\input texinfo
@c %**start of header
@setfilename dynare.info
@documentencoding UTF-8
@settitle Dynare Reference Manual
@afourwide
@dircategory Math
@direntry
* Dynare: (dynare). A platform for handling a wide class
of economic models.
@end direntry
@include version.texi
@c Define some macros
@macro descriptionhead
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@sp 1
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@emph{Description}
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@macro optionshead
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@emph{Options}
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@macro flagshead
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@emph{Flags}
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@macro examplehead
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@emph{Example}
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@macro outputhead
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@emph{Output}
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@macro algorithmhead
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@emph{Algorithm}
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@macro algorithmshead
@iftex
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@emph{Algorithms}
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@macro customhead{title}
@iftex
@sp 1
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@emph{\title\}
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@c %**end of header
@copying
Copyright @copyright{} 1996-2013, Dynare Team.
@quotation
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 @uref{http://www.gnu.org/licenses/fdl.txt}.
@end quotation
@end copying
@titlepage
@title Dynare
@subtitle Reference Manual, version @value{VERSION}
@author Stéphane Adjemian
@author Houtan Bastani
@author Frédéric Karamé
@author Michel Juillard
@author Junior Maih
@author Ferhat Mihoubi
@author George Perendia
@author Johannes Pfeifer
@author Marco Ratto
@author Sébastien Villemot
@page
@vskip 0pt plus 1filll
@insertcopying
@end titlepage
@contents
@ifnottex
@node Top
@top Dynare
This is Dynare Reference Manual, version @value{VERSION}.
@insertcopying
@end ifnottex
@menu
* Introduction::
* Installation and configuration::
* Running Dynare::
* The Model file::
* The Configuration File::
* Time Series::
* Reporting::
* Examples::
* Dynare internal documentation and unitary tests::
* Bibliography::
* Command and Function Index::
* Variable Index::
@detailmenu
--- The Detailed Node Listing ---
Introduction
* What is Dynare ?::
* Documentation sources::
* Citing Dynare in your research::
Installation and configuration
* Software requirements::
* Installation of Dynare::
* Configuration::
Installation of Dynare
* On Windows::
* On Debian GNU/Linux and Ubuntu::
* On Mac OS X::
* For other systems::
Configuration
* For MATLAB::
* For GNU Octave::
* Some words of warning::
Running Dynare
* Dynare invocation::
* Dynare hooks::
* Understanding Preprocessor Error Messages::
Dynare invocation
* Dynare hooks
* Understanding Preprocessor Error Messages::
The Model file
* Conventions::
* Variable declarations::
* Expressions::
* Parameter initialization::
* Model declaration::
* Auxiliary variables::
* Initial and terminal conditions::
* Shocks on exogenous variables::
* Other general declarations::
* Steady state::
* Getting information about the model::
* Deterministic simulation::
* Stochastic solution and simulation::
* Estimation::
* Forecasting::
* Optimal policy::
* Sensitivity and identification analysis::
* Markov-switching SBVAR::
* Displaying and saving results::
* Macro-processing language::
* Misc commands::
Expressions
* Parameters and variables::
* Operators::
* Functions::
* A few words of warning in stochastic context::
Parameters and variables
* Inside the model::
* Outside the model::
Functions
* Built-in Functions::
* External Functions::
Steady state
* Finding the steady state with Dynare nonlinear solver::
* Using a steady state file::
* Replace some equations during steady state computations::
Stochastic solution and simulation
* Computing the stochastic solution::
* Typology and ordering of variables::
* First order approximation::
* Second order approximation::
* Third order approximation::
Sensitivity and identification analysis
* Sampling::
* Stability Mapping::
* Reduced Form Mapping::
* RMSE::
* Screening Analysis::
* Identification Analysis::
* Performing Sensitivity and Identification Analysis::
Macro-processing language
* Macro expressions::
* Macro directives::
* Typical usages::
* MATLAB/Octave loops versus macro-processor loops::
Typical usages
* Modularization::
* Indexed sums or products::
* Multi-country models::
* Endogeneizing parameters::
The Configuration File
* Dynare Configuration::
* Parallel Configuration::
@end detailmenu
@end menu
@node Introduction
@chapter Introduction
@menu
* What is Dynare ?::
* Documentation sources::
* Citing Dynare in your research::
@end menu
@node What is Dynare ?
@section 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 @i{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, @dots{}
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
@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
@uref{http://www.mathworks.com/products/matlab/, 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
@uref{http://www.octave.org, 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
@uref{http://www.cepremap.ens.fr, 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 du Maine, Gains and Cepremap), Junior Maih (IMF),
Ferhat Mihoubi (Université d'Évry, Epee and Cepremap), George
Perendia, Johannes Pfeifer (Universität Tübingen), Marco Ratto (JRC)
and Sébastien Villemot (Cepremap).
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.
Interaction between developers and users of Dynare is central to the
project. A @uref{http://www.dynare.org/phpBB3, 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.
@node Documentation sources
@section 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 (@cite{Mancini
(2007)}), distributed with Dynare and also available from the
@uref{http://www.dynare.org,official Dynare web site}.
Other useful sources of information include the
@uref{http://www.dynare.org,Dynare wiki} and the
@uref{http://www.dynare.org/phpBB3, Dynare forums}.
@node Citing Dynare in your research
@section 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:
@quotation
Stéphane Adjemian, Houtan Bastani, Michel Juillard, Frédéric Karamé,
Ferhat Mihoubi, George Perendia, Johannes Pfeifer, Marco Ratto and
Sébastien Villemot (2011), ``Dynare: Reference Manual, Version 4,''
@i{Dynare Working Papers}, 1, CEPREMAP
@end quotation
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:
@uref{http://www.dynare.org}.
@node Installation and configuration
@chapter Installation and configuration
@menu
* Software requirements::
* Installation of Dynare::
* Configuration::
@end menu
@node Software requirements
@section Software requirements
Packaged versions of Dynare are available for Windows XP/Vista/7/8,
@uref{http://www.debian.org,Debian GNU/Linux},
@uref{http://www.ubuntu.com/,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:
@itemize
@item
MATLAB version 7.3 (R2006b) or above;
@item
GNU Octave version 3.6 or above.
@end itemize
Packages of GNU Octave can be downloaded on the
@uref{http://www.dynare.org/download/octave,Dynare website}.
The following optional extensions are also useful to benefit from extra
features, but are in no way required:
@itemize
@item
If under MATLAB: the optimization toolbox, the statistics toolbox, the
control system toolbox;
@item
If under GNU Octave, the following
@uref{http://octave.sourceforge.net/,Octave-Forge} packages: optim,
io, java, statistics, control.
@end itemize
If you plan to use the @code{use_dll} option of the @code{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
@uref{http://www.dynare.org/DynareWiki/ConfigureMatlabWindowsForMexCompilation,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
@file{liboctave-dev}). If you are
using Octave or MATLAB under Mac OS X, you should install the latest
version of XCode: see
@uref{http://www.dynare.org/DynareWiki/InstallOnMacOSX,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.
@node Installation of Dynare
@section 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.
@menu
* On Windows::
* On Debian GNU/Linux and Ubuntu::
* On Mac OS X::
* For other systems::
@end menu
@node On Windows
@subsection On Windows
Execute the automated installer called @file{dynare-4.@var{x}.@var{y}-win.exe}
(where 4.@var{x}.@var{y} is the version number), and follow the instructions. The
default installation directory is @file{c:\dynare\4.@var{x}.@var{y}}.
After installation, this directory will contain several sub-directories,
among which are @file{matlab}, @file{mex} and @file{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 @file{c:\dynare}), as long as you correctly adjust your path
settings (@pxref{Some words of warning}).
@node On Debian GNU/Linux and Ubuntu
@subsection On Debian GNU/Linux and Ubuntu
Please refer to the
@uref{http://www.dynare.org/DynareWiki/InstallOnDebianOrUbuntu,Dynare
Wiki} for detailed instructions.
Dynare will be installed under @file{/usr/share/dynare} and
@file{/usr/lib/dynare}. Documentation will be under
@file{/usr/share/doc/dynare}.
@node On Mac OS X
@subsection On Mac OS X
Execute the automated installer called
@file{dynare-4.@var{x}.@var{y}.pkg} (where
4.@var{x}.@var{y} is the version number), and follow the
instructions. The default installation directory is
@file{/Applications/Dynare/4.@var{x}.@var{y}}.
Please refer to the
@uref{http://www.dynare.org/DynareWiki/InstallOnMacOSX,Dynare Wiki} for
detailed instructions.
After installation, this directory will contain several sub-directories,
among which are @file{matlab}, @file{mex} and @file{doc}.
