# NormannR / LRESolve.jl

Solving Systems of Linear Rational Expectations Equations in Julia
Jupyter Notebook Julia

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# LRESolve.jl

Solving Systems of Linear Rational Expectations Equations in Julia

## Installation

• `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 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)`
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  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)`
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 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])`
1. Call the `solve_am` method over the newly created model
`B = solve_am(M0)`

The different methods can be tested using Binder. You can’t perform that action at this time.