there may exist multiple misspecification equilibria. We show that these findings have im?portant implications for business cycle dynamics and for the design of monetary policy.