Note that you can have several versions of Dynare coexisting (for
example in @file{/Applications/Dynare}), as long as you correctly
adjust your path settings (@pxref{Some words of warning}).
@node For other systems
@subsection For other systems
You need to download Dynare source code from the
@uref{http://www.dynare.org,Dynare website} and unpack it somewhere.
Then you will need to recompile the pre-processor and the dynamic
loadable libraries. Please refer to
@uref{https://github.com/DynareTeam/dynare/blob/master/README.md,README.md}.
@node Configuration
@section Configuration
@menu
* For MATLAB::
* For GNU Octave::
* Some words of warning::
@end menu
@node For MATLAB
@subsection For MATLAB
You need to add the @file{matlab} subdirectory of your Dynare
installation to MATLAB path. You have two options for doing that:
@itemize
@item
Using the @code{addpath} command in the MATLAB command window:
Under Windows, assuming that you have installed Dynare in the standard
location, and replacing @code{4.@var{x}.@var{y}} with the correct
version number, type:
@example
addpath c:\dynare\4.@var{x}.@var{y}\matlab
@end example
Under Debian GNU/Linux or Ubuntu, type:
@example
addpath /usr/share/dynare/matlab
@end example
Under Mac OS X, assuming that you have installed Dynare in the standard
location, and replacing @code{4.@var{x}.@var{y}} with the correct version
number, type:
@example
addpath /Applications/Dynare/4.@var{x}.@var{y}/matlab
@end example
MATLAB will not remember this setting next time you run it, and you
will have to do it again.
@item
Via the menu entries:
Select the ``Set Path'' entry in the ``File'' menu, then click on
``Add Folder@dots{}'', and select the @file{matlab} subdirectory of your
Dynare installation. Note that you @emph{should not} use ``Add with
Subfolders@dots{}''. Apply the settings by clicking on ``Save''. Note that
MATLAB will remember this setting next time you run it.
@end itemize
@node For GNU Octave
@subsection For GNU Octave
You need to add the @file{matlab} subdirectory of your Dynare
installation to Octave path, using the @code{addpath} at the Octave
command prompt.
Under Windows, assuming that you have installed Dynare in the standard
location, and replacing ``4.@var{x}.@var{y}'' with the correct version
number, type:
@example
addpath c:\dynare\4.@var{x}.@var{y}\matlab
@end example
Under Debian GNU/Linux or Ubuntu, there is no need to use the
@code{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.@var{x}.@var{y}'' with the correct
version number, type:
@example
addpath /Applications/Dynare/4.@var{x}.@var{y}/matlab
@end example
If you don't want to type this command every time you run Octave, you
can put it in a file called @file{.octaverc} in your home directory
(under Windows this will generally be @file{c:\Documents and
Settings\USERNAME\} while under Mac OS X it is @file{/Users/USERNAME/}).
This file is run by Octave at every startup.
@node Some words of warning
@subsection 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 @code{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 @file{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 any of your M-files have the same name
as a Dynare file. Your file would then override the Dynare file, making
Dynare unusable.
@node Running Dynare
@chapter Running Dynare
In order to give instructions to Dynare, the user has to write a
@emph{model file} whose filename extension must be @file{.mod}. This
file contains the description of the model and the computing tasks
required by the user. Its contents is described in @ref{The Model file}.
@menu
* Dynare invocation::
* Dynare hooks::
* Understanding Preprocessor Error Messages::
@end menu
@node Dynare invocation
@section Dynare invocation
Once the model file is written, Dynare is invoked using the
@code{dynare} command at the MATLAB or Octave prompt (with the filename
of the @file{.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 @emph{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 @code{dynare} command.
@deffn {MATLAB/Octave command} dynare @var{FILENAME}[.mod] [@var{OPTIONS}@dots{}]
@descriptionhead
This command launches Dynare and executes the instructions included in
@file{@var{FILENAME}.mod}. This user-supplied file contains the model
and the processing instructions, as described in @ref{The Model file}.
@code{dynare} begins by launching the preprocessor on the @file{.mod}
file. By default (unless @code{use_dll} option has been given to
@code{model}), the preprocessor creates three intermediary files:
@table @file
@item @var{FILENAME}.m
Contains variable declarations, and computing tasks
@item @var{FILENAME}_dynamic.m
Contains the dynamic model equations
@item @var{FILENAME}_static.m
Contains the long run static model equations
@end table
@noindent
These files may be looked at to understand errors reported at the simulation stage.
@code{dynare} will then run the computing tasks by executing @file{@var{FILENAME}.m}.
@optionshead
@table @code
@item noclearall
By default, @code{dynare} will issue a @code{clear all} command to
MATLAB or Octave, thereby deleting all workspace variables; this options
instructs @code{dynare} not to clear the workspace
@item debug
Instructs the preprocessor to write some debugging information about the
scanning and parsing of the @file{.mod} file
@item 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
@item savemacro[=@var{FILENAME}]
Instructs @code{dynare} to save the intermediary file which is obtained
after macro-processing (@pxref{Macro-processing language}); the saved
output will go in the file specified, or if no file is specified in
@file{@var{FILENAME}-macroexp.mod}
@item 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.
@item nolinemacro
Instructs the macro-preprocessor to omit line numbering information in
the intermediary @file{.mod} file created after the maco-processing
step. Useful in conjunction with @code{savemacro} when one wants that to
reuse the intermediary @file{.mod} file, without having it cluttered by
line numbering directives.
@item nolog
Instructs Dynare to no create a logfile of this run in
@file{@var{FILENAME}.log}. The default is to create the logfile.
@item nowarn
Suppresses all warnings.
@item warn_uninit
Display a warning for each variable or parameter which is not
initialized. @xref{Parameter initialization}, or
@ref{load_params_and_steady_state} for initialization of parameters.
@xref{Initial and terminal conditions}, or
@ref{load_params_and_steady_state} for initialization of endogenous
and exogenous variables.
@item console
Activate console mode. In addition to the behavior of
@code{nodisplay}, Dynare will not use graphical waitbars for long
computations.
@item cygwin
Tells Dynare that your MATLAB is configured for compiling MEX files with
Cygwin (@pxref{Software requirements}). This option is only available
under Windows, and is used in conjunction with @code{use_dll}.
@item msvc
Tells Dynare that your MATLAB is configured for compiling MEX files with
Microsoft Visual C++ (@pxref{Software requirements}). This option is
only available under Windows, and is used in conjunction with
@code{use_dll}.
@item parallel[=@var{CLUSTER_NAME}]
Tells Dynare to perform computations in parallel. If @var{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. @xref{The Configuration File}, for more
information about the configuration file.
@item conffile=@var{FILENAME}
Specifies the location of the configuration file if it differs from the
default. @xref{The Configuration File}, for more information about the
configuration file and its default location.
@item 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.
@item parallel_test
Tests the parallel setup specified in the configuration file without
executing the @file{.mod} file. @xref{The Configuration File}, for more
information about the configuration file.
@item -D@var{MACRO_VARIABLE}=@var{MACRO_EXPRESSION}
Defines a macro-variable from the command line (the same effect as using
the Macro directive @code{@@#define} in a model file, @pxref{Macro-processing language}).
@end table
@outputhead
Depending on the computing tasks requested in the @file{.mod} file,
executing command @code{dynare} will leave in the workspace variables
containing results available for further processing. More details are
given under the relevant computing tasks.
The @code{M_}, @code{oo_} and @code{options_} structures are also saved
in a file called @file{@var{FILENAME}_results.mat}.
@examplehead
@example
dynare ramst
dynare ramst.mod savemacro
@end example
@end deffn
The output of Dynare is left into three main variables in the
MATLAB/Octave workspace:
@defvr {MATLAB/Octave variable} M_
Structure containing various informations about the model.
@end defvr
@defvr {MATLAB/Octave variable} options_
Structure contains the values of the various options used by Dynare
during the computation.
@end defvr
@defvr {MATLAB/Octave variable} oo_
Structure containing the various results of the computations.
@end defvr
@node Dynare hooks
@section Dynare hooks
It is possible to call pre and post dynare preprocessor hooks written as matlab scripts.
The script @file{@var{FILENAME}_pre_dynare_preprocessor_hook.m} is executed before the
call to Dynare's preprocessor, and can be used to programatically transform the mod file
that will be read by the preprocessor. The script @file{@var{FILENAME}_post_dynare_preprocessor_hook.m}
is executed just after the call to Dynare's preprocessor, and can be used to programatically
transform the files generated by Dynare's preprocessor before actual computations start. The
pre and/or post dynare preprocessor hooks are executed if and only if the aforementioned scripts
are detected in the same folder as the the model file, @file{@var{FILENAME}.mod}.
