This post gives an short introduction to the gEcon R package, which provides a variety of functionalities for DSGE (Dynamic Stochastic General Equilibrium) or CGE (Computational General Equilibrium) model. It is typical that the former is solved by Matlab with Dynare, the latter by GAMS. In this post, we take a simple example of basic RBC model to understand how to use gEcon R package.

Introduction

Using gEcon (https://gecon.r-forge.r-project.org/) R package, we can perform the calibration or (Bayesian) estimation of DSGE model as well as RBC model. These days, New Keynesian DSGE (NK DSGE) model is widely used for economic policy analysis and simulation (or forecast). For monetary policy analysis, price stickiness is needed and reflected in NK DSGE model.

Authors of gEcon published the following paper, frmo which we can learn a lot of advanced methodologies.


But this post deals with a basic RBC model which is a simpler version of NK DSGE model because our focus is to learn how to use gEcon package not investigate policy effects. But when we understand how to estimate or calibrate RBC model, we can apply this approach to NK DSGE model. This is possible since the same solution technique is used for these two types of model although NK DSGE model is so complicated in nature.

Installing

Installation of gEcon package is not available in CRAN. In particular, you need to install nleqslv R package in advance. If you haven’t installed the following packages, you are recommended to install these packages as a prerequisite.

After installing the above prerequisite packages, type the following command at console.

install.packages(“gEcon”, repos=”http://R-Forge.R-project.org”)

After a long display of installation process, we can find that gEcon package is installed.

Model Structure File (*.gcn)

gEcon estimates a macro model with two files. Firstly, we need a model structure file (*.gcn) to describe a model structure (objective function, constraints, control variables, and so on). Secondly, we need a model running file (*.r file) to run this model structure file.

You can find lots of example code at https://gecon.r-forge.r-project.org/models.html.

As an example of a model structure file, a basic RBC model code(rbc_shlee.gcn) is written as follows. (this example is also found at the above link.)



At first, \(X\) variable has the following timing.



Now let’s investigate the above RBC model code (*.gcn) line by line.

block CONSUMER

block CONSUMER describes the following the consumer utility maximization problem with two constraints: budget constraint and capital accumulation.
\begin{align} \max_{K^{\mathrm{s}}_{t}, C_{t}, L^{\mathrm{s}}_{t}, I_{t} } U_{t} &= {\beta} {\mathrm{E}_{t}\left[U_{t+1}\right]} + \left(1 – \eta\right)^{-1} {\left({{C_{t}}^{\mu}} {\left(1 – L^{\mathrm{s}}_{t}\right)^{1 – \mu}}\right)^{1 – \eta}}\\ \mathrm{s.t.}&\nonumber\\ C_{t} + I_{t} &= \pi_{t} + {K^{\mathrm{s}}_{t-1}} {r_{t}} + {L^{\mathrm{s}}_{t}} {w_{t}}\\ K^{\mathrm{s}}_{t} &= I_{t} + {K^{\mathrm{s}}_{t-1}} \left(1 – \delta\right) \end{align}

block FIRM

block FIRM describes the following the firm profit(\(\pi_t\)) maximization problem with the constraint of the Cobb-Douglas production function.
\begin{align} \max_{K_{t}, L_{t}, Y_{t} } \pi_{t} &= Y_{t} – {w_{t}}{L_{t}} – {r_{t}} {K_{t}}\\ \mathrm{s.t.}&\nonumber\\ Y_{t} &= {Z_{t}} {{K_{t}}^{\alpha}} {{L_{t}}^{1 – \alpha}} \end{align}

block EQUILIBRIUM

The equilibrium occurs where the quantity demanded is equal to the quantity supplied for the labor and capital.
\begin{align} K_{t} &= K^{\mathrm{s}}_{t-1} \\ L_{t} &= L^{\mathrm{s}}_{t} \end{align}

block EXOG

In this RBC model, business cycles result from the aggregate productivity shock (\(Z_{t}\)) which follows an exogenous stochastic process. \begin{equation} Z_{t} = e^{\epsilon^{\mathrm{Z}}_{t} + {\phi} {\log{Z_{t-1}}}} \end{equation}

Model Running File (*.R)

This model running file consists of three parts.

Results

After running the above R code, we can get the following results: 1) IRFs, 2) calibrated model results with statistics and moments.

The following figures shows the impulse response functions of endogenous variables to the exogenous shock (\(\epsilon^{\mathrm{Z}}_{t}\))

The following output shows calibrated model results with statistics and moments. Since we don’t use observable data such as GDP, investment flow, and inflation rate, these output are based on calibration not estimation.


Besides the above output, shock covariance matrix, correlation matrix, autocorrelations, cross correlations are also produced (These are not reported).

Conclusion

This post deals with the calibration of a basic RBC model using gEcon R package. Authors of gEcon also provides the gEcon.estimation package which deals with the Bayesian estimation for DSGE. It will be interesting to learn how to do Bayesian estimation with these packages in R. \(\blacksquare\)