Dynare
Dynare Working Papers Series
http://www.dynare.org/wp/
Dynare: Reference Manual
Version 4
Stéphane Adjemian
Houtan Bastani
Fréderic Karamé
Michel Juillard
Junior Maih
Ferhat Mihoubi
George Perendia
Marco Ratto
Sébastien Villemot
Working Paper no. 1
Initial revision: April 2011
This revision: June 2012
142, rue du Chevaleret — 75013 Paris — France
http://www.cepremap.ens.fr
Dynare
Reference Manual, version 4.3.0
Stéphane Adjemian
Houtan Bastani
Michel Juillard
Junior Maih
Ferhat Mihoubi
George Perendia
Marco Ratto
Sébastien Villemot
c 1996-2012, Dynare Team.
Copyright Permission is granted to copy, distribute and/or modify this document under the terms
of the GNU Free Documentation License, Version 1.3 or any later version published by
the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and
no Back-Cover Texts.
A copy of the license can be found at http://www.gnu.org/licenses/fdl.txt.
i
Table of Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1
1.2
1.3
2
What is Dynare ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Documentation sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Citing Dynare in your research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Installation and configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1
2.2
Software requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Installation of Dynare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 On Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 On Debian GNU/Linux and Ubuntu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 On Mac OS X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 For other systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 For MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 For GNU Octave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Some words of warning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
3
3
3
4
4
4
4
4
5
3
Dynare invocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4
The Model file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.1
4.2
4.3
Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Variable declarations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3.1 Parameters and variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3.1.1 Inside the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3.1.2 Outside the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3.2 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3.3.1 Built-in Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3.3.2 External Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4 Parameter initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.5 Model declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.6 Auxiliary variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.7 Initial and terminal conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.8 Shocks on exogenous variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.9 Other general declarations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.10 Steady state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.10.1 Finding the steady state with Dynare nonlinear solver . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.10.2 Using a steady state file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.11 Getting information about the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.12 Deterministic simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.13 Stochastic solution and simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.13.1 Computing the stochastic solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.13.2 Typology and ordering of variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.13.3 First order approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.13.4 Second order approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.13.5 Third order approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.14 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
ii
4.15 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.16 Optimal policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.17 Sensitivity and identification analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.17.1 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.17.2 Stability Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.17.3 Reduced Form Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.17.4 RMSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.17.5 Screening Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.17.6 Identification Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.17.7 Performing Sensitivity and Identification Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.18 Markov-switching SBVAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.19 Displaying and saving results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20 Macro-processing language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20.1 Macro expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20.2 Macro directives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20.3 Typical usages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20.3.1 Modularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20.3.2 Indexed sums or products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20.3.3 Multi-country models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20.3.4 Endogeneizing parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20.4 MATLAB/Octave loops versus macro-processor loops . . . . . . . . . . . . . . . . . . . . . . . . . .
4.21 Misc commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
54
58
60
60
60
61
61
63
63
63
68
76
77
77
78
80
80
80
81
81
82
83
The Configuration File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.1
5.2
Dynare Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Parallel Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7
Dynare internal documentation and unitary tests . . . . . . . . . . . 89
8
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Command and Function Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Variable Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Chapter 1: Introduction
1
1 Introduction
1.1 What is Dynare ?
Dynare is a software platform for handling a wide class of economic models, in particular dynamic
stochastic general equilibrium (DSGE) and overlapping generations (OLG) models. The models
solved by Dynare include those relying on the rational expectations hypothesis, wherein agents form
their expectations about the future in a way consistent with the model. But Dynare is also able
to handle models where expectations are formed differently: on one extreme, models where agents
perfectly anticipate the future; on the other extreme, models where agents have limited rationality
or imperfect knowledge of the state of the economy and, hence, form their expectations through a
learning process. In terms of types of agents, models solved by Dynare can incorporate consumers,
productive firms, governments, monetary authorities, investors and financial intermediaries. Some
degree of heterogeneity can be achieved by including several distinct classes of agents in each of
the aforementioned agent categories.
Dynare offers a user-friendly and intuitive way of describing these models. It is able to perform
simulations of the model given a calibration of the model parameters and is also able to estimate
these parameters given a dataset. In practice, the user will write a text file containing the list of
model variables, the dynamic equations linking these variables together, the computing tasks to be
performed and the desired graphical or numerical outputs.
A large panel of applied mathematics and computer science techniques are internally employed
by Dynare: multivariate nonlinear solving and optimization, matrix factorizations, local functional
approximation, Kalman filters and smoothers, MCMC techniques for Bayesian estimation, graph
algorithms, optimal control, . . .
Various public bodies (central banks, ministries of economy and finance, international organisations) and some private financial institutions use Dynare for performing policy analysis exercises
and as a support tool for forecasting exercises. In the academic world, Dynare is used for research
and teaching purposes in postgraduate macroeconomics courses.
Dynare is a free software, which means that it can be downloaded free of charge, that its source
code is freely available, and that it can be used for both non-profit and for-profit purposes. Most of
the source files are covered by the GNU General Public Licence (GPL) version 3 or later (there are
some exceptions to this, see the file ‘license.txt’ in Dynare distribution). It is available for the
Windows, Mac and Linux platforms and is fully documented through a user guide and a reference
manual. Part of Dynare is programmed in C++, while the rest is written using the MATLAB programming language. The latter implies that commercially-available MATLAB software is required
in order to run Dynare. However, as an alternative to MATLAB, Dynare is also able to run on top
of GNU Octave (basically a free clone of MATLAB): this possibility is particularly interesting for
students or institutions who cannot afford, or do not want to pay for, MATLAB and are willing to
bear the concomitant performance loss.
The development of Dynare is mainly done at Cepremap by a core team of researchers who
devote part of their time to software development. Currently the development team of Dynare
is composed of Stéphane Adjemian (Université du Maine, Gains and Cepremap), Houtan Bastani
(Cepremap), Michel Juillard (Banque de France), Frédéric Karamé (Université d’Évry, Epee and
Cepremap), Junior Maih (Norges Bank), Ferhat Mihoubi (Université d’Évry, Epee and Cepremap),
George Perendia, Johannes Pfeifer, Marco Ratto (JRC) and Sébastien Villemot (Cepremap and
Paris School of Economics). Increasingly, the developer base is expanding, as tools developed
by researchers outside of Cepremap are integrated into Dynare. Financial support is provided
by Cepremap, Banque de France and DSGE-net (an international research network for DSGE
modeling). The Dynare project also received funding through the Seventh Framework Programme
for Research (FP7) of the European Commission’s Socio-economic Sciences and Humanities (SSH)
Program from October 2008 to September 2011 under grant agreement SSH-CT-2009-225149.
Chapter 1: Introduction
2
Interaction between developers and users of Dynare is central to the project. A web forum is
available for users who have questions about the usage of Dynare or who want to report bugs.
Training sessions are given through the Dynare Summer School, which is organized every year and
is attended by about 40 people. Finally, priorities in terms of future developments and features to
be added are decided in cooperation with the institutions providing financial support.
1.2 Documentation sources
The present document is the reference manual for Dynare. It documents all commands and features
in a systematic fashion.
New users should rather begin with Dynare User Guide (Mancini (2007)), distributed with
Dynare and also available from the official Dynare web site.
Other useful sources of information include the Dynare wiki and the Dynare forums.
1.3 Citing Dynare in your research
If you would like to refer to Dynare in a research article, the recommended way is to cite the present
manual, as follows:
Stéphane Adjemian, Houtan Bastani, Michel Juillard, Ferhat Mihoubi, George Perendia, Marco Ratto and Sébastien Villemot (2011), “Dynare: Reference Manual, Version
4,” Dynare Working Papers, 1, CEPREMAP
Note that citing the Dynare Reference Manual in your research is a good way to help the Dynare
project.
If you want to give a URL, use the address of the Dynare website: http://www.dynare.org.
Chapter 2: Installation and configuration
3
2 Installation and configuration
2.1 Software requirements
Packaged versions of Dynare are available for Windows XP/Vista/Seven, Debian GNU/Linux,
Ubuntu and Mac OS X Leopard/Snow Leopard. Dynare should work on other systems, but some
compilation steps are necessary in that case.
In order to run Dynare, you need one of the following:
• MATLAB version 7.0 (R14) or above;
• GNU Octave version 3.2.2 or above.
Some installation instructions for GNU Octave can be found on the Dynare Wiki.
The following optional extensions are also useful to benefit from extra features, but are in no
way required:
• If under MATLAB: the optimization toolbox, the statistics toolbox, the control system toolbox;
• If under GNU Octave, the following Octave-Forge packages: optim, io, java, statistics, control.
If you plan to use the use_dll option of the model command, you will need to install the
necessary requirements for compiling MEX files on your machine. If you are using MATLAB
under Windows, install a C++ compiler on your machine and configure it with MATLAB: see
instructions on the Dynare wiki. Users of Octave under Linux should install the package for MEX
file compilation (under Debian or Ubuntu, it is called ‘liboctave-dev’ or ‘octave3.2-headers’). If
you are using Octave or MATLAB under Mac OS X, you should install the latest version of XCode:
see instructions on the Dynare wiki. Mac OS X Octave users will also need to install gnuplot if
they want graphing capabilities. Users of MATLAB under Linux and Mac OS X, and users of
Octave under Windows, normally need to do nothing, since a working compilation environment is
available by default.
2.2 Installation of Dynare
After installation, Dynare can be used in any directory on your computer. It is best practice to
keep your model files in directories different from the one containing the Dynare toolbox. That
way you can upgrade Dynare and discard the previous version without having to worry about your
own files.
2.2.1 On Windows
Execute the automated installer called ‘dynare-4.x.y-win.exe’ (where 4.x.y is the version number), and follow the instructions. The default installation directory is ‘c:\dynare\4.x.y’.
After installation, this directory will contain several sub-directories, among which are ‘matlab’,
‘mex’ and ‘doc’.
The installer will also add an entry in your Start Menu with a shortcut to the documentation
files and uninstaller.
Note that you can have several versions of Dynare coexisting (for example in ‘c:\dynare’), as
long as you correctly adjust your path settings (see Section 2.3.3 [Some words of warning], page 5).
2.2.2 On Debian GNU/Linux and Ubuntu
Please refer to the Dynare Wiki for detailed instructions.
Dynare will be installed under ‘/usr/share/dynare’ and ‘/usr/lib/dynare’. Documentation
will be under ‘/usr/share/doc/dynare’.
Chapter 2: Installation and configuration
4
2.2.3 On Mac OS X
Execute the automated installer called ‘dynare-4.x.y-macosx-10.5+10.6.pkg’ (where 4.x.y
is the version number), and follow the instructions. The default installation directory is
‘/Applications/Dynare/4.x.y’.
Please refer to the Dynare Wiki for detailed instructions.
After installation, this directory will contain several sub-directories, among which are ‘matlab’,
‘mex’ and ‘doc’.
Note that you can have several versions of Dynare coexisting (for example in
‘/Applications/Dynare’), as long as you correctly adjust your path settings (see Section 2.3.3
[Some words of warning], page 5).
2.2.4 For other systems
You need to download Dynare source code from the Dynare website and unpack it somewhere.
Then you will need to recompile the pre-processor and the dynamic loadable libraries. Please
refer to Dynare Wiki.
2.3 Configuration
2.3.1 For MATLAB
You need to add the ‘matlab’ subdirectory of your Dynare installation to MATLAB path. You
have two options for doing that:
• Using the addpath command in the MATLAB command window:
Under Windows, assuming that you have installed Dynare in the standard location, and replacing 4.x.y with the correct version number, type:
addpath c:\dynare\4.x.y\matlab
Under Debian GNU/Linux or Ubuntu, type:
addpath /usr/share/dynare/matlab
Under Mac OS X, assuming that you have installed Dynare in the standard location, and
replacing 4.x.y with the correct version number, type:
addpath /Applications/Dynare/4.x.y/matlab
MATLAB will not remember this setting next time you run it, and you will have to do it again.
• Via the menu entries:
Select the “Set Path” entry in the “File” menu, then click on “Add Folder. . . ”, and select the
‘matlab’ subdirectory of your Dynare installation. Note that you should not use “Add with
Subfolders. . . ”. Apply the settings by clicking on “Save”. Note that MATLAB will remember
this setting next time you run it.
2.3.2 For GNU Octave
You need to add the ‘matlab’ subdirectory of your Dynare installation to Octave path, using the
addpath at the Octave command prompt.
Under Windows, assuming that you have installed Dynare in the standard location, and replacing “4.x.y” with the correct version number, type:
addpath c:\dynare\4.x.y\matlab
Under Debian GNU/Linux or Ubuntu, there is no need to use the addpath command; the
packaging does it for you.
Under Mac OS X, assuming that you have installed Dynare in the standard location, and
replacing “4.x.y” with the correct version number, type:
Chapter 2: Installation and configuration
5
addpath /Applications/Dynare/4.x.y/matlab
If you are using an Octave version strictly older than 3.2.0, you will also want to tell to Octave
to accept the short syntax (without parentheses and quotes) for the dynare command, by typing:
mark_as_command dynare
If you don’t want to type this command every time you run Octave, you can put it in a file
called ‘.octaverc’ in your home directory (under Windows this will generally by ‘c:\Documents
and Settings\USERNAME\’). This file is run by Octave at every startup.
2.3.3 Some words of warning
You should be very careful about the content of your MATLAB or Octave path. You can display
its content by simply typing path in the command window.
The path should normally contain system directories of MATLAB or Octave, and some subdirectories of your Dynare installation. You have to manually add the ‘matlab’ subdirectory, and
Dynare will automatically add a few other subdirectories at runtime (depending on your configuration). You must verify that there is no directory coming from another version of Dynare than
the one you are planning to use.
You have to be aware that adding other directories to your path can potentially create problems,
if some of your M-files have the same names than Dynare files. Your files would then override Dynare
files, and make Dynare unusable.
Chapter 3: Dynare invocation
6
3 Dynare invocation
In order to give instructions to Dynare, the user has to write a model file whose filename extension
must be ‘.mod’. This file contains the description of the model and the computing tasks required
by the user. Its contents is described in Chapter 4 [The Model file], page 9.
Once the model file is written, Dynare is invoked using the dynare command at the MATLAB
or Octave prompt (with the filename of the ‘.mod’ given as argument).
In practice, the handling of the model file is done in two steps: in the first one, the model
and the processing instructions written by the user in a model file are interpreted and the proper
MATLAB or GNU Octave instructions are generated; in the second step, the program actually
runs the computations. Boths steps are triggered automatically by the dynare command.
dynare FILENAME[.mod] [OPTIONS . . . ]
[MATLAB/Octave command]
Description
This command launches Dynare and executes the instructions included in ‘FILENAME.mod’. This
user-supplied file contains the model and the processing instructions, as described in Chapter 4
[The Model file], page 9.
dynare begins by launching the preprocessor on the ‘.mod’ file. By default (unless use_dll
option has been given to model), the preprocessor creates three intermediary files:
‘FILENAME.m’
Contains variable declarations, and computing tasks
‘FILENAME_dynamic.m’
Contains the dynamic model equations
‘FILENAME_static.m’
Contains the long run static model equations
These files may be looked at to understand errors reported at the simulation stage.
dynare will then run the computing tasks by executing ‘FILENAME.m’.
Options
noclearall
By default, dynare will issue a clear all command to MATLAB or Octave, thereby
deleting all workspace variables; this options instructs dynare not to clear the
workspace
debug
Instructs the preprocessor to write some debugging information about the scanning
and parsing of the ‘.mod’ file
notmpterms
Instructs the preprocessor to omit temporary terms in the static and dynamic files;
this generally decreases performance, but is used for debugging purposes since it
makes the static and dynamic files more readable
savemacro[=FILENAME]
Instructs dynare to save the intermediary file which is obtained after macroprocessing (see Section 4.20 [Macro-processing language], page 77); the saved output
will go in the file specified, or if no file is specified in ‘FILENAME-macroexp.mod’
onlymacro
Instructs the preprocessor to only perform the macro-processing step, and stop
just after. Mainly useful for debugging purposes or for using the macro-processor
independently of the rest of Dynare toolbox.
Chapter 3: Dynare invocation
7
nolinemacro
Instructs the macro-preprocessor to omit line numbering information in the intermediary ‘.mod’ file created after the maco-processing step. Useful in conjunction
with savemacro when one wants that to reuse the intermediary ‘.mod’ file, without
having it cluttered by line numbering directives.
nolog
Instructs Dynare to no create a logfile of this run in ‘FILENAME.log’. The default
is to create the logfile.
warn_uninit
Display a warning for each variable or parameter which is not initialized. See
Section 4.4 [Parameter initialization], page 15, or [load params and steady state],
page 83 for initialization of parameters. See Section 4.7 [Initial and terminal conditions], page 19, or [load params and steady state], page 83 for initialization of
endogenous and exogenous variables.
console
Activate console mode: Dynare will not use graphical waitbars for long computations. Note that this option is only useful under MATLAB, since Octave does not
provide graphical waitbar capabilities.
cygwin
Tells Dynare that your MATLAB is configured for compiling MEX files with Cygwin
(see Section 2.1 [Software requirements], page 3). This option is only available under
Windows, and is used in conjunction with use_dll.
msvc
Tells Dynare that your MATLAB is configured for compiling MEX files with Microsoft Visual C++ (see Section 2.1 [Software requirements], page 3). This option is
only available under Windows, and is used in conjunction with use_dll.
parallel[=CLUSTER_NAME]
Tells Dynare to perform computations in parallel. If CLUSTER NAME is passed,
Dynare will use the specified cluster to perform parallel computations. Otherwise,
Dynare will use the first cluster specified in the configuration file. See Chapter 5
[The Configuration File], page 84, for more information about the configuration file.
conffile=FILENAME
Specifies the location of the configuration file if it differs from the default. See
Chapter 5 [The Configuration File], page 84, for more information about the configuration file and its default location.
parallel_slave_open_mode
Instructs Dynare to leave the connection to the slave node open after computation
is complete, closing this connection only when Dynare finishes processing.
parallel_test
Tests the parallel setup specified in the configuration file without executing the
‘.mod’ file. See Chapter 5 [The Configuration File], page 84, for more information
about the configuration file.
-DMACRO_VARIABLE=MACRO_EXPRESSION
Defines a macro-variable from the command line (the same effect as using the Macro
directive @#define in a model file, see Section 4.20 [Macro-processing language],
page 77).
Output
Depending on the computing tasks requested in the ‘.mod’ file, executing command dynare will
leave in the workspace variables containing results available for further processing. More details
are given under the relevant computing tasks.
The M_, oo_ and options_ structures are also saved in a file called ‘FILENAME_results.mat’.
Chapter 3: Dynare invocation
8
Example
dynare ramst
dynare ramst.mod savemacro
The output of Dynare is left into three main variables in the MATLAB/Octave workspace:
[MATLAB/Octave variable]
M_
Structure containing various informations about the model.
[MATLAB/Octave variable]
Structure contains the values of the various options used by Dynare during the computation.
options_
oo_
Structure containing the various results of the computations.
[MATLAB/Octave variable]
Chapter 4: The Model file
9
4 The Model file
4.1 Conventions
A model file contains a list of commands and of blocks. Each command and each element of a
block is terminated by a semicolon (;). Blocks are terminated by end;.
Most Dynare commands have arguments and several accept options, indicated in parentheses
after the command keyword. Several options are separated by commas.
In the description of Dynare commands, the following conventions are observed:
• optional arguments or options are indicated between square brackets: ‘[]’;
• repreated arguments are indicated by ellipses: “. . . ”;
• mutually exclusive arguments are separated by vertical bars: ‘|’;
• INTEGER indicates an integer number;
• DOUBLE indicates a double precision number. The following syntaxes are valid: 1.1e3,
1.1E3, 1.1d3, 1.1D3;
• NUMERICAL VECTOR indicates a vector of numbers separated by spaces, enclosed by square
brackets;
• EXPRESSION indicates a mathematical expression valid outside the model description (see
Section 4.3 [Expressions], page 12);
• MODEL EXPRESSION indicates a mathematical expression valid in the model description
(see Section 4.3 [Expressions], page 12 and Section 4.5 [Model declaration], page 16);
• MACRO EXPRESSION designates an expression of the macro-processor (see Section 4.20.1
[Macro expressions], page 77);
• VARIABLE NAME indicates a variable name starting with an alphabetical character and
can’t contain: ‘()+-*/^=!;:@#.’ or accentuated characters;
• PARAMETER NAME indicates a parameter name starting with an alphabetical character
and can’t contain: ‘()+-*/^=!;:@#.’ or accentuated characters;
• LATEX NAME indicates a valid LaTeX expression in math mode (not including the dollar
signs);
• FUNCTION NAME indicates a valid MATLAB function name;
• FILENAME indicates a filename valid in the underlying operating system; it is necessary to put
it between quotes when specifying the extension or if the filename contains a non-alphanumeric
character;
4.2 Variable declarations
Declarations of variables and parameters are made with the following commands:
var VARIABLE_NAME [$LATEX_NAME$] . . . ;
var (deflator = MODEL_EXPRESSION) VARIABLE_NAME [$LATEX_NAME$] . . . ;
[Command]
[Command]
Description
This required command declares the endogenous variables in the model. See Section 4.1 [Conventions], page 9, for the syntax of VARIABLE NAME and MODEL EXPRESSION. Optionally
it is possible to give a LaTeX name to the variable or, if it is nonstationary, provide information
regarding its deflator.
var commands can appear several times in the file and Dynare will concatenate them.
Options
Chapter 4: The Model file
10
If the model is nonstationary and is to be written as such in the model block, Dynare will need
the trend deflator for the appropriate endogenous variables in order to stationarize the model.
The trend deflator must be provided alongside the variables that follow this trend.
deflator = MODEL_EXPRESSION
The expression used to detrend an endogenous variable. All trend variables, endogenous variables and parameters referenced in MODEL EXPRESSION must already
have been declared by the trend_var, var and parameters commands.
Example
var c gnp q1 q2;
var(deflator=A) i b;
varexo VARIABLE_NAME [$LATEX_NAME$] . . . ;
[Command]
Description
This optional command declares the exogenous variables in the model. See Section 4.1 [Conventions], page 9, for the syntax of VARIABLE NAME. Optionally it is possible to give a LaTeX
name to the variable.
Exogenous variables are required if the user wants to be able to apply shocks to her model.
varexo commands can appear several times in the file and Dynare will concatenate them.
Example
varexo m gov;
varexo_det VARIABLE_NAME [$LATEX_NAME$] . . . ;
[Command]
Description
This optional command declares exogenous deterministic variables in a stochastic model. See
Section 4.1 [Conventions], page 9, for the syntax of VARIABLE NAME. Optionally it is possible
to give a LaTeX name to the variable.
It is possible to mix deterministic and stochastic shocks to build models where agents know
from the start of the simulation about future exogenous changes. In that case stoch_simul will
compute the rational expectation solution adding future information to the state space (nothing
is shown in the output of stoch_simul) and forecast will compute a simulation conditional
on initial conditions and future information.
varexo_det commands can appear several times in the file and Dynare will concatenate them.
Example
varexo m gov;
varexo_det tau;
parameters PARAMETER_NAME [$LATEX_NAME$] . . . ;
[Command]
Description
This command declares parameters used in the model, in variable initialization or in shocks
declarations. See Section 4.1 [Conventions], page 9, for the syntax of PARAMETER NAME.
Optionally it is possible to give a LaTeX name to the parameter.
Chapter 4: The Model file
11
The parameters must subsequently be assigned values (see Section 4.4 [Parameter initialization],
page 15).
parameters commands can appear several times in the file and Dynare will concatenate them.
Example
parameters alpha, bet;
change_type (var | varexo | varexo det | parameters) VARIABLE_NAME |
PARAMETER_NAME . . . ;
[Command]
Description
Changes the types of the specified variables/parameters to another type: endogenous, exogenous,
exogenous deterministic or parameter.
It is important to understand that this command has a global effect on the ‘.mod’ file: the type
change is effective after, but also before, the change_type command. This command is typically
used when flipping some variables for steady state calibration: typically a separate model file is
used for calibration, which includes the list of variable declarations with the macro-processor,
and flips some variable.
