Expectational Stability in Multivariate Models

Expectational Stability in Multivariate Models

This paper shows that the concept of Expectational stability (E-stability) in a multivariate framework is inherently model-dependent. Whereas a Rational Expectations equilibrium (REE) is subject to model-specific parameter restrictions from the economic model at hand, a perceived law of motion (PLM) is postulated without such restrictions because economic agents are not likely to know the restrictions a priori. Therefore, an unrestricted PLM is in general overparameterized relative to an REE of interest in multivariate models even when the functional form is the same as the REE. Since E-stability necessarily reflects model-specific extents of overparameterization, it is model-dependent as well. Consequently, E-stability is not directly comparable across multivariate models or different representations of a given model. This implies that one may draw different conclusions on E-stability of an REE to one model under alternative representations of the same model and the REE. Our finding is independent of the information structure, the stationarity of solutions or the determinacy of a given model. We provide several economic examples analyzed in the literature. In particular, we show that a fundamental solution to a canonical New-Keynesian model can be E-stable or not depending on representations even in the case of determinacy.