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

TL;DR

This paper investigates the number of solutions and parameters in linear multivariate rational expectations models, focusing on zero structures, predetermined variables, and conditions for unique causal stationary solutions.

Contribution

It provides new insights into how the structure of zeros and predetermined variables affect the solution space and uniqueness in rational expectations models.

Findings

Number of free parameters depends on zero structure of a matrix polynomial.

Predetermined variables influence the solution set.

A condition for existence and uniqueness of causal stationary solutions is established.

Abstract

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.