Example
var y, w;
parameters alpha, bet;
...
change_type(var) alpha, bet;
change_type(parameters) y, w;
Here, in the whole model file, alpha and beta will be endogenous and y and w will be parameters.
predetermined_variables VARIABLE_NAME . . . ;
[Command]
Description
In Dynare, the default convention is that the timing of a variable reflects when this variable
is decided. The typical example is for capital stock: since the capital stock used at current
period is actually decided at the previous period, then the capital stock entering the production
function is k(-1), and the law of motion of capital must be written:
k = i + (1-delta)*k(-1)
Put another way, for stock variables, the default in Dynare is to use a “stock at the end of the
period” concept, instead of a “stock at the beginning of the period” convention.
The predetermined_variables is used to change that convention. The endogenous variables
declared as predetermined variables are supposed to be decided one period ahead of all other
endogenous variables. For stock variables, they are supposed to follow a “stock at the beginning
of the period” convention.
Example
The following two program snippets are strictly equivalent.
Using default Dynare timing convention:
var y, k, i;
...
model;
y = k(-1)^alpha;
k = i + (1-delta)*k(-1);
Chapter 4: The Model file
12
...
end;
Using the alternative timing convention:
var y, k, i;
predetermined_variables k;
...
model;
y = k^alpha;
k(+1) = i + (1-delta)*k;
...
end;
trend_var (growth factor = MODEL_EXPRESSION) VARIABLE_NAME
[$LATEX_NAME$] . . . ;
[Command]
Description
This optional command declares the trend variables in the model. See Section 4.1 [Conventions],
page 9, for the syntax of MODEL EXPRESSION and VARIABLE NAME. Optionally it is
possible to give a LaTeX name to the variable.
Trend variables are required if the user wants to be able to write a nonstationary model in the
model block. The trend_var command must appear before the var command that references
the trend variable.
trend_var commands can appear several times in the file and Dynare will concatenate them.
If the model is nonstationary and is to be written as such in the model block, Dynare will
need the growth factor of every trend variable in order to stationarize the model. The growth
factor must be provided within the declaration of the trend variable, using the growth_factor
keyword. All endogenous variables and parameters referenced in MODEL EXPRESSION must
already have been declared by the var and parameters commands.
Example
trend_var (growth_factor=gA) A;
4.3 Expressions
Dynare distinguishes between two types of mathematical expressions: those that are used to describe the model, and those that are used outside the model block (e.g. for initializing parameters or
variables, or as command options). In this manual, those two types of expressions are respectively
denoted by MODEL EXPRESSION and EXPRESSION.
Unlike MATLAB or Octave expressions, Dynare expressions are necessarily scalar ones: they
cannot contain matrices or evaluate to matrices1 .
Expressions can be constructed using integers (INTEGER), floating point numbers (DOUBLE),
parameter names (PARAMETER NAME), variable names (VARIABLE NAME), operators and
functions.
The following special constants are also accepted in some contexts:
inf
[Constant]
Represents infinity.
1
Note that arbitrary MATLAB or Octave expressions can be put in a ‘.mod’ file, but those expressions have to
be on separate lines, generally at the end of the file for post-processing purposes. They are not interpreted by
Dynare, and are simply passed on unmodified to MATLAB or Octave. Those constructions are not addresses in
this section.
Chapter 4: The Model file
nan
13
[Constant]
“Not a number”: represents an undefined or unrepresentable value.
4.3.1 Parameters and variables
Parameters and variables can be introduced in expressions by simply typing their names. The
semantics of parameters and variables is quite different whether they are used inside or outside the
model block.
4.3.1.1 Inside the model
Parameters used inside the model refer to the value given through parameter initialization (see
Section 4.4 [Parameter initialization], page 15) or homotopy_setup when doing a simulation, or are
the estimated variables when doing an estimation.
Variables used in a MODEL EXPRESSION denote current period values when neither a lead
or a lag is given. A lead or a lag can be given by enclosing an integer between parenthesis just after
the variable name: a positive integer means a lead, a negative one means a lag. Leads or lags of
more than one period are allowed. For example, if c is an endogenous variable, then c(+1) is the
variable one period ahead, and c(-2) is the variable two periods before.
When specifying the leads and lags of endogenous variables, it is important to respect the
following convention: in Dynare, the timing of a variable reflects when that variable is decided. A
control variable — which by definition is decided in the current period — must have no lead. A
predetermined variable — which by definition has been decided in a previous period — must have
a lag. A consequence of this is that all stock variables must use the “stock at the end of the period”
convention. Please refer to Mancini-Griffoli (2007) for more details and concrete examples.
Leads and lags are primarily used for endogenous variables, but can be used for exogenous
variables. They have no effect on parameters and are forbidden for local model variables (see
Section 4.5 [Model declaration], page 16).
4.3.1.2 Outside the model
When used in an expression outside the model block, a parameter or a variable simply refers to
the last value given to that variable. More precisely, for a parameter it refers to the value given
in the corresponding parameter initialization (see Section 4.4 [Parameter initialization], page 15);
for an endogenous or exogenous variable, it refers to the value given in the most recent initval or
endval block.
4.3.2 Operators
The following operators are allowed in both MODEL EXPRESSION and EXPRESSION :
• binary arithmetic operators: +, -, *, /, ^
• unary arithmetic operators: +, • binary comparison operators (which evaluate to either 0 or 1): <, >, <=, >=, ==, !=
The following special operators are accepted in MODEL EXPRESSION (but not in EXPRESSION ):
STEADY_STATE (MODEL_EXPRESSION)
[Operator]
This operator is used to take the value of the enclosed expression at the steady state. A typical
usage is in the Taylor rule, where you may want to use the value of GDP at steady state to
compute the output gap.
EXPECTATION (INTEGER) (MODEL_EXPRESSION)
[Operator]
This operator is used to take the expectation of some expression using a different information
set than the information available at current period. For example, EXPECTATION(-1)(x(+1))
is equal to the expected value of variable x at next period, using the information set available
Chapter 4: The Model file
14
at the previous period. See Section 4.6 [Auxiliary variables], page 19, for an explanation of how
this operator is handled internally and how this affects the output.
4.3.3 Functions
4.3.3.1 Built-in Functions
The following standard functions are supported internally for both MODEL EXPRESSION and
EXPRESSION :
exp (x)
[Function]
Natural exponential.
log (x)
ln (x)
[Function]
[Function]
Natural logarithm.
log10 (x)
[Function]
Base 10 logarithm.
sqrt (x)
[Function]
Square root.
abs (x)
[Function]
Absolute value.
sign (x)
[Function]
Signum function.
sin (x)
cos (x)
tan (x)
asin (x)
acos (x)
atan (x)
[Function]
[Function]
[Function]
[Function]
[Function]
[Function]
Trigonometric functions.
max (a, b)
min (a, b)
[Function]
[Function]
Maximum and minimum of two reals.
normcdf (x)
normcdf (x, mu, sigma)
[Function]
[Function]
Gaussian cumulative density function, with mean mu and standard deviation sigma. Note that
normcdf(x) is equivalent to normcdf(x,0,1).
normpdf (x)
normpdf (x, mu, sigma)
[Function]
[Function]
Gaussian probability density function, with mean mu and standard deviation sigma. Note that
normpdf(x) is equivalent to normpdf(x,0,1).
erf (x)
Gauss error function.
[Function]
Chapter 4: The Model file
15
4.3.3.2 External Functions
Any other user-defined (or built-in) MATLAB or Octave function may be used in both a
MODEL EXPRESSION and an EXPRESSION, provided that this function has a scalar argument as a return value.
To use an external function in a MODEL EXPRESSION, one must declare the function using the external_function statement. This is not necessary for external functions used in an
EXPRESSION.
external_function (OPTIONS . . . );
[Command]
Description
This command declares the external functions used in the model block. It is required for every
unique function used in the model block.
external_function commands can appear several times in the file and must come before the
model block.
Options
name = NAME
The name of the function, which must also be the name of the M-/MEX file implementing it. This option is mandatory.
nargs = INTEGER
The number of arguments of the function. If this option is not provided, Dynare
assumes nargs = 1.
first_deriv_provided [= NAME]
If NAME is provided, this tells Dynare that the Jacobian is provided as the only
output of the M-/MEX file given as the option argument. If NAME is not provided,
this tells Dynare that the M-/MEX file specified by the argument passed to name
returns the Jacobian as its second output argument.
second_deriv_provided [= NAME]
If NAME is provided, this tells Dynare that the Hessian is provided as the only
output of the M-/MEX file given as the option argument. If NAME is not provided,
this tells Dynare that the M-/MEX file specified by the argument passed to name
returns the Hessian as its third output argument. NB: This option can only be
used if the first_deriv_provided option is used in the same external_function
command.
Example
external_function(name = funcname);
external_function(name = otherfuncname, nargs = 2,
first_deriv_provided, second_deriv_provided);
external_function(name = yetotherfuncname, nargs = 3,
first_deriv_provided = funcname_deriv);
4.4 Parameter initialization
When using Dynare for computing simulations, it is necessary to calibrate the parameters of the
model. This is done through parameter initialization.
The syntax is the following:
PARAMETER_NAME = EXPRESSION;
Here is an example of calibration:
Chapter 4: The Model file
16
parameters alpha, bet;
beta = 0.99;
alpha = 0.36;
A = 1-alpha*beta;
Internally, the parameter values are stored in M_.params:
[MATLAB/Octave variable]
Contains the values of model parameters. The parameters are in the order that was used in the
parameters command.
M_.params
4.5 Model declaration
The model is declared inside a model block:
model ;
model (OPTIONS . . . );
[Block]
[Block]
Description
The equations of the model are written in a block delimited by model and end keywords.
There must be as many equations as there are endogenous variables in the model, except when
computing the unconstrained optimal policy with ramsey_policy or discretionary_policy.
The syntax of equations must follow the conventions for MODEL EXPRESSION as described
in Section 4.3 [Expressions], page 12. Each equation must be terminated by a semicolon (‘;’).
A normal equation looks like:
MODEL_EXPRESSION = MODEL_EXPRESSION;
When the equations are written in homogenous form, it is possible to omit the ‘=0’ part and
write only the left hand side of the equation. A homogenous equation looks like:
MODEL_EXPRESSION;
Inside the model block, Dynare allows the creation of model-local variables, which constitute a
simple way to share a common expression between several equations. The syntax consists of a
pound sign (#) followed by the name of the new model local variable (which must not be declared
as in Section 4.2 [Variable declarations], page 9), an equal sign, and the expression for which
this new variable will stand. Later on, every time this variable appears in the model, Dynare
will substitute it by the expression assigned to the variable. Note that the scope of this variable
is restricted to the model block; it cannot be used outside. A model local variable declaration
looks like:
# VARIABLE_NAME = MODEL_EXPRESSION;
Options
2
linear
Declares the model as being linear. It spares oneself from having to declare initial
values for computing the steady state, and it sets automatically order=1 in stoch_
simul.
use_dll
Instructs the preprocessor to create dynamic loadable libraries (DLL) containing
the model equations and derivatives, instead of writing those in M-files. You need
a working compilation environment, i.e. a working mex command (see Section 2.1
[Software requirements], page 3 for more details). Using this option can result in
faster simulations or estimations, at the expense of some initial compilation time.2
In particular, for big models, the compilation step can be very time-consuming, and use of this option may be
counter-productive in those cases.
Chapter 4: The Model file
17
block
Perform the block decomposition of the model, and exploit it in computations
(steady-state, deterministic simulation, stochastic simulation with first order approximation and estimation). See Dynare wiki for details on the algorithms used in
deterministic simulation and steady-state computation.
bytecode
Instead of M-files, use a bytecode representation of the model, i.e. a binary file
containing a compact representation of all the equations.
cutoff = DOUBLE
Threshold under which a jacobian element is considered as null during the model
normalization. Only available with option block. Default: 1e-15
mfs = INTEGER
Controls the handling of minimum feedback set of endogenous variables. Only available with option block. Possible values:
0
All the endogenous variables are considered as feedback variables (Default).
1
The endogenous variables assigned to equation naturally normalized
(i.e. of the form x = f (Y ) where x does not appear in Y ) are potentially
recursive variables. All the other variables are forced to belong to the
set of feedback variables.
2
In addition of variables with mfs = 1 the endogenous variables related
to linear equations which could be normalized are potential recursive
variables. All the other variables are forced to belong to the set of
feedback variables.
3
In addition of variables with mfs = 2 the endogenous variables related to
non-linear equations which could be normalized are potential recursive
variables. All the other variables are forced to belong to the set of
feedback variables.
no_static
Don’t create the static model file. This can be useful for models which don’t have
a steady state.
Example 1: elementary RBC model
var c k;
varexo x;
parameters aa alph bet delt gam;
model;
c = - k + aa*x*k(-1)^alph + (1-delt)*k(-1);
c^(-gam) = (aa*alph*x(+1)*k^(alph-1) + 1 - delt)*c(+1)^(-gam)/(1+bet);
end;
Example 2: use of model local variables
The following program:
model;
# gamma = 1 - 1/sigma;
u1 = c1^gamma/gamma;
u2 = c2^gamma/gamma;
end;
. . . is formally equivalent to:
Chapter 4: The Model file
18
model;
u1 = c1^(1-1/sigma)/(1-1/sigma);
u2 = c2^(1-1/sigma)/(1-1/sigma);
end;
Example 3: a linear model
model(linear);
x = a*x(-1)+b*y(+1)+e_x;
y = d*y(-1)+e_y;
end;
Dynare has the ability to output the list of model equations to a LaTeX file, using the write_
latex_dynamic_model command. The static model can also be written with the write_latex_
static_model command.
write_latex_dynamic_model ;
[Command]
Description
This command creates a LaTeX file containing the (dynamic) model.
If your ‘.mod’ file is ‘FILENAME.mod’, then Dynare will create a file called
‘FILENAME_dynamic.tex’, containing the list of all the dynamic model equations.
If LaTeX names were given for variables and parameters (see Section 4.2 [Variable declarations],
page 9), then those will be used; otherwise, the plain text names will be used.
Time subscripts (t, t+1, t-1, . . . ) will be appended to the variable names, as LaTeX subscripts.
Note that the model written in the TeX file will differ from the model declared by the user in
the following dimensions:
• the timing convention of predetermined variables (see [predetermined variables], page 11)
will have been changed to the default Dynare timing convention; in other words, variables
declared as predetermined will be lagged on period back,
• the expectation operators (see [expectation], page 13) will have been removed, replaced by
auxiliary variables and new equations as explained in the documentation of the operator,
• endogenous variables with leads or lags greater or equal than two will have been removed,
replaced by new auxiliary variables and equations,
• for a stochastic model, exogenous variables with leads or lags will also have been replaced
by new auxiliary variables and equations.
Compiling the TeX file requires the following Latex packages: geometry, fullpage, breqn.
write_latex_static_model ;
[Command]
Description
This command creates a LaTeX file containing the static model.
If your ‘.mod’ file is ‘FILENAME.mod’, then Dynare will create a file called
‘FILENAME_static.tex’, containing the list of all the equations of the steady state
model.
If LaTeX names were given for variables and parameters (see Section 4.2 [Variable declarations],
page 9), then those will be used; otherwise, the plain text names will be used.
Note that the model written in the TeX file will differ from the model declared by the user in
the some dimensions (see [write latex dynamic model], page 18 for details).
Also note that this command will not output the contents of the optional steady_state_model
block (see [steady state model], page 29); it will rather output a static version (i.e. without
leads and lags) of the dynamic model declared in the model block.
Chapter 4: The Model file
19
Compiling the TeX file requires the following Latex packages: geometry, fullpage, breqn.
4.6 Auxiliary variables
The model which is solved internally by Dynare is not exactly the model declared by the user.
In some cases, Dynare will introduce auxiliary endogenous variables—along with corresponding
auxiliary equations—which will appear in the final output.
The main transformation concerns leads and lags. Dynare will perform a transformation of the
model so that there is only one lead and one lag on endogenous variables and, in the case of a
stochastic model, no leads/lags on exogenous variables.
This transformation is achieved by the creation of auxiliary variables and corresponding equations. For example, if x(+2) exists in the model, Dynare will create one auxiliary variable AUX_
ENDO_LEAD = x(+1), and replace x(+2) by AUX_ENDO_LEAD(+1).
A similar transformation is done for lags greater than 2 on endogenous (auxiliary variables will
have a name beginning with AUX_ENDO_LAG), and for exogenous with leads and lags (auxiliary
variables will have a name beginning with AUX_EXO_LEAD or AUX_EXO_LAG respectively).
Another transformation is done for the EXPECTATION operator. For each occurence of this operator, Dynare creates an auxiliary variable defined by a new equation, and replaces the expectation
operator by a reference to the new auxiliary variable. For example, the expression EXPECTATION(1)(x(+1)) is replaced by AUX_EXPECT_LAG_1(-1), and the new auxiliary variable is declared as
AUX_EXPECT_LAG_1 = x(+2).
Auxiliary variables are also introduced by the preprocessor for the ramsey_policy command.
In this case, they are used to represent the Lagrange multipliers when first order conditions of the
Ramsey problem are computed. The new variables take the form MULT_i, where i represents the
constraint with which the multiplier is associated (counted from the order of declaration in the
model block).
Once created, all auxiliary variables are included in the set of endogenous variables. The output
of decision rules (see below) is such that auxiliary variable names are replaced by the original
variables they refer to.
The number of endogenous variables before the creation of auxiliary variables is stored in M_
.orig_endo_nbr, and the number of endogenous variables after the creation of auxiliary variables
is stored in M_.endo_nbr.
See Dynare Wiki for more technical details on auxiliary variables.
4.7 Initial and terminal conditions
For most simulation exercises, it is necessary to provide initial (and possibly terminal) conditions.
It is also necessary to provide initial guess values for non-linear solvers. This section describes the
statements used for those purposes.
In many contexts (determistic or stochastic), it is necessary to compute the steady state of a
non-linear model: initval then specifies numerical initial values for the non-linear solver. The
command resid can be used to compute the equation residuals for the given initial values.
Used in perfect foresight mode, the types of forward-loking models for which Dynare was designed require both initial and terminal conditions. Most often these initial and terminal conditions
are static equilibria, but not necessarily.
One typical application is to consider an economy at the equilibrium, trigger a shock in first
period, and study the trajectory of return at the initial equilbrium. To do that, one needs initval
and shocks (see Section 4.8 [Shocks on exogenous variables], page 23.
Another one is to study, how an economy, starting from arbitrary initial conditions converges
toward equilibrium. To do that, one needs initval and endval.
For models with lags on more than one period, the command histval permits to specify different
historical initial values for periods before the beginning of the simulation.
Chapter 4: The Model file
initval ;
20
[Block]
Description
The initval block serves two purposes: declaring the initial (and possibly terminal) conditions
in a simulation exercise, and providing guess values for non-linear solvers.
This block is terminated by end;, and contains lines of the form:
VARIABLE_NAME = EXPRESSION;
In a deterministic (i.e. perfect foresight) model
First, it provides the initial conditions for all the endogenous and exogenous variables at all the
periods preceeding the first simulation period (unless some of these initial values are modified
by histval).
Second, in the absence of an endval block, it sets the terminal conditions for all the periods
succeeding the last simulation period.
Third, in the absence of an endval block, it provides initial guess values at all simulation dates
for the non-linear solver implemented in simul.
For this last reason, it necessary to provide values for all the endogenous variables in an initval
block (even though, theoretically, initial conditions are only necessary for lagged variables). If
some variables, endogenous or exogenous, are not mentionned in the initval block, a zero value
is assumed.
Note that if the initval block is immediately followed by a steady command, its semantics is
changed. The steady command will compute the steady state of the model for all the endogenous
variables, assuming that exogenous variables are kept constant to the value declared in the
initval block, and using the values declared for the endogenous as initial guess values for the
non-linear solver. An initval block followed by steady is formally equivalent to an initval
block with the same values for the exogenous, and with the associated steady state values for
the endogenous.
In a stochastic model
The main purpose of initval is to provide initial guess values for the non-linear solver in
the steady state computation. Note that if the initval block is not followed by steady,
the steady state computation will still be triggered by subsequent commands (stoch_simul,
estimation. . . ).
It is not necessary to declare 0 as initial value for exogenous stochastic variables, since it is the
only possible value.
This steady state will be used as the initial condition at all the periods preceeding the first
simulation period for the two possible types of simulations in stochastic mode:
• in stoch_simul, if the periods options is specified
• in forecast (in this case, note that it is still possible to modify some of these initial values
with histval)
Example
initval;
c = 1.2;
k = 12;
x = 1;
end;
steady;
Chapter 4: The Model file
endval ;
21
[Block]
Description
This block is terminated by end;, and contains lines of the form:
VARIABLE_NAME = EXPRESSION;
The endval block makes only sense in a determistic model, and serves two purposes.
First, it sets the terminal conditions for all the periods succeeding the last simulation period.
Second, it provides initial guess values at all the simulation dates for the non-linear solver
implemented in simul.
For this last reason, it necessary to provide values for all the endogenous variables in an endval
block (even though, theoretically, initial conditions are only necessary for forward variables). If
some variables, endogenous or exogenous, are not mentionned in the endval block, a zero value
is assumed.
Note that if the endval block is immediately followed by a steady command, its semantics
is changed. The steady command will compute the steady state of the model for all the
endogenous variables, assuming that exogenous variables are kept constant to the value declared
in the endval block, and using the values declared for the endogenous as initial guess values for
the non-linear solver. An endval block followed by steady is formally equivalent to an endval
block with the same values for the exogenous, and with the associated steady state values for
the endogenous.
Example
var c k;
varexo x;
...
initval;
c = 1.2;
k = 12;
x = 1;
end;
steady;
endval;
c = 2;
k = 20;
x = 2;
end;
steady;
The initial equilibrium is computed by steady for x=1, and the terminal one, for x=2.
histval ;
[Block]
Description
In models with lags on more than one period, the histval block permits to specify different
historical initial values for different periods.
This block is terminated by end;, and contains lines of the form:
VARIABLE_NAME(INTEGER) = EXPRESSION;
Chapter 4: The Model file
22
EXPRESSION is any valid expression returning a numerical value and can contain already
initialized variable names.
By convention in Dynare, period 1 is the first period of the simulation. Going backward in time,
the first period before the start of the simulation is period 0, then period -1, and so on.
If your lagged variables are linked by identities, be careful to satisfy these identities when you
set historical initial values.
Variables not initialized in the histval block are assumed to have a value of zero at period 0
and before. Note that this behavior differs from the case where there is no histval block, where
all variables are initialized at their steady state value at period 0 and before (except when a
steady command doesn’t follow an initval block).
Example
var x y;
varexo e;
model;
x = y(-1)^alpha*y(-2)^(1-alpha)+e;
...
end;
initval;
x = 1;
y = 1;
e = 0.5;
end;
steady;
histval;
y(0) = 1.1;
y(-1) = 0.9;
end;
resid ;
[Command]
This command will display the residuals of the static equations of the model, using the values
given for the endogenous in the last initval or endval block (or the steady state file if you
provided one, see Section 4.10 [Steady state], page 26).
initval_file (filename = FILENAME);
[Command]
Description
In a deterministic setup, this command is used to specify a path for all endogenous and exogenous
variables. The length of these paths must be equal to the number of simulation periods, plus the
number of leads and the number of lags of the model (for example, with 50 simulation periods,
in a model with 2 lags and 1 lead, the paths must have a length of 53). Note that these paths
cover two different things:
• the constraints of the problem, which are given by the path for exogenous and the initial
and terminal values for endogenous
• the initial guess for the non-linear solver, which is given by the path for endogenous variables
for the simulation periods (excluding initial and terminal conditions)
The command accepts three file formats:
Chapter 4: The Model file
23
• M-file (extension ‘.m’): for each endogenous and exogenous variable, the file must contain
a row vector of the same name.
• MAT-file (extension ‘.mat’): same as for M-files.
• Excel file (extension ‘.xls’): for each endogenous and exogenous, the file must contain
a column of the same name (supported under Octave if the io and java packages from
Octave-Forge are installed, along with a Java Runtime Environment).
Warning
The extension must be omitted in the command argument. Dynare will automatically figure
out the extension and select the appropriate file type.
4.8 Shocks on exogenous variables
In a deterministic context, when one wants to study the transition of one equilibrium position to
another, it is equivalent to analyze the consequences of a permanent shock and this in done in
Dynare through the proper use of initval and endval.
