A finite set of equilibria for the indeterminacy of linear rational expectations models

TL;DR

This paper proves that linear rational expectations models with indeterminacy have a finite number of equilibria, determined by eigenvector selection, replacing the usual uncountable sunspot equilibria.

Contribution

It establishes the existence of a finite set of equilibria in indeterminate linear rational expectations models based on eigenvector selection.

Findings

Finite set of equilibria exists for indeterminate models

Number of equilibria equals eigenvector combinations

Replaces uncountable sunspot equilibria in certain cases

Abstract

This paper demonstrates the existence of a finite set of equilibria in the case of the indeterminacy of linear rational expectations models. The number of equilibria corresponds to the number of ways to select n eigenvectors among a larger set of eigenvectors related to stable eigenvalues. A finite set of equilibria is a substitute to continuous (uncountable) sets of sunspots equilibria, when the number of independent eigenvectors for each stable eigenvalue is equal to one.