Bayesian forecasting of U.S. recessions using new Keynesian models with heterogeneous expectations

ABSTRACT

In this paper, the Bayesian point forecasting performances of small-scale and medium-scale New Keynesian models, each augmented to include heterogeneous expectations via the Euler equation adaptive learning method, are compared to their homogeneous expectations counterparts during the three most recent U.S. recessions. Forecasting performance is assessed based on root mean squared error. Results show that, in general, the models with heterogeneous expectations forecast recessions better than their homogeneous expectations counterparts.

KEYWORDS:

• Heterogeneous expectations
• adaptive learning
• Bayesian econometrics
• new Keynesian model
• forecasting

JEL CLASSIFICATION:

• C11
• D83
• D84
• E12
• E17

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the author upon reasonable request.

Notes

¹ A notable exception is Elias (2021), who does some analysis of the forecasting performance of a medium-scale New Keynesian model. The work in the current paper, however, examines the predictive power of New Keynesian models specifically during recessions, and also examines a small-scale New Keynesian model, which has much different dynamics than the medium-scale model.

² The shock processes in the medium-scale model analysed in this paper are all AR(1) processes, which is a slight modification to the model in Smets and Wouters (2007).

³ The auxiliary variables are necessary to incorporate lagged endogenous variables into the state-space measurement equation.

⁴ Dating is determined by the National Bureau of Economic Research’s (NBER) Business Cycle Dating Committee. According to the NBER, the business cycle peaked in the first quarter of 2001, the fourth quarter of 2007, and the fourth quarter of 2019. This information is available at https://www.nber.org/research/data/us-business-cycle-expansions-and-contractions.

⁵ The values are the ‘relative’ root mean squared error (RMSE), which is the RMSE of the homogeneous expectations model (HO) divided by the RMSE of the heterogeneous expectations model (HE). Also shown are the median relative RMSEs for each forecasted variable, and the median relative RMSEs for all variables at each forecasted time horizon.

⁶ The values are the ‘relative’ root mean squared error (RMSE), which is the RMSE of the homogeneous expectations model (HO) divided by the RMSE of the heterogeneous expectations model (HE). Also shown are the median relative RMSEs for each forecasted variable, and the median relative RMSEs for all variables at each forecasted time horizon.