The DSGE model with endogenous and time-varying sticky information in Dräger (2010) is extended by allowing agents’ recursive choice between forecasts under rational or sticky information to affect the model solution. Dynamic equilibrium paths generate highly persistent series for output, inflation and the nominal interest rate. Agents choose predictors in a near-rational manner and we find that the share of agents with rational expectations reacts to the overall variability of aggregate variables. The model can generate hump-shaped responses of inflation and output to a monetary policy shock if the degree of inattentiveness is sufficiently high. Finally, feedback from agents’ degree of inattentiveness to the model solution affects the determinacy region of the model. The Taylor principle is then only a necessary condition for determinacy, and monetary policy should target the output gap as well in order to ensure a unique and stable solution.Endogenous sticky information, heterogeneous expectations, DSGE models, persistence.