Accelerating Non Linear Perfect Foresight Model Solution by Exploiting the Steady State Linearization

Abstract

Consider the model

$$h({x_{t - \tau }},{x_{t - \tau + 1}},...{x_{t + 0 - 1}},{x_{t + 0}}) = 0$$

((1))

Where χ ∈ ℜ^L and h:ℜ^L(τ+1+θ) → ℜ^L. We want to determine the solutions to Equation 1 with initial conditions

$${x_i} = {\bar x_i}{\text{ }}for{\text{ }}i = - \tau ,..., - 1$$

((2))

$$\mathop {\lim }\limits_{t \to \infty } {x_t} = x*.$$

((3))

satisfying