@node Understanding Preprocessor Error Messages
@section Understanding Preprocessor Error Messages
If the preprocessor runs into an error while processing your
@file{.mod} file, it will issue an error. Due to the way that a parser
works, sometimes these errors can be misleading. Here, we aim to
demystify these error messages.
The preprocessor issues error messages of the form:
@enumerate
@item @code{ERROR: <>: line A, col B: <>}
@item @code{ERROR: <>: line A, cols B-C: <>}
@item @code{ERROR: <>: line A, col B - line C, col D: <>}
@end enumerate
@noindent The first two errors occur on a single line, with error
two spanning multiple columns. Error three spans multiple rows.
Often, the line and column numbers are precise, leading you directly
to the offending syntax. Infrequently however, because of the way the
parser works, this is not the case. The most common example of
misleading line and column numbers (and error message for that matter)
is the case of a missing semicolon, as seen in the following example:
@example
varexo a, b
parameters c, ...;
@end example
@noindent In this case, the parser doesn't know a semicolon is missing at the
end of the @code{varexo} command until it begins parsing the second
line and bumps into the @code{parameters} command. This is because we
allow commands to span multiple lines and, hence, the parser cannot
know that the second line will not have a semicolon on it until it
gets there. Once the parser begins parsing the second line, it
realizes that it has encountered a keyword, @code{parameters}, which
it did not expect. Hence, it throws an error of the form: @code{ERROR:
<>: line 2, cols 0-9: syntax error, unexpected
PARAMETERS}. In this case, you would simply place a semicolon at the
end of line one and the parser would continue processing.
@node The Model file
@chapter The Model file
@menu
* Conventions::
* Variable declarations::
* Expressions::
* Parameter initialization::
* Model declaration::
* Auxiliary variables::
* Initial and terminal conditions::
* Shocks on exogenous variables::
* Other general declarations::
* Steady state::
* Getting information about the model::
* Deterministic simulation::
* Stochastic solution and simulation::
* Estimation::
* Forecasting::
* Optimal policy::
* Sensitivity and identification analysis::
* Markov-switching SBVAR::
* Displaying and saving results::
* Macro-processing language::
* Misc commands::
@end menu
@node Conventions
@section 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
(@code{;}). Blocks are terminated by @code{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:
@itemize
@item
optional arguments or options are indicated between square brackets:
@samp{[]};
@item
repreated arguments are indicated by ellipses: ``@dots{}'';
@item
mutually exclusive arguments are separated by vertical bars: @samp{|};
@item
@var{INTEGER} indicates an integer number;
@item
@var{DOUBLE} indicates a double precision number. The following syntaxes
are valid: @code{1.1e3}, @code{1.1E3}, @code{1.1d3}, @code{1.1D3}. In
some places, infinite values @code{Inf} and @code{-Inf} are also allowed;
@item
@var{NUMERICAL_VECTOR} indicates a vector of numbers separated by spaces,
enclosed by square brackets;
@item
@var{EXPRESSION} indicates a mathematical expression valid outside the
model description (@pxref{Expressions});
@item
@var{MODEL_EXPRESSION} indicates a mathematical expression valid in the
model description (@pxref{Expressions} and @ref{Model declaration});
@item
@var{MACRO_EXPRESSION} designates an expression of the macro-processor
(@pxref{Macro expressions});
@item
@var{VARIABLE_NAME} indicates a variable name starting with an
alphabetical character and can't contain: @samp{()+-*/^=!;:@@#.} or
accentuated characters;
@item
@var{PARAMETER_NAME} indicates a parameter name starting with an
alphabetical character and can't contain: @samp{()+-*/^=!;:@@#.} or
accentuated characters;
@item
@var{LATEX_NAME} indicates a valid @LaTeX{} expression in math mode
(not including the dollar signs);
@item
@var{FUNCTION_NAME} indicates a valid MATLAB function name;
@item
@var{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;
@end itemize
@node Variable declarations
@section Variable declarations
Declarations of variables and parameters are made with the following commands:
@deffn Command var @var{VARIABLE_NAME} [$@var{LATEX_NAME}$]@dots{};
@deffnx Command var (deflator = @var{MODEL_EXPRESSION}) @var{VARIABLE_NAME} [$@var{LATEX_NAME}$]@dots{};
@deffnx Command var (log_deflator = @var{MODEL_EXPRESSION}) @var{VARIABLE_NAME} [$@var{LATEX_NAME}$]@dots{};
@descriptionhead
This required command declares the endogenous variables in the
model. @xref{Conventions}, for the syntax of @var{VARIABLE_NAME} and
@var{MODEL_EXPRESSION}. Optionally it is possible to give a @LaTeX{}
name to the variable or, if it is nonstationary, provide information
regarding its deflator.
@code{var} commands can appear several times in the file and Dynare will
concatenate them.
@optionshead
If the model is nonstationary and is to be written as such in the
@code{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.
@table @code
@item deflator = @var{MODEL_EXPRESSION}
The expression used to detrend an endogenous variable. All trend
variables, endogenous variables and parameters referenced in
@var{MODEL_EXPRESSION} must already have been declared by the
@code{trend_var}, @code{log_trend_var}, @code{var} and
@code{parameters} commands. The deflator is assumed to be
multiplicative; for an additive deflator, use @code{log_deflator}.
@item log_deflator = @var{MODEL_EXPRESSION}
Same as @code{deflator}, except that the deflator is assumed to be
additive instead of multiplicative (or, to put it otherwise, the
declared variable is equal to the log of a variable with a
multiplicative trend).
@end table
@examplehead
@example
var c gnp q1 q2;
var(deflator=A) i b;
@end example
@end deffn
@deffn Command varexo @var{VARIABLE_NAME} [$@var{LATEX_NAME}$]@dots{};
@descriptionhead
This optional command declares the exogenous variables in the model.
@xref{Conventions}, for the syntax of @var{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.
@code{varexo} commands can appear several times in the file and Dynare
will concatenate them.
@examplehead
@example
varexo m gov;
@end example
@end deffn
@deffn Command varexo_det @var{VARIABLE_NAME} [$@var{LATEX_NAME}$]@dots{};
@descriptionhead
This optional command declares exogenous deterministic variables in a
stochastic model. See @ref{Conventions}, for the syntax of
@var{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 @code{stoch_simul} will compute the
rational expectation solution adding future information to the state
space (nothing is shown in the output of @code{stoch_simul}) and
@code{forecast} will compute a simulation conditional on initial
conditions and future information.
@code{varexo_det} commands can appear several times in the file and
Dynare will concatenate them.
@examplehead
@example
varexo m gov;
varexo_det tau;
@end example
@end deffn
@deffn Command parameters @var{PARAMETER_NAME} [$@var{LATEX_NAME}$]@dots{};
@descriptionhead
This command declares parameters used in the model, in variable
initialization or in shocks declarations. See @ref{Conventions}, for the
syntax of @var{PARAMETER_NAME}. Optionally it is possible to give a
@LaTeX{} name to the parameter.
The parameters must subsequently be assigned values (@pxref{Parameter
initialization}).
@code{parameters} commands can appear several times in the file and
Dynare will concatenate them.
@examplehead
@example
parameters alpha, bet;
@end example
@end deffn
@deffn Command change_type (var | varexo | varexo_det | parameters) @var{VARIABLE_NAME} | @var{PARAMETER_NAME}@dots{};
@descriptionhead
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 @file{.mod} file: the type change is effective after, but also
before, the @code{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.
@examplehead
@example
var y, w;
parameters alpha, bet;
@dots{}
change_type(var) alpha, bet;
change_type(parameters) y, w;
@end example
Here, in the whole model file, @code{alpha} and @code{beta} will be
endogenous and @code{y} and @code{w} will be parameters.
@end deffn
@anchor{predetermined_variables}
@deffn Command predetermined_variables @var{VARIABLE_NAME}@dots{};
@descriptionhead
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 @code{k(-1)}, and the law of motion of
capital must be written:
@example
k = i + (1-delta)*k(-1)
@end example
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 @code{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.
@examplehead
The following two program snippets are strictly equivalent.
@emph{Using default Dynare timing convention:}
@example
var y, k, i;
@dots{}
model;
y = k(-1)^alpha;
k = i + (1-delta)*k(-1);
@dots{}
end;
@end example
@emph{Using the alternative timing convention:}
@example
var y, k, i;
predetermined_variables k;
@dots{}
model;
y = k^alpha;
k(+1) = i + (1-delta)*k;
@dots{}
end;
@end example
@end deffn
@deffn Command trend_var (growth_factor = @var{MODEL_EXPRESSION}) @var{VARIABLE_NAME} [$@var{LATEX_NAME}$]@dots{};
@descriptionhead
This optional command declares the trend variables in the
model. @xref{Conventions}, for the syntax of @var{MODEL_EXPRESSION}
and @var{VARIABLE_NAME}. Optionally it is possible to give a @LaTeX{}
name to the variable.
