MacroModelling.jl

The goal of MacroModelling.jl is to reduce coding time and speed up model development.

The package currently supports dicsrete-time DSGE models with end-of-period timing.

As of now the package can:

parse a model written with user friendly syntax (variables are followed by time indices ...[2], [1], [0], [-1], [-2]..., or [x] for shocks)
(attempt to) solve the model only knowing the model equations and parameter values (no steady state file, no variable and parameter declaration needed)
calculate first, second, and third order perturbation solutions using (forward) automatic differentiation (AD)
calculate (generalised) impulse response functions, and simulate the model
calibrate parameters using (non stochastic) steady state relationships
match model moments
estimate the model on data (kalman filter using first order perturbation)
differentiate (forward AD) the model solution (first order perturbation), kalman filter loglikelihood, model moments, steady state, with respect to the parameters

Getting started

Installation

MacroModelling.jl requires julia version 1.8 or higher and an IDE is recommended (e.g. VS Code with the julia extension).

Once set up you can install MacroModelling.jl by typing the following in the julia REPL:

using Pkg; Pkg.add("MacroModelling")

Example

See below for example code of a simple RBC model. For more details see the documentation.

using MacroModelling

@model RBC begin
    1  /  c[0] = (β  /  c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
    c[0] + k[0] = (1 - δ) * k[-1] + q[0]
    q[0] = exp(z[0]) * k[-1]^α
    z[0] = ρ * z[-1] + std_z * eps_z[x]
end;

@parameters RBC begin
    std_z = 0.01
    ρ = 0.2
    δ = 0.02
    α = 0.5
    β = 0.95
end;

plot_irfs(RBC)

Comparison with other packages

	MacroModelling.jl	dynare	RISE	DSGE.jl	StateSpaceEcon.jl	SolveDSGE.jl	dolo.py	DifferentiableStateSpaceModels.jl	gEcon
Host language	julia	MATLAB	MATLAB	julia	julia	julia	Python	julia	R
Non stochastic steady state solver	symbolic or numerical solver of recursive blocks; symbolic removal of variables redundant in steady state; inclusion of calibration equations in problem	numerical solver of recursive blocks or user-supplied values/functions	numerical solver of recursive blocks or user-supplied values/functions		numerical solver of recursive blocks or user-supplied values/functions	numerical solver	numerical solver or user supplied values/equations	numerical solver or user supplied values/equations	numerical solver; inclusion of calibration equations in problem
Automatic declaration of variables and parameters	yes
Derivatives (Automatic Differentiation) wrt parameters	yes - for all 1st order perturbation solution related output						yes - for all 1st, 2nd order perturbation solution related output if user supplied steady state equations
Perturbation solution order	1, 2, 3	k	1 to 5	1	1	1, 2, 3	1, 2, 3	1, 2	1
Automatic derivation of first order conditions								yes
Handles occasionally binding constraints		yes	yes	yes		yes	yes
Global solution						yes	yes
Estimation	yes	yes	yes	yes					yes
Balanced growth path		yes	yes	yes	yes
Model input	macro (julia)	text file	text file	text file	module (julia)	text file	text file	macro (julia)	text file
Timing convention	end-of-period	end-of-period	end-of-period		end-of-period	start-of period	end-of-period	start-of period	end-of-period

Bibliography

Levintal, O., (2017), "Fifth-Order Perturbation Solution to DSGE models", Journal of Economic Dynamics and Control, 80, pp. 1---16.

Villemot, S., (2011), "Solving rational expectations models at first order: what Dynare does", Dynare Working Papers 2, CEPREMAP.

azev77 / MacroModelling.jl