diff --git a/joss.05598/10.21105.joss.05598.crossref.xml b/joss.05598/10.21105.joss.05598.crossref.xml new file mode 100644 index 0000000000..5af8477bb4 --- /dev/null +++ b/joss.05598/10.21105.joss.05598.crossref.xml @@ -0,0 +1,225 @@ + + + + 20230925T175210-71a90f82b1d1ba77147c32b63632ecc488c2e432 + 20230925175210 + + JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 09 + 2023 + + + 8 + + 89 + + + + MacroModelling.jl: A Julia package for developing and +solving dynamic stochastic general equilibrium models + + + + Thore + Kockerols + https://orcid.org/0000-0002-0068-1809 + + + + 09 + 25 + 2023 + + + 5598 + + + 10.21105/joss.05598 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.8374466 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/5598 + + + + 10.21105/joss.05598 + https://joss.theoj.org/papers/10.21105/joss.05598 + + + https://joss.theoj.org/papers/10.21105/joss.05598.pdf + + + + + + Time series analysis by state space methods, +2nd edn + Durbin + 10.1093/acprof:oso/9780199641178.001.0001 + 2012 + Durbin, J., & Koopman, S. J. +(2012). Time series analysis by state space methods, 2nd edn. Oxford +University Press. +https://doi.org/10.1093/acprof:oso/9780199641178.001.0001 + + + The Pruned State-Space System for Non-Linear +DSGE Models: Theory and Empirical Applications + Andreasen + The Review of Economic +Studies + 1 + 85 + 10.1093/restud/rdx037 + 0034-6527 + 2017 + Andreasen, M. M., +Fernández-Villaverde, J., & Rubio-Ramírez, J. F. (2017). The Pruned +State-Space System for Non-Linear DSGE Models: Theory and Empirical +Applications. The Review of Economic Studies, 85(1), 1–49. +https://doi.org/10.1093/restud/rdx037 + + + Julia: A fresh approach to numerical +computing + Bezanson + SIAM Review + 1 + 59 + 10.1137/141000671 + 2017 + Bezanson, J., Edelman, A., Karpinski, +S., & Shah, V. B. (2017). Julia: A fresh approach to numerical +computing. SIAM Review, 59(1), 65–98. +https://doi.org/10.1137/141000671 + + + Fifth-order perturbation solution to DSGE +models + Levintal + Journal of Economic Dynamics and +Control + 80 + 10.1016/j.jedc.2017.04.007 + 2017 + Levintal, O. (2017). Fifth-order +perturbation solution to DSGE models. Journal of Economic Dynamics and +Control, 80, 1–16. +https://doi.org/10.1016/j.jedc.2017.04.007 + + + Solving rational expectations models at first +order: What dynare does + Villemot + 2011 + Villemot, S. (2011). Solving rational +expectations models at first order: What dynare does. Dynare Working +Papers 2, CEPREMAP. + + + Time to build and aggregate +fluctuations + Kydland + Econometrica + 6 + 50 + 10.2307/1913386 + 1982 + Kydland, F. E., & Prescott, E. C. +(1982). Time to build and aggregate fluctuations. Econometrica, 50(6), +1345–1370. https://doi.org/10.2307/1913386 + + + Dynare: Reference manual version +5 + Adjemian + 2022 + Adjemian, S., Bastani, H., Juillard, +M., Karamé, F., Mihoubi, F., Mutschler, W., Pfeifer, J., Ratto, M., +Rion, N., & Villemot, S. (2022). Dynare: Reference manual version 5 +(Dynare Working Papers No. 72). CEPREMAP. + + + Efficient perturbation methods for solving +regime-switching DSGE models + Maih + 10.2139/ssrn.2602453 + 2015 + Maih, J. (2015). Efficient +perturbation methods for solving regime-switching DSGE models (Working +Paper No. 2015/01). Norges Bank. +https://doi.org/10.2139/ssrn.2602453 + + + Taylor Projection: A New Solution Method For +Dynamic General Equilibrium Models + Levintal + International Economic Review + 3 + 59 + 10.1111/iere.12306 + 2018 + Levintal, O. (2018). Taylor +Projection: A New Solution Method For Dynamic General Equilibrium +Models. International Economic Review, 59(3), 1345–1373. +https://doi.org/10.1111/iere.12306 + + + Smets-Wouters ’03 model revisited - an +implementation in gEcon + Klima + 2015 + Klima, G., Podemski, K., +Retkiewicz-Wijtiwiak, K., & Sowińska, A. E. (2015). Smets-Wouters +’03 model revisited - an implementation in gEcon (MPRA Paper No. 64440). +University Library of Munich, Germany. + + + Differentiable State-Space Models and +Hamiltonian Monte Carlo Estimation + Childers + 10.3386/w30573 + 2022 + Childers, D., Fernández-Villaverde, +J., Perla, J., Rackauckas, C., & Wu, P. (2022). Differentiable +State-Space Models and Hamiltonian Monte Carlo Estimation (NBER Working +Papers No. 30573). National Bureau of Economic Research, Inc. +https://doi.org/10.3386/w30573 + + + + + + diff --git a/joss.05598/10.21105.joss.05598.jats b/joss.05598/10.21105.joss.05598.jats new file mode 100644 index 0000000000..aa23766022 --- /dev/null +++ b/joss.05598/10.21105.joss.05598.jats @@ -0,0 +1,408 @@ + + +
+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +5598 +10.21105/joss.05598 + +MacroModelling.jl: A Julia package for developing and +solving dynamic stochastic general equilibrium models + + + +https://orcid.org/0000-0002-0068-1809 + +Kockerols +Thore + + + + + +Norges Bank, Norway + + + + +1 +9 +2023 + +8 +89 +5598 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +DSGE +macroeconomics +perturbation +difference equations +dynamical systems + + + + + + Summary +

