MacroModelling.jl

Macros and functions to work with DSGE models.
Author thorek1
Popularity
18 Stars
Updated Last
11 Months Ago
Started In
November 2022

MacroModelling.jl

Documentation: Documentation

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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] =/  c[1]) ** exp(z[1]) * k[0]^- 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)

RBC IRF

The package contains the following models in the models folder:

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.