Estimating a medium–scale DSGE model with expectations based on small forecasting models

In this paper we evaluate the empirical performance of a medium–scale DSGE model (Smets andWouters 2007) when agents form expectations about forward variables by using small forecasting models. Agents learn about these simple AR and VAR forecasting models through Kalman filter estimation and they combine them either using a prediction basedweighting scheme or fixed weights. The results indicate that a model, in which agents use a mixture of simple forecasting models to form expectations, does fit the data better than the full rational expectations model. Adaptive learning leads to substantial time variation in the coefficients of the forecasting models. Especially the beliefs about the dynamics of the inflation process turn out to be very important for the overall performance of the model. Agents’ beliefs about the persistence of inflation display a peak the late seventies, and follow a clear downward trend starting during the Volcker disinflation period. This pattern in beliefs, which is in line with other recent evidence in the literature on inflation persistence, implies that the response of inflation to the various shocks declined significantly over the last 25 years. In this way, adaptive learning about inflation persistence also explains the observed decline in both the mean and the volatility of inflation as well as the flattening of the Phillips curve. Allowing for learning about inflation dynamics also results in lower estimates for the persistence of the exogenous processes that drive price and wage dynamics in the Rational Expectation version. We also find that the implicit beliefs of agents based on small forecasting models are more closely related to the survey evidence on inflation expectations than the beliefs under rational expectations. JEL codes: C11, D84, E30, E52