Another typical experiment is to study the effects of a temporary shock after which the system
goes back to the original equilibrium (if the model is stable. . . ). A temporary shock is a temporary
change of value of one or several exogenous variables in the model. Temporary shocks are specified
with the command shocks.
In a stochastic framework, the exogenous variables take random values in each period. In
Dynare, these random values follow a normal distribution with zero mean, but it belongs to the
user to specify the variability of these shocks. The non-zero elements of the matrix of variancecovariance of the shocks can be entered with the shocks command. Or, the entire matrix can be
direclty entered with Sigma_e (this use is however deprecated).
If the variance of an exogenous variable is set to zero, this variable will appear in the report
on policy and transition functions, but isn’t used in the computation of moments and of Impulse
Response Functions. Setting a variance to zero is an easy way of removing an exogenous shock.
shocks ;
[Block]
In deterministic context
For deterministic simulations, the shocks block specifies temporary changes in the value of
exogenous variables. For permanent shocks, use an endval block.
The block should contain one or more occurrences of the following group of three lines:
var VARIABLE_NAME;
periods INTEGER[:INTEGER] [[,] INTEGER[:INTEGER]]...;
values DOUBLE | (EXPRESSION) [[,] DOUBLE | (EXPRESSION) ]...;
It is possible to specify shocks which last several periods and which can vary over time. The
periods keyword accepts a list of several dates or date ranges, which must be matched by as
many shock values in the values keyword. Note that a range in the periods keyword can be
matched by only one value in the values keyword. If values represents a scalar, the same value
applies to the whole range. If values represents a vector, it must have as many elements as
there are periods in the range.
Note that shock values are not restricted to numerical constants: arbitrary expressions are also
allowed, but you have to enclose them inside parentheses.
Here is an example:
shocks;
var e;
periods 1;
Chapter 4: The Model file
24
values 0.5;
var u;
periods 4:5;
values 0;
var v;
periods 4:5 6 7:9;
values 1 1.1 0.9;
var w;
periods 1 2;
values (1+p) (exp(z));
end;
A second example with a vector of values:
xx = [1.2; 1.3; 1];
shocks;
var e;
periods 1:3;
values (xx);
end;
In stochastic context
For stochastic simulations, the shocks block specifies the non zero elements of the covariance
matrix of the shocks of exogenous variables.
You can use the following types of entries in the block:
var VARIABLE_NAME; stderr EXPRESSION;
Specifies the standard error of a variable.
var VARIABLE_NAME = EXPRESSION;
Specifies the variance error of a variable.
var VARIABLE_NAME, VARIABLE_NAME = EXPRESSION;
Specifies the covariance of two variables.
corr VARIABLE_NAME, VARIABLE_NAME = EXPRESSION;
Specifies the correlation of two variables.
In an estimation context, it is also possible to specify variances and covariances on endogenous
variables: in that case, these values are interpreted as the calibration of the measurement errors
on these variables.
Here is an example:
shocks;
var e = 0.000081;
var u; stderr 0.009;
corr e, u = 0.8;
var v, w = 2;
end;
Mixing determininistic and stochastic shocks
It is possible to mix deterministic and stochastic shocks to build models where agents know
from the start of the simulation about future exogenous changes. In that case stoch_simul will
compute the rational expectation solution adding future information to the state space (nothing
is shown in the output of stoch_simul) and forecast will compute a simulation conditional
on initial conditions and future information.
Chapter 4: The Model file
25
Here is an example:
varexo_det tau;
varexo e;
...
shocks;
var e; stderr 0.01;
var tau;
periods 1:9;
values -0.15;
end;
stoch_simul(irf=0);
forecast;
mshocks ;
[Block]
The purpose of this block is similar to that of the shocks block for deterministic shocks, except
that the numeric values given will be interpreted in a multiplicative way. For example, if a value
of 1.05 is given as shock value for some exogenous at some date, it means 5% above its steady
state value (as given by the last initval or endval block).
The syntax is the same than shocks in a deterministic context.
This command is only meaningful in two situations:
• on exogenous variables with a non-zero steady state, in a deterministic setup,
• on deterministic exogenous variables with a non-zero steady state, in a stochastic setup.
Sigma_e
[Special variable]
Warning
The use of this special variable is deprecated and is strongly discouraged. You should use a
shocks block instead.
Description
This special variable specifies directly the covariance matrix of the stochastic shocks, as an upper
(or lower) triangular matrix. Dynare builds the corresponding symmetrix matrix. Each row of
the triangular matrix, except the last one, must be terminated by a semi-colon ;. For a given
element, an arbitrary EXPRESSION is allowed (instead of a simple constant), but in that case
you need to enclose the expression in parentheses. The order of the covariances in the matrix is
the same as the one used in the varexo declaration.
Example
varexo u, e;
...
Sigma_e = [ 0.81 (phi*0.9*0.009);
0.000081];
This sets the variance of u to 0.81, the variance of e to 0.000081, and the correlation between e
and u to phi.
Chapter 4: The Model file
26
4.9 Other general declarations
dsample INTEGER [INTEGER];
[Command]
Reduces the number of periods considered in subsequent output commands.
periods INTEGER;
[Command]
Description
This command is now deprecated (but will still work for older model files). It is not necessary
when no simulation is performed and is replaced by an option periods in simul and stoch_
simul.
This command sets the number of periods in the simulation. The periods are numbered from 1
to INTEGER. In perfect foresight simulations, it is assumed that all future events are perfectly
known at the beginning of period 1.
Example
periods 100;
4.10 Steady state
There are two ways of computing the steady state (i.e. the static equilibrium) of a model. The first
way is to let Dynare compute the steady state using a nonlinear Newton-type solver; this should
work for most models, and is relatively simple to use. The second way is to give more guidance to
Dynare, using your knowledge of the model, by providing it with a “steady state file”.
4.10.1 Finding the steady state with Dynare nonlinear solver
steady ;
steady (OPTIONS . . . );
[Command]
[Command]
Description
This command computes the steady state of a model using a nonlinear Newton-type solver and
displays it. When a steady state file is used steady displays the steady state and checks that it
is a solution of the static model.
More precisely, it computes the equilibrium value of the endogenous variables for the value of
the exogenous variables specified in the previous initval or endval block.
steady uses an iterative procedure and takes as initial guess the value of the endogenous variables
set in the previous initval or endval block.
For complicated models, finding good numerical initial values for the endogenous variables is
the trickiest part of finding the equilibrium of that model. Often, it is better to start with a
smaller model and add new variables one by one.
Options
maxit = INTEGER
Determines the maximum number of iterations used in the non-linear solver. The
default value of maxit is 10. The maxit option is shared with the simul command.
So a change in maxit in a steady command will also be considered in the following
simul commands.
solve_algo = INTEGER
Determines the non-linear solver to use. Possible values for the option are:
Chapter 4: The Model file
27
0
Use fsolve (under MATLAB, only available if you have the Optimization Toolbox; always available under Octave)
1
Use Dynare’s own nonlinear equation solver
2
Splits the model into recursive blocks and solves each block in turn
3
Use Chris Sims’ solver
4
Similar to value 2, except that it deals differently with nearly singular
Jacobian
5
Newton algorithm with a sparse Gaussian elimination (SPE) (requires
bytecode option, see Section 4.5 [Model declaration], page 16)
6
Newton algorithm with a sparse LU solver at each iteration (requires
bytecode and/or block option, see Section 4.5 [Model declaration],
page 16)
7
Newton algorithm with a Generalized Minimal Residual (GMRES)
solver at each iteration (requires bytecode and/or block option, see
Section 4.5 [Model declaration], page 16; not available under Octave)
8
Newton algorithm with a Stabilized Bi-Conjugate Gradient
(BICGSTAB) solver at each iteration (requires bytecode and/or
block option, see Section 4.5 [Model declaration], page 16)
Default value is 2.
homotopy_mode = INTEGER
Use a homotopy (or divide-and-conquer) technique to solve for the steady state. If
you use this option, you must specify a homotopy_setup block. This option can
take three possible values:
1
In this mode, all the parameters are changed simultaneously, and the
distance between the boudaries for each parameter is divided in as many
intervals as there are steps (as defined by homotopy_steps option); the
problem is solves as many times as there are steps.
2
Same as mode 1, except that only one parameter is changed at a time;
the problem is solved as many times as steps times number of parameters.
3
Dynare tries first the most extreme values. If it fails to compute the
steady state, the interval between initial and desired values is divided by
two for all parameters. Every time that it is impossible to find a steady
state, the previous interval is divided by two. When it succeeds to find
a steady state, the previous interval is multiplied by two. In that last
case homotopy_steps contains the maximum number of computations
attempted before giving up.
homotopy_steps = INTEGER
Defines the number of steps when performing a homotopy. See homotopy_mode
option for more details.
homotopy_force_continue = INTEGER
This option controls what happens when homotopy fails.
0
steady fails with an error message
1
steady keeps the values of the last homotopy step that was successful
and continues. BE CAREFUL: parameters and/or exogenous variables
are NOT at the value expected by the user
Chapter 4: The Model file
28
Default is 0.
nocheck
Don’t check the steady state values when they are provided explicitely either by a
steady state file or a steady_state_model block. This is useful for models with
unit roots as, in this case, the steady state is not unique or doesn’t exist.
Example
See Section 4.7 [Initial and terminal conditions], page 19.
After computation, the steady state is available in the following variable:
oo_.steady_state
[MATLAB/Octave variable]
Contains the computed steady state.
Endogenous variables are ordered in order of declaration used in var command (which is also
the order used in M_.endo_names).
homotopy_setup ;
[Block]
Description
This block is used to declare initial and final values when using a homotopy method. It is used
in conjunction with the option homotopy_mode of the steady command.
The idea of homotopy (also called divide-and-conquer by some authors) is to subdivide the
problem of finding the steady state into smaller problems. It assumes that you know how to
compute the steady state for a given set of parameters, and it helps you finding the steady state
for another set of parameters, by incrementally moving from one to another set of parameters.
The purpose of the homotopy_setup block is to declare the final (and possibly also the initial)
values for the parameters or exogenous that will be changed during the homotopy. It should
contain lines of the form:
VARIABLE_NAME, EXPRESSION, EXPRESSION;
This syntax specifies the initial and final values of a given parameter/exogenous.
There is an alternative syntax:
VARIABLE_NAME, EXPRESSION;
Here only the final value is specified for a given parameter/exogenous; the initial value is taken
from the preceeding initval block.
A necessary condition for a successful homotopy is that Dynare must be able to solve the steady
state for the initial parameters/exogenous without additional help (using the guess values given
in the initval block).
If the homotopy fails, a possible solution is to increase the number of steps (given in homotopy_
steps option of steady).
Example
In the following example, Dynare will first compute the steady state for the initial values
(gam=0.5 and x=1), and then subdivide the problem into 50 smaller problems to find the steady
state for the final values (gam=2 and x=2).
var c k;
varexo x;
parameters alph gam delt bet aa;
alph=0.5;
delt=0.02;
Chapter 4: The Model file
29
aa=0.5;
bet=0.05;
model;
c + k - aa*x*k(-1)^alph - (1-delt)*k(-1);
c^(-gam) - (1+bet)^(-1)*(aa*alph*x(+1)*k^(alph-1) + 1 - delt)*c(+1)^(-gam);
end;
initval;
x = 1;
k = ((delt+bet)/(aa*x*alph))^(1/(alph-1));
c = aa*x*k^alph-delt*k;
end;
homotopy_setup;
gam, 0.5, 2;
x, 2;
end;
steady(homotopy_mode = 1, homotopy_steps = 50);
4.10.2 Using a steady state file
If you know how to compute the steady state for your model, you can provide a MATLAB/Octave
function doing the computation instead of using steady. If your MOD-file is called ‘FILENAME.mod’,
the steady state file should be called ‘FILENAME_steadystate.m’.
Again, there are two options for creating this file:
• The easiest way is to write a steady_state_model block.
• You can write the corresponding Matlab function by hand. See ‘fs2000_steadystate.m’ in
the ‘examples’ directory for an example. This option gives a bit more flexibility, at the expense
of a heavier programming burden and a lesser efficiency.
steady_state_model ;
[Block]
Description
When the analytical solution of the model is known, this command can be used to help Dynare
find the steady state in a more efficient and reliable way, especially during estimation where the
steady state has to be recomputed for every point in the parameter space.
Each line of this block consists of a variable (either an endogenous, a temporary variable or
a parameter) which is assigned an expression (which can contain parameters, exogenous at
the steady state, or any endogenous or temporary variable already declared above). Each line
therefore looks like:
VARIABLE_NAME = EXPRESSION;
Note that it is also possible to assign several variables at the same time, if the main function in
the right hand side is a MATLAB/Octave function returning several arguments:
[ VARIABLE_NAME, VARIABLE_NAME... ] = EXPRESSION;
Dynare will automatically generate a steady state file using the information provided in this
block.
Steady state file for deterministic models
steady_state_model block works also with deterministic models. An initval block and, when
necessary, an endval block, is used to set the value of the exogenous variables. Each initval
Chapter 4: The Model file
30
or endval block must be followed by steady to execute the function created by steady_state_
model and set the initial, respectively terminal, steady state.
Example
var m P c e W R k d n l gy_obs gp_obs y dA;
varexo e_a e_m;
parameters alp bet gam mst rho psi del;
...
// parameter calibration, (dynamic) model declaration, shock calibration...
...
steady_state_model;
dA = exp(gam);
gst = 1/dA; // A temporary variable
m = mst;
// Three other temporary variables
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
n
P
k
= xist/(nust+xist);
= xist + nust;
= khst*n;
l
c
d
y
R
=
=
=
=
=
psi*mst*n/( (1-psi)*(1-n) );
mst/P;
l - mst + 1;
k^alp*n^(1-alp)*gst^alp;
mst/bet;
// You can use MATLAB functions which return several arguments
[W, e] = my_function(l, n);
gp_obs = m/dA;
gy_obs = dA;
end;
steady;
4.11 Getting information about the model
check ;
check (solve algo = INTEGER) ;
[Command]
[Command]
Description
Computes the eigenvalues of the model linearized around the values specified by the last initval,
endval or steady statement. Generally, the eigenvalues are only meaningful if the linearization
is done around a steady state of the model. It is a device for local analysis in the neighborhood
of this steady state.
Chapter 4: The Model file
31
A necessary condition for the uniqueness of a stable equilibrium in the neighborhood of the
steady state is that there are as many eigenvalues larger than one in modulus as there are
forward looking variables in the system. An additional rank condition requires that the square
submatrix of the right Schur vectors corresponding to the forward looking variables (jumpers)
and to the explosive eigenvalues must have full rank.
Options
solve_algo = INTEGER
See [solve algo], page 26, for the possible values and their meaning.
Output
check returns the eigenvalues in the global variable oo_.dr.eigval.
[MATLAB/Octave variable]
Contains the eigenvalues of the model, as computed by the check command.
oo_.dr.eigval
model_info ;
model_info (OPTIONS . . . );
[Command]
[Command]
Description
This command provides information about:
• the normalization of the model: an endogenous variable is attributed to each equation of
the model;
• the block structure of the model: for each block model info indicates its type, the equations
number and endogenous variables belonging to this block.
This command can only be used in conjunction with the block option of the model block.
There are five different types of blocks depending on the simulation method used:
‘EVALUATE FORWARD’
In this case the block contains only equations where endogenous variable attributed
to the equation appears currently on the left hand side and where no forward looking
endogenous variables appear. The block has the form: yj,t = fj (yt , yt−1 , . . . , yt−k ).
‘EVALUATE BACKWARD’
The block contains only equations where endogenous variable attributed to the
equation appears currently on the left hand side and where no backward looking
endogenous variables appear. The block has the form: yj,t = fj (yt , yt+1 , . . . , yt+k ).
‘SOLVE FORWARD x’
The block contains only equations where endogenous variable attributed to the equation does not appear currently on the left hand side and where no forward looking
endogenous variables appear. The block has the form: gj (yj,t , yt , yt−1 , . . . , yt−k ) = 0.
x is equal to ‘SIMPLE’ if the block has only one equation. If several equation appears
in the block, x is equal to ‘COMPLETE’.
‘SOLVE FORWARD x’
The block contains only equations where endogenous variable attributed to the equation does not appear currently on the left hand side and where no backward looking
endogenous variables appear. The block has the form: gj (yj,t , yt , yt+1 , . . . , yt+k ) = 0.
x is equal to ‘SIMPLE’ if the block has only one equation. If several equation appears
in the block, x is equal to ‘COMPLETE’.
Chapter 4: The Model file
32
‘SOLVE TWO BOUNDARIES x’
The block contains equations depending on both forward and backward variables.
The block looks like: gj (yj,t , yt , yt−1 , . . . , yt−k , yt , yt+1 , . . . , yt+k ) = 0. x is equal to
‘SIMPLE’ if the block has only one equation. If several equation appears in the block,
x is equal to ‘COMPLETE’.
Options
’static’
Prints out the block decomposition of the static model. Without ’static’ option
model info displays the block decomposition of the dynamic model.
’incidence’
Displays the gross incidence matrix and the reordered incidence matrix of the block
decomposed model.
print_bytecode_dynamic_model ;
[Command]
Prints the equations and the Jacobian matrix of the dynamic model stored in the bytecode
binary format file. Can only be used in conjunction with the bytecode option of the model
block.
print_bytecode_static_model ;
[Command]
Prints the equations and the Jacobian matrix of the static model stored in the bytecode binary
format file. Can only be used in conjunction with the bytecode option of the model block.
4.12 Deterministic simulation
When the framework is deterministic, Dynare can be used for models with the assumption of perfect
foresight. Typically, the system is supposed to be in a state of equilibrium before a period ‘1’ when
the news of a contemporaneous or of a future shock is learned by the agents in the model. The
purpose of the simulation is to describe the reaction in anticipation of, then in reaction to the shock,
until the system returns to the old or to a new state of equilibrium. In most models, this return
to equilibrium is only an asymptotic phenomenon, which one must approximate by an horizon of
simulation far enough in the future. Another exercise for which Dynare is well suited is to study the
transition path to a new equilibrium following a permanent shock. For deterministic simulations,
Dynare uses a Newton-type algorithm, first proposed by Laffargue (1990) and Boucekkine (1995),
instead of a first order technique like the one proposed by Fair and Taylor (1983), and used in
earlier generation simulation programs. We believe this approach to be in general both faster and
more robust. The details of the algorithm can be found in Juillard (1996).
simul ;
simul (OPTIONS . . . );
[Command]
[Command]
Description
Triggers the computation of a deterministic simulation of the model for the number of periods
set in the option periods.
Options
periods = INTEGER
Number of periods of the simulation
maxit = INTEGER
Determines the maximum number of iterations used in the non-linear solver. The
default value of maxit is 10. The maxit option is shared with the steady command.
So a change in maxit in a simul command will also be considered in the following
steady commands.
Chapter 4: The Model file
33
stack_solve_algo = INTEGER
Algorithm used for computing the solution. Possible values are:
0
Newton method to solve simultaneously all the equations for every period, using sparse matrices (Default).
1
Use a Newton algorithm with a sparse LU solver at each iteration (requires bytecode and/or block option, see Section 4.5 [Model declaration], page 16).
2
Use a Newton algorithm with a Generalized Minimal Residual (GMRES) solver at each iteration (requires bytecode and/or block option,
see Section 4.5 [Model declaration], page 16; not available under Octave)
3
Use a Newton algorithm with a Stabilized Bi-Conjugate Gradient
(BICGSTAB) solver at each iteration (requires bytecode and/or block
option, see Section 4.5 [Model declaration], page 16).
4
Use a Newton algorithm with a optimal path length at each iteration
(requires bytecode and/or block option, see Section 4.5 [Model declaration], page 16).
5
Use a Newton algorithm with a sparse Gaussian elimination (SPE)
solver at each iteration (requires bytecode option, see Section 4.5
[Model declaration], page 16).
6
Use the historical algorithm proposed in Juillard (1996): it is slower
than stack_solve_algo=0, but may be less memory consuming on big
models (not available with bytecode and/or block options).
markowitz = DOUBLE
Value of the Markowitz criterion, used to select the pivot. Only used when stack_
solve_algo = 5. Default: 0.5.
minimal_solving_periods = INTEGER
Specify the minimal number of periods where the model has to be solved, before
using a constant set of operations for the remaining periods. Only used when stack_
solve_algo = 5. Default: 1.
datafile = FILENAME
If the variables of the model are not constant over time, their initial values, stored in
a text file, could be loaded, using that option, as initial values before a deteministic
simulation.
Output
The simulated endogenous variables are available in global matrix oo_.endo_simul.
[MATLAB/Octave variable]
This variable stores the result of a deterministic simulation (computed by simul) or of a stochastic simulation (computed by stoch_simul with the periods option or by extended_path).
The variables are arranged row by row, in order of declaration (as in M_.endo_names). Note
that this variable also contains initial and terminal conditions, so it has more columns than the
value of periods option.
oo_.endo_simul
[MATLAB/Octave variable]
This variable stores the path of exogenous variables during a simulation (computed by simul,
stoch_simul or extended_path).
The variables are arranged in columns, in order of declaration (as in M_.endo_names). Periods
are in rows. Note that this convention regarding columns and rows is the opposite of the
convention for oo_.endo_simul!
oo_.exo_simul
Chapter 4: The Model file
34
4.13 Stochastic solution and simulation
In a stochastic context, Dynare computes one or several simulations corresponding to a random
draw of the shocks.
The main algorithm for solving stochastic models relies on a Taylor approximation, up to third
order, of the expectation functions (see Judd (1996), Collard and Juillard (2001a), Collard and
Juillard (2001b), and Schmitt-Grohé and Urı́be (2004)). The details of the Dynare implementation
of the first order solution are given in Villemot (2011). Such a solution is computed using the
stoch_simul command.
As an alternative, it is possible to compute a simulation to a stochastic model using the extended
path method presented by Fair and Taylor (1983). This method is especially useful when there are
strong nonlinearities or binding constraints. Such a solution is computed using the extended_path
command.
4.13.1 Computing the stochastic solution
stoch_simul [VARIABLE_NAME . . . ];
stoch_simul (OPTIONS . . . ) [VARIABLE_NAME . . . ];
[Command]
[Command]
Description
stoch_simul solves a stochastic (i.e. rational expectations) model, using perturbation techniques.
More precisely, stoch_simul computes a Taylor approximation of the decision and transition
functions for the model. Using this, it computes impulse response functions and various descriptive statistics (moments, variance decomposition, correlation and autocorrelation coefficients).
For correlated shocks, the variance decomposition is computed as in the VAR literature through
a Cholesky decomposition of the covariance matrix of the exogenous variables. When the shocks
are correlated, the variance decomposition depends upon the order of the variables in the varexo
command.
The Taylor approximation is computed around the steady state (see Section 4.10 [Steady state],
page 26).
The IRFs are computed as the difference between the trajectory of a variable following a shock
at the beginning of period 1 and its steady state value. More details on the computation of IRFs
can be found on the DynareWiki.
Variance decomposition, correlation, autocorrelation are only displayed for variables with positive variance. Impulse response functions are only plotted for variables with response larger
than 10−10 .
Variance decomposition is computed relative to the sum of the contribution of each shock.
Normally, this is of course equal to aggregate variance, but if a model generates very large
variances, it may happen that, due to numerical error, the two differ by a significant amount.
Dynare issues a warning if the maximum relative difference between the sum of the contribution
of each shock and aggregate variance is larger than 0.01%.
Currently, the IRFs are only plotted for 12 variables. Select the ones you want to see, if your
model contains more than 12 endogenous variables.
The covariance matrix of the shocks is specified with the shocks command (see Section 4.8
[Shocks on exogenous variables], page 23).
When a list of VARIABLE NAME is specified, results are displayed only for these variables.
The stoch_simul command with a first order approximation can benefit from the block decomposition of the model (see [block], page 17).