The variable is assumed to have a multiplicative growth trend. For an
additive growth trend, use @code{log_trend_var} instead.
Trend variables are required if the user wants to be able to write a
nonstationary model in the @code{model} block. The @code{trend_var}
command must appear before the @code{var} command that references the
trend variable.
@code{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
@code{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
@code{growth_factor} keyword. All endogenous variables and
parameters referenced in @var{MODEL_EXPRESSION} must already have been
declared by the @code{var} and @code{parameters} commands.
@examplehead
@example
trend_var (growth_factor=gA) A;
@end example
@end deffn
@deffn Command log_trend_var (log_growth_factor = @var{MODEL_EXPRESSION}) @var{VARIABLE_NAME} [$@var{LATEX_NAME}$]@dots{};
@descriptionhead
Same as @code{trend_var}, except that the variable is supposed to have
an additive trend (or, to put it otherwise, to be equal to the log of
a variable with a multiplicative trend).
@end deffn
@node Expressions
@section 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 (@i{e.g.} for initializing parameters or
variables, or as command options). In this manual, those two types of
expressions are respectively denoted by @var{MODEL_EXPRESSION} and
@var{EXPRESSION}.
Unlike MATLAB or Octave expressions, Dynare expressions are necessarily
scalar ones: they cannot contain matrices or evaluate to
matrices@footnote{Note that arbitrary MATLAB or Octave expressions can
be put in a @file{.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.}.
Expressions can be constructed using integers (@var{INTEGER}), floating
point numbers (@var{DOUBLE}), parameter names (@var{PARAMETER_NAME}),
variable names (@var{VARIABLE_NAME}), operators and functions.
The following special constants are also accepted in some contexts:
@deffn Constant inf
Represents infinity.
@end deffn
@deffn Constant nan
``Not a number'': represents an undefined or unrepresentable value.
@end deffn
@menu
* Parameters and variables::
* Operators::
* Functions::
* A few words of warning in stochastic context::
@end menu
@node Parameters and variables
@subsection 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.
@menu
* Inside the model::
* Outside the model::
@end menu
@node Inside the model
@subsubsection Inside the model
Parameters used inside the model refer to the value given through
parameter initialization (@pxref{Parameter initialization}) or
@code{homotopy_setup} when doing a simulation, or are the estimated
variables when doing an estimation.
Variables used in a @var{MODEL_EXPRESSION} denote @emph{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
@code{c} is an endogenous variable, then @code{c(+1)} is the variable
one period ahead, and @code{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 @cite{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 (@pxref{Model declaration}).
@node Outside the model
@subsubsection 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 (@pxref{Parameter
initialization}); for an endogenous or exogenous variable, it refers to
the value given in the most recent @code{initval} or @code{endval} block.
@node Operators
@subsection Operators
The following operators are allowed in both @var{MODEL_EXPRESSION} and
@var{EXPRESSION}:
@itemize
@item
binary arithmetic operators: @code{+}, @code{-}, @code{*}, @code{/}, @code{^}
@item
unary arithmetic operators: @code{+}, @code{-}
@item
binary comparison operators (which evaluate to either @code{0} or
@code{1}): @code{<}, @code{>}, @code{<=}, @code{>=}, @code{==},
@code{!=}
Note that these operators are differentiable everywhere except on a
line of the 2-dimensional real plane. However for facilitating
convergence of Newton-type methods, Dynare assumes that, at the points
of non-differentiability, the partial derivatives of these operators
with respect to both arguments is equal to @math{0} (since this is the
value of the partial derivatives everywhere else).
@end itemize
The following special operators are accepted in @var{MODEL_EXPRESSION}
(but not in @var{EXPRESSION}):
@deffn Operator STEADY_STATE (@var{MODEL_EXPRESSION})
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.
@end deffn
@anchor{expectation}
@deffn Operator EXPECTATION (@var{INTEGER}) (@var{MODEL_EXPRESSION})
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, @code{EXPECTATION(-1)(x(+1))} is equal to the
expected value of variable @code{x} at next period, using the
information set available at the previous period. @xref{Auxiliary
variables}, for an explanation of how this operator is handled
internally and how this affects the output.
@end deffn
@node Functions
@subsection Functions
@menu
* Built-in Functions::
* External Functions::
@end menu
@node Built-in Functions
@subsubsection Built-in Functions
The following standard functions are supported internally for both
@var{MODEL_EXPRESSION} and @var{EXPRESSION}:
@defun exp (@var{x})
Natural exponential.
@end defun
@defun log (@var{x})
@defunx ln (@var{x})
Natural logarithm.
@end defun
@defun log10 (@var{x})
Base 10 logarithm.
@end defun
@defun sqrt (@var{x})
Square root.
@end defun
@defun abs (@var{x})
Absolute value.
Note that this function is not differentiable at @math{x=0}. However,
for facilitating convergence of Newton-type methods, Dynare assumes
that the derivative at @math{x=0} is equal to @math{0} (this
assumption comes from the observation that the derivative of
@math{abs(x)} is equal to @math{sign(x)} for @math{x\neq 0} and from
the convention for the derivative of @math{sign(x)} at @math{x=0}).
@end defun
@defun sign (@var{x})
Signum function.
Note that this function is not differentiable at @math{x=0}. However,
for facilitating convergence of Newton-type methods, Dynare assumes
that the derivative at @math{x=0} is equal to @math{0} (this assumption
comes from the observation that both the right- and left-derivatives
at this point exist and are equal to @math{0}).
@end defun
@defun sin (@var{x})
@defunx cos (@var{x})
@defunx tan (@var{x})
@defunx asin (@var{x})
@defunx acos (@var{x})
@defunx atan (@var{x})
Trigonometric functions.
@end defun
@defun max (@var{a}, @var{b})
@defunx min (@var{a}, @var{b})
Maximum and minimum of two reals.
Note that these functions are differentiable everywhere except on a
line of the 2-dimensional real plane defined by @math{a=b}. However
for facilitating convergence of Newton-type methods, Dynare assumes
that, at the points of non-differentiability, the partial derivative
of these functions with respect to the first (resp. the second)
argument is equal to @math{1} (resp. to @math{0}) (@i{i.e.} the
derivatives at the kink are equal to the derivatives observed on the
half-plane where the function is equal to its first argument).
@end defun
@defun normcdf (@var{x})
@defunx normcdf (@var{x}, @var{mu}, @var{sigma})
Gaussian cumulative density function, with mean @var{mu} and standard
deviation @var{sigma}. Note that @code{normcdf(@var{x})} is equivalent
to @code{normcdf(@var{x},0,1)}.
@end defun
@defun normpdf (@var{x})
@defunx normpdf (@var{x}, @var{mu}, @var{sigma})
Gaussian probability density function, with mean @var{mu} and standard
deviation @var{sigma}. Note that @code{normpdf(@var{x})} is equivalent
to @code{normpdf(@var{x},0,1)}.
@end defun
@defun erf (@var{x})
Gauss error function.
@end defun
@node External Functions
@subsubsection External Functions
Any other user-defined (or built-in) MATLAB or Octave function may be
used in both a @var{MODEL_EXPRESSION} and an @var{EXPRESSION}, provided
that this function has a scalar argument as a return value.
To use an external function in a @var{MODEL_EXPRESSION}, one must
declare the function using the @code{external_function} statement. This
is not necessary for external functions used in an @var{EXPRESSION}.
@deffn Command external_function (@var{OPTIONS}@dots{});
@descriptionhead
This command declares the external functions used in the model block. It
is required for every unique function used in the model block.
@code{external_function} commands can appear several times in the file
and must come before the model block.
@optionshead
@table @code
@item name = @var{NAME}
The name of the function, which must also be the name of the M-/MEX file
implementing it. This option is mandatory.
@item nargs = @var{INTEGER}
The number of arguments of the function. If this option is not provided,
Dynare assumes @code{nargs = 1}.
@item first_deriv_provided [= @var{NAME}]
If @var{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 @var{NAME} is not provided, this tells Dynare that the
M-/MEX file specified by the argument passed to @code{name} returns the
Jacobian as its second output argument.
@item second_deriv_provided [= @var{NAME}]
If @var{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 @var{NAME} is not provided, this tells Dynare that the
M-/MEX file specified by the argument passed to @code{name} returns the
Hessian as its third output argument. NB: This option can only be used
if the @code{first_deriv_provided} option is used in the same
@code{external_function} command.
