This paper evaluates the empirical performance of a medium-scale DSGE model with agents forming expectations using small forecasting models updated by the Kalman filter. The adaptive learning model fits the data better than the rational expectations (RE) model.
Beliefs about the inflation persistence explain the observed decline in the mean and the volatility of inflation as well as Phillips curve flattening. Learning about inflation results in lower estimates for the persistence of the exogenous shocks that drive price and wage dynamics in the RE version of the model.
Expectations based on small forecasting models are closely related to the survey evidence on inflation expectations.