Options
Chapter 4: The Model file
35
ar = INTEGER
Order of autocorrelation coefficients to compute and to print. Default: 5.
drop = INTEGER
Number of points dropped at the beginning of simulation before computing the
summary statistics. Default: 100.
hp_filter = DOUBLE
Uses HP filter with λ = DOUBLE before computing moments. Default: no filter.
hp_ngrid = INTEGER
Number of points in the grid for the discrete Inverse Fast Fourier Transform used
in the HP filter computation. It may be necessary to increase it for highly autocorrelated processes. Default: 512.
irf = INTEGER
Number of periods on which to compute the IRFs. Setting irf=0, suppresses the
plotting of IRF’s. Default: 40.
irf_shocks = ( VARIABLE_NAME [[,] VARIABLE_NAME ...] )
The exogenous variables for which to compute IRFs. Default: all.
relative_irf
Requests the computation of normalized IRFs in percentage of the standard error
of each shock.
linear
Indicates that the original model is linear (put it rather in the model command).
nocorr
Don’t print the correlation matrix (printing them is the default).
nofunctions
Don’t print the coefficients of the approximated solution (printing them is the default).
nomoments
Don’t print moments of the endogenous variables (printing them is the default).
nograph
Do not create graphs (which implies that they are not saved to the disk nor displayed). If this option is not used, graphs will be saved to disk (to the format
specified by graph_format option) and displayed to screen (unless nodisplay option is used).
nodisplay
Do not display the graphs, but still save them to disk (unless nograph is used).
graph_format = FORMAT
Specify the file format for graphs saved to disk. Possible values are eps (the default),
pdf and fig (the latter is not available under Octave).
noprint
Don’t print anything. Useful for loops.
print
Print results (opposite of noprint).
order = INTEGER
Order of Taylor approximation. Acceptable values are 1, 2 and 3. Note that for
third order, k_order_solver option is implied and only empirical moments are
available (you must provide a value for periods option). Default: 2 (except after an estimation command, in which case the default is the value used for the
estimation).
k_order_solver
Use a k-order solver (implemented in C++) instead of the default Dynare solver.
This option is not yet compatible with the bytecode option (see Section 4.5 [Model
declaration], page 16. Default: disabled for order 1 and 2, enabled otherwise
Chapter 4: The Model file
36
periods = INTEGER
If different from zero, empirical moments will be computed instead of theoretical
moments. The value of the option specifies the number of periods to use in the
simulations. Values of the initval block, possibly recomputed by steady, will be
used as starting point for the simulation. The simulated endogenous variables are
made available to the user in a vector for each variable and in the global matrix oo_
.endo_simul (see [oo .endo simul], page 33). The simulated exogenous variables
are made available in oo_.exo_simul (see [oo .exo simul], page 33). Default: 0.
qz_criterium = DOUBLE
Value used to split stable from unstable eigenvalues in reordering the Generalized
Schur decomposition used for solving 1^st order problems. Default: 1.000001 (except when estimating with lik_init option equal to 1: the default is 0.999999 in
that case; see Section 4.14 [Estimation], page 41).
replic = INTEGER
Number of simulated series used to compute the IRFs. Default: 1 if order=1, and
50 otherwise.
simul_replic = INTEGER
Number of series to simulate when empirical moments are requested (i.e. periods
> 0). Note that if this option is greater than 1, the additional series will not be used
for computing the empirical moments but will simply be saved in binary form to
the file ‘FILENAME_simul’. Default: 1.
solve_algo = INTEGER
See [solve algo], page 26, for the possible values and their meaning.
aim_solver
Use the Anderson-Moore Algorithm (AIM) to compute the decision rules, instead
of using Dynare’s default method based on a generalized Schur decomposition. This
option is only valid for first order approximation. See AIM website for more details
on the algorithm.
conditional_variance_decomposition = INTEGER
See below.
conditional_variance_decomposition = [INTEGER1:INTEGER2]
See below.
conditional_variance_decomposition = [INTEGER1 INTEGER2 ...]
Computes a conditional variance decomposition for the specified period(s). The
periods must be strictly positive. Conditional variances are given by var(yt+k |t).
For period 1, the conditional variance decomposition provides the decomposition
of the effects of shocks upon impact. The results are stored in oo_.conditional_
variance_decomposition (see [oo .conditional variance decomposition], page 41).
pruning
Discard higher order terms when iteratively computing simulations of the solution,
as in Kim, Kim, Schaumburg and Sims (2008).
partial_information
Computes the solution of the model under partial information, along the lines of
Pearlman, Currie and Levine (1986). Agents are supposed to observe only some
variables of the economy. The set of observed variables is declared using the varobs
command. Note that if varobs is not present or contains all endogenous variables,
then this is the full information case and this option has no effect. More references
can be found at http://www.dynare.org/DynareWiki/PartialInformation.
Chapter 4: The Model file
37
sylvester = OPTION
Determines the algorithm used to solve the Sylvester equation for block decomposed
model. Possible values for OPTION are:
default
Uses the default solver for Sylvester equations (gensylv) based on Ondra Kamenik algorithm (see the Dynare Website for more information).
fixed_point
Uses a fixed point algorithm to solve the Sylvester equation (gensylv_
fp). This method is faster than the default one for large scale models.
Default value is default
sylvester_fixed_point_tol = DOUBLE
It is the convergence criterion used in the fixed point sylvester solver. Its default
value is 1e-12.
Output
This command sets oo_.dr, oo_.mean, oo_.var and oo_.autocorr, which are described below.
If option periods is present, sets oo_.endo_simul (see [oo .endo simul], page 33), and also
saves the simulated variables in MATLAB/Octave vectors of the global workspace with the
same name as the endogenous variables.
If options irf is different from zero, sets oo_.irfs (see below) and also saves the IRFs in
MATLAB/Octave vectors of the global workspace (this latter way of accessing the IRFs is
deprecated and will disappear in a future version).
Example 1
shocks;
var e;
stderr 0.0348;
end;
stoch_simul;
Performs the simulation of the 2nd order approximation of a model with a single stochastic
shock e, with a standard error of 0.0348.
Example 2
stoch_simul(linear,irf=60) y k;
Performs the simulation of a linear model and displays impulse response functions on 60 periods
for variables y and k.
[MATLAB/Octave variable]
After a run of stoch_simul, contains the mean of the endogenous variables. Contains theoretical
mean if the periods option is not present, and empirical mean otherwise. The variables are
arranged in declaration order.
oo_.mean
[MATLAB/Octave variable]
After a run of stoch_simul, contains the variance-covariance of the endogenous variables. Contains theoretical variance if the periods option is not present, and empirical variance otherwise.
The variables are arranged in declaration order.
oo_.var
[MATLAB/Octave variable]
After a run of stoch_simul, contains a cell array of the autocorrelation matrices of the endogenous variables. The element number of the matrix in the cell array corresponds to the
oo_.autocorr
Chapter 4: The Model file
38
order of autocorrelation. The option ar specifies the number of autocorrelation matrices available. Contains theoretical autocorrelations if the periods option is not present, and empirical
autocorrelations otherwise.
l
The element oo_.autocorr{i}(k,l) is equal to the correlation between ytk and yt−i
, where y k
l
(resp. y ) is the k-th (resp. l-th) endogenous variable in the declaration order.
Note that if theoretical moments have been requested, oo_.autocorr{i} is the same than oo_
.gamma_y{i+1}.
[MATLAB/Octave variable]
After a run of stoch_simul, if theoretical moments have been requested (i.e. if the periods
option is not present), this variable contains a cell array with the following values (where ar is
the value of the option of the same name):
oo_.gamma_y
oo_.gamma{1}
Variance/co-variance matrix.
oo_.gamma{i+1} (for i=1:ar)
Autocorrelation function. see [oo .autocorr], page 37 for more details. Beware, this
is the autocorrelation function, not the autocovariance function.
oo_.gamma{nar+2}
Variance decomposition.
oo_.gamma{nar+3}
If a second order approximation has been requested, contains the vector of the mean
correction terms.
[MATLAB/Octave variable]
After a run of stoch_simul with option irf different from zero, contains the impulse responses,
with the following naming convention: VARIABLE_NAME_SHOCK_NAME.
For example, oo_.irfs.gnp_ea contains the effect on gnp of a one standard deviation shock on
ea.
oo_.irfs
The approximated solution of a model takes the form of a set of decision rules or transition
equations expressing the current value of the endogenous variables of the model as function of the
previous state of the model and shocks oberved at the beginning of the period. The decision rules
are stored in the structure oo_.dr which is described below.
extended_path ;
extended_path (OPTIONS . . . ) ;
[Command]
[Command]
Description
extended_path solves a stochastic (i.e. rational expectations) model, using the extended path
method presented by Fair and Taylor (1983).
This function first computes a random path for the exogenous variables (stored in oo_.exo_
simul, see [oo .exo simul], page 33) and then computes the corresponding path for endogenous
variables, taking the steady state as starting point. The result of the simulation is stored in
oo_.endo_simul (see [oo .endo simul], page 33).
Options
periods = INTEGER
The number of periods for which the simulation is to be computed. No default
value, mandatory option.
solver_periods = INTEGER
The number of periods used to compute the approximate solution at every iteration
of the algorithm. Default: 200.
Chapter 4: The Model file
39
4.13.2 Typology and ordering of variables
Dynare distinguishes four types of endogenous variables:
Purely backward (or purely predetermined) variables
Those that appear only at current and past period in the model, but not at future
period (i.e. at t and t − 1 but not t + 1). The number of such variables is equal to
oo_.dr.npred - oo_.dr.nboth.
Purely forward variables
Those that appear only at current and future period in the model, but not at past
period (i.e. at t and t + 1 but not t − 1). The number of such variables is stored in
oo_.dr.nfwrd.
Mixed variables
Those that appear at current, past and future period in the model (i.e. at t, t + 1 and
t − 1). The number of such variables is stored in oo_.dr.nboth.
Static variables
Those that appear only at current, not past and future period in the model (i.e. only
at t, not at t + 1 or t − 1). The number of such variables is stored in oo_.dr.nstatic.
Note that all endogenous variables fall into one of these four categories, since after the creation
of auxiliary variables (see Section 4.6 [Auxiliary variables], page 19), all endogenous have at most
one lead and one lag. We therefore have the following identity:
oo_.dr.npred + oo_.dr.nfwrd + oo_.dr.nstatic = M_.endo_nbr
Internally, Dynare uses two orderings of the endogenous variables: the order of declaration
(which is reflected in M_.endo_names), and an order based on the four types described above,
which we will call the DR-order (“DR” stands for decision rules). Most of the time, the declaration
order is used, but for elements of the decision rules, the DR-order is used.
The DR-order is the following: static variables appear first, then purely backward variables, then
mixed variables, and finally purely forward variables. Inside each category, variables are arranged
according to the declaration order.
Variable oo_.dr.order_var maps DR-order to declaration order, and variable oo_.dr.inv_
order_var contains the inverse map. In other words, the k-th variable in the DR-order corresponds
to the endogenous variable numbered oo_.dr_order_var(k) in declaration order. Conversely, k-th
declared variable is numbered oo_.dr.inv_order_var(k) in DR-order.
Finally, the state variables of the model are the purely backward variables and the mixed
variables. They are orderer in DR-order when they appear in decision rules elements. There are
oo_.dr.npred such variables.
4.13.3 First order approximation
The approximation has the form:
h
yt = y s + Ayt−1
+ But
where y s is the steady state value of y and yth = yt − y s .
The coefficients of the decision rules are stored as follows:
• y s is stored in oo_.dr.ys. The vector rows correspond to all endogenous in the declaration
order.
• A is stored in oo_.dr.ghx. The matrix rows correspond to all endogenous in DR-order. The
matrix columns correspond to state variables in DR-order.
• B is stored oo_.dr.ghu. The matrix rows correspond to all endogenous in DR-order. The
matrix columns correspond to exogenous variables in declaration order.
Chapter 4: The Model file
40
4.13.4 Second order approximation
The approximation has the form:
h
h
h
h
yt = y s + 0.5Δ2 + Ayt−1
+ But + 0.5C(yt−1
⊗ yt−1
) + 0.5D(ut ⊗ ut ) + E(yt−1
⊗ ut )
s
h
s
2
where y is the steady state value of y, yt = yt − y , and Δ is the shift effect of the variance of
future shocks.
The coefficients of the decision rules are stored in the variables described for first order approximation, plus the following variables:
• Δ2 is stored in oo_.dr.ghs2. The vector rows correspond to all endogenous in DR-order.
• C is stored in oo_.dr.ghxx. The matrix rows correspond to all endogenous in DR-order.
The matrix columns correspond to the Kronecker product of the vector of state variables in
DR-order.
• D is stored in oo_.dr.ghuu. The matrix rows correspond to all endogenous in DR-order. The
matrix columns correspond to the Kronecker product of exogenous variables in declaration
order.
• E is stored in oo_.dr.ghxu. The matrix rows correspond to all endogenous in DR-order.
The matrix columns correspond to the Kronecker product of the vector of state variables (in
DR-order) by the vector of exogenous variables (in declaration order).
4.13.5 Third order approximation
The approximation has the form:
yt = y s + G0 + G1 zt + G2 (zt ⊗ zt ) + G3 (zt ⊗ zt ⊗ zt )
where y s is the steady state value of y, and zt is a vector consisting of the deviation from the
steady state of the state variables (in DR-order) at date t − 1 followed by the exogenous variables at
date t (in declaration order). The vector zt is therefore of size nz = oo_.dr.npred + M_.exo_nbr.
The coefficients of the decision rules are stored as follows:
• y s is stored in oo_.dr.ys. The vector rows correspond to all endogenous in the declaration
order.
• G0 is stored in oo_.dr.g_0. The vector rows correspond to all endogenous in DR-order.
• G1 is stored in oo_.dr.g_1. The matrix rows correspond to all endogenous in DR-order. The
matrix columns correspond to state variables in DR-order, followed by exogenous in declaration
order.
• G2 is stored in oo_.dr.g_2. The matrix rows correspond to all endogenous in DR-order. The
matrix columns correspond to the Kronecker product of state variables (in DR-order), followed
by exogenous (in declaration order). Note that the Kronecker product is stored in a folded way,
i.e. symmetric elements are stored only once, which implies that the matrix has nz (nz + 1)/2
columns. More precisely, each column of this matrix corresponds to a pair (i1 , i2 ) where each
index represents an element of zt and is therefore between 1 and nz . Only non-decreasing
pairs are stored, i.e. those for which i1 ≤ i2 . The columns are arranged in the lexicographical
order of non-decreasing pairs. Also note that for those pairs where i1 6= i2 , since the element
is stored only once but appears two times in the unfolded G2 matrix, it must be multiplied by
2 when computing the decision rules.
• G3 is stored in oo_.dr.g_3. The matrix rows correspond to all endogenous in DR-order. The
matrix columns correspond to the third Kronecker power of state variables (in DR-order),
followed by exogenous (in declaration order). Note that the third Kronecker power is stored
in a folded way, i.e. symmetric elements are stored only once, which implies that the matrix
has nz (nz + 1)(nz + 2)/6 columns. More precisely, each column of this matrix corresponds to
a tuple (i1 , i2 , i3 ) where each index represents an element of zt and is therefore between 1 and
nz . Only non-decreasing tuples are stored, i.e. those for which i1 ≤ i2 ≤ i3 . The columns
are arranged in the lexicographical order of non-decreasing tuples. Also note that for tuples
Chapter 4: The Model file
41
that have three distinct indices (i.e. i1 6= i2 and i1 6= i3 and i2 6= i3 , since these elements are
stored only once but appears six times in the unfolded G3 matrix, they must be multiplied by
6 when computing the decision rules. Similarly, for those tuples that have two equal indices
(i.e. of the form (a, a, b) or (a, b, a) or (b, a, a)), since these elements are stored only once but
appears three times in the unfolded G3 matrix, they must be multiplied by 3 when computing
the decision rules.
[MATLAB/Octave variable]
After a run of stoch_simul with the conditional_variance_decomposition option, contains a
three-dimensional array with the result of the decomposition. The first dimension corresponds to
forecast horizons (as declared with the option), the second dimension corresponds to endogenous
variables (in the order of declaration), the third dimension corresponds to exogenous variables
(in the order of declaration).
oo_.conditional_variance_decomposition
4.14 Estimation
Provided that you have observations on some endogenous variables, it is possible to use Dynare to
estimate some or all parameters. Both maximum likelihood (as in Ireland (2004)) and Bayesian
techniques (as in Rabanal and Rubio-Ramirez (2003), Schorfheide (2000) or Smets and Wouters
(2003)) are available. Using Bayesian methods, it is possible to estimate DSGE models, VAR
models, or a combination of the two techniques called DSGE-VAR.
Note that in order to avoid stochastic singularity, you must have at least as many shocks or
measurement errors in your model as you have observed variables.
The estimation using a first order approximation can benefit from the block decomposition of
the model (see [block], page 17).
varobs VARIABLE_NAME . . . ;
[Command]
Description
This command lists the name of observed endogenous variables for the estimation procedure.
These variables must be available in the data file (see [estimation cmd], page 44).
Alternatively, this command is also used in conjunction with the partial_information option
of stoch_simul, for declaring the set of observed variables when solving the model under partial
information.
Only one instance of varobs is allowed in a model file. If one needs to declare observed variables
in a loop, the macroprocessor can be used as shown in the second example below.
Simple example
varobs C y rr;
Example with a loop
varobs
@#for co in countries
GDP_@{co}
@#endfor
;
observation_trends ;
[Block]
Description
This block specifies linear trends for observed variables as functions of model parameters.
Each line inside of the block should be of the form:
Chapter 4: The Model file
42
VARIABLE_NAME(EXPRESSION);
In most cases, variables shouldn’t be centered when observation_trends is used.
Example
observation_trends;
Y (eta);
P (mu/eta);
end;
estimated_params ;
[Block]
Description
This block lists all parameters to be estimated and specifies bounds and priors as necessary.
Each line corresponds to an estimated parameter.
In a maximum likelihood estimation, each line follows this syntax:
stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME
, INITIAL_VALUE [, LOWER_BOUND, UPPER_BOUND ];
In a Bayesian estimation, each line follows this syntax:
stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 |
PARAMETER_NAME | DSGE_PRIOR_WEIGHT
[, INITIAL_VALUE [, LOWER_BOUND, UPPER_BOUND]], PRIOR_SHAPE,
PRIOR_MEAN, PRIOR_STANDARD_ERROR [, PRIOR_3RD_PARAMETER [,
PRIOR_4TH_PARAMETER [, SCALE_PARAMETER ] ] ];
The first part of the line consists of one of the three following alternatives:
stderr VARIABLE_NAME
Indicates that the standard error of the exogenous variable VARIABLE NAME,
or of the observation error associated with endogenous observed variable VARIABLE NAME, is to be estimated
corr VARIABLE_NAME1, VARIABLE_NAME2
Indicates that the correlation between the exogenous variables VARIABLE NAME1 and VARIABLE NAME2, or the correlation of the observation
errors associated with endogenous observed variables VARIABLE NAME1 and
VARIABLE NAME2, is to be estimated
PARAMETER_NAME
The name of a model parameter to be estimated
DSGE_PRIOR_WEIGHT
...
The rest of the line consists of the following fields, some of them being optional:
INITIAL_VALUE
Specifies a starting value for maximum likelihood estimation
LOWER_BOUND
Specifies a lower bound for the parameter value in maximum likelihood estimation
UPPER_BOUND
Specifies an upper bound for the parameter value in maximum likelihood estimation
PRIOR_SHAPE
A keyword specifying the shape of the prior density. The possible values are:
beta_pdf, gamma_pdf, normal_pdf, uniform_pdf, inv_gamma_pdf, inv_gamma1_
pdf, inv_gamma2_pdf. Note that inv_gamma_pdf is equivalent to inv_gamma1_pdf
Chapter 4: The Model file
43
PRIOR_MEAN
The mean of the prior distribution
PRIOR_STANDARD_ERROR
The standard error of the prior distribution
PRIOR_3RD_PARAMETER
A third parameter of the prior used for generalized beta distribution, generalized
gamma and for the uniform distribution. Default: 0
PRIOR_4TH_PARAMETER
A fourth parameter of the prior used for generalized beta distribution and for the
uniform distribution. Default: 1
SCALE_PARAMETER
The scale parameter to be used for the jump distribution of the Metropolis-Hasting
algorithm
Note that INITIAL VALUE, LOWER BOUND, UPPER BOUND, PRIOR MEAN,
PRIOR STANDARD ERROR, PRIOR 3RD PARAMETER, PRIOR 4TH PARAMETER
and SCALE PARAMETER can be any valid EXPRESSION. Some of them can be empty, in
which Dynare will select a default value depending on the context and the prior shape.
As one uses options more towards the end of the list, all previous options must be
filled: for example, if you want to specify SCALE PARAMETER, you must specify
PRIOR 3RD PARAMETER and PRIOR 4TH PARAMETER. Use empty values, if these
parameters don’t apply.
Example
The following line:
corr eps_1, eps_2, 0.5, , , beta_pdf, 0, 0.3, -1, 1;
sets a generalized beta prior for the correlation between eps_1 and eps_2 with mean 0 and
variance 0.3. By setting PRIOR 3RD PARAMETER to -1 and PRIOR 4TH PARAMETER
to 1 the standard beta distribution with support [0,1] is changed to a generalized beta with
support [-1,1]. Note that LOWER BOUND and UPPER BOUND are left empty and thus
default to -1 and 1, respectively. The initial value is set to 0.5.
Similarly, the following line:
corr eps_1, eps_2, 0.5, -0.5, 1, beta_pdf, 0, 0.3, -1, 1;
sets the same generalized beta distribution as before, but now truncates this distribution to
[-0.5,1] through the use of LOWER BOUND and UPPER BOUND. Hence, the prior does not
integrate to 1 anymore.
Parameter transformation
Sometimes, it is desirable to estimate a transformation of a parameter appearing in the model,
rather than the parameter itself. It is of course possible to replace the original parameter by a
function of the estimated parameter everywhere is the model, but it is often unpractical.
In such a case, it is possible to declare the parameter to be estimated in the parameters
statement and to define the transformation, using a pound sign (#) expression (see Section 4.5
[Model declaration], page 16).
Example
parameters bet;
model;
Chapter 4: The Model file
44
# sig = 1/bet;
c = sig*c(+1)*mpk;
end;
estimated_params;
bet, normal_pdf, 1, 0.05;
end;
estimated_params_init ;
[Block]
This block declares numerical initial values for the optimizer when these ones are different from
the prior mean.
Each line has the following syntax:
stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME
, INITIAL_VALUE;
See [estimated params], page 42, for the meaning and syntax of the various components.
estimated_params_bounds ;
[Block]
This block declares lower and upper bounds for parameters in maximum likelihood estimation.
Each line has the following syntax:
stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME
, LOWER_BOUND, UPPER_BOUND;
See [estimated params], page 42, for the meaning and syntax of the various components.
estimation [VARIABLE_NAME . . . ];
estimation (OPTIONS . . . ) [VARIABLE_NAME . . . ];
[Command]
[Command]
Description
This command runs Bayesian or maximum likelihood estimation.
The following information will be displayed by the command:
• results from posterior optimization (also for maximum likelihood)
• marginal log density
• mean and shortest confidence interval from posterior simulation
• Metropolis-Hastings convergence graphs that still need to be documented
• graphs with prior, posterior and mode
• graphs of smoothed shocks, smoothed observation errors, smoothed and historical variables
Options
datafile = FILENAME
The datafile: a ‘.m’ file, a ‘.mat’ file or, a ‘.xls’ file (the latter format is supported
under Octave if the io and java packages from Octave-Forge are installed, along with
a Java Runtime Environment)
xls_sheet = NAME
The name of the sheet with the data in an Excel file
xls_range = RANGE
The range with the data in an Excel file
nobs = INTEGER
The number of observations to be used. Default: all observations in the file
Chapter 4: The Model file
45
nobs = [INTEGER1:INTEGER2]
Runs a recursive estimation and forecast for samples of size ranging of INTEGER1
to INTEGER2. Option forecast must also be specified
first_obs = INTEGER
The number of the first observation to be used. Default: 1
prefilter = INTEGER
A value of 1 means that the estimation procedure will demean the data. Default:
0, i.e. no prefiltering
presample = INTEGER
The number of observations to be skipped before evaluating the likelihood. Default:
0
loglinear
Computes a log-linear approximation of the model instead of a linear approximation.
The data must correspond to the definition of the variables used in the model.
