Causality, Structure, and the Uniqueness of Rational Expectations Equilibria

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.