@end table
@examplehead
@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);
@end example
@end deffn
@node A few words of warning in stochastic context
@subsection A few words of warning in stochastic context
The use of the following functions and operators is strongly
discouraged in a stochastic context: @code{max}, @code{min},
@code{abs}, @code{sign}, @code{<}, @code{>}, @code{<=}, @code{>=},
@code{==}, @code{!=}.
The reason is that the local approximation used by @code{stoch_simul}
or @code{estimation} will by nature ignore the non-linearities
introduced by these functions if the steady state is away from the
kink. And, if the steady state is exactly at the kink, then the
approximation will be bogus because the derivative of these functions
at the kink is bogus (as explained in the respective documentations of
these functions and operators).
Note that @code{extended_path} is not affected by this problem,
because it does not rely on a local approximation of the model.
@node Parameter initialization
@section 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:
@example
@var{PARAMETER_NAME} = @var{EXPRESSION};
@end example
Here is an example of calibration:
@example
parameters alpha, bet;
beta = 0.99;
alpha = 0.36;
A = 1-alpha*beta;
@end example
Internally, the parameter values are stored in @code{M_.params}:
@defvr {MATLAB/Octave variable} M_.params
Contains the values of model parameters. The parameters are in the
order that was used in the @code{parameters} command.
@end defvr
@node Model declaration
@section Model declaration
The model is declared inside a @code{model} block:
@deffn Block model ;
@deffnx Block model (@var{OPTIONS}@dots{});
@descriptionhead
The equations of the model are written in a block delimited by
@code{model} and @code{end} keywords.
There must be as many equations as there are endogenous variables in the
model, except when computing the unconstrained optimal policy with
@code{ramsey_policy} or @code{discretionary_policy}.
The syntax of equations must follow the conventions for
@var{MODEL_EXPRESSION} as described in @ref{Expressions}. Each equation
must be terminated by a semicolon (@samp{;}). A normal equation looks
like:
@example
@var{MODEL_EXPRESSION} = @var{MODEL_EXPRESSION};
@end example
When the equations are written in homogenous form, it is possible to
omit the @samp{=0} part and write only the left hand side of the
equation. A homogenous equation looks like:
@example
@var{MODEL_EXPRESSION};
@end example
Inside the model block, Dynare allows the creation of @emph{model-local
variables}, which constitute a simple way to share a common expression
between several equations. The syntax consists of a pound sign
(@code{#}) followed by the name of the new model local variable (which
must @strong{not} be declared as in @ref{Variable declarations}), 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:
@example
# @var{VARIABLE_NAME} = @var{MODEL_EXPRESSION};
@end example
@optionshead
@table @code
@item linear
Declares the model as being linear. It spares oneself from having to
declare initial values for computing the steady state of a stationary
linear model. This options can't be used with non-linear models, it will
NOT trigger linearization of the model.
@item use_dll
@anchor{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{i.e.}
a working @code{mex} command (see @ref{Software requirements} for more
details). Using this option can result in faster simulations or
estimations, at the expense of some initial compilation
time.@footnote{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.}
@item block
@anchor{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
@uref{http://www.dynare.org/DynareWiki/FastDeterministicSimulationAndSteadyStateComputation,Dynare
wiki} for details on the algorithms used in deterministic simulation and steady-state computation.
@item bytecode
@anchor{bytecode}
Instead of M-files, use a bytecode representation of the model, @i{i.e.}
a binary file containing a compact representation of all the equations.
@item cutoff = @var{DOUBLE}
Threshold under which a jacobian element is considered as null during
the model normalization. Only available with option
@code{block}. Default: @code{1e-15}
@item mfs = @var{INTEGER}
Controls the handling of minimum feedback set of endogenous
variables. Only available with option @code{block}. Possible values:
@table @code
@item 0
All the endogenous variables are considered as feedback variables (Default).
@item 1
The endogenous variables assigned to equation naturally normalized
(@i{i.e.} of the form @math{x=f(Y)} where @math{x} does not appear in
@math{Y}) are potentially recursive variables. All the other variables
are forced to belong to the set of feedback variables.
@item 2
In addition of variables with @code{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.
@item 3
In addition of variables with @code{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.
@end table
@item no_static
Don't create the static model file. This can be useful for models which
don't have a steady state.
@item differentiate_forward_vars
@itemx differentiate_forward_vars = ( @var{VARIABLE_NAME} [@var{VARIABLE_NAME} @dots{}] )
Tells Dynare to create a new auxiliary variable for each endogenous
variable that appears with a lead, such that the new variable is the
time differentiate of the original one. More precisely, if the model
contains @code{x(+1)}, then a variable @code{AUX_DIFF_VAR} will be
created such that @code{AUX_DIFF_VAR=x-x(-1)}, and @code{x(+1)} will
be replaced with @code{x+AUX_DIFF_VAR(+1)}.
The transformation is applied to all endogenous variables with a lead
if the option is given without a list of variables. If there is a
list, the transformation is restricted to endogenous with a lead that
also appear in the list.
This option can useful for some deterministic simulations where
convergence is hard to obtain. Bad values for terminal conditions in
the case of very persistent dynamics or permanent shocks can hinder
correct solutions or any convergence. The new differentiated variables
have obvious zero terminal conditions (if the terminal condition is a
steady state) and this in many cases helps convergence of simulations.
@item parallel_local_files = ( @var{FILENAME} [, @var{FILENAME}]@dots{} )
Declares a list of extra files that should be transferred to slave
nodes when doing a parallel computation (@pxref{Parallel Configuration}).
@end table
@customhead{Example 1: elementary RBC model}
@example
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;
@end example
@customhead{Example 2: use of model local variables}
The following program:
@example
model;
# gamma = 1 - 1/sigma;
u1 = c1^gamma/gamma;
u2 = c2^gamma/gamma;
end;
@end example
@noindent
@dots{}is formally equivalent to:
@example
model;
u1 = c1^(1-1/sigma)/(1-1/sigma);
u2 = c2^(1-1/sigma)/(1-1/sigma);
end;
@end example
@customhead{Example 3: a linear model}
@example
model(linear);
x = a*x(-1)+b*y(+1)+e_x;
y = d*y(-1)+e_y;
end;
@end example
@end deffn
Dynare has the ability to output the list of model equations to a
@LaTeX{} file, using the @code{write_latex_dynamic_model} command. The
static model can also be written with the
@code{write_latex_static_model} command.
@anchor{write_latex_dynamic_model}
@deffn Command write_latex_dynamic_model ;
@descriptionhead
This command creates a @LaTeX{} file containing the (dynamic) model.
If your @file{.mod} file is @file{@var{FILENAME}.mod}, then Dynare
will create a file called @file{@var{FILENAME}_dynamic.tex},
containing the list of all the dynamic model equations.
If @LaTeX{} names were given for variables and parameters
(@pxref{Variable declarations}), then those will be used; otherwise,
the plain text names will be used.
Time subscripts (@code{t}, @code{t+1}, @code{t-1}, @dots{}) 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:
@itemize
@item
the timing convention of predetermined variables
(@pxref{predetermined_variables}) will have been changed to the
default Dynare timing convention; in other words, variables declared
as predetermined will be lagged on period back,
@item
the expectation operators (@pxref{expectation}) will have
been removed, replaced by auxiliary variables and new equations as
explained in the documentation of the operator,
@item
endogenous variables with leads or lags greater or equal than two will
have been removed, replaced by new auxiliary variables and equations,
@item
for a stochastic model, exogenous variables with leads or lags will
also have been replaced by new auxiliary variables and equations.
@end itemize
Compiling the @TeX{} file requires the following @LaTeX{} packages:
@code{geometry}, @code{fullpage}, @code{breqn}.
@end deffn
@deffn Command write_latex_static_model ;
@descriptionhead
This command creates a @LaTeX{} file containing the static model.
If your @file{.mod} file is @file{@var{FILENAME}.mod}, then Dynare
will create a file called @file{@var{FILENAME}_static.tex}, containing
the list of all the equations of the steady state model.
If @LaTeX{} names were given for variables and parameters
(@pxref{Variable declarations}), 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
(@pxref{write_latex_dynamic_model} for details).
Also note that this command will not output the contents of the
optional @code{steady_state_model} block (@pxref{steady_state_model});
it will rather output a static version (@i{i.e.} without leads and
lags) of the dynamic model declared in the @code{model} block.
Compiling the @TeX{} file requires the following @LaTeX{} packages:
@code{geometry}, @code{fullpage}, @code{breqn}.
@end deffn
@node Auxiliary variables
@section 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 @code{x(+2)}
exists in the model, Dynare will create one auxiliary variable
@code{AUX_ENDO_LEAD = x(+1)}, and replace @code{x(+2)} by
@code{AUX_ENDO_LEAD(+1)}.