Default: computes a linear approximation
plot_priors = INTEGER
Control the plotting of priors:
0
No prior plot
1
Prior density for each estimated parameter is plotted. It is important
to check that the actual shape of prior densities matches what you have
in mind. Ill choosen values for the prior standard density can result in
absurd prior densities.
Default value is 1.
nograph
See [nograph], page 35.
nodisplay
See [nodisplay], page 35.
graph_format = FORMAT
See [graph format], page 35.
lik_init = INTEGER
Type of initialization of Kalman filter:
1
For stationary models, the initial matrix of variance of the error of
forecast is set equal to the unconditional variance of the state variables
2
For nonstationary models: a wide prior is used with an initial matrix of
variance of the error of forecast diagonal with 10 on the diagonal
3
For nonstationary models: use a diffuse filter (use rather the diffuse_
filter option)
4
The filter is initialized with the fixed point of the Riccati equation
Default value is 1. For advanced use only.
lik_algo = INTEGER
For internal use and testing only.
conf_sig = DOUBLE
See [conf sig], page 55.
mh_replic = INTEGER
Number of replications for Metropolis-Hastings algorithm. For the time being, mh_
replic should be larger than 1200. Default: 20000
Chapter 4: The Model file
46
sub_draws = INTEGER
number of draws from the Metropolis iterations that are used to compute posterior distribution of various objects (smoothed variable, smoothed shocks, forecast,
moments, IRF). sub_draws should be smaller than the total number of Metropolis
draws available. Default: min(1200,0.25*Total number of draws)
mh_nblocks = INTEGER
Number of parallel chains for Metropolis-Hastings algorithm. Default: 2
mh_drop = DOUBLE
The fraction of initially generated parameter vectors to be dropped before using
posterior simulations. Default: 0.5
mh_jscale = DOUBLE
The scale to be used for the jumping distribution in Metropolis-Hastings algorithm.
The default value is rarely satisfactory. This option must be tuned to obtain, ideally,
an acceptation rate of 25% in the Metropolis-Hastings algorithm. Default: 0.2
mh_init_scale = DOUBLE
The scale to be used for drawing the initial value of the Metropolis-Hastings chain.
Default: 2*mh_scale
mh_recover
Attempts to recover a Metropolis-Hastings simulation that crashed prematurely.
Shouldn’t be used together with load_mh_file
mh_mode = INTEGER
...
mode_file = FILENAME
Name of the file containing previous value for the mode. When computing the
mode, Dynare stores the mode (xparam1) and the hessian (hh) in a file called
‘MODEL_FILENAME_mode.mat’
mode_compute = INTEGER | FUNCTION_NAME
Specifies the optimizer for the mode computation:
0
The mode isn’t computed. When mode_file option is specified, the
mode is simply read from that file.
When mode_file option is not specified, Dynare reports the value of
the log posterior (log likelihood) evaluated at the initial value of the
parameters.
When mode_file option is not specified and there is no estimated_
params block, but the smoother option is used, it is a roundabout way to
compute the smoothed value of the variables of a model with calibrated
parameters.
1
Uses fmincon optimization routine (not available under Octave)
2
Value no longer used
3
Uses fminunc optimization routine
4
Uses Chris Sims’s csminwel
5
Uses Marco Ratto’s newrat. This value is not compatible with non
linear filters or DSGE-VAR models
6
Uses a Monte-Carlo based optimization routine (see Dynare wiki for
more details)
Chapter 4: The Model file
47
7
Uses fminsearch, a simplex based optimization routine (available under MATLAB if the optimization toolbox is installed; available under
Octave if the optim package from Octave-Forge is installed)
8
Uses Dynare implementation of the Nelder-Mead simplex based optimization routine (generally more efficient than the MATLAB or Octave
implementation available with mode_compute=7)
9
Uses the CMA-ES (Covariance Matrix Adaptation Evolution Strategy)
algorithm, an evolutionary algorithm for difficult non-linear non-convex
optimization
FUNCTION_NAME
It is also possible to give a FUNCTION NAME to this option, instead
of an INTEGER. In that case, Dynare takes the return value of that
function as the posterior mode.
Default value is 4.
mode_check
Tells Dynare to plot the posterior density for values around the computed mode for
each estimated parameter in turn. This is helpful to diagnose problems with the
optimizer
prior_trunc = DOUBLE
Probability of extreme values of the prior density that is ignored when computing
bounds for the parameters. Default: 1e-32
load_mh_file
Tells Dynare to add to previous Metropolis-Hastings simulations instead of starting
from scratch. Shouldn’t be used together with mh_recover
optim = (fmincon options)
Can be used to set options for fmincon, the optimizing function of MATLAB
Optimization toolbox. Use MATLAB’s syntax for these options. Default:
(’display’,’iter’,’LargeScale’,’off’,’MaxFunEvals’,100000,’TolFun’,1e8,’TolX’,1e-6)
nodiagnostic
Doesn’t compute the convergence diagnostics for Metropolis-Hastings. Default: diagnostics are computed and displayed
bayesian_irf
Triggers the computation of the posterior distribution of IRFs.
The
length of the IRFs are controlled by the irf option. Results are stored in
oo_.PosteriorIRF.dsge (see below for a description of this variable)
dsge_var
Triggers the estimation of a DSGE-VAR model, where the weight of the DSGE prior
of the VAR model will be estimated. The prior on the weight of the DSGE prior,
dsge_prior_weight, must be defined in the estimated_params section. NB: The
previous method of declaring dsge_prior_weight as a parameter and then placing
it in estimated_params is now deprecated and will be removed in a future release
of Dynare.
dsge_var = DOUBLE
Triggers the estimation of a DSGE-VAR model, where the weight of the DSGE
prior of the VAR model is calibrated to the value passed. NB: The previous method
of declaring dsge_prior_weight as a parameter and then calibrating it is now
deprecated and will be removed in a future release of Dynare.
Chapter 4: The Model file
48
dsge_varlag = INTEGER
The number of lags used to estimate a DSGE-VAR model. Default: 4.
moments_varendo
Triggers the computation of the posterior distribution of the theoretical moments of the endogenous variables.
Results are stored in
oo_.PosteriorTheoreticalMoments (see below for a description of this variable)
conditional_variance_decomposition = INTEGER
See below.
conditional_variance_decomposition = [INTEGER1:INTEGER2]
See below.
conditional_variance_decomposition = [INTEGER1 INTEGER2 ...]
Computes the posterior distribution of the conditional variance decomposition for the specified period(s).
The periods must be strictly
positive.
Conditional variances are given by var(yt+k |t).
For period
1, the conditional variance decomposition provides the decomposition
of the effects of shocks upon impact.
The results are stored in oo_
.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition,
but currently there is not output. Note that this option requires the option
moments_varendo to be specified.
filtered_vars
Triggers the computation of the posterior distribution of filtered endogenous variables and shocks. Results are stored in oo_.FilteredVariables (see below for a
description of this variable)
smoother
Triggers the computation of the posterior distribution of smoothered endogenous variables and shocks. Results are stored in oo_.SmoothedVariables, oo_
.SmoothedShocks and oo_.SmoothedMeasurementErrors. Also triggers the computation of oo_.UpdatedVariables, which contains the estimation of the expected
value of variables given the information available at the current date. See below for
a description of all these variables.
forecast = INTEGER
Computes the posterior distribution of a forecast on INTEGER periods after the
end of the sample used in estimation. If no Metropolis-Hastings is computed, the
result is stored in variable oo_.forecast and corresponds to the forecast at the
posterior mode. If a Metropolis-Hastings is computed, the distribution of forecasts
is stored in variables oo_.PointForecast and oo_.MeanForecast. See Section 4.15
[Forecasting], page 54) for a description of these variables.
tex
Requests the printing of results and graphs in TeX tables and graphics that can be
later directly included in LaTeX files (not yet implemented)
kalman_algo = INTEGER
...
kalman_tol = DOUBLE
...
filter_covariance
Saves the series of one step ahead error of forecast covariance matrices.
filter_step_ahead = [INTEGER1:INTEGER2]
Triggers the computation k-step ahead filtered values.
results
in
oo_.FilteredVariablesKStepAhead
and
.FilteredVariablesKStepAheadVariances.
Stores
oo_
Chapter 4: The Model file
49
filter_decomposition
Triggers the computation of the shock decomposition of the above k-step ahead
filtered values.
constant
...
noconstant
...
diffuse_filter
Uses the diffuse Kalman filter (as described in Durbin and Koopman (2001) and
Koopman and Durbin (2003)) to estimate models with non-stationary observed
variables.
When diffused_filter is used the lik_init option of estimation has no effect.
When there are nonstationary variables in a model, there is no unique deterministic
steady state. The user must supply a MATLAB/Octave function that computes
the steady state values of the stationary variables in the model and returns dummy
values for the nonstationary ones. The function should be called with the name of the
‘.mod’ file followed by ‘_steadystate’. See ‘fs2000_steadystate.m’ in ‘examples’
directory for an example.
Note that the nonstationary variables in the model must be integrated processes
(their first difference or k-difference must be stationary).
selected_variables_only
Only run the smoother on the variables listed just after the estimation command.
Default: run the smoother on all the declared endogenous variables.
cova_compute = INTEGER
When 0, the covariance matrix of estimated parameters is not computed after the
computation of posterior mode (or maximum likelihood). This increases speed of
computation in large models during development, when this information is not always necessary. Of course, it will break all successive computations that would
require this covariance matrix. Default is 1.
solve_algo = INTEGER
See [solve algo], page 26.
order = INTEGER
Order of approximation, either 1 or 2. When equal to 2, the likelihood is evaluated
with a particle filter based on a second order approximation of the model (see
Fernandez-Villaverde and Rubio-Ramirez (2005)). Default is 1, ie the lilkelihood of
the linearized model is evaluated using a standard Kalman filter.
irf = INTEGER
See [irf], page 35. Only used if [bayesian irf], page 47 is passed.
irf_shocks = ( VARIABLE_NAME [[,] VARIABLE_NAME ...] )
See [irf shocks], page 35. Only used if [bayesian irf], page 47 is passed. Cannot be
used with [dsge var], page 47.
aim_solver
See [aim solver], page 36.
sylvester = OPTION
See [sylvester], page 37.
sylvester_fixed_point_tol = DOUBLE
See [sylvester fixed point tol], page 37.
Chapter 4: The Model file
50
lyapunov = OPTION
Determines the algorithm used to solve the Laypunov equation to initialized the
variance-covariance matrix of the Kalman filter using the steady-state value of state
variables. Possible values for OPTION are:
default
Uses the default solver for Lyapunov equations based on Bartels-Stewart
algorithm.
fixed_point
Uses a fixed point algorithm to solve the Lyapunov equation. This
method is faster than the default one for large scale models, but it
could require a large amount of iterations.
doubling
Uses a doubling algorithm to solve the Lyapunov equation (disclyap_
fast). This method is faster than the two previous one for large scale
models.
square_root_solver
Uses a square-root solver for Lyapunov equations (dlyapchol). This
method is fast for large scale models (available under MATLAB if the
control system toolbox is installed; available under Octave if the control
package from Octave-Forge is installed)
Default value is default
lyapunov_fixed_point_tol = DOUBLE
This is the convergence criterion used in the fixed point lyapunov solver. Its default
value is 1e-10.
lyapunov_doubling_tol = DOUBLE
This is the convergence criterion used in the doubling algorithm to solve the lyapunov
equation. Its default value is 1e-16.
analytic_derivation
Triggers estimation with analytic gradient. The final hessian is also computed analytically. Only works for stationary models without missing observations.
Note
If no mh_jscale parameter is used in estimated params, the procedure uses mh_jscale for all
parameters. If mh_jscale option isn’t set, the procedure uses 0.2 for all parameters.
Output
After running estimation, the parameters M_.params and the variance matrix M_.Sigma_e of
the shocks are set to the mode for maximum likelihood estimation or posterior mode computation
without Metropolis iterations.
After estimation with Metropolis iterations (option mh_replic > 0 or option load_mh_file
set) the parameters M_.params and the variance matrix M_.Sigma_e of the shocks are set to the
posterior mean.
Depending on the options, estimation stores results in various fields of the oo_ structure,
described below.
Running the smoother with calibrated parameters
It is possible to compute smoothed value of the endogenous variables and the shocks with calibrated parameters, without estimation proper. For this usage, there should be no estimated_
params block. Observed variables must be declared. A dataset must be specified in
Chapter 4: The Model file
51
the estimation instruction. In addition, use the following options: mode_compute=0,mh_
replic=0,smoother. Currently, there is no specific output for this usage of the estimation
command. The results are made available in fields of oo_ structure. An example is available in
‘./tests/smoother/calibrated_model.mod’.
In the following variables, we will adopt the following shortcuts for specific field names:
MOMENT NAME
This field can take the following values:
HPDinf
Lower bound of a 90% HPD interval3
HPDsup
Upper bound of a 90% HPD interval
Mean
Mean of the posterior distribution
Median
Median of the posterior distribution
Std
Standard deviation of the posterior distribution
deciles
Deciles of the distribution.
density
Non parametric estimate of the posterior density. First and second columns
are respectively abscissa and ordinate coordinates.
ESTIMATED OBJECT
This field can take the following values:
measurement_errors_corr
Correlation between two measurement errors
measurement_errors_std
Standard deviation of measurement errors
parameters
Parameters
shocks_corr
Correlation between two structural shocks
shocks_std
Standard deviation of structural shocks
oo_.MarginalDensity.LaplaceApproximation
[MATLAB/Octave variable]
Variable set by the estimation command.
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with mh_replic > 0 or load_mh_file
option.
oo_.MarginalDensity.ModifiedHarmonicMean
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with the filtered_vars option. Fields
are of the form:
oo_.FilteredVariables.VARIABLE_NAME
oo_.FilteredVariables
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with the filter_step_ahead option.
oo_.FilteredVariablesKStepAhead
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with the filter_step_ahead option.
oo_.FilteredVariablesKStepAheadVariances
3
See option [conf sig], page 55 to change the size of the HPD interval
Chapter 4: The Model file
52
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with the bayesian_irf option. Fields
are of the form:
oo_.PosteriorIRF.dsge.MOMENT_NAME.VARIABLE_NAME_SHOCK_NAME
oo_.PosteriorIRF.dsge
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with the smoother option. Fields are of
the form:
oo_.SmoothedMeasurementErrors.VARIABLE_NAME
oo_.SmoothedMeasurementErrors
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with the smoother option. Fields are of
the form:
oo_.SmoothedShocks.VARIABLE_NAME
oo_.SmoothedShocks
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with the smoother option. Fields are of
the form:
oo_.SmoothedVariables.VARIABLE_NAME
oo_.SmoothedVariables
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with the smoother option. Contains the
estimation of the expected value of variables given the information available at the current date.
Fields are of the form:
oo_.UpdatedVariables.VARIABLE_NAME
oo_.UpdatedVariables
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with the moments_varendo option. Fields
are of the form:
oo_.PosteriorTheoreticalMoments.dsge.THEORETICAL_MOMENT.ESTIMATED_OBJECT.MOMENT_
NAME.VARIABLE_NAME
where THEORETICAL MOMENT is one of the following:
oo_.PosteriorTheoreticalMoments
covariance
Variance-covariance of endogenous variables
correlation
Correlation between endogenous variables
VarianceDecomposition
Decomposition of variance4
ConditionalVarianceDecomposition
Only if the conditional_variance_decomposition option has been specified
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with mh_replic > 0 or load_mh_file
option. Fields are of the form:
oo_.posterior_density.PARAMETER_NAME
oo_.posterior_density
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with mh_replic > 0 or load_mh_file
option. Fields are of the form:
oo_.posterior_hpdinf.ESTIMATED_OBJECT.VARIABLE_NAME
oo_.posterior_hpdinf
4
When the shocks are correlated, it is the decomposition of orthogonalized shocks via Cholesky decompostion
according to the order of declaration of shocks (see Section 4.2 [Variable declarations], page 9)
Chapter 4: The Model file
53
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with mh_replic > 0 or load_mh_file
option. Fields are of the form:
oo_.posterior_hpdsup.ESTIMATED_OBJECT.VARIABLE_NAME
oo_.posterior_hpdsup
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with mh_replic > 0 or load_mh_file
option. Fields are of the form:
oo_.posterior_mean.ESTIMATED_OBJECT.VARIABLE_NAME
oo_.posterior_mean
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with mh_replic > 0 or load_mh_file
option. Fields are of the form:
oo_.posterior_mode.ESTIMATED_OBJECT.VARIABLE_NAME
oo_.posterior_mode
[MATLAB/Octave variable]
Variable set by the estimation command, if it is used with mh_replic > 0 or load_mh_file
option. Fields are of the form:
oo_.posterior_std.ESTIMATED_OBJECT.VARIABLE_NAME
oo_.posterior_std
Here are some examples of generated variables:
oo_.posterior_mode.parameters.alp
oo_.posterior_mean.shocks_std.ex
oo_.posterior_hpdsup.measurement_errors_corr.gdp_conso
model_comparison FILENAME[(DOUBLE)] . . . ;
model_comparison (marginal density = laplace | modifiedharmonicmean)
FILENAME[(DOUBLE)] . . . ;
[Command]
[Command]
Description
This command computes odds ratios and estimate a posterior density over a collection of models.
The priors over models can be specified as the DOUBLE values, otherwise a uniform prior is
assumed.
Example
model_comparison my_model(0.7) alt_model(0.3);
This example attributes a 70% prior over my_model and 30% prior over alt_model.
shock_decomposition [VARIABLE_NAME] . . . ;
shock_decomposition (OPTIONS . . . ) [VARIABLE_NAME] . . . ;
[Command]
[Command]
Description
This command computes and displays shock decomposition according to the model for a given
sample.
Note that this command must come after either estimation (in case of an estimated model) or
stoch_simul (in case of a calibrated model).
Options
parameter_set = PARAMETER_SET
Specify the parameter set to use for running the smoother. The PARAMETER SET can take one of the following five values: calibration, prior_
mode, prior_mean, posterior_mode, posterior_mean, posterior_median. Default value: posterior_mean if Metropolis has been run, else posterior_mode.
Chapter 4: The Model file
54
shocks = (VARIABLE_NAME [VARIABLE_NAME ...] [ ; VARIABLE_NAME [VARIABLE_NAME ...]
...] )
...
labels = ( VARIABLE_NAME [VARIABLE_NAME ...] )
...
datafile = FILENAME
See [datafile], page 44. Useful when computing the shock decomposition on a calibrated model.
unit_root_vars VARIABLE_NAME . . . ;
[Command]
This command is deprecated. Use estimation option diffuse_filter instead for estimating a
model with non-stationary observed variables or steady option nocheck to prevent steady to
check the steady state returned by your steady state file.
Dynare also has the ability to estimate Bayesian VARs:
bvar_density ;
[Command]
Computes the marginal density of an estimated BVAR model, using Minnesota priors.
See ‘bvar-a-la-sims.pdf’, which comes with Dynare distribution, for more information on this
command.
calib_smoother [VARIABLE_NAME] . . . ;
calib_smoother (OPTIONS . . . ) [VARIABLE_NAME] . . . ;
[Command]
[Command]
Description
This command computes the smoothed variables (and possible the filtered variables) on a
calibrated model.
A datafile must be provided, and the observable variables declared with varobs. The smoother
is based on a first-order approximation of the model.
By default, the command computes the smoothed variables and shocks and stores the results in
oo_.SmoothedVariables and oo_.SmoothedShocks. It also fills oo_.UpdatedVariables.
Options
datafile = FILENAME
See [datafile], page 44.
filtered_vars
Triggers the computation of filtered variables. See [filtered vars], page 48 for more
details.
filter_step_ahead = [INTEGER1:INTEGER2]
See [filter step ahead], page 48.
4.15 Forecasting
On a calibrated model, forecasting is done using the forecast command. On an estimated model,
use the forecast option of estimation command.
It is also possible to compute forecasts on a calibrated or estimated model for a given constrained
path of the future endogenous variables. This is done, from the reduced form representation of the
DSGE model, by finding the structural shocks that are needed to match the restricted paths.
Use conditional_forecast, conditional_forecast_paths and plot_conditional_forecast
for that purpose.
Finally, it is possible to do forecasting with a Bayesian VAR using the bvar_forecast command.
Chapter 4: The Model file
forecast [VARIABLE_NAME . . . ];
forecast (OPTIONS . . . ) [VARIABLE_NAME . . . ];
55
[Command]
[Command]
Description
This command computes a simulation of a stochastic model from an arbitrary initial point.
When the model also contains deterministic exogenous shocks, the simulation is computed conditionaly to the agents knowing the future values of the deterministic exogenous variables.
forecast must be called after stoch_simul.
forecast plots the trajectory of endogenous variables. When a list of variable names follows
the command, only those variables are plotted. A 90% confidence interval is plotted around the
mean trajectory. Use option conf_sig to change the level of the confidence interval.
Options
periods = INTEGER
Number of periods of the forecast. Default: 40
conf_sig = DOUBLE
Level of significance for confidence interval. Default: 0.90
nograph
See [nograph], page 35.
nodisplay
See [nodisplay], page 35.
graph_format = FORMAT
See [graph format], page 35.
Initial Values
forecast computes the forecast taking as initial values the values specified in histval (see
Section 4.7 [Initial and terminal conditions], page 19). When no histval block is present, the
initial values are the one stated in initval. When initval is followed by command steady,
the initial values are the steady state (see Section 4.10 [Steady state], page 26).
Output
The results are stored in oo_.forecast, which is described below.
Example
varexo_det tau;
varexo e;
...
shocks;
var e; stderr 0.01;
var tau;
periods 1:9;
values -0.15;
end;
stoch_simul(irf=0);
forecast;
Chapter 4: The Model file
56
[MATLAB/Octave variable]
Variable set by the forecast command, or by the estimation command if used with the
forecast option and if no Metropolis-Hastings has been computed (in that case, the forecast is
computed for the posterior mode). Fields are of the form:
oo_.forecast.FORECAST_MOMENT.VARIABLE_NAME
where FORECAST MOMENT is one of the following:
oo_.forecast
HPDinf
Lower bound of a 90% HPD interval5 of forecast due to parameter uncertainty
HPDsup
Lower bound of a 90% HPD interval due to parameter uncertainty
HPDTotalinf
Lower bound of a 90% HPD interval of forecast due to parameter uncertainty and
future shocks (only with the estimation command)
HPDTotalsup
Lower bound of a 90% HPD interval due to parameter uncertainty and future shocks
(only with the estimation command)
Mean
Mean of the posterior distribution of forecasts
Median
Median of the posterior distribution of forecasts
Std
Standard deviation of the posterior distribution of forecasts
[MATLAB/Octave variable]
Set by the estimation command, if it is used with the forecast option and if either mh_replic
> 0 or load_mh_file option is used.
Contains the distribution of forecasts taking into account the uncertainty about both parameters
and shocks.
Fields are of the form:
oo_.PointForecast.MOMENT_NAME.VARIABLE_NAME
oo_.PointForecast
[MATLAB/Octave variable]
Set by the estimation command, if it is used with the forecast option and if either mh_replic
> 0 or load_mh_file option is used.
Contains the distribution of forecasts where the uncertainty about shocks is averaged out. The
distribution of forecasts therefore only represents the uncertainty about parameters.
Fields are of the form:
oo_.MeanForecast.MOMENT_NAME.VARIABLE_NAME
oo_.MeanForecast
conditional_forecast (OPTIONS . . . ) [VARIABLE_NAME . . . ];
[Command]
Description
This command computes forecasts on an estimated model for a given constrained path of some
future endogenous variables. This is done, from the reduced form representation of the DSGE
model, by finding the structural shocks that are needed to match the restricted paths. This
command has to be called after estimation.
Use conditional_forecast_paths block to give the list of constrained endogenous, and their
constrained future path. Option controlled_varexo is used to specify the structural shocks
which will be matched to generate the constrained path.
Use plot_conditional_forecast to graph the results.
Options
5
See option [conf sig], page 55 to change the size of the HPD interval
Chapter 4: The Model file
57
parameter_set = calibration | prior_mode | prior_mean | posterior_mode |
posterior_mean | posterior_median
Specify the parameter set to use for the forecasting. No default value, mandatory
option.
controlled_varexo = (VARIABLE_NAME...)
