Determinacy and Stability under Learning of Rational Expectations Equilibria

Stéphane Gauthier (1, 2)

1 CREST - Centre de Recherche en Économie et Statistique
2 ERMES - Equipe de recherche sur les marches, l'emploi et la simulation

This paper studies relationships between the local determinacy of a stationary equilibrium in the perfect foresight dynamics, and its local stability in dynamics arising from econometric learning procedures. Attention is focused on linear scalar economies where agents forecast only one period ahead, and with an arbitrary, but fixed, number of predetermined variables. In such a framework, it is well known that there are no clear links between the determinacy of the stationary state in the perfect foresight dynamics on the levels of the state variable, and its stability under learning. The paper emphasizes, however, that this is not the right perfect foresight dynamics to look at whenever agents try to learn the coefficients of the perfect foresight dynamics restricted to an eigenspace of lower dimension. Indeed the paper introduces a growth rate perfect foresight dynamics on these coefficients and proves equivalence between determinacy in that dynamics and stability under learning provided that a simple sign condition is satisfied.

Mots clés: rational expectations; determinacy; learning; expectational stability

Domaines: Economies et finances

Stéphane Gauthier. Determinacy and Stability under Learning of Rational Expectations Equilibria. Journal of Economic Theory, 2002, 102 (2), pp.354-374. ⟨10.1006/jeth.2000.2768⟩. ⟨hal-00731065⟩