A similar transformation is done for lags greater than 2 on endogenous
(auxiliary variables will have a name beginning with
@code{AUX_ENDO_LAG}), and for exogenous with leads and lags (auxiliary
variables will have a name beginning with @code{AUX_EXO_LEAD} or
@code{AUX_EXO_LAG} respectively).
Another transformation is done for the @code{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 @code{EXPECTATION(-1)(x(+1))} is replaced by
@code{AUX_EXPECT_LAG_1(-1)}, and the new auxiliary variable is
declared as @code{AUX_EXPECT_LAG_1 = x(+2)}.
Auxiliary variables are also introduced by the preprocessor for the
@code{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 @code{MULT_@var{i}}, where @var{i} represents
the constraint with which the multiplier is associated (counted from the
order of declaration in the model block).
The last type of auxiliary variables is introduced by the
@code{differentiate_forward_vars} option of the @code{model} block.
The new variables take the form @code{AUX_DIFF_FWRD_@var{i}}, and are
equal to @code{x-x(-1)} for some endogenous variable @code{x}.
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.
@vindex M_.orig_endo_nbr
@vindex M_.endo_nbr
The number of endogenous variables before the creation of auxiliary
variables is stored in @code{M_.orig_endo_nbr}, and the number of
endogenous variables after the creation of auxiliary variables is
stored in @code{M_.endo_nbr}.
See @uref{http://www.dynare.org/DynareWiki/AuxiliaryVariables,Dynare
Wiki} for more technical details on auxiliary variables.
@node Initial and terminal conditions
@section 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: @code{initval} then
specifies numerical initial values for the non-linear solver. The
command @code{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 @code{initval} and
@code{shocks} (@pxref{Shocks on exogenous variables}.
Another one is to study, how an economy, starting from arbitrary
initial conditions converges toward equilibrium. To do that, one needs
@code{initval} and @code{endval}.
For models with lags on more than one period, the command
@code{histval} permits to specify different historical initial values
for periods before the beginning of the simulation.
@deffn Block initval ;
@deffnx Block initval (@var{OPTIONS}@dots{});
@descriptionhead
The @code{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 @code{end;}, and contains lines of the
form:
@example
@var{VARIABLE_NAME} = @var{EXPRESSION};
@end example
@customhead{In a deterministic (@i{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
@code{histval}).
Second, in the absence of an @code{endval} block, it sets the terminal
conditions for all the periods succeeding the last simulation period.
Third, in the absence of an @code{endval} block, it provides initial
guess values at all simulation dates for the non-linear solver
implemented in @code{simul}.
For this last reason, it necessary to provide values for all the
endogenous variables in an @code{initval} block (even though,
theoretically, initial conditions are only necessary for lagged
variables). If some variables, endogenous or exogenous, are not mentionned in the
@code{initval} block, a zero value is assumed.
Note that if the @code{initval} block is immediately followed by a
@code{steady} command, its semantics is changed. The @code{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 @code{initval} block, and using
the values declared for the endogenous as initial guess values for the
non-linear solver. An @code{initval} block followed by @code{steady}
is formally equivalent to an @code{initval} block with the same values
for the exogenous, and with the associated steady state values for the
endogenous.
@customhead{In a stochastic model}
The main purpose of @code{initval} is to provide initial guess values
for the non-linear solver in the steady state computation. Note that
if the @code{initval} block is not followed by @code{steady}, the
steady state computation will still be triggered by subsequent
commands (@code{stoch_simul}, @code{estimation}@dots{}).
It is not necessary to declare @code{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:
@itemize
@item
in @code{stoch_simul}, if the @code{periods} options is specified
@item
in @code{forecast} (in this case, note that it is still possible to
modify some of these initial values with @code{histval})
@end itemize
@optionshead
@table @code
@item all_values_required
@anchor{all_values_required}
Issues an error and stops processing the @file{.mod} file if there is at least
one endogenous or exogenous variable that has not been set in the @code{initval}
block.
@end table
@examplehead
@example
initval;
c = 1.2;
k = 12;
x = 1;
end;
steady;
@end example
@end deffn
@deffn Block endval ;
@deffnx Block endval (@var{OPTIONS}@dots{});
@descriptionhead
This block is terminated by @code{end;}, and contains lines of the
form:
@example
@var{VARIABLE_NAME} = @var{EXPRESSION};
@end example
The @code{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 @code{simul}.
For this last reason, it necessary to provide values for all the
endogenous variables in an @code{endval} block (even though,
theoretically, initial conditions are only necessary for forward
variables). If some variables, endogenous or exogenous, are not mentionned in the
@code{endval} block, the value assumed is that of the last
@code{initval} block or @code{steady} command.
Note that if the @code{endval} block is immediately followed by a
@code{steady} command, its semantics is changed. The @code{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 @code{endval} block, and using
the values declared for the endogenous as initial guess values for the
non-linear solver. An @code{endval} block followed by @code{steady} is
formally equivalent to an @code{endval} block with the same values for
the exogenous, and with the associated steady state values for the
endogenous.
@optionshead
@table @code
@item all_values_required
@xref{all_values_required}.
@end table
@examplehead
@example
var c k;
varexo x;
@dots{}
initval;
c = 1.2;
k = 12;
x = 1;
end;
steady;
endval;
c = 2;
k = 20;
x = 2;
end;
steady;
@end example
The initial equilibrium is computed by @code{steady} for @code{x=1},
and the terminal one, for @code{x=2}.
@end deffn
@deffn Block histval ;
@descriptionhead
In models with lags on more than one period, the @code{histval} block
permits to specify different historical initial values for different
periods.
This block is terminated by @code{end;}, and contains lines of the
form:
@example
@var{VARIABLE_NAME}(@var{INTEGER}) = @var{EXPRESSION};
@end example
@var{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 @code{0}, then period @code{-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 @code{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 @code{histval} block, where all
variables are initialized at their steady state value at period 0 and
before (except when a @code{steady} command doesn't follow an
@code{initval} block).
@examplehead
@example
var x y;
varexo e;
model;
x = y(-1)^alpha*y(-2)^(1-alpha)+e;
@dots{}
end;
initval;
x = 1;
y = 1;
e = 0.5;
end;
steady;
histval;
y(0) = 1.1;
y(-1) = 0.9;
end;
@end example
@end deffn
@deffn Command resid ;
This command will display the residuals of the static equations of the
model, using the values given for the endogenous in the last
@code{initval} or @code{endval} block (or the steady state file if you
provided one, @pxref{Steady state}).
@end deffn
@deffn Command initval_file (filename = @var{FILENAME});
@descriptionhead
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:
@itemize
@item
the constraints of the problem, which are given by the path for
exogenous and the initial and terminal values for endogenous
@item
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)
@end itemize
The command accepts three file formats:
@itemize
@item
M-file (extension @file{.m}): for each endogenous and exogenous
variable, the file must contain a row vector of the same name.
@item
MAT-file (extension @file{.mat}): same as for M-files.
@item
Excel file (extension @file{.xls} or @file{.xlsx}): for each
endogenous and exogenous, the file must contain a column of the same
name (supported under Octave if the
@uref{http://octave.sourceforge.net/io/,io} and
@uref{http://octave.sourceforge.net/java/,java} packages from
Octave-Forge are installed, along with a
@uref{http://www.java.com/download,Java Runtime Environment}).
@end itemize
@customhead{Warning}
The extension must be omitted in the command argument. Dynare will
automatically figure out the extension and select the appropriate file
type.
@end deffn
@node Shocks on exogenous variables
@section 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 @code{initval} and @code{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@dots{}). 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 @code{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
variance-covariance of the shocks can be entered with the @code{shocks}
command. Or, the entire matrix can be direclty entered with
@code{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.
@deffn Block shocks ;
@customhead{In deterministic context}
For deterministic simulations, the @code{shocks} block specifies
temporary changes in the value of exogenous variables. For
permanent shocks, use an @code{endval} block.
The block should contain one or more occurrences of the following
group of three lines:
@example
var @var{VARIABLE_NAME};
periods @var{INTEGER}[:@var{INTEGER}] [[,] @var{INTEGER}[:@var{INTEGER}]]@dots{};
values @var{DOUBLE} | (@var{EXPRESSION}) [[,] @var{DOUBLE} | (@var{EXPRESSION}) ]@dots{};
@end example
It is possible to specify shocks which last several periods and which can
vary over time. The @code{periods} keyword accepts a list of
several dates or date ranges, which must be matched by as many shock values
in the @code{values} keyword. Note that a range in the
@code{periods} keyword can be matched by only one value in the
@code{values} keyword. If @code{values} represents a scalar, the same
value applies to the whole range. If @code{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:
@example
shocks;
var e;
periods 1;
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;
@end example
A second example with a vector of values:
@example
xx = [1.2; 1.3; 1];
shocks;
var e;
periods 1:3;
values (xx);
end;
@end example
In case of conditional forecasts using an extended path method,
the shock command is extended in order to determine the nature of the expectation
on the endogenous variable paths. The command @code{expectation} has, in this case,
to be added after the @code{values} command (@pxref{Forecasting}).
