Calibrate, estimate and analyze linearized DSGE models.
This is a Python library to specify, calibrate, solve, simulate, estimate and
analyze linearized DSGE models. The specification interface is inpired by
dynare, which allows for symbolic declarations of parameters, variables and
equations. Once a model is calbrated or estimated, it is solved using Sims
(2002) methodology.
Simulated trajectories can be generated from a calibrated model. Estimation
uses bayesian methods, specifically markov chain monte carlo (MCMC), to
simulate the posterior distributions of the parameters. Analysis tools include
impulse-response functions, historical decompostion and extraction of latent
variables.
This library is an effort to bring the DSGE toolset into the open-source world
in a full python implementation, which allows to embrace the advantages of this
programming language when working with DSGEs.
You can install this development version using:
pip install dsgepy
A full example on how to use this library with a small New Keynesian model is available in
this Jupyter notebook. The model used
in the example is descibred briefly by the following equations:
\tilde{y}_{t}=E_{t}\left(\tilde{y}_{t+1}\right)-\frac{1}{\sigma}\left[\hat{i}_{t}-E_{t}\left(\pi_{t+1}\right)\right]+\psi_{ya}^{n}\left(\rho_{a}-1\right)a_{t}
\pi_{t}=\beta E_{t}\left(\pi_{t+1}\right)+\kappa\tilde{y}_{t}+\sigma_{\pi}\varepsilon_{t}^{\pi}
\hat{i}_{t}=\phi_{\pi}\pi_{t}+\phi_{y}\tilde{y}_{t}+v_{t}
a{t}=\rho\{a}a_{t-1}+\sigma_{a}\varepsilon_{t}^{a}
v{t}=\rho{v}v{t-1}+\sigma{v}\varepsilon_{t}^{v}
For now, the model equations have to be linearized around its steady-state.
Soon, there will be a functionality that allows for declaration with
non-linearized equilibrium conditions.
The solution method used is based on the implementation of Christopher A. Sims’ gensys function. You can find the
author’s original matlab code here. The paper explaining the solution
method is this one.
The models are estimated using Bayesian methdos, specifically, by simulating the posterior distribution using MCMC
sampling. This process is slow, so there is a functionality that allows you to stop a simulation and continue
it later from where it stoped.
There are functionalities for computing Impulse-Response funcions for both state variables and observed variables.
Historical decomposition is also available, but only when the number of exogenous shocks matches the number of
observed variables.
Since there is symbolic declaration of variables and equations, methdos
involving them are slow. Also, MCMC methods for macroeconomic models require
many iterations to achieve convergence. Clearly, there is room for improvement
on the efficiency of these estimation algorithms. Contributions are welcome.
Speaking of contributions…
If you would like to contribute to this repository, plese check the
contributing guidelines here. A
list of feature suggestions is available on the projects page of this
repository.
If you need more information and help, specially about contributing, you can
contact Gustavo Amarante on developer@dsgepy.com