MacroModelling.jl is a Julia + (Bezanson + et al., 2017) 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).

+

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. The package includes several pre-defined + models from prominent economic papers, providing an immediate starting + point for users. The target audience for the package includes central + bankers, regulators, graduate students, and others working in academia + with an interest in DSGE modelling.

+

The package supports programmatic model definition. Once the model + is defined, the package finds the solution for the model dynamics + knowing only the model equations and parameter values. The model + dynamics can be solved for using first, (pruned) second, and (pruned) + third-order perturbation solutions + (Andreasen + et al., 2017; + O. + Levintal, 2017; + Villemot, + 2011), leveraging symbolic and automatic differentiation. + Furthermore, the package can be used to calibrate parameters, match + model moments, and estimate the model on data using the Kalman filter + (Durbin + & Koopman, 2012). The package is designed to be + user-friendly and efficient. Once the functions are compiled and the + non-stochastic steady state (NSSS) has been found, the users benefit + from fast and convenient functions to generate outputs or change + parameters.

+ + + Statement of Need +

Due to the complexity of DSGE 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.

+

MacroModelling.jl differentiates itself + among macroeconomic modelling packages by offering a unique blend of + capabilities and conveniences, such as automatic declaration of + variables and parameters, automatic differentiation with respect to + parameters, and support for perturbation solutions up to 3rd order. + While it operates within the Julia environment, it presents an + alternative to the MATLAB-dominated field, which includes + dynare + (Adjemian + et al., 2022), + RISE + (Maih, + 2015), + Taylor + Projection + (Oren + Levintal, 2018), + NBTOOLBOX, + and + IRIS, + the latter two being capable of providing only 1st order perturbation + solutions.

+

Other Julia-based packages such as + DSGE.jl, + StateSpaceEcon.jl, + SolveDSGE.jl, + and + DifferentiableStateSpaceModels.jl + (Childers + et al., 2022) have functionalities similar to those of + MacroModelling.jl. However, the former are not + as general and convenience-focused as the MATLAB packages and + MacroModelling.jl. The Julia-based packages are + missing convenience functionalities such as automatic creation of + auxiliary variables for variables in lead and lags larger than 1, or + programmatic model definition. These functionalities are convenient to + the user but require significant effort to implement in the parser. + Furthermore, the other Julia-based packages do not possess the unique + feature set of MacroModelling.jl regarding + variable declaration and automatic differentiation. Notably, the + Python-based + dolo.py + offers global solutions, but does not include estimation features + which are available in MacroModelling.jl.

+

MacroModelling.jl stands out as one of the + few packages that can solve non-stochastic steady states symbolically, + a feature shared only with + gEcon + (Klima + et al., 2015), an R-based package. When, as in most cases, + symbolic solution is not possible + MacroModelling.jl uses symbolic simplification, + search space transformation, automatic domain restrictions, restarts + with different initial values, warm starts using previous solutions, + and a Levenberg-Marquardt-type optimizer. The combination of these + elements makes it possible to solve all 16 models currently + implemented in the examples out-of-the box. This is remarkable because + all other packages rely either on analytical NSSS derivation by hand, + or on a smaller subset of the features outlined above. In general this + makes the other packages far less reliable in finding the NSSS without + further information (e.g. a close enough initial guess). Furthermore, + unlike many of its competitors, the domain-specific model language of + MacroModelling.jl is integrated into the Julia + language, which makes for convenient reading and coding, with the help + of Julia macros.