@customhead{In stochastic context}
For stochastic simulations, the @code{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:
@table @code
@item var @var{VARIABLE_NAME}; stderr @var{EXPRESSION};
Specifies the standard error of a variable.
@item var @var{VARIABLE_NAME} = @var{EXPRESSION};
Specifies the variance error of a variable.
@item var @var{VARIABLE_NAME}, @var{VARIABLE_NAME} = @var{EXPRESSION};
Specifies the covariance of two variables.
@item corr @var{VARIABLE_NAME}, @var{VARIABLE_NAME} = @var{EXPRESSION};
Specifies the correlation of two variables.
@end table
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. This requires the @code{var_obs}-command to be specified before the @code{shocks}-block.
Here is an example:
@example
shocks;
var e = 0.000081;
var u; stderr 0.009;
corr e, u = 0.8;
var v, w = 2;
end;
@end example
@customhead{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 @code{stoch_simul} will compute the
rational expectation solution adding future information to the state
space (nothing is shown in the output of @code{stoch_simul}) and
@code{forecast} will compute a simulation conditional on initial
conditions and future information.
Here is an example:
@example
varexo_det tau;
varexo e;
@dots{}
shocks;
var e; stderr 0.01;
var tau;
periods 1:9;
values -0.15;
end;
stoch_simul(irf=0);
forecast;
@end example
@end deffn
@deffn Block mshocks ;
The purpose of this block is similar to that of the @code{shocks}
block for deterministic shocks, except that the numeric values given
will be interpreted in a multiplicative way. For example, if a value
of @code{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
@code{initval} or @code{endval} block).
The syntax is the same than @code{shocks} in a deterministic context.
This command is only meaningful in two situations:
@itemize
@item
on exogenous variables with a non-zero steady state, in a deterministic setup,
@item
on deterministic exogenous variables with a non-zero steady state, in
a stochastic setup.
@end itemize
@end deffn
@defvr {Special variable} Sigma_e
@customhead{Warning}
@strong{The use of this special variable is deprecated and is strongly
discouraged.} You should use a @code{shocks} block instead.
@descriptionhead
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
@code{;}. For a given element, an arbitrary @var{EXPRESSION} is
allowed (instead of a simple constant), but in that case you need to
enclose the expression in parentheses. @emph{The order of the
covariances in the matrix is the same as the one used in the
@code{varexo} declaration.}
@examplehead
@example
varexo u, e;
@dots{}
Sigma_e = [ 0.81 (phi*0.9*0.009);
0.000081];
@end example
This sets the variance of @code{u} to 0.81, the variance of @code{e}
to 0.000081, and the correlation between @code{e} and @code{u} to
@code{phi}.
@end defvr
@node Other general declarations
@section Other general declarations
@deffn {Command} dsample @var{INTEGER} [@var{INTEGER}];
Reduces the number of periods considered in subsequent output commands.
@end deffn
@deffn {Command} periods @var{INTEGER};
@descriptionhead
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 @code{periods} in @code{simul} and
@code{stoch_simul}.
This command sets the number of periods in the simulation. The periods
are numbered from @code{1} to @var{INTEGER}. In perfect foresight
simulations, it is assumed that all future events are perfectly known
at the beginning of period @code{1}.
@examplehead
@example
periods 100;
@end example
@end deffn
@node Steady state
@section Steady state
There are two ways of computing the steady state (@i{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''.
@menu
* Finding the steady state with Dynare nonlinear solver::
* Using a steady state file::
* Replace some equations during steady state computations::
@end menu
@node Finding the steady state with Dynare nonlinear solver
@subsection Finding the steady state with Dynare nonlinear solver
@deffn Command steady ;
@deffnx Command steady (@var{OPTIONS}@dots{});
@descriptionhead
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 @code{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 @code{initval} or @code{endval} block.
@code{steady} uses an iterative procedure and takes as initial guess
the value of the endogenous variables set in the previous
@code{initval} or @code{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.
@optionshead
@table @code
@item maxit = @var{INTEGER}
Determines the maximum number of iterations used in the non-linear solver.
The default value of @code{maxit} is 10. The @code{maxit} option is shared with the
@code{simul} command. So a change in @code{maxit} in a @code{steady} command will
also be considered in the following @code{simul} commands.
@item solve_algo = @var{INTEGER}
@anchor{solve_algo}
Determines the non-linear solver to use. Possible values for the option are:
@table @code
@item 0
Use @code{fsolve} (under MATLAB, only available if you have the
Optimization Toolbox; always available under Octave)
@item 1
Use Dynare's own nonlinear equation solver
@item 2
Splits the model into recursive blocks and solves each block in turn
@item 3
Use Chris Sims' solver
@item 4
Similar to value @code{2}, except that it deals differently with
nearly singular Jacobian
@item 5
Newton algorithm with a sparse Gaussian elimination (SPE) (requires
@code{bytecode} option, @pxref{Model declaration})
@item 6
Newton algorithm with a sparse LU solver at each iteration (requires
@code{bytecode} and/or @code{block} option, @pxref{Model declaration})
@item 7
Newton algorithm with a Generalized Minimal Residual (GMRES) solver at
each iteration (requires @code{bytecode} and/or @code{block} option,
@pxref{Model declaration}; not available under Octave)
@item 8
Newton algorithm with a Stabilized Bi-Conjugate Gradient (BICGSTAB)
solver at each iteration (requires @code{bytecode} and/or @code{block}
option, @pxref{Model declaration})
@end table
@noindent
Default value is @code{2}.
@item homotopy_mode = @var{INTEGER}
Use a homotopy (or divide-and-conquer) technique to solve for the
steady state. If you use this option, you must specify a
@code{homotopy_setup} block. This option can take three possible
values:
@table @code
@item 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 @code{homotopy_steps}
option); the problem is solves as many times as there are steps.
@item 2
Same as mode @code{1}, except that only one parameter is changed at a
time; the problem is solved as many times as steps times number of
parameters.
@item 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 @code{homotopy_steps} contains the maximum
number of computations attempted before giving up.
@end table
@item homotopy_steps = @var{INTEGER}
Defines the number of steps when performing a homotopy. See
@code{homotopy_mode} option for more details.
@item homotopy_force_continue = @var{INTEGER}
This option controls what happens when homotopy fails.
@table @code
@item 0
@code{steady} fails with an error message
@item 1
@code{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
@end table
@noindent
Default is @code{0}.
@item nocheck
Don't check the steady state values when they are provided explicitely either by a steady state file or a @code{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.
@item markowitz = @var{DOUBLE}
Value of the Markowitz criterion, used to select the pivot. Only used
when @code{solve_algo = 5}. Default: @code{0.5}.
@end table
@examplehead
@xref{Initial and terminal conditions}.
@end deffn
After computation, the steady state is available in the following
variable:
@defvr {MATLAB/Octave variable} oo_.steady_state
Contains the computed steady state.
Endogenous variables are ordered in order of declaration used in
@code{var} command (which is also the order used in @code{M_.endo_names}).
@end defvr
@deffn Block homotopy_setup ;
@descriptionhead
This block is used to declare initial and final values when using
a homotopy method. It is used in conjunction with the option
@code{homotopy_mode} of the @code{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 @code{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:
@example
@var{VARIABLE_NAME}, @var{EXPRESSION}, @var{EXPRESSION};
@end example
This syntax specifies the initial and final values of a given
parameter/exogenous.
There is an alternative syntax:
@example
@var{VARIABLE_NAME}, @var{EXPRESSION};
@end example
Here only the final value is specified for a given
parameter/exogenous; the initial value is taken from the preceeding
@code{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
@code{initval} block).
If the homotopy fails, a possible solution is to increase the number
of steps (given in @code{homotopy_steps} option of @code{steady}).
@examplehead
In the following example, Dynare will first compute the steady state
for the initial values (@code{gam=0.5} and @code{x=1}), and then
subdivide the problem into 50 smaller problems to find the steady
state for the final values (@code{gam=2} and @code{x=2}).
@example
var c k;
varexo x;
parameters alph gam delt bet aa;
alph=0.5;
delt=0.02;
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);
@end example
@end deffn
@node Using a steady state file
@subsection 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 @code{steady}. If your MOD-file is called
@file{@var{FILENAME}.mod}, the steady state file should be called
@file{@var{FILENAME}_steadystate.m}.
Again, there are two options for creating this file:
@itemize
@item
The easiest way is to write a @code{steady_state_model} block.
