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
- Define the model through the
ModelSims
structure. The syntax is typically
M0 = ModelSims(Γ₀,Γ₁,C,Ψ,Π)
- 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
- Define the model through the
ModelUhlig
structure. The syntax is typically
M0 = ModelUhlig(F,G,H,L,M,N)
- 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
- Define the model through the
ModelAM
structure. The syntax is typically
M0 = ModelAM(τ,θ,[Hmτ,...,Hθ])
- Call the
solve_am
method over the newly created model
B = solve_am(M0)
The different methods can be tested using Binder.