A continuum of path-dependent equilibrium solutions induced by sticky expectations

TL;DR

This paper introduces a macroeconomic model with sticky inflation expectations, revealing a continuum of equilibria influenced by past states, and explores how shocks and policy variations affect system dynamics and stability.

Contribution

It presents a novel mathematical operator for modeling sticky expectations, demonstrating a continuum of equilibria and analyzing their stability under shocks and policy changes.

Findings

A line segment of equilibria replaces the rational expectations solution.

Small shocks revert the system to the original equilibrium, larger shocks lead to different equilibria.

Exogenous shocks can cause runaway inflation under certain conditions.

Abstract

We analyze a simple macroeconomic model where rational inflation expectations is replaced by a boundedly rational, and genuinely sticky, response to changes in the actual inflation rate. The stickiness is introduced in a novel way using a mathematical operator that is amenable to rigorous analysis. We prove that, when exogenous noise is absent from the system, the unique equilibrium of the rational expectations model is replaced by an entire line segment of possible equilibria with the one chosen depending, in a deterministic way, upon the previous states of the system. The agents are sufficiently far-removed from the rational expectations paradigm that problems o indeterminacy do not arise. The response to exogenous noise is far more subtle than in a unique equilibrium model. After sufficiently small shocks the system will indeed revert to the same equilibrium but larger ones will move the system to a different one (at the same model parameters). The path to this new equilibrium may be very long with a highly unpredictable endpoint. At certain model parameters exogenously-triggered runaway inflation can occur. Finally, we analyze a variant model in which the same form of sticky response is introduced into the interest rate rule instead.