LRESolve.jl

Solving Systems of Linear Rational Expectations Equations in Julia

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")

Sims (2001) solves LRE systems of the form

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

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)

2. Call the solve_sims method over the newly created model

Θ, Θ₀, Θ₁ = solve_sims(M0)

Uhlig (1998) solves LRE systems of the form

where

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

The solution takes the form

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)

2. Call the solve_uhlig method over the newly created model

P,Q = solve_uhlig(M0)

Anderson and Moore (1985) solves systems of the form

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

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])

2. Call the solve_am method over the newly created model

B = solve_am(M0)

The different methods can be tested using Binder.