Fit and Forecasting: Real-time Forecasting in the New Keynesian Model with Constant Gain Learning

This paper explores the empirical fit and real-time forecasting performance of the canonical three-equation New Keynesian model when expectations are formed  via adaptive learning with a constant gain.  Research has found that constant gain learning significantly improves the in-sample fit of the model when compared to the rational expectations case.  This paper investigates the origins of this improvement and uses real-time out-of-sample forecasting exercises to determine if in-sample improvements are meaningful.  We find that constant gain learning can provide large increases in-sample fit that are not in general matched by similar improvements in out-of-sample forecast performance.  This suggests that some proportion of the improvement is likely due to overfitting.  The model with constant gain learning though does show some fairly impressive out-of-sample forecasting power relative to univariate time-series models and parsimonious VARs.

We also identify a number of issues relating to estimating and forecasting with adaptive learning models heretofore undiscussed in the empirical literature.  In particular, we show that even a small relaxation of the rational expectations hypothesis results in significant improvements in fit and modest improvements in out-of-sample forecasting.  In addition, we document the crucial role initial beliefs play in generating better in sample fit and influencing the monetary policy parameter estimates.  We show that the monetary policy parameters obtained from estimation are a function of initial beliefs and move in predictable patterns based on the assumption of these beliefs.  Finally, we show that forecasts are extremely sensitive to the choice of initial beliefs making the use of a constant gain model risky. We therefore recommend using the forecasts as part of combined forecast with other models and different specification, which is shown to result in reliable increases in forecast accuracy.