# Causality, Structure, and the Uniqueness of Rational Expectations Equilibria

26 Pages Posted: 18 Aug 2009 Last revised: 18 Aug 2010

See all articles by Bennett T. McCallum

## Bennett T. McCallum

Carnegie Mellon University - David A. Tepper School of Business; National Bureau of Economic Research (NBER)

Date Written: August 2009

### Abstract

Consider a rational expectations (RE) model that includes a relationship between variables x_t and z_(t+1). To be considered structural and potentially useful as a guide to actual behavior, this model must specify whether x_t is influenced by the expectation at t of z_(t+1) or, alternatively, that z_(t+1) is directly influenced (via some inertial mechanism) by x_t (i.e., that z_t is influenced by x_(t-1)). These are quite different phenomena. Here it is shown that, for a very broad class of multivariate linear RE models, distinct causal specifications involving both expectational and inertial influences will be uniquely associated with distinct solutions--which will result operationally from different specifications concerning which of the model's variables are predetermined. It follows that for a given structure, and with a natural continuity assumption, there is only one RE solution that is fully consistent with the model's specification. Furthermore, this solution does not involve "sunspot" phenomena.

Suggested Citation

McCallum, Bennett T., Causality, Structure, and the Uniqueness of Rational Expectations Equilibria (August 2009). NBER Working Paper No. w15234, Available at SSRN: https://ssrn.com/abstract=1454969