Specify the exogenous variables to use as control variables. No default value, mandatory option.
periods = INTEGER
Number of periods of the forecast. Default: 40. periods cannot be less than the
number of constrained periods.
replic = INTEGER
Number of simulations. Default: 5000.
conf_sig = DOUBLE
Level of significance for confidence interval. Default: 0.80
Example
var y a
varexo e u;
...
estimation(...);
conditional_forecast_paths;
var y;
periods 1:3, 4:5;
values 2, 5;
var a;
periods 1:5;
values 3;
end;
conditional_forecast(parameter_set = calibration, controlled_varexo = (e, u), replic =
plot_conditional_forecast(periods = 10) a y;
conditional_forecast_paths ;
[Block]
Describes the path of constrained endogenous, before calling conditional_forecast. The
syntax is similar to deterministic shocks in shocks, see conditional_forecast for an example.
The syntax of the block is the same than the deterministic shocks in the shocks blocks (see
Section 4.8 [Shocks on exogenous variables], page 23).
plot_conditional_forecast [VARIABLE_NAME . . . ];
plot_conditional_forecast (periods = INTEGER) [VARIABLE_NAME . . . ];
Description
Plots the conditional (plain lines) and unconditional (dashed lines) forecasts.
To be used after conditional_forecast.
Options
[Command]
[Command]
Chapter 4: The Model file
58
periods = INTEGER
Number of periods to be plotted. Default: equal to periods in conditional_
forecast. The number of periods declared in plot_conditional_forecast cannot
be greater than the one declared in conditional_forecast.
bvar_forecast ;
[Command]
This command computes in-sample or out-sample forecasts for an estimated BVAR model, using
Minnesota priors.
See ‘bvar-a-la-sims.pdf’, which comes with Dynare distribution, for more information on this
command.
4.16 Optimal policy
Dynare has tools to compute optimal policies for various types of objectives. You can either solve
for optimal policy under commitment with ramsey_policy, for optimal policy under discretion
with discretionary_policy or for optimal simple rule with osr.
osr [VARIABLE_NAME . . . ];
osr (OPTIONS . . . ) [VARIABLE_NAME . . . ];
[Command]
[Command]
Description
This command computes optimal simple policy rules for linear-quadratic problems of the form:
maxγ E(yt0 W yt )
such that:
A1 Et yt+1 + A2 yt + A3 yt−1 + Cet = 0
where:
• γ are parameters to be optimized. They must be elements of matrices A1 , A2 , A3 ;
• y are the endogenous variables;
• e are the exogenous stochastic shocks;
The parameters to be optimized must be listed with osr_params.
The quadratic objectives must be listed with optim_weights.
This problem is solved using a numerical optimizer.
Options
This command accept the same options than stoch_simul (see Section 4.13.1 [Computing the
stochastic solution], page 34).
The value of the objective is stored in the variable oo_.osr.objective_function, which is
described below.
osr_params PARAMETER_NAME . . . ;
[Command]
This command declares parameters to be optimized by osr.
optim_weights ;
[Block]
This block specifies quadratic objectives for optimal policy problems
More precisely, this block specifies the nonzero elements of the quadratic weight matrices for
the objectives in osr.
A element of the diagonal of the weight matrix is given by a line of the form:
VARIABLE_NAME EXPRESSION;
An off-the-diagonal element of the weight matrix is given by a line of the form:
VARIABLE_NAME, VARIABLE_NAME EXPRESSION;
Chapter 4: The Model file
59
[MATLAB/Octave variable]
After an execution of the osr command, this variable contains the value of the objective under
optimal policy.
oo_.osr.objective_function
ramsey_policy [VARIABLE_NAME . . . ];
ramsey_policy (OPTIONS . . . ) [VARIABLE_NAME . . . ];
[Command]
[Command]
Description
This command computes the first order approximation of the policy that maximizes the policy
maker objective function submitted to the constraints provided by the equilibrium path of the
economy.
The planner objective must be declared with the planner_objective command.
See Section 4.6 [Auxiliary variables], page 19, for an explanation of how this operator is handled
internally and how this affects the output.
Options
This command accepts all options of stoch_simul, plus:
planner_discount = EXPRESSION
Declares the discount factor of the central planner. Default: 1.0
instruments = (VARIABLE_NAME,...)
Declares instrument variables for the computation of the steady state under optimal
policy. Requires a steady_state_model block or a ..._steadystate.m file. See
below.
Note that only first order approximation is available (i.e. order=1 must be specified).
Output
This command generates all the output variables of stoch_simul.
In addition, it stores the value of planner objective function under Ramsey policy in oo_
.planner_objective_value.
Steay state
Dynare takes advantage of the fact that the Lagrange multipliers appear linearly in the equations
of the steady state of the model under optimal policy. Nevertheless, it is in general very difficult
to compute the steady state with simply a numerical guess in initval for the endogenous
variables.
It greatly facilitates the computation, if the user provides an analytical solution for the steady
state (in steady_state_model block or in a ..._steadystate.m file). In this case, it is necessary
to provide a steady state solution CONDITIONAL on the value of the instruments in the optimal
policy problem and declared with option instruments. Note that choosing the instruments
is partly a matter of interpretation and you can choose instruments that are handy from a
mathematical point of view but different from the instruments you would refer to in the analysis
of the paper. Typical example is choosing inflation or nominal interest rate as an instrument.
discretionary_policy [VARIABLE_NAME . . . ];
discretionary_policy (OPTIONS . . . ) [VARIABLE_NAME . . . ];
[Command]
[Command]
Description
This command computes an approximation of the optimal policy under discretion. The algorithm implemented is essentially an LQ solver, and is described by Dennis (2007).
Chapter 4: The Model file
60
Options
This command accepts the same options than ramsey_policy, plus:
discretionary_tol = NON-NEGATIVE DOUBLE
Sets the tolerance level used to assess convergence of the solution algorithm. Default:
1e-7.
planner_objective MODEL_EXPRESSION;
[Command]
This command declares the policy maker objective, for use with ramsey_policy or
discretionary_policy.
You need to give the one-period objective, not the discounted lifetime objective. The discount
factor is given by the planner_discount option of ramsey_policy and discretionary_policy.
Note that with this command you are not limited to quadratic objectives: you can give any
arbitrary nonlinear expression.
4.17 Sensitivity and identification analysis
Dynare provides an interface to the global sensitivity analysis (GSA) toolbox (developed by the
Joint Research Center (JRC) of the European Commission), which is now part of the official Dynare
distribution. The GSA toolbox can be used to answer the following questions:
1. What is the domain of structural coefficients assuring the stability and determinacy of a DSGE
model?
2. Which parameters mostly drive the fit of, e.g., GDP and which the fit of inflation? Is there
any conflict between the optimal fit of one observed series versus another?
3. How to represent in a direct, albeit approximated, form the relationship between structural
parameters and the reduced form of a rational expectations model?
The discussion of the methodologies and their application is described in Ratto (2008).
With respect to the previous version of the toolbox, in order to work properly, the GSA toolbox
no longer requires that the Dynare estimation environment is setup.
Sensitivity analysis results are saved locally in <mod_file>/GSA, where <mod_file>.mod is the
name of the DYNARE model file.
4.17.1 Sampling
The following binary files are produced:
• <mod_file>_prior.mat: this file stores information about the analyses performed sampling
from the prior ranges, i.e. pprior=1 and ppost=0;
• <mod_file>_mc.mat: this file stores information about the analyses performed sampling from
multivariate normal, i.e. pprior=0 and ppost=0;
• <mod_file>_post.mat: this file stores information about analyses performed using the
Metropolis posterior sample, i.e. ppost=1.
4.17.2 Stability Mapping
Figure files produced are of the form <mod_file>_prior_*.fig and store results for stability
mapping from prior Monte-Carlo samples:
• <mod_file>_prior_stab_SA_*.fig: plots of the Smirnov test analyses confronting the cdf of
the sample fulfilling Blanchard-Kahn conditions with the cdf of the rest of the sample;
• <mod_file>_prior_stab_indet_SA_*.fig: plots of the Smirnov test analyses confronting the
cdf of the sample producing indeterminacy with the cdf of the original prior sample;
• <mod_file>_prior_stab_unst_SA_*.fig: plots of the Smirnov test analyses confronting the
cdf of the sample producing unstable (explosive roots) behavior with the cdf of the original
prior sample;
Chapter 4: The Model file
61
• <mod_file>_prior_stable_corr_*.fig: plots of bivariate projections of the sample fulfilling
Blanchard-Kahn conditions;
• <mod_file>_prior_indeterm_corr_*.fig: plots of bivariate projections of the sample producing indeterminacy;
• <mod_file>_prior_unstable_corr_*.fig: plots of bivariate projections of the sample producing instability;
• <mod_file>_prior_unacceptable_corr_*.fig: plots of bivariate projections of the sample
producing unacceptable solutions, i.e. either instability or indeterminacy or the solution could
not be found (e.g. the steady state solution could not be found by the solver).
Similar conventions apply for <mod_file>_mc_*.fig files, obtained when samples from multivariate normal are used.
4.17.3 Reduced Form Mapping
The mapping of the reduced form solution forces the use of samples from prior ranges or prior
distributions, i.e.: pprior=1 and ppost=0. It uses 250 samples to optimize smoothing parameters
and 1000 samples to compute the fit. The rest of the sample is used for out-of-sample validation.
One can also load a previously estimated mapping with a new Monte-Carlo sample, to look at the
forecast for the new Monte-Carlo sample.
The following synthetic figures are produced:
• <mod_file>_redform_<endo name>_vs_lags_*.fig: shows bar charts of the sensitivity indices for the ten most important parameters driving the reduced form coefficients of the selected
endogenous variables (namendo) versus lagged endogenous variables (namlagendo); suffix log
indicates the results for log-transformed entries;
• <mod_file>_redform_<endo name>_vs_shocks_*.fig: shows bar charts of the sensitivity indices for the ten most important parameters driving the reduced form coefficients of the selected
endogenous variables (namendo) versus exogenous variables (namexo); suffix log indicates the
results for log-transformed entries;
• <mod_file>_redform_GSA(_log).fig: shows bar chart of all sensitivity indices for each parameter: this allows one to notice parameters that have a minor effect for any of the reduced
form coefficients.
Detailed results of the analyses are shown in the subfolder <mod_file>/GSA/redform_stab,
where the detailed results of the estimation of the single functional relationships between parameters
θ and reduced form coefficient are stored in separate directories named as:
• <namendo>_vs_<namlagendo>: for the entries of the transition matrix;
• <namendo>_vs_<namexo>: for entries of the matrix of the shocks.
Moreover, analyses for log-transformed entries are denoted with the following suffixes (y denotes
the generic reduced form coefficient):
• log: y ∗ = log(y);
• minuslog: y ∗ = log(−y);
• logsquared: y ∗ = log(y 2 ) for symmetric fat tails;
• logskew: y ∗ = log(|y + λ|) for asymmetric fat tails.
The optimal type of transformation is automatically selected without the need of user intervention.
4.17.4 RMSE
The RMSE analysis can be performed with different types of sampling options:
Chapter 4: The Model file
62
1. When pprior=1 and ppost=0, the toolbox analyzes the RMSEs for the Monte-Carlo sample
obtained by sampling parameters from their prior distributions (or prior ranges): this analysis
provides some hints about what parameter drives the fit of which observed series, prior to the
full estimation;
2. When pprior=0 and ppost=0, the toolbox analyzes the RMSEs for a multivariate normal
Monte-Carlo sample, with covariance matrix based on the inverse Hessian at the optimum: this
analysis is useful when maximum likelihood estimation is done (i.e. no Bayesian estimation);
3. When ppost=1 the toolbox analyzes the RMSEs for the posterior sample obtained by Dynare’s
Metropolis procedure.
The use of cases 2 and 3 requires an estimation step beforehand. To facilitate the sensitivity
analysis after estimation, the dynare_sensitivity command also allows you to indicate some
options of the estimation command. These are:
• datafile
• nobs
• first_obs
• prefilter
• presample
• nograph
• nodisplay
• graph_format
• conf_sig
• loglinear
• mode_file
Binary files produced my RMSE analysis are:
• <mod_file>_prior_*.mat: these files store the filtered and smoothed variables for the prior
Monte-Carlo sample, generated when doing RMSE analysis (pprior=1 and ppost=0);
• <mode_file>_mc_*.mat: these files store the filtered and smoothed variables for the multivariate normal Monte-Carlo sample, generated when doing RMSE analysis (pprior=0 and
ppost=0).
Figure files <mod_file>_rmse_*.fig store results for the RMSE analysis.
• <mod_file>_rmse_prior*.fig: save results for the analysis using prior Monte-Carlo samples;
• <mod_file>_rmse_mc*.fig: save results for the analysis using multivariate normal MonteCarlo samples;
• <mod_file>_rmse_post*.fig: save results for the analysis using Metropolis posterior samples.
The following types of figures are saved (we show prior sample to fix ideas, but the same
conventions are used for multivariate normal and posterior):
• <mod_file>_rmse_prior_*.fig: for each parameter, plots the cdfs corresponding to the best
10% RMSEs of each observed series;
• <mod_file>_rmse_prior_dens_*.fig: for each parameter, plots the pdfs corresponding to
the best 10% RMESs of each observed series;
• <mod_file>_rmse_prior_<name of observedseries>_corr_*.fig: for each observed series
plots the bi-dimensional projections of samples with the best 10% RMSEs, when the correlation
is significant;
• <mod_file>_rmse_prior_lnlik*.fig: for each observed series, plots in red the cdf of the
log-likelihood corresponding to the best 10% RMSEs, in green the cdf of the rest of the sample
and in blue the cdf of the full sample; this allows one to see the presence of some idiosyncratic
behavior;
Chapter 4: The Model file
63
• <mod_file>_rmse_prior_lnpost*.fig: for each observed series, plots in red the cdf of the
log-posterior corresponding to the best 10% RMSEs, in green the cdf of the rest of the sample
and in blue the cdf of the full sample; this allows one to see idiosyncratic behavior;
• <mod_file>_rmse_prior_lnprior*.fig: for each observed series, plots in red the cdf of the
log-prior corresponding to the best 10% RMSEs, in green the cdf of the rest of the sample and
in blue the cdf of the full sample; this allows one to see idiosyncratic behavior;
• <mod_file>_rmse_prior_lik_SA_*.fig: when lik_only=1, this shows the Smirnov tests for
the filtering of the best 10% log-likelihood values;
• <mod_file>_rmse_prior_post_SA_*.fig: when lik_only=1, this shows the Smirnov test for
the filtering of the best 10% log-posterior values.
4.17.5 Screening Analysis
Screening analysis does not require any additional options with respect to those listed in [Sampling
Options], page 64. The toolbox performs all the analyses required and displays results.
The results of the screening analysis with Morris sampling design are stored in the subfolder
<mod_file>/GSA/SCREEN. The data file <mod_file>_prior stores all the information of the analysis (Morris sample, reduced form coefficients, etc.).
Screening analysis merely concerns reduced form coefficients. Similar synthetic bar charts as for
the reduced form analysis with Monte-Carlo samples are saved:
• <mod_file>_redform_<endo name>_vs_lags_*.fig: shows bar charts of the elementary effect
tests for the ten most important parameters driving the reduced form coefficients of the selected
endogenous variables (namendo) versus lagged endogenous variables (namlagendo);
• <mod_file>_redform_<endo name>_vs_shocks_*.fig: shows bar charts of the elementary
effect tests for the ten most important parameters driving the reduced form coefficients of the
selected endogenous variables (namendo) versus exogenous variables (namexo);
• <mod_file>_redform_screen.fig: shows bar chart of all elementary effect tests for each
parameter: this allows one to identify parameters that have a minor effect for any of the
reduced form coefficients.
4.17.6 Identification Analysis
Setting the option identification=1, an identification analysis based on theoretical moments is
performed. Sensitivity plots are provided that allow to infer which parameters are most likely to
be less identifiable.
Prerequisite for properly running all the identification routines, is the keyword identification;
in the Dynare model file. This keyword triggers the computation of analytic derivatives of the
model with respect to estimated parameters and shocks. This is required for option morris=2,
which implements Iskrev (2010) identification analysis.
For example, the placing identification; dynare_sensitivity(identification=1,
morris=2); in the Dynare model file trigger identification analysis using analytic derivatives
Iskrev (2010), jointly with the mapping of the acceptable region.
The identification analysis with derivatives can also be triggered by the commands
identification; This does not do the mapping of acceptable regions for the model and uses
the standard random sampler of Dynare. It completely offsets any use of the sensitivity analysis
toolbox.
4.17.7 Performing Sensitivity and Identification Analysis
dynare_sensitivity ;
dynare_sensitivity (OPTIONS . . . );
Description
[Command]
[Command]
Chapter 4: The Model file
64
This command triggers sensitivity analysis on a DSGE model.
Options
Sampling Options
nsam = INTEGER
Size of the Monte-Carlo sample. Default: 2048
ilptau = INTEGER
If equal to 1, use LPτ quasi-Monte-Carlo. If equal to 0, use LHS Monte-Carlo.
Default: 1
pprior = INTEGER
If equal to 1, sample from the prior distributions. If equal to 0, sample from the
multivariate normal N (θ̄, Σ), where θ̄ is the posterior mode and Σ = H −1 , H is the
Hessian at the mode. Default: 1
prior_range = INTEGER
If equal to 1, sample uniformly from prior ranges. If equal to 0, sample from prior
distributions. Default: 1
morris = INTEGER
If equal to 0, ANOVA mapping (Type I error) If equal to 1, Screening analysis
(Type II error) If equal to 2, Analytic derivatives (similar to Type II error, only
valid when identification=1).Default: 1 when identification=1, 0 otherwise
morris_nliv = INTEGER
Number of levels in Morris design. Default: 6
morris_ntra = INTEGER
Number trajectories in Morris design. Default: 20
ppost = INTEGER
If equal to 1, use Metropolis posterior sample. If equal to 0, do not use Metropolis
posterior sample. NB: This overrides any other sampling option. Default: 0
neighborhood_width = DOUBLE
When pprior=0 and ppost=0, allows for the sampling
eters around the value specified in the mode_file, in
xparam1± |xparam1 × neighborhood_width|. Default: 0
of paramthe range
Stability Mapping Options
stab = INTEGER
If equal to 1, perform stability mapping. If equal to 0, do not perform stability
mapping. Default: 1
load_stab = INTEGER
If equal to 1, load a previously created sample. If equal to 0, generate a new sample.
Default: 0
alpha2_stab = DOUBLE
Critical value for correlations ρ in filtered samples: plot couples of parmaters with
|ρ| > alpha2_stab. Default: 0.3
ksstat = DOUBLE
Critical value for Smirnov statistics d: plot parameters with d > ksstat. Default:
0.1
Chapter 4: The Model file
65
pvalue_ks = DOUBLE
The threshold pvalue for significant Kolmogorov-Smirnov test (i.e. plot parameters
with pvalue < pvalue_ks). Default: 0.001
pvalue_corr = DOUBLE
The threshold pvalue for significant correlation in filtered samples (i.e. plot bivariate
samples when pvalue < pvalue_corr). Default: 0.001
Reduced Form Mapping Options
redform = INTEGER
If equal to 1, prepare Monte-Carlo sample of reduced form matrices. If equal to 0,
do not prepare Monte-Carlo sample of reduced form matrices. Default: 0
load_redform = INTEGER
If equal to 1, load previously estimated mapping. If equal to 0, estimate the mapping
of the reduced form model. Default: 0
logtrans_redform = INTEGER
If equal to 1, use log-transformed entries. If equal to 0, use raw entries. Default: 0
threshold_redform = [DOUBLE DOUBLE]
The range over which the filtered Monte-Carlo entries of the reduced form coefficients
should be analyzed. The first number is the lower bound and the second is the upper
bound. An empty vector indicates that these entries will not be filtered. Default:
empty
ksstat_redform = DOUBLE
Critical value for Smirnov statistics d when reduced form entries are filtered. Default: 0.1
alpha2_redform = DOUBLE
Critical value for correlations ρ when reduced form entries are filtered. Default: 0.3
namendo = (VARIABLE_NAME...)
List of endogenous variables. ‘:’ indicates all endogenous variables. Default: empty
namlagendo = (VARIABLE_NAME...)
List of lagged endogenous variables. ‘:’ indicates all lagged endogenous variables.
Analyze entries [namendo×namlagendo] Default: empty
namexo = (VARIABLE_NAME...)
List of exogenous variables. ‘:’ indicates all exogenous variables. Analyze entries
[namendo×namexo]. Default: empty
RMSE Options
rmse = INTEGER
If equal to 1, perform RMSE analysis. If equal to 0, do not perform RMSE analysis.
Default: 0
load_rmse = INTEGER
If equal to 1, load previous RMSE analysis. If equal to 0, make a new RMSE
analysis. Default: 0
lik_only = INTEGER
If equal to 1, compute only likelihood and posterior. If equal to 0, compute RMSE’s
for all observed series. Default: 0
Chapter 4: The Model file
66
var_rmse = (VARIABLE_NAME...)
List of observed series to be considered. ‘:’ indicates all observed variables. Default:
varobs
pfilt_rmse = DOUBLE
Filtering threshold for RMSE’s. Default: 0.1
istart_rmse = INTEGER
Value at which to start computing RMSE’s (use 2 to avoid big intitial error). Default: presample+1
alpha_rmse = DOUBLE
Critical value for Smirnov statistics d: plot parameters with d > alpha_rmse. Default: 0.002
alpha2_rmse = DOUBLE
Critical value for correlation ρ: plot couples of parmaters with |ρ| = alpha2_rmse.
Default: 1.0
datafile = FILENAME
See [datafile], page 44.
nobs = INTEGER
nobs = [INTEGER1:INTEGER2]
See [nobs], page 44.
first_obs = INTEGER
See [first obs], page 45.
prefilter = INTEGER
See [prefilter], page 45.
presample = INTEGER
See [presample], page 45.
nograph
See [nograph], page 35.
nodisplay
See [nodisplay], page 35.
graph_format = FORMAT
See [graph format], page 35.
conf_sig = DOUBLE
See [conf sig], page 55.
loglinear
See [loglinear], page 45.
mode_file = FILENAME
See [mode file], page 46.
kalman_algo = INTEGER
See [kalman algo], page 48.
Identification Analysis Options
identification = INTEGER
If equal to 1, performs identification anlysis (forcing redform=0 and morris=1) If
equal to 0, no identification analysis. Default: 0
morris = INTEGER
See [morris], page 64.
Chapter 4: The Model file
67
morris_nliv = INTEGER
See [morris nliv], page 64.
morris_ntra = INTEGER
See [morris ntra], page 64.
load_ident_files = INTEGER
Loads previously performed identification analysis. Default: 0
useautocorr = INTEGER
Use autocorrelation matrices in place of autocovariance matrices in moments for
identification analysis. Default: 0
ar = INTEGER
Maximum number of lags for moments in identification analysis. Default: 1
lik_init = INTEGER
See [lik init], page 45.
identification ;
identification (OPTIONS . . . );
[Command]
[Command]
Description
This command triggers identification analysis.
Options
ar = INTEGER
Number of lags of computed autocorrelations (theoretical moments). Default: 1
useautocorr = INTEGER
If equal to 1, compute derivatives of autocorrelation. If equal to 0, compute derivatives of autocovariances. Default: 0
load_ident_files = INTEGER
If equal to 1, allow Dynare to load previously computed analyzes. Default: 0
prior_mc = INTEGER
Size of Monte-Carlo sample. Default: 1
prior_range = INTEGER
Triggers uniform sample within the range implied by the prior specifications (when
prior_mc>1). Default: 0
advanced = INTEGER
Shows a more detailed analysis, comprised of an analysis for the linearized rational
expectation model as well as the associated reduced form solution. Further performs
a brute force search of the groups of parameters best reproducing the behavior of
each single parameter. The maximum dimension of the group searched is triggered
by max_dim_cova_group. Default: 0
max_dim_cova_group = INTEGER
In the brute force search (performed when advanced=1) this option sets the maximum dimension of groups of parameters that best reproduce the behavior of each
single model parameter. Default: 2
periods = INTEGER
When the analytic Hessian is not available (i.e. with missing values or diffuse
Kalman filter or univariate Kalman filter), this triggers the length of stochastic
simulation to compute Simulated Moments Uncertainty. Default: 300
Chapter 4: The Model file
68
replic = INTEGER
When the analytic Hessian is not available, this triggers the number of replicas to
compute Simulated Moments Uncertainty. Default: 100
gsa_sample_file = INTEGER
If equal to 0, do not use sample file. If equal to 1, triggers gsa prior sample. If
equal to 2, triggers gsa Monte-Carlo sample (i.e. loads a sample corresponding to
pprior=0 and ppost=0 in the dynare_sensitivity options). Default: 0
gsa_sample_file = FILENAME
Uses the provided path to a specific user defined sample file. Default: 0
parameter_set = calibration | prior_mode | prior_mean | posterior_mode |
posterior_mean | posterior_median
Specify the parameter set to use. Default: prior_mean
lik_init = INTEGER
See [lik init], page 45.
kalman_algo = INTEGER
See [kalman algo], page 48.
nograph
See [nograph], page 35.
nodisplay
See [nodisplay], page 35.
graph_format = FORMAT
See [graph format], page 35.
