The Linear Systems Approach to Linear Rational Expectations Models

• BSE Working Paper: 110348 | February 16
• Keywords: rational expectations , cointegration , linear systems , Wiener-Hopf factorization , vector autoregressive processes , exogeneity , stationarity
• JEL codes: C32, C51, C62, C63, C65
• rational expectations
• cointegration
• linear systems
• Wiener-Hopf factorization
• vector autoregressive processes
• exogeneity
• stationarity

This paper considers linear rational expectations models from the linear systems point of view. Using a generalization of the Wiener-Hopf factorization, the linear systems approach is able to furnish very simple conditions for existence and uniqueness of both particular and generic linear rational expectations models. To illustrate the applicability of this approach, the paper characterizes the structure of stationary and cointegrated solutions, including a generalization of Granger’s representation theorem.