The Dimension of the Set of Causal Solutions of Linear Multivariate Rational Expectations Models

This paper analyses the number of free parameters and solutions of the structural difference equation obtained from a linear multivariate rational expectations model. First, it is shown that the number of free parameters depends on the structure of the zeros at zero of a certain matrix polynomial of the structural difference equation and the number of inputs of the rational expectations model. Second, the implications of requiring that some components of the endogenous variables be predetermined are analysed. Third, a condition for existence and uniqueness of a causal stationary solution is given.