+ + + Example +

One relatively simple example to study with the package is a real + business cycle model (see e.g. + (Kydland + & Prescott, 1982)). The model describes the dynamics of an + economy with households consuming a consumption good + c, produced by competitive firms using the + capital stock k, and an exogenous technology + process z. The households maximize their + utility (log(c)) and decide whether to invest + in the capital stock or consume. The firms decide the amount of + production inputs and the quantity of output with the goal to maximize + their profits while minimizing their costs. The capital stock + depreciates by the factor δ and the production + technology takes the form: k^α. All agents + discount the future with β and the exogenous + AR(1) technology process is governed by parameters + ρ and σ_z. Given the + optimization problems of the households and firms one can write down + the first-order optimality conditions as follows:

+ using MacroModelling +import StatsPlots + +@model RBC begin + 1 / c[0] = (β / c[1]) * (α * z[1] * k[0]^(α - 1) + (1 - δ)) + c[0] + k[0] = (1 - δ) * k[-1] + q[0] + q[0] = z[0] * k[-1]^α + z[0] = (1 - ρ) + ρ * z[-1] + σ_z * eps_z[x] +end + +@parameters RBC begin + σ_z = 0.01 + ρ = 0.2 + δ = 0.02 + α = 0.5 + β = 0.95 +end + +plot_irf(RBC) +

+ Impulse response to a positive 1 standard deviation + shock. + The plot shows both the level, percentage deviation + from the NSSS as well as the NSSS itself. Note that the code to + generate the impulse response function (IRF) plot contains only the + equations, parameter values, and the command to plot. Solving the + model using first-order perturbation happens automatically in the + background.

+ + + Acknowledgements +

The author thanks everybody who opened issues, reported bugs, + contributed ideas, and was supportive in driving + MacroModelling.jl forward.

+ + + + + + + + DurbinJ + KoopmanS. J. + + Time series analysis by state space methods, 2nd edn + Oxford University Press + 2012 + 10.1093/acprof:oso/9780199641178.001.0001 + + + + + + AndreasenMartin M + Fernández-VillaverdeJesús + Rubio-RamírezJuan F + + The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications + The Review of Economic Studies + 201706 + 85 + 1 + 0034-6527 + https://doi.org/10.1093/restud/rdx037 + 10.1093/restud/rdx037 + 1 + 49 + + + + + + BezansonJeff + EdelmanAlan + KarpinskiStefan + ShahViral B. + + Julia: A fresh approach to numerical computing + SIAM Review + 2017 + 59 + 1 + https://doi.org/10.1137/141000671 + 10.1137/141000671 + 65 + 98 + + + + + + LevintalO. + + Fifth-order perturbation solution to DSGE models + Journal of Economic Dynamics and Control + 2017 + 80 + https://doi.org/10.1016/j.jedc.2017.04.007 + 10.1016/j.jedc.2017.04.007 + 1 + 16 + + + + + + VillemotS. + + Solving rational expectations models at first order: What dynare does + Dynare Working Papers 2, CEPREMAP + 2011 + + + + + + KydlandFinn E. + PrescottEdward C. + + Time to build and aggregate fluctuations + Econometrica + [Wiley, Econometric Society] + 1982 + 20230831 + 50 + 6 + http://www.jstor.org/stable/1913386 + 10.2307/1913386 + 1345 + 1370 + + + + + + AdjemianStéphane + BastaniHoutan + JuillardMichel + KaraméFréderic + MihoubiFerhat + MutschlerWilli + PfeiferJohannes + RattoMarco + RionNormann + VillemotSébastien + + Dynare: Reference manual version 5 + CEPREMAP + 2022 + + + + + + MaihJunior + + Efficient perturbation methods for solving regime-switching DSGE models + Norges Bank + 201501 + 10.2139/ssrn.2602453 + + + + + + LevintalOren + + Taylor Projection: A New Solution Method For Dynamic General Equilibrium Models + International Economic Review + 2018 + 59 + 3 + 10.1111/iere.12306 + 1345 + 1373 + + + + + + KlimaGrzegorz + PodemskiKarol + Retkiewicz-WijtiwiakKaja + SowińskaAnna E. + + Smets-Wouters ’03 model revisited - an implementation in gEcon + University Library of Munich, Germany + 201502 + + + + + + ChildersDavid + Fernández-VillaverdeJesús + PerlaJesse + RackauckasChristopher + WuPeifan + + Differentiable State-Space Models and Hamiltonian Monte Carlo Estimation + National Bureau of Economic Research, Inc + 202210 + 10.3386/w30573 + + + + +
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