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MacroModelling.jl

Author: Thore Kockerols (@thorek1)

MacroModelling.jl is a Julia package for developing and solving dynamic stochastic general equilibrium (DSGE) models.

These kinds of models describe the behavior of a macroeconomy and are particularly suited for counterfactual analysis (economic policy evaluation) and exploring / quantifying specific mechanisms (academic research). Due to the complexity of these models, efficient numerical tools are required, as analytical solutions are often unavailable. MacroModelling.jl serves as a tool for handling the complexities involved, such as forward-looking expectations, nonlinearity, and high dimensionality.

The goal of this package is to reduce coding time and speed up model development by providing functions for working with discrete-time DSGE models. The user-friendly syntax, automatic variable declaration, and effective steady state solver facilitate fast prototyping of models. Furthermore, the package allows the user to work with nonlinear model solutions (up to third order (pruned) perturbation) and estimate the model using gradient based samplers (e.g. NUTS, of HMC). Currently, DifferentiableStateSpaceModels.jl is the only other package providing functionality to estimate using gradient based samplers but the use is limited to models with an analytical solution of the non stochastic steady state (NSSS). Larger models tend to not have an analytical solution of the NSSS and MacroModelling.jl can also use gradient based sampler in this case. The target audience for the package includes central bankers, regulators, graduate students, and others working in academia with an interest in DSGE modelling.

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 (pruned) perturbation solutions (see Villemot (2011), Andreasen et al. (2017) and Levintal (2017)) using symbolic derivatives
  • handle occasionally binding constraints for linear and nonlinear solutions
  • calculate (generalised) impulse response functions, simulate the model, or do conditional forecasts for linear and nonlinear solutions
  • calibrate parameters using (non stochastic) steady state relationships
  • match model moments (also for pruned higher order solutions)
  • estimate the model on data (Kalman filter using first order perturbation; see Durbin and Koopman (2012)) with gradient based samplers (e.g. NUTS, HMC) or estimate nonlinear models using the inversion filter
  • differentiate (forward AD) the model solution, Kalman filter loglikelihood (forward and reverse-mode AD), model moments, steady state, with respect to the parameters

The package is not:

  • guaranteed to find the non stochastic steady state
  • the fastest package around if you already have a fast way to find the NSSS

The former has to do with the fact that solving systems of nonlinear equations is hard (an active area of research). Especially in cases where the values of the solution are far apart (have a high standard deviation - e.g. sol = [-46.324, .993457, 23523.3856]), the algorithms have a hard time finding a solution. The recommended way to tackle this is to set bounds in the @parameters part (e.g. r < 0.2), so that the initial points are closer to the final solution (think of steady state interest rates not being higher than 20% - meaning not being higher than 0.2 or 1.2 depending on the definition).

The latter has to do with the fact that julia code is fast once compiled, and that the package can spend more time finding the non stochastic steady state. This means that it takes more time from executing the code to define the model and parameters for the first time to seeing the first plots than with most other packages. But, once the functions are compiled and the non stochastic steady state has been found the user can benefit from the object oriented nature of the package and generate outputs or change parameters very fast.

The package contains the following models in the models folder:

Comparison with other packages

MacroModelling.jldynareDSGE.jldolo.pySolveDSGE.jlDifferentiableStateSpaceModels.jlStateSpaceEcon.jlIRISRISENBTOOLBOXgEconGDSGETaylor Projection
Host languagejuliaMATLABjuliaPythonjuliajuliajuliaMATLABMATLABMATLABRMATLABMATLAB
Non stochastic steady state solversymbolic or numerical solver of independent blocks; symbolic removal of variables redundant in steady state; inclusion of calibration equations in problemnumerical solver of independent blocks or user-supplied values/functionsnumerical solver of independent blocks or user-supplied values/functionsnumerical solvernumerical solver or user supplied values/equationsnumerical solver of independent blocks or user-supplied values/functionsnumerical solver of independent blocks or user-supplied values/functionsnumerical solver of independent blocks or user-supplied values/functionsuser-supplied steady state file or numerical solvernumerical solver; inclusion of calibration equations in problem
Automatic declaration of variables and parametersyes
Derivatives (Automatic Differentiation) wrt parametersyesyes - for all 1st, 2nd order perturbation solution related output if user supplied steady state equations
Perturbation solution order1, 2, 3k11, 2, 31, 2, 31, 2111 to 5111 to 5
Pruningyesyesyesyes
Automatic derivation of first order conditionsyes
Handles occasionally binding constraintsyesyesyesyesyesyesyes
Global solutionyesyesyes
Estimationyesyesyesyesyesyesyes
Balanced growth pathyesyesyesyesyesyes
Model inputmacro (julia)text filetext filetext filetext filemacro (julia)module (julia)text filetext filetext filetext filetext filetext file
Timing conventionend-of-periodend-of-periodend-of-periodstart-of-periodstart-of-periodend-of-periodend-of-periodend-of-periodend-of-periodend-of-periodstart-of-periodstart-of-period

Bibliography