4.18 Markov-switching SBVAR
Given a list of variables, observed variables and a data file, Dynare can be used to solve a Markovswitching SBVAR model according to Sims, Waggoner and Zha (2008). Having done this, you can
create forecasts and compute the marginal data density, regime probabilities, IRFs, and variance
decomposition of the model.
The commands have been modularized, allowing for multiple calls to the same command within
a <mod_file>.mod file. The default is to use <mod_file> to tag the input (output) files used
(produced) by the program. Thus, to call any command more than once within a <mod_file>.mod
file, you must use the *_tag options described below.
markov_switching (OPTIONS . . . );
[Command]
Description
Declares the Markov state variable information of a Markov-switching SBVAR model.
Options
chain = INTEGER
The Markov chain. Default: none
state = INTEGER
This state has duration equal to duration. Exactly one of state and number_of_
states must be passed. Default: none
number_of_states = INTEGER
Total number of states. Implies that all states have the same duration. Exactly one
of state and number_of_states must be passed. Default: none
duration = DOUBLE | inf
The duration of the state or states. Default: none
Chapter 4: The Model file
svar (OPTIONS . . . );
69
[Command]
Description
Each Makov chain can control the switching of a set of parameters. We allow the parameters to
be divided equation by equation and by variance or slope and intercept.
Options
coefficients
Specifies that only the slope and intercept in the given equations are controlled by
the given chain. One, but not both, of coefficients or variances must appear.
Default: none
variances
Specifies that only variances in the given equations are controlled by the given chain.
One, but not both, of coefficients or variances must appear. Default: none
equations
Defines the equation controlled by the given chain. If not specificed, then all equations are controlled by chain. Default: none
chain = INTEGER
Specifies a Markov chain defined by [markov switching], page 68. Default: none
ms_estimation (OPTIONS . . . );
[Command]
Description
Triggers the creation of an initialization file for, and the estimation of, a Markov-switching
SBVAR model. At the end of the run, the A0 , A+ , Q and ζ matrices are contained in the
oo_.ms structure.
Options
General Options
file_tag = FILENAME
The portion of the filename associated with this run. This will create the model
initialization file, init_<file_tag>.dat. Default: <mod_file>
output_file_tag = FILENAME
The portion of the output filename that will be assigned to this run. This will create, among other files, est_final_<output_file_tag>.out, est_intermediate_
<output_file_tag>.out. Default: <file_tag>
no_create_init
Do not create an initialization file for the model. Passing this option will cause
the Initialization Options to be ignored. Further, the model will be generated
from the output files associated with the previous estimation run (i.e. est_final_
<file_tag>.out, est_intermediate_<file_tag>.out or init_<file_tag>.dat,
searched for in sequential order). This functionality can be useful for continuing a
previous estimation run to ensure convergence was reached or for reusing an initialization file. NB: If this option is not passed, the files from the previous estimation
run will be overwritten. Default: off (i.e. create initialization file)
Initialization Options
Chapter 4: The Model file
70
coefficients_prior_hyperparameters = [DOUBLE1 DOUBLE2 DOUBLE3 DOUBLE4 DOUBLE5
DOUBLE6]
Sets the hyper parameters for the model. The six elements of the argument vector
have the following interpretations:
Position
Interpretation
1
Overall tightness for A0 and A+
2
Relative tightness for A+
3
Relative tightness for the constant term
4
Tightness on lag decay (range: 1.2 - 1.5); a faster decay produces better
inflation process
5
Weight on nvar sums of coeffs dummy observations (unit roots)
6
Weight on single dummy initial observation including constant
Default: [1.0 1.0 0.1 1.2 1.0 1.0]
freq = INTEGER | monthly | quarterly | yearly
Frequency of the data (e.g. monthly, 12). Default: 4
initial_year = INTEGER
The first year of data. Default: none
initial_subperiod = INTEGER
The first period of data (i.e. for quarterly data, an integer in [1,4]). Default: 1
final_year = INTEGER
The last year of data. Default: none
final_subperiod = INTEGER
The final period of data (i.e. for monthly data, an integer in [1,12]. Default: 4
datafile = FILENAME
See [datafile], page 44.
xls_sheet = NAME
See [xls sheet], page 44.
xls_range = RANGE
See [xls range], page 44.
nlags = INTEGER
The number of lags in the model. Default: 1
cross_restrictions
Use cross A0 and A+ restrictions. Default: off
contemp_reduced_form
Use contemporaneous recursive reduced form. Default: off
no_bayesian_prior
Do not use bayesian prior. Default: off (i.e. use bayesian prior)
alpha = INTEGER
Alpha value for squared time-varying structural shock lambda. Default: 1
beta = INTEGER
Beta value for squared time-varying structural shock lambda. Default: 1
gsig2_lmdm = INTEGER
The variance for each independent λ parameter under SimsZha restrictions. Default:
50^2
Chapter 4: The Model file
71
specification = sims_zha | none
This controls how restrictions are imposed to reduce the number of parameters.
Default: Random Walk
Estimation Options
convergence_starting_value = DOUBLE
This is the tolerance criterion for convergence and refers to changes in the objective
function value. It should be rather loose since it will gradually be tighened during
estimation. Default: 1e-3
convergence_ending_value = DOUBLE
The convergence criterion ending value. Values much smaller than square root
machine epsilon are probably overkill. Default: 1e-6
convergence_increment_value = DOUBLE
Determines how quickly the convergence criterion moves from the starting value to
the ending value. Default: 0.1
max_iterations_starting_value = INTEGER
This is the maximum number of iterations allowed in the hill-climbing optimization routine and should be rather small since it will gradually be increased during
estimation. Default: 50
max_iterations_increment_value = DOUBLE
Determines how quickly the maximum number of iterations is increased. Default: 2
max_block_iterations = INTEGER
The parameters are divided into blocks and optimization proceeds over each block.
After a set of blockwise optimizations are performed, the convergence criterion is
checked and the blockwise optimizations are repeated if the criterion is violated.
This controls the maximum number of times the blockwise optimization can be
performed. Note that after the blockwise optimizations have converged, a single
optimization over all the parameters is performed before updating the convergence
value and maximum number of iterations. Default: 100
max_repeated_optimization_runs = INTEGER
The entire process described by [max block iterations], page 71 is repeated until
improvement has stopped. This is the maximum number of times the process is
allowed to repeat. Set this to 0 to not allow repetitions. Default: 10
function_convergence_criterion = DOUBLE
The convergence criterion for the objective function when max_repeated_
optimizations_runs is positive. Default: 0.1
parameter_convergence_criterion = DOUBLE
The convergence criterion for parameter
optimizations_runs is positive. Default: 0.1
values
when
max_repeated_
number_of_large_perturbations = INTEGER
The entire process described by [max block iterations], page 71 is repeated with
random starting values drawn from the posterior. This specifies the number of
random starting values used. Set this to 0 to not use random starting values. A
larger number should be specified to ensure that the entire parameter space has
been covererd. Default: 5
number_of_small_perturbations = INTEGER
The number of small perturbations to make after the large perturbations have
stopped improving. Setting this number much above 10 is probably overkill. Default: 5
Chapter 4: The Model file
72
number_of_posterior_draws_after_perturbation = INTEGER
The number of consecutive posterior draws to make when producing a small perturbation. Because the posterior draws are serially correlated, a small number will
result in a small perturbation. Default: 1
max_number_of_stages = INTEGER
The small and large perturbation are repeated until improvement has stopped. This
specifices the maximum number of stages allowed. Default: 20
random_function_convergence_criterion = DOUBLE
The convergence criterion for the objective function when number_of_large_
perturbations is positive. Default: 0.1
random_parameter_convergence_criterion = DOUBLE
The convergence criterion for parameter values when number_of_large_
perturbations is positive. Default: 0.1
Example
ms_estimation(datafile=data, initial_year=1959, final_year=2005,
nlags=4, max_repeated_optimization_runs=1, max_number_of_stages=0);
ms_estimation(file_tag=second_run, datafile=data, initial_year=1959,
final_year=2005, nlags=4, max_repeated_optimization_runs=1,
max_number_of_stages=0);
ms_estimation(file_tag=second_run, output_file_tag=third_run,
no_create_init, max_repeated_optimization_runs=5,
number_of_large_perturbations=10);
ms_simulation ;
ms_simulation (OPTIONS . . . );
[Command]
[Command]
Description
Simulates a Markov-switching SBVAR model.
Options
file_tag = FILENAME
The portion of the filename associated with the ms_estimation run. Default: <mod_
file>
output_file_tag = FILENAME
The portion of the output filename that will be assigned to this run. Default:
<file_tag>
mh_replic = INTEGER
The number of draws to save. Default: 10,000
drop = INTEGER
The number of burn-in draws. Default: 0.1*mh_replic*thinning_factor
thinning_factor = INTEGER
The total number of draws is equal to thinning_factor*mh_replic+drop. Default:
1
adaptive_mh_draws = INTEGER
Tuning period for Metropolis-Hasting draws. Default: 30,000
Chapter 4: The Model file
73
Example
ms_simulation(file_tag=second_run);
ms_simulation(file_tag=third_run, mh_replic=5000, thinning_factor=3);
ms_compute_mdd ;
ms_compute_mdd (OPTIONS . . . );
[Command]
[Command]
Description
Computes the marginal data density of a Markov-switching SBVAR model from the posterior
draws. At the end of the run, the Muller and Bridged log marginal densities are contained in
the oo_.ms structure.
Options
file_tag = FILENAME
See [file tag], page 72.
output_file_tag = FILENAME
See [output file tag], page 72.
simulation_file_tag = FILENAME
The portion of the filename associated with the simulation run. Defualt: <file_
tag>
proposal_type = INTEGER
The proposal type:
1
Gaussian
2
Power
3
Truncated Power
4
Step
5
Truncated Gaussian
Default: 3
proposal_lower_bound = DOUBLE
The lower cutoff in terms of probability. Not used for proposal_type in [1,2].
Required for all other proposal types. Default: 0.1
proposal_upper_bound = DOUBLE
The upper cutoff in terms of probability. Not used for proposal_type equal to 1.
Required for all other proposal types. Default: 0.9
mdd_proposal_draws = INTEGER
The number of proposal draws. Default: 100,000
mdd_use_mean_center
Use the posterior mean as center. Default: off
ms_compute_probabilities ;
ms_compute_probabilities (OPTIONS . . . );
[Command]
[Command]
Description
Computes smoothed regime probabilities of a Markov-switching SBVAR model. Output .eps
files are contained in <output_file_tag/Output/Probabilities>.
Options
Chapter 4: The Model file
74
file_tag = FILENAME
See [file tag], page 72.
output_file_tag = FILENAME
See [output file tag], page 72.
filtered_probabilities
Filtered probabilities are computed instead of smoothed. Default: off
real_time_smoothed
Smoothed probabilities are computed based on time t information for 0 ≤ t ≤ nobs.
Default: off
ms_irf ;
ms_irf (OPTIONS . . . );
[Command]
[Command]
Description
Computes impulse response functions for a Markov-switching SBVAR model. Output .eps files
are contained in <output_file_tag/Output/IRF>, while data files are contained in <output_
file_tag/IRF>.
Options
file_tag = FILENAME
See [file tag], page 72.
output_file_tag = FILENAME
See [output file tag], page 72.
simulation_file_tag = FILENAME
See [simulation file tag], page 73.
horizon = INTEGER
The forecast horizon. Default: 12
filtered_probabilities
Uses filtered probabilities at the end of the sample as initial conditions for regime
probabilities. Only one of filtered_probabilities, regime and regimes may be
passed. Default: off
error_band_percentiles = [DOUBLE1 ...]
The percentiles to compute. Default: [0.16 0.50 0.84]. If median is passed, the
default is [0.5]
shock_draws = INTEGER
The number of regime paths to draw. Default: 10,000
shocks_per_parameter = INTEGER
The number of regime paths to draw under parameter uncertainty. Default: 10
thinning_factor = INTEGER
Only 1/thinning_factor of the draws in posterior draws file are used. Default: 1
free_parameters = NUMERICAL_VECTOR
A vector of free parameters to initialize theta of the model. Default: use estimated
parameters
parameter_uncertainty
Calculate IRFs under parameter uncertainty. Requires that ms_simulation has
been run. Default: off
Chapter 4: The Model file
75
regime = INTEGER
Given the data and model parameters, what is the ergodic probability of being in
the specified regime. Only one of filtered_probabilities, regime and regimes
may be passed. Default: off
regimes
Describes the evolution of regimes. Only one of filtered_probabilities, regime
and regimes may be passed. Default: off
median
A shortcut to setting error_band_percentiles=[0.5]. Default: off
ms_forecast ;
ms_forecast (OPTIONS . . . );
[Command]
[Command]
Description
Generates forecasts for a Markov-switching SBVAR model. Output .eps files are contained
in <output_file_tag/Output/Forecast>, while data files are contained in <output_file_
tag/Forecast>.
Options
file_tag = FILENAME
See [file tag], page 72.
output_file_tag = FILENAME
See [output file tag], page 72.
simulation_file_tag = FILENAME
See [simulation file tag], page 73.
data_obs_nbr = INTEGER
The number of data points included in the output. Default: 0
error_band_percentiles = [DOUBLE1 ...]
See [error band percentiles], page 74.
shock_draws = INTEGER
See [shock draws], page 74.
shocks_per_parameter = INTEGER
See [shocks per parameter], page 74.
thinning_factor = INTEGER
See [thinning factor], page 74.
free_parameters = NUMERICAL_VECTOR
See [free parameters], page 74.
parameter_uncertainty
See [parameter uncertainty], page 74.
regime = INTEGER
See [regime], page 75.
regimes
See [regimes], page 75.
median
See [median], page 75.
Chapter 4: The Model file
ms_variance_decomposition ;
ms_variance_decomposition (OPTIONS . . . );
76
[Command]
[Command]
Description
Computes the variance decomposition for a Markov-switching SBVAR model. Output .eps files
are contained in <output_file_tag/Output/Variance_Decomposition>, while data files are
contained in <output_file_tag/Variance_Decomposition>.
Options
file_tag = FILENAME
See [file tag], page 72.
output_file_tag = FILENAME
See [output file tag], page 72.
simulation_file_tag = FILENAME
See [simulation file tag], page 73.
horizon = INTEGER
See [horizon], page 74.
filtered_probabilities
See [filtered probabilities], page 74.
no_error_bands
Do not output percentile error bands (i.e. compute mean). Default: off (i.e.
output error bands)
error_band_percentiles = [DOUBLE1 ...]
See [error band percentiles], page 74.
shock_draws = INTEGER
See [shock draws], page 74.
shocks_per_parameter = INTEGER
See [shocks per parameter], page 74.
thinning_factor = INTEGER
See [thinning factor], page 74.
free_parameters = NUMERICAL_VECTOR
See [free parameters], page 74.
parameter_uncertainty
See [parameter uncertainty], page 74.
regime = INTEGER
See [regime], page 75.
regimes
See [regimes], page 75.
4.19 Displaying and saving results
Dynare has comments to plot the results of a simulation and to save the results.
rplot VARIABLE_NAME . . . ;
[Command]
Plots the simulated path of one or several variables, as stored in oo .endo simul by either simul
(see Section 4.12 [Deterministic simulation], page 32) or stoch simul with option periods (see
Section 4.13.1 [Computing the stochastic solution], page 34). The variables are plotted in levels.
Chapter 4: The Model file
dynatype (FILENAME) [VARIABLE_NAME . . . ];
This command prints the listed variables in a text file named FILENAME.
ABLE NAME is listed, all endogenous variables are printed.
77
[Command]
If no VARI-
dynasave (FILENAME) [VARIABLE_NAME . . . ];
[Command]
This command saves the listed variables in a binary file named FILENAME. If no VARIABLE NAME are listed, all endogenous variables are saved.
In MATLAB or Octave, variables saved with the dynasave command can be retrieved by the
command:
load -mat FILENAME
4.20 Macro-processing language
It is possible to use “macro” commands in the ‘.mod’ file for doing the following tasks: including
modular source files, replicating blocks of equations through loops, conditionally executing some
code, writing indexed sums or products inside equations. . .
The Dynare macro-language provides a new set of macro-commands which can be inserted inside
‘.mod’ files. It features:
• file inclusion
• loops (for structure)
• conditional inclusion (if/then/else structures)
• expression substitution
Technically, this macro language is totally independent of the basic Dynare language, and is
processed by a separate component of the Dynare pre-processor. The macro processor transforms
a ‘.mod’ file with macros into a ‘.mod’ file without macros (doing expansions/inclusions), and then
feeds it to the Dynare parser. The key point to understand is that the macro-processor only does
text substitution (like the C preprocessor or the PHP language). Note that it is possible to see
the output of the macro-processor by using the savemacro option of the dynare command (see
Chapter 3 [Dynare invocation], page 6).
The macro-processor is invoked by placing macro directives in the ‘.mod’ file. Directives begin
with an at-sign followed by a pound sign (@#). They produce no output, but give instructions to
the macro-processor. In most cases, directives occupy exactly one line of text. In case of need, two
anti-slashes (\\) at the end of the line indicates that the directive is continued on the next line.
The main directives are:
• @#include, for file inclusion,
• @#define, for defining a macro-processor variable,
• @#if, @#ifdef, @#else, @#endif for conditional statements,
• @#for, @#endfor for constructing loops.
The macro-processor maintains its own list of variables (distinct of model variables and of
MATLAB/Octave variables). These macro-variables are assigned using the @#define directive,
and can be of four types: integer, character string, array of integers, array of strings.
4.20.1 Macro expressions
It is possible to construct macro-expressions which can be assigned to macro-variables or used within
a macro-directive. The expressions are constructed using literals of the four basic types (integers,
strings, arrays of strings, arrays of integers), macro-variables names and standard operators.
String literals have to be enclosed between double quotes (like "name"). Arrays are enclosed
within brackets, and their elements are separated by commas (like [1,2,3] or ["US", "EA"]).
Note that there is no boolean type: false is represented by integer zero and true is any non-null
integer.
Chapter 4: The Model file
78
The following operators can be used on integers:
• arithmetic operators: +, -, *, /
• comparison operators: <, >, <=, >=, ==, !=
• logical operators: &&, ||, !
• integer ranges, using the following syntax: INTEGER1:INTEGER2 (for example, 1:4 is equivalent
to integer array [1,2,3,4])
The following operators can be used on strings:
• comparison operators: ==, !=
• concatenation of two strings: +
• extraction of substrings: if s is a string, then s[3] is a string containing only the third character
of s, and s[4:6] contains the characters from 4th to 6th
The following operators can be used on arrays:
• dereferencing: if v is an array, then v[2] is its 2nd element
• concatenation of two arrays: +
• difference -: returns the first operand from which the elements of the second operand have
been removed
• extraction of sub-arrays: e.g. v[4:6]
• testing membership of an array: in operator (for example: "b" in ["a", "b", "c"] returns
1)
Macro-expressions can be used at two places:
• inside macro directives, directly;
• in the body of the .mod file, between an at-sign and curly braces (like @{expr}): the macro
processor will substitute the expression with its value.
In the following, MACRO EXPRESSION designates an expression constructed as explained
above.
4.20.2 Macro directives
[Macro directive]
This directive simply includes the content of another file at the place where it is inserted. It is
exactly equivalent to a copy/paste of the content of the included file. Note that it is possible to
nest includes (i.e. to include a file from an included file).
@#include "FILENAME"
Example
@#include "modelcomponent.mod"
@#define MACRO_VARIABLE = MACRO_EXPRESSION
Defines a macro-variable.
Example 1
@#define
@#define
@#define
@#define
@#define
@#define
Example 2
x
y
v
w
z
t
=
=
=
=
=
=
5
// Integer
"US"
// String
[ 1, 2, 4 ]
// Integer array
[ "US", "EA" ] // String array
3 + v[2]
// Equals 5
("US" in w)
// Equals 1 (true)
[Macro directive]
Chapter 4: The Model file
79
@#define x = [ "B", "C" ]
@#define i = 2
model;
A = @{x[i]};
end;
is strictly equivalent to:
model;
A = C;
end;
[Macro directive]
[Macro directive]
[Macro directive]
[Macro directive]
Conditional inclusion of some part of the ‘.mod’ file. The lines between @#if or @#ifdef and
the next @#else or @#endif is executed only if the condition evaluates to a non-null integer.
The @#else branch is optional and, if present, is only evaluated if the condition evaluates to 0.
@#if MACRO_EXPRESSION
@#ifdef MACRO_VARIABLE
@#else
@#endif
Example
Choose between two alternative monetary policy rules using a macro-variable:
@#define linear_mon_pol = 0 // or 1
...
model;
@#if linear_mon_pol
i = w*i(-1) + (1-w)*i_ss + w2*(pie-piestar);
@#else
i = i(-1)^w * i_ss^(1-w) * (pie/piestar)^w2;
@#endif
...
end;
Example
Choose between two alternative monetary policy rules using a macro-variable. As linear_mon_
pol was not previously defined in this example, the second equation will be chosen:
model;
@#ifdef linear_mon_pol
i = w*i(-1) + (1-w)*i_ss + w2*(pie-piestar);
@#else
i = i(-1)^w * i_ss^(1-w) * (pie/piestar)^w2;
@#endif
...
end;
@#for MACRO_VARIABLE in MACRO_EXPRESSION
@#endfor
[Macro directive]
[Macro directive]
Loop construction for replicating portions of the ‘.mod’ file. Note that this construct can enclose
variable/parameters declaration, computational tasks, but not a model declaration.
Example
Chapter 4: The Model file
80
model;
@#for country in [ "home", "foreign" ]
GDP_@{country} = A * K_@{country}^a * L_@{country}^(1-a);
@#endfor
end;
is equivalent to:
model;
GDP_home = A * K_home^a * L_home^(1-a);
GDP_foreign = A * K_foreign^a * L_foreign^(1-a);
end;
[Macro directive]
Asks the preprocessor to display some message on standard output. The argument must evaluate
to a string.
@#echo MACRO_EXPRESSION
[Macro directive]
Asks the preprocessor to display some error message on standard output and to abort. The
argument must evaluate to a string.
@#error MACRO_EXPRESSION
4.20.3 Typical usages
4.20.3.1 Modularization
The @#include directive can be used to split ‘.mod’ files into several modular components.
Example setup:
‘modeldesc.mod’
Contains variable declarations, model equations and shocks declarations
‘simul.mod’
Includes ‘modeldesc.mod’, calibrates parameters and runs stochastic simulations
‘estim.mod’
Includes ‘modeldesc.mod’, declares priors on parameters and runs bayesian estimation
Dynare can be called on ‘simul.mod’ and ‘estim.mod’, but it makes no sense to run it on
‘modeldesc.mod’.
The main advantage is that it is no longer needed to manually copy/paste the whole model (at
the beginning) or changes to the model (during development).
4.20.3.2 Indexed sums or products
The following example shows how to construct a moving average:
@#define window = 2
var x MA_x;
...
model;
...
MA_x = 1/@{2*window+1}*(
@#for i in -window:window
+x(@{i})
@#endfor
);
...
end;
After macro-processing, this is equivalent to:
Chapter 4: The Model file
81
var x MA_x;
...
model;
...
