Slow learning challenges rational expectations models

A new Federal Reserve paper finds that learning in macroeconomic models converges to rational expectations equilibrium (REE) at an extraordinarily slow pace. This slow convergence can render analysis based on rational expectations misleading, especially in empirically plausible New-Keynesian models.

Self-fulfilling beliefs slow learning

The paper analytically characterizes the speed of convergence under learning to a rational expectations equilibrium (REE) for a large class of multivariate models.

A central finding is that learning is significantly slower when people's beliefs about model outcomes are more self-fulfilling.

This phenomenon, driven by a scalar statistic 'b' of the system, means that analysis based on rational expectations can be misleading if convergence is too slow.

For empirically plausible New-Keynesian (NK) models, convergence to the REE is measured in decades.

In the benchmark DSGE model by Christiano et al. (2005), meaningful convergence extends to centuries.

Even more dramatically, when the zero lower bound (ZLB) is binding in the simple NK model, progress is measured in millennia.

This extraordinary slowness challenges the practical utility of RE models.

Robustness across model specifications

The authors demonstrate the robustness of their conclusions across various model specifications.

This includes different nominal rigidities, such as Rotemberg and Calvo-style models, and whether the zero lower bound on nominal interest rates is binding.

The findings also hold for different learning approaches, comparing Kreps's anticipated utility with internally rational learning.

Monetary policy plays a crucial role: more aggressive responses to inflation by the monetary authority reduce the self-fulfilling nature of inflation expectations, thereby potentially speeding up convergence.

Conversely, less aggressive policy can exacerbate slow learning.

A fundamental challenge to modeling

This research poses a fundamental challenge to the widespread use of rational expectations in economic modeling.

Its findings suggest that many policy analyses based on REE might be fundamentally flawed due to the extraordinary slowness of learning in realistic scenarios.

Policymakers and researchers must reconsider the practical applicability of RE models, especially when beliefs are highly self-fulfilling and policy responses are less aggressive.