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Solving Systems of Linear Rational Expectations Equations in Julia
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LRESolve.jl

Solving Systems of Linear Rational Expectations Equations in Julia

Installation

These commands install the latest version of LRESolve.jl

  • import Pkg; Pkg.add("https://github.com/NormannR/LRESolve.jl.git")
  • import Pkg; Pkg.add("LRESolve.jl")

Methods

Sims (2001)

Sims (2001) solves LRE systems of the form

image

where

  • x is the vector of endogenous variables
  • z is the vector of exogenous shocks
  • η is the vector of expectation errors

The solution verifies

image

To solve a LRE system using this method

  1. Define the model through the ModelSims structure. The syntax is typically
M0 = ModelSims(Γ₀,Γ₁,C,Ψ,Π)
  1. Call the solve_sims method over the newly created model
Θ, Θ₀, Θ₁ = solve_sims(M0)

Uhlig (1998)

Uhlig (1998) solves LRE systems of the form

image

image

where

  • x is the vector of endogenous variables
  • f is the vector of exogenous variables

The solution takes the form

image

To solve a LRE system using this method

  1. Define the model through the ModelUhlig structure. The syntax is typically
M0 = ModelUhlig(F,G,H,L,M,N)
  1. Call the solve_uhlig method over the newly created model
P,Q = solve_uhlig(M0)

Anderson and Moore (1985)

Anderson and Moore (1985) solves systems of the form

image

where

  • x is the vector of all variables
  • τ is the number of past lags
  • θ is the number of future lags

The solution is of the form

image

To solve a system using this method

  1. Define the model through the ModelAM structure. The syntax is typically
M0 = ModelAM(τ,θ,[Hmτ,...,Hθ])
  1. Call the solve_am method over the newly created model
B = solve_am(M0)

The different methods can be tested using Binder.

Binder

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