MacroModelling.jl

Documentation:

Author: Thore Kockerols (@thorek1)

MacroModelling.jl is a package for developing and solving dynamic stochastic general equilibrium (DSGE) models. The package provides functions for creating, calibrating, simulating and estimating discrete-time DSGE models.

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

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)
(tries to) solve the model only knowing the model equations and parameter values (no steady state file needed)
calculate first, second, and third order perturbation solutions using (forward or reverse-mode) automatic differentiation (AD)
calculate (generalised) impulse response functions, simulate the model, or do conditional forecasts
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, Kalman filter loglikelihood (reverse-mode AD), model moments, steady state, with respect to the parameters

The package is not:

guaranteed to find the non stochastic steady state (solving systems of nonlinear equations is an active area of research)
the fastest package around if you already have a fast way to find the NSSS (time to first plot is long, time to second plot (with new parameters) is very short)

For more details have a look at the documentation.

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 (and StatsPlots in order to plot) by typing the following in the Julia REPL:

using Pkg; Pkg.add(["MacroModelling", "StatsPlots"])

Example

See below an implementation of a simple RBC model. You can find more detailed tutorials in the documentation.

using MacroModelling
import StatsPlots

@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_irf(RBC)

The package contains the following models in the models folder:

Aguiar and Gopinath (2007) Aguiar_Gopinath_2007.jl
Ascari and Sbordone (2014) Ascari_sbordone_2014.jl
Caldara et al. (2012) Caldara_et_al_2012.jl
Gali (2015) - Chapter 3 Gali_2015_chapter_3_nonlinear.jl
Gali and Monacelli (2005) - CPI inflation-based Taylor rule Gali_Monacelli_2005_CITR.jl
Gerali, Neri, Sessa, and Signoretti (2010) GNSS_2010.jl
Ghironi and Melitz (2005) Ghironi_Melitz_2005.jl
Ireland (2004) Ireland_2004.jl
Jermann and Quadrini (2012) - RBC JQ_2012_RBC.jl
New Area-Wide Model (2008) - Euro Area - US NAWM_EAUS_2008.jl
Schmitt-Grohé and Uribe (2003) - debt premium SGU_2003_debt_premium.jl
Schorfheide (2000) FS2000.jl
Smets and Wouters (2003) SW03.jl
Smets and Wouters (2007) SW07.jl

Comparison with other packages

	MacroModelling.jl	dynare	RISE	NBTOOLBOX	IRIS	DSGE.jl	StateSpaceEcon.jl	SolveDSGE.jl	dolo.py	DifferentiableStateSpaceModels.jl	gEcon	GDSGE	Taylor Projection
Host language	julia	MATLAB	MATLAB	MATLAB	MATLAB	julia	julia	julia	Python	julia	R	MATLAB	MATLAB
Non stochastic steady state solver	symbolic or numerical solver of independent blocks; symbolic removal of variables redundant in steady state; inclusion of calibration equations in problem	numerical solver of independent blocks or user-supplied values/functions	numerical solver of independent blocks or user-supplied values/functions	user-supplied steady state file or numerical solver	numerical solver of independent blocks or user-supplied values/functions		numerical solver of independent 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									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	1	1, 2, 3	1, 2, 3	1, 2	1		1 to 5
Automatic derivation of first order conditions											yes
Handles occasionally binding constraints		yes	yes			yes		yes	yes			yes
Global solution								yes	yes			yes
Estimation	yes	yes	yes	yes	yes	yes					yes
Balanced growth path		yes	yes	yes	yes	yes	yes
Model input	macro (julia)	text file	text file	text file	text file	text file	module (julia)	text file	text file	macro (julia)	text file	text file	text file
Timing convention	end-of-period	end-of-period	end-of-period	end-of-period	end-of-period		end-of-period	start-of-period	end-of-period	start-of-period	end-of-period	start-of-period	start-of-period

Bibliography

Durbin, J, and Koopman, S. J. (2012), "Time Series Analysis by State Space Methods, 2nd edn", Oxford University Press.

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.