Do heterogenous beliefs drive the US business cycles?

This paper estimates a Behavioural New Keynesian (BNK) model incorporating belief heterogeneity through a switching mechanism. Agents form expectations using either a forward-looking (rational) or backward-looking (extrapolative) rule, and their weights evolve endogenously based on past forecast performance. To identify the latent structural shocks and the time-varying composition of beliefs over the business cycle, we apply a simulation-based nonlinear filtering and backward smoothing routine, which recovers full-sample paths of unobserved states consistent with both equilibrium restrictions and observed macroeconomic data. Our results show that belief heterogeneity has moderate quantitative effects during normal times but significantly amplifies macroeconomic dynamics during periods of large shocks, such as the COVID-19 crisis. This highlights some limitations of rational expectations models and points to the relevance of endogenous expectation formation for business cycle analysis.