MA_x = 1/5*(
+x(-2)
+x(-1)
+x(0)
+x(1)
+x(2)
);
...
end;
4.20.3.3 Multi-country models
Here is a skeleton example for a multi-country model:
@#define countries = [ "US", "EA", "AS", "JP", "RC" ]
@#define nth_co = "US"
@#for co in countries
var Y_@{co} K_@{co} L_@{co} i_@{co} E_@{co} ...;
parameters a_@{co} ...;
varexo ...;
@#endfor
model;
@#for co in countries
Y_@{co} = K_@{co}^a_@{co} * L_@{co}^(1-a_@{co});
...
@# if co != nth_co
(1+i_@{co}) = (1+i_@{nth_co}) * E_@{co}(+1) / E_@{co}; // UIP relation
@# else
E_@{co} = 1;
@# endif
@#endfor
end;
4.20.3.4 Endogeneizing parameters
When doing the steady state calibration of the model, it may be useful to consider a parameter as
an endogenous (and vice-versa).
For example, suppose production is defined by a CES function:
ξ/(ξ−1)
y = α1/ξ `1−1/ξ + (1 − α)1/ξ k 1−1/ξ
The labor share in GDP is defined as:
lab_rat = (w`)/(py)
In the model, α is a (share) parameter, and lab_rat is an endogenous variable.
It is clear that calibrating α is not straigthforward; but on the contrary, we have real world data
for lab_rat, and it is clear that these two variables are economically linked.
The solution is to use a method called variable flipping, which consist in changing the way of
computing the steady state. During this computation, α will be made an endogenous variable and
lab_rat will be made a parameter. An economically relevant value will be calibrated for lab_rat,
and the solution algorithm will deduce the implied value for α.
Chapter 4: The Model file
82
An implementation could consist of the following files:
‘modeqs.mod’
This file contains variable declarations and model equations. The code for the declaration of α and lab_rat would look like:
@#if steady
var alpha;
parameter lab_rat;
@#else
parameter alpha;
var lab_rat;
@#endif
‘steady.mod’
This file computes the steady state. It begins with:
@#define steady = 1
@#include "modeqs.mod"
Then it initializes parameters (including lab_rat, excluding α, computes the steady
state (using guess values for endogenous, including α, then saves values of parameters
and endogenous at steady state in a file, using the save_params_and_steady_state
command.
‘simul.mod’
This file computes the simulation. It begins with:
@#define steady = 0
@#include "modeqs.mod"
Then it loads values of parameters and endogenous at steady state from file, using the
load_params_and_steady_state command, and computes the simulations.
4.20.4 MATLAB/Octave loops versus macro-processor loops
Suppose you have a model with a parameter ρ, and you want to make simulations for three values:
ρ = 0.8, 0.9, 1. There are several ways of doing this:
With a MATLAB/Octave loop
rhos = [ 0.8, 0.9, 1];
for i = 1:length(rhos)
rho = rhos(i);
stoch_simul(order=1);
end
Here the loop is not unrolled, MATLAB/Octave manages the iterations. This is interesting when there are a lot of iterations.
With a macro-processor loop (case 1)
rhos = [ 0.8, 0.9, 1];
@#for i in 1:3
rho = rhos(@{i});
stoch_simul(order=1);
@#endfor
This is very similar to previous example, except that the loop is unrolled. The macroprocessor manages the loop index but not the data array (rhos).
With a macro-processor loop (case 2)
@#for rho_val in [ "0.8", "0.9", "1"]
rho = @{rho_val};
Chapter 4: The Model file
83
stoch_simul(order=1);
@#endfor
The advantage of this method is that it uses a shorter syntax, since list of values
directly given in the loop construct. Note that values are given as character strings
(the macro-processor does not know floating point values. The inconvenient is that you
can not reuse an array stored in a MATLAB/Octave variable.
4.21 Misc commands
(INTEGER)
(’default’)
(’reset’)
(’ALGORITHM’, INTEGER)
Sets the seed used for random number generation.
set_dynare_seed
set_dynare_seed
set_dynare_seed
set_dynare_seed
[Command]
[Command]
[Command]
[Command]
save_params_and_steady_state (FILENAME);
[Command]
For all parameters, endogenous and exogenous variables, stores their value in a text file, using
a simple name/value associative table.
• for parameters, the value is taken from the last parameter initialization
• for exogenous, the value is taken from the last initval block
• for endogenous, the value is taken from the last steady state computation (or, if no steady
state has been computed, from the last initval block)
Note that no variable type is stored in the file, so that the values can be reloaded with load_
params_and_steady_state in a setup where the variable types are different.
The typical usage of this function is to compute the steady-state of a model by calibrating the
steady-state value of some endogenous variables (which implies that some parameters must be
endogeneized during the steady-state computation).
You would then write a first ‘.mod’ file which computes the steady state and saves the result of
the computation at the end of the file, using save_params_and_steady_state.
In a second file designed to perform the actual simulations, you would use load_params_and_
steady_state just after your variable declarations, in order to load the steady state previously
computed (including the parameters which had been endogeneized during the steady state computation).
The need for two separate ‘.mod’ files arises from the fact that the variable declarations differ
between the files for steady state calibration and for simulation (the set of endogenous and
parameters differ between the two); this leads to different var and parameters statements.
Also note that you can take advantage of the @#include directive to share the model equations
between the two files (see Section 4.20 [Macro-processing language], page 77).
load_params_and_steady_state (FILENAME);
[Command]
For all parameters, endogenous and exogenous variables, loads their value from a file created
with save_params_and_steady_state.
• for parameters, their value will be initialized as if they had been calibrated in the ‘.mod’
file
• for endogenous and exogenous, their value will be initialized as they would have been from
an initval block
This function is used in conjunction with save_params_and_steady_state; see the documentation of that function for more information.
Chapter 5: The Configuration File
84
5 The Configuration File
The configuration file is used to provide Dynare with information not related to the model (and
hence not placed in the model file). At the moment, it is only used when using Dynare to run
parallel computations.
On Linux and Mac OS X, the default location of the configuration file is
‘$HOME/.dynare’, while on Windows it is ‘%APPDATA%\dynare.ini’ (typically ‘C:\Documents
and Settings\USERNAME\Application Data\dynare.ini’
under
Windows
XP,
or
‘C:\Users\USERNAME\AppData\dynare.ini’ under Windows Vista or Windows 7). You can
specify a non standard location using the conffile option of the dynare command (see Chapter 3
[Dynare invocation], page 6).
The parsing of the configuration file is case-sensitive and it should take the following form, with
each option/choice pair placed on a newline:
[command0]
option0 = choice0
option1 = choice1
[command1]
option0 = choice0
option1 = choice1
The configuration file follows a few conventions (self-explanatory conventions such as
USER NAME have been excluded for concision):
COMPUTER NAME
Indicates the valid name of a server (e.g. localhost, server.cepremap.org) or an IP
address.
DRIVE NAME
Indicates a valid drive name in Windows, without the trailing colon (e.g. C).
PATH
Indicates a valid path in
/home/user/dynare/matlab/).
the
underlying
operating
system
(e.g.
PATH AND FILE
Indicates a valid path to a file in the underlying operating system (e.g.
/usr/local/MATLAB/R2010b/bin/matlab).
BOOLEAN
Is true or false.
5.1 Dynare Configuration
This section explains how to configure Dynare for general processing. Currently, there is only one
option available.
[hooks]
[Configuration block]
Description
The [hooks] block can be used to specify configuration options that will be used when running
dynare.
Options
GlobalInitFile = PATH_AND_FILE
The location of the global initialization file to be run at the end of global_
initialization.m
Chapter 5: The Configuration File
85
Example
[hooks]
GlobalInitFile = /home/usern/dynare/myInitFile.m
5.2 Parallel Configuration
This section explains how to configure Dynare for parallelizing some tasks which require very little
inter-process communication.
The parallelization is done by running several MATLAB or Octave processes, either on local or
on remote machines. Communication between master and slave processes are done through SMB
on Windows and SSH on UNIX. Input and output data, and also some short status messages, are
exchanged through network filesystems. Currently the system works only with homogenous grids:
only Windows or only Unix machines.
The following routines are currently parallelized:
• the Metropolis-Hastings algorithm;
• the Metropolis-Hastings diagnostics;
• the posterior IRFs;
• the prior and posterior statistics;
• some plotting routines.
Note that creating the configuration file is not enough in order to trigger parallelization of
the computations: you also need to specify the parallel option to the dynare command. For
more details, and for other options related to the parallelization engine, see see Chapter 3 [Dynare
invocation], page 6.
You also need to verify that the following requirements are met by your cluster (which is composed of a master and of one or more slaves):
For a Windows grid
• a standard Windows network (SMB) must be in place;
• PsTools must be installed in the path of the master Windows machine;
• the Windows user on the master machine has to be user of any other slave machine
in the cluster, and that user will be used for the remote computations.
For a UNIX grid
• SSH must be installed on the master and on the slave machines;
• SSH keys must be installed so that the SSH connection from the master to the
slaves can be done without passwords, or using an SSH agent
We now turn to the description of the configuration directives:
[cluster]
[Configuration block]
Description
When working in parallel, [cluster] is required to specify the group of computers that will be
used. It is required even if you are only invoking multiple processes on one computer.
Options
Name = CLUSTER_NAME
The reference name of this cluster.
Chapter 5: The Configuration File
86
Members = NODE_NAME[(WEIGHT)] NODE_NAME[(WEIGHT)] ...
A list of nodes that comprise the cluster with an optional computing weight specified
for that node. The computing weight indicates how much more powerful one node
is with respect to the others (e.g. n1(2) n2(1) n3(3), means that n1 is two times
more powerful than n2 whereas n3 is three times more powerful than n2). Each
node is separated by at least one space and the weights are in parenthesis with no
spaces separating them from their node.
Example
[cluster]
Name = c1
Members = n1 n2 n3
[cluster]
Name = c2
Members = n1(4) n2 n3
[node]
[Configuration block]
Description
When working in parallel, [node] is required for every computer that will be used. The options
that are required differ, depending on the underlying operating system and whether you are
working locally or remotely.
Options
Name = NODE_NAME
The reference name of this node.
CPUnbr = INTEGER | [INTEGER:INTEGER]
If just one integer is passed, the number of processors to use. If a range of integers
is passed, the specific processors to use (processor counting is defined to begin at
one as opposed to zero). Note that using specific processors is only possible under
Windows; under Linux and Mac OS X, if a range is passed the same number of
processors will be used but the range will be adjusted to begin at one.
ComputerName = COMPUTER_NAME
The name or IP address of the node. If you want to run locally, use localhost
(case-sensitive).
Port = INTEGER
The port number to connect to on the node. The default is empty, meaning that
the connection will be made to the default SSH port (22).
UserName = USER_NAME
The username used to log into a remote system. Required for remote runs on all
platforms.
Password = PASSWORD
The password used to log into the remote system. Required for remote runs originating from Windows.
RemoteDrive = DRIVE_NAME
The drive to be used for remote computation. Required for remote runs originating
from Windows.
Chapter 5: The Configuration File
87
RemoteDirectory = PATH
The directory to be used for remote computation. Required for remote runs on all
platforms.
DynarePath = PATH
The path to the ‘matlab’ subdirectory within the Dynare installation directory. The
default is the empty string.
MatlabOctavePath = PATH_AND_FILE
The path to the MATLAB or Octave executable. The default value is matlab.
SingleCompThread = BOOLEAN
Whether or not to disable MATLAB’s native multithreading. The default value is
true. Option meaningless under Octave.
OperatingSystem = OPERATING_SYSTEM
The operating system associated with a node. Only necessary when creating a
cluster with nodes from different operating systems. Possible values are unix or
windows. There is no default value.
Example
[node]
Name = n1
ComputerName = localhost
CPUnbr = 1
[node]
Name = n2
ComputerName = dynserv.cepremap.org
CPUnbr = 5
UserName = usern
RemoteDirectory = /home/usern/Remote
DynarePath = /home/usern/dynare/matlab
MatlabOctavePath = matlab
[node]
Name = n3
ComputerName = dynserv.dynare.org
Port = 3333
CPUnbr = [2:4]
UserName = usern
RemoteDirectory = /home/usern/Remote
DynarePath = /home/usern/dynare/matlab
MatlabOctavePath = matlab
Chapter 6: Examples
88
6 Examples
Dynare comes with a database of example ‘.mod’ files, which are designed to show a broad range
of Dynare features, and are taken from academic papers for most of them. You should have these
files in the ‘examples’ subdirectory of your distribution.
Here is a short list of the examples included. For a more complete description, please refer to
the comments inside the files themselves.
‘ramst.mod’
An elementary real business cycle (RBC) model, simulated in a deterministic setup.
‘example1.mod’
‘example2.mod’
Two examples of a small RBC model in a stochastic setup, presented in Collard (2001)
(see the file ‘guide.pdf’ which comes with Dynare).
‘fs2000.mod’
A cash in advance model, estimated by Schorfheide (2000).
‘fs2000_nonstationary.mod’
The same model than ‘fs2000.mod’, but written in non-stationary form. Detrending
of the equations is done by Dynare.
‘bkk.mod’
Multi-country RBC model with time to build, presented in Backus, Kehoe and Kydland
(1992).
‘agtrend.mod’
Small open economy RBC model with shocks to the growth trend, presented in Aguiar
and Gopinath (2004).
Chapter 7: Dynare internal documentation and unitary tests
89
7 Dynare internal documentation and unitary tests
One can obtain internal documentation of matlab/octave’s routines or perform unitary tests using
the internals command. This is a new feature, and, at this time, will work properly for a small
number of routines. At the top of the (available) matlab/octave routines a commented block for
the internal documentation is written in the GNU texinfo documentation format. This block is
processed by calling texinfo from matlab. Consequently, texinfo has to be installed on your machine.
internals FLAG ROUTINENAME[.m]
[MATLAB/Octave command]
Description
Depending on the FLAG this command prints internal documentation of a matlab/octave routine or triggers unitary tests associated to this routine.
Flags
--info
Prints on screen the internal documentation of ROUTINENAME (if this routine exists and if this routine has texinfo internal documentation header). If the command
is executed in the matlab directory of Dynare, then the path to ROUTINENAME
has to be provided.
--test
Performs the unitary test associated to ROUTINENAME (if this routine exists and
if the matalab/octave m file has unitary test sections).
Example
internals --info particle/local_state_iteration
internals --test particle/local_state_iteration
Chapter 8: Bibliography
90
8 Bibliography
• Aguiar, Mark and Gopinath, Gita (2004): “Emerging Market Business Cycles: The Cycle is
the Trend,” NBER Working Paper, 10734
• Backus, David K., Patrick J. Kehoe, and Finn E. Kydland (1992): “International Real Business
Cycles,” Journal of Political Economy, 100(4), 745–775
• Boucekkine, Raouf (1995): “An alternative methodology for solving nonlinear forward-looking
models,” Journal of Economic Dynamics and Control, 19, 711–734
• Collard, Fabrice (2001): “Stochastic simulations with Dynare: A practical guide”
• Collard, Fabrice and Michel Juillard (2001a): “Accuracy of stochastic perturbation methods:
The case of asset pricing models,” Journal of Economic Dynamics and Control, 25, 979–999
• Collard, Fabrice and Michel Juillard (2001b): “A Higher-Order Taylor Expansion Approach
to Simulation of Stochastic Forward-Looking Models with an Application to a Non-Linear
Phillips Curve,” Computational Economics, 17, 125–139
• Dennis, Richard (2007): “Optimal Policy In Rational Expectations Models: New Solution
Algorithms,” Macroeconomic Dynamics, 11(1), 31–55
• Durbin, J. and S. J. Koopman (2001), Time Series Analysis by State Space Methods, Oxford
University Press
• Fair, Ray and John Taylor (1983): “Solution and Maximum Likelihood Estimation of Dynamic
Nonlinear Rational Expectation Models,” Econometrica, 51, 1169–1185
• Fernández-Villaverde, Jesús and Juan Rubio-Ramı́rez (2004): “Comparing Dynamic Equilibrium Economies to Data: A Bayesian Approach,” Journal of Econometrics, 123, 153–187
• Fernández-Villaverde, Jesús and Juan Rubio-Ramı́rez (2005): “Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood,” Journal of Applied Econometrics, 20,
891–910
• Ireland, Peter (2004): “A Method for Taking Models to the Data,” Journal of Economic
Dynamics and Control, 28, 1205–26
• Iskrev, Nikolay (2010): “Local identification in DSGE models,” Journal of Monetary Economics, 57(2), 189–202
• Judd, Kenneth (1996): “Approximation, Perturbation, and Projection Methods in Economic
Analysis”, in Handbook of Computational Economics, ed. by Hans Amman, David Kendrick,
and John Rust, North Holland Press, 511–585
• Juillard, Michel (1996): “Dynare: A program for the resolution and simulation of dynamic
models with forward variables through the use of a relaxation algorithm,” CEPREMAP, Couverture Orange, 9602
• Kim, Jinill, Sunghyun Kim, Ernst Schaumburg, and Christopher A. Sims (2008): “Calculating and using second-order accurate solutions of discrete time dynamic equilibrium models,”
Journal of Economic Dynamics and Control, 32(11), 3397–3414
• Koopman, S. J. and J. Durbin (2003): “Filtering and Smoothing of State Vector for Diffuse
State Space Models,” Journal of Time Series Analysis, 24(1), 85–98
• Laffargue, Jean-Pierre (1990): “Résolution d’un modèle macroéconomique avec anticipations
rationnelles”, Annales d’Économie et Statistique, 17, 97–119
• Lubik, Thomas and Frank Schorfheide (2007): “Do Central Banks Respond to Exchange Rate
Movements? A Structural Investigation,” Journal of Monetary Economics, 54(4), 1069–1087
• Mancini-Griffoli, Tommaso (2007): “Dynare User Guide: An introduction to the solution and
estimation of DSGE models”
• Pearlman, Joseph, David Currie, and Paul Levine (1986): “Rational expectations models with
partial information,” Economic Modelling, 3(2), 90–105
Chapter 8: Bibliography
91
• Rabanal, Pau and Juan Rubio-Ramirez (2003): “Comparing New Keynesian Models of the
Business Cycle: A Bayesian Approach,” Federal Reserve of Atlanta, Working Paper Series,
2003-30.
• Ratto, Marco (2008): “Analysing DSGE models with global sensitivity analysis”, Computational Economics, 31, 115–139
• Schorfheide, Frank (2000): “Loss Function-based evaluation of DSGE models,” Journal of
Applied Econometrics, 15(6), 645–670
• Schmitt-Grohé, Stephanie and Martin Urı́be (2004): “Solving Dynamic General Equilibrium
Models Using a Second-Order Approximation to the Policy Function,” Journal of Economic
Dynamics and Control, 28(4), 755–775
• Sims, Christopher A., Daniel F. Waggoner and Tao Zha (2008): “Methods for inference in
large multiple-equation Markov-switching models,” Journal of Econometrics, 146, 255–274
• Smets, Frank and Rafael Wouters (2003): “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area,” Journal of the European Economic Association, 1(5), 1123–1175
• Villemot, Sébastien (2011): “Solving rational expectations models at first order: what Dynare
does,” Dynare Working Papers, 2, CEPREMAP
Command and Function Index
92
Command and Function Index
F
@
@#define . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
@#echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
@#else . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
@#endfor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
@#endif . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
@#error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
@#for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
@#if . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
@#ifdef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
@#include . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
80
79
79
79
80
79
79
79
78
[
[cluster] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
[hooks] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
[node] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
A
abs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
acos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
asin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
atan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
14
14
14
B
bvar_density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
bvar_forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
C
calib_smoother . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
change_type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
conditional_forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . .
conditional_forecast_paths . . . . . . . . . . . . . . . . . . . . .
cos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
11
30
56
57
14
D
discretionary_policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
dsample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
dynare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
dynare_sensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
dynasave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
dynatype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
E
endval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
erf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
estimated_params . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
estimated_params_bounds . . . . . . . . . . . . . . . . . . . . . . . . .
estimated_params_init . . . . . . . . . . . . . . . . . . . . . . . . . . .
estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
exp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
EXPECTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
extended_path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
external_function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
14
42
44
44
44
14
13
38
15
forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
H
histval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
homotopy_setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
I
identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
inf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
initval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
initval_file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
internals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
12
20
22
89
L
ln . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
load_params_and_steady_state . . . . . . . . . . . . . . . . . . .
log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
log10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
83
14
14
M
markov_switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
model_comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
model_info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ms_compute_mdd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ms_compute_probabilities . . . . . . . . . . . . . . . . . . . . . . . .
ms_estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ms_forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ms_irf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ms_simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ms_variance_decomposition . . . . . . . . . . . . . . . . . . . . . .
mshocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
14
14
16
53
31
73
73
69
75
74
72
76
25
N
nan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
normcdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
normpdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
O
observation_trends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
optim_weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
osr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
osr_params . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
58
58
58
P
parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
planner_objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
plot_conditional_forecast . . . . . . . . . . . . . . . . . . . . . .
predetermined_variables . . . . . . . . . . . . . . . . . . . . . . . . .
print_bytecode_dynamic_model . . . . . . . . . . . . . . . . . . .
10
26
60
57
11
32
Command and Function Index
93
print_bytecode_static_model . . . . . . . . . . . . . . . . . . . . 32
svar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
R
T
ramsey_policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
resid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
rplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
tan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
trend_var . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
U
S
save_params_and_steady_state . . . . . . . . . . . . . . . . . . .
set_dynare_seed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
shock_decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
simul . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
sin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
sqrt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
steady . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
STEADY_STATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
steady_state_model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
stoch_simul . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
unit_root_vars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
83
83
53
23
14
32
14
14
26
13
29
34
V
var . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
varexo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
varexo_det . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
varobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
W
write_latex_dynamic_model . . . . . . . . . . . . . . . . . . . . . . 18
write_latex_static_model . . . . . . . . . . . . . . . . . . . . . . . . 18
Variable Index
94
Variable Index
M
M_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
M_.endo_nbr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
M_.orig_endo_nbr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
M_.params . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16, 50
M_.Sigma_e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
O
oo_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
oo_.autocorr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
oo_.conditional_variance_decomposition. . . . . . . . 41
oo_.dr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
oo_.dr.eigval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
oo_.dr.g_0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
oo_.dr.g_1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
oo_.dr.g_2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
oo_.dr.g_3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
oo_.dr.ghs2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
oo_.dr.ghu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
oo_.dr.ghuu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
oo_.dr.ghx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
oo_.dr.ghxu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
oo_.dr.ghxx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
oo_.dr.inv_order_var . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
oo_.dr.nboth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
oo_.dr.nfwrd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
oo_.dr.npred . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
oo_.dr.nstatic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
oo_.dr.order_var . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
oo_.dr.ys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39, 40
oo_.endo_simul. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33, 36
oo_.exo_simul . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
oo_.FilteredVariables . . . . . . . . . . . . . . . . . . . . . . . 48, 51
oo_.FilteredVariablesKStepAhead . . . . . . . . . . . . 48, 51
oo_.FilteredVariablesKStepAheadVariances . . 48, 51
oo_.forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48, 56
oo_.gamma_y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
oo_.irfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
oo_.MarginalDensity.LaplaceApproximation . . . . . 51
oo_.MarginalDensity.ModifiedHarmonicMean . . . . . 51
oo_.mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
oo_.MeanForecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
oo_.osr.objective_function . . . . . . . . . . . . . . . . . . . . . 59
oo_.planner_objective_value . . . . . . . . . . . . . . . . . . . . 59
oo_.PointForecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
oo_.posterior_density . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
oo_.posterior_hpdinf . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
oo_.posterior_hpdsup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
oo_.posterior_mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
oo_.posterior_mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
oo_.posterior_std . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
oo_.PosteriorIRF.dsge . . . . . . . . . . . . . . . . . . . . . . . 47, 52
oo_.PosteriorTheoreticalMoments . . . . . . . . . . . . 48, 52
oo_.SmoothedMeasurementErrors . . . . . . . . . . . . . . 48, 52
oo_.SmoothedShocks . . . . . . . . . . . . . . . . . . . . . . . 48, 52, 54
oo_.SmoothedVariables . . . . . . . . . . . . . . . . . . . . 48, 52, 54
oo_.steady_state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
oo_.UpdatedVariables . . . . . . . . . . . . . . . . . . . . . 48, 52, 54
oo_.var . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
options_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
S
Sigma_e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
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