dsgepy 1.1

Solve and estimate linearized DSGE models

dsgepy

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.

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Installation

You can install this development version using:

pip install dsgepy

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Example

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:

$$\tilde{y}_{t}=E_{t}\left(\tilde{y}_{t+1}\right)-\frac{1}{\sigma}\left[\hat{i}_{t}-E_{t}\left(\pi_{t+1}\right)\right]+\psi_{ya}^{n}\left(\rho_{a}-1\right)a_{t}$$

$$\pi_{t}=\beta E_{t}\left(\pi_{t+1}\right)+\kappa\tilde{y}_{t}+\sigma_{\pi}\varepsilon_{t}^{\pi}$$

$$\hat{i}_{t}=\phi_{\pi}\pi_{t}+\phi_{y}\tilde{y}_{t}+v_{t}$$

$$a_{t}=\rho_{a}a_{t-1}+\sigma_{a}\varepsilon_{t}^{a}$$

$$v_{t}=\rho_{v}v_{t-1}+\sigma_{v}\varepsilon_{t}^{v}$$

Model Especification

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.

Model Solution

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.

Model Estimation

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.

Analysis

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.

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Drawbacks

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...

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Contributing

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.

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More Information and Help

If you need more information and help, specially about contributing, you can contact Gustavo Amarante on [e-mail]