WORK IN PROGRESS

LinearRationalExpectations provides tools to solve economic linear rational expectations models.

Linear rational expectations models have the general form

E_t { A y_{t+1} + B y_t + C y_{t-1} + D u_t + e} = 0

The deterministic steady state of the model is defined as

\bar y = -(I - A - B - C)^{-1}e

The solution takes the form

y_t - \bar y= G_y (y_{t-1} - \bar y) + G_u u_t

where G_y is the solution of the polynomial matrix equation

A G_y G_y + B G_y + C = 0

Two different algorithms are provided by package PolynomialMatrixEquations: one based on generalized Schur decomposition and one based on cyclic reduction.

G_u = -(A G_y + B)^{-1}Du_t

In addition the LinearRationalExpectations package provides functions to reduce the problem size by eliminating static variables.