@item
You can write the corresponding Matlab function by hand. See @file{fs2000_steadystate.m}
in the @file{examples} directory for an example. This option
gives a bit more flexibility, at the expense of a heavier
programming burden and a lesser efficiency.
@end itemize
@anchor{steady_state_model}
@deffn Block steady_state_model ;
@descriptionhead
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:
@example
@var{VARIABLE_NAME} = @var{EXPRESSION};
@end example
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:
@example
[ @var{VARIABLE_NAME}, @var{VARIABLE_NAME}@dots{} ] = @var{EXPRESSION};
@end example
Dynare will automatically generate a steady state file (of the form
@file{@var{FILENAME}_steadystate2.m}) using the information provided in
this block.
@customhead{Steady state file for deterministic models}
@code{steady_state_model} block works also with deterministic
models. An @code{initval} block and, when necessary, an @code{endval}
block, is used to set the value of the exogenous variables. Each
@code{initval} or @code{endval} block must be followed by @code{steady}
to execute the function created by @code{steady_state_model} and set the
initial, respectively terminal, steady state.
@examplehead
@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;
@dots{}
// parameter calibration, (dynamic) model declaration, shock calibration@dots{}
@dots{}
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 = xist/(nust+xist);
P = xist + nust;
k = khst*n;
l = psi*mst*n/( (1-psi)*(1-n) );
c = mst/P;
d = l - mst + 1;
y = k^alp*n^(1-alp)*gst^alp;
R = 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;
@end example
@end deffn
@node Replace some equations during steady state computations
@subsection Replace some equations during steady state computations
When there is no steady state file, Dynare computes the steady state
by solving the static model, @i{i.e.} the model from the @file{.mod}
file from which leads and lags have been removed.
In some specific cases, one may want to have more control over the way
this static model is created. Dynare therefore offers the possibility
to explicitly give the form of equations that should be in the static
model.
More precisely, if an equation is prepended by a @code{[static]} tag,
then it will appear in the static model used for steady state
computation, but that equation will not be used for other
computations. For every equation tagged in this way, you must tag
another equation with @code{[dynamic]}: that equation will not be used
for steady state computation, but will be used for other computations.
This functionality can be useful on models with a unit root, where
there is an infinity of steady states. An equation (tagged
@code{[dynamic]}) would give the law of motion of the nonstationary
variable (like a random walk). To pin down one specific steady state,
an equation tagged @code{[static]} would affect a constant value to
the nonstationary variable.
@examplehead
This is a trivial example with two endogenous variables. The second equation
takes a different form in the static model.
@example
var c k;
varexo x;
@dots{}
model;
c + k - aa*x*k(-1)^alph - (1-delt)*k(-1);
[dynamic] c^(-gam) - (1+bet)^(-1)*(aa*alph*x(+1)*k^(alph-1) + 1 - delt)*c(+1)^(-gam);
[static] k = ((delt+bet)/(x*aa*alph))^(1/(alph-1));
end;
@end example
@node Getting information about the model
@section Getting information about the model
@deffn Command check ;
@deffnx Command check (solve_algo = @var{INTEGER}) ;
@descriptionhead
Computes the eigenvalues of the model linearized around the values
specified by the last @code{initval}, @code{endval} or @code{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.
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.
@optionshead
@table @code
@item solve_algo = @var{INTEGER}
@xref{solve_algo}, for the possible values and their meaning.
@item qz_zero_threshold = @var{DOUBLE}
Value used to test if a generalized eigenvalue is 0/0 in the generalized
Schur decomposition (in which case the model does not admit a unique
solution). Default: @code{1e-6}.
@end table
@outputhead
@code{check} returns the eigenvalues in the global variable
@code{oo_.dr.eigval}.
@end deffn
@defvr {MATLAB/Octave variable} oo_.dr.eigval
Contains the eigenvalues of the model, as computed by the @code{check}
command.
@end defvr
@deffn Command model_diagnostics ;
This command performs various sanity checks on the model, and prints a
message if a problem is detected (missing variables at current period,
invalid steady state, singular Jacobian of static model).
@end deffn
@deffn Command model_info ;
@deffnx Command model_info (@var{OPTIONS}@dots{});
@descriptionhead
This command provides information about:
@itemize
@item
the normalization of the model: an endogenous variable is attributed
to each equation of the model;
@item
the block structure of the model: for each block model_info indicates
its type, the equations number and endogenous variables belonging to
this block.
@end itemize
This command can only be used in conjunction with the @code{block}
option of the @code{model} block.
There are five different types of blocks depending on the simulation
method used:
@table @samp
@item 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: @math{y_{j,t} = f_j(y_t, y_{t-1}, \ldots, y_{t-k})}.
@item 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:
@math{y_{j,t} = f_j(y_t, y_{t+1}, \ldots, y_{t+k})}.
@item SOLVE FORWARD @var{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: @math{g_j(y_{j,t}, y_t, y_{t-1}, \ldots, y_{t-k})=0}.
@var{x} is equal to @samp{SIMPLE} if the block has only one
equation. If several equation appears in the block, @var{x} is equal
to @samp{COMPLETE}.
@item SOLVE FORWARD @var{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: @math{g_j(y_{j,t}, y_t, y_{t+1}, \ldots,
y_{t+k})=0}. @var{x} is equal to @samp{SIMPLE} if the block has only
one equation. If several equation appears in the block, @var{x} is
equal to @samp{COMPLETE}.
@item SOLVE TWO BOUNDARIES @var{x}
The block contains equations depending on both forward and backward
variables. The block looks like: @math{g_j(y_{j,t}, y_t, y_{t-1},
\ldots, y_{t-k} ,y_t, y_{t+1}, \ldots, y_{t+k})=0}. @var{x} is equal
to @samp{SIMPLE} if the block has only one equation. If several
equation appears in the block, @var{x} is equal to @samp{COMPLETE}.
@end table
@optionshead
@table @code
@item 'static'
Prints out the block decomposition of the static model.
Without 'static' option model_info displays the block decomposition
of the dynamic model.
@item 'incidence'
Displays the gross incidence matrix and the reordered incidence matrix
of the block decomposed model.
@end table
@end deffn
@deffn Command print_bytecode_dynamic_model ;
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 @code{bytecode} option of the @code{model} block.
@end deffn
@deffn Command print_bytecode_static_model ;
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 @code{bytecode} option of the @code{model} block.
@end deffn
@node Deterministic simulation
@section 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 @samp{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 @cite{Laffargue (1990)} and
@cite{Boucekkine (1995)}, instead of a first order technique like the
one proposed by @cite{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 @cite{Juillard (1996)}.
@deffn Command simul ;
@deffnx Command simul (@var{OPTIONS}@dots{});
@descriptionhead
Triggers the computation of a deterministic simulation of the model
for the number of periods set in the option @code{periods}.
@optionshead
@table @code
@item periods = @var{INTEGER}
Number of periods of the simulation
@item maxit = @var{INTEGER}
Determines the maximum number of iterations used in the non-linear solver.
The default value of @code{maxit} is 10. The @code{maxit} option is shared with the
@code{steady} command. So a change in @code{maxit} in a @code{simul} command will
also be considered in the following @code{steady} commands.
@item stack_solve_algo = @var{INTEGER}
Algorithm used for computing the solution. Possible values are:
@table @code
@item 0
Newton method to solve simultaneously all the equations for every
period, using sparse matrices (Default).
@item 1
Use a Newton algorithm with a sparse LU solver at each iteration
(requires @code{bytecode} and/or @code{block} option, @pxref{Model
declaration}).
@item 2
Use a Newton algorithm with a Generalized Minimal Residual (GMRES)
solver at each iteration (requires @code{bytecode} and/or @code{block}
option, @pxref{Model declaration}; not available under Octave)
@item 3
Use a Newton algorithm with a Stabilized Bi-Conjugate Gradient
(BICGSTAB) solver at each iteration (requires @code{bytecode} and/or
@code{block} option, @pxref{Model declaration}).
@item 4
Use a Newton algorithm with a optimal path length at each iteration
(requires @code{bytecode} and/or @code{block} option, @pxref{Model
declaration}).
@item 5
Use a Newton algorithm with a sparse Gaussian elimination (SPE) solver
at each iteration (requires @code{bytecode} option, @pxref{Model
declaration}).
@item 6
Use the historical algorithm proposed in @cite{Juillard (1996)}: it is
slower than @code{stack_solve_algo=0}, but may be less memory consuming
on big models (not available with @code{bytecode} and/or @code{block}
options).
@end table
@item markowitz = @var{DOUBLE}
Value of the Markowitz criterion, used to select the pivot. Only used
when @code{stack_solve_algo = 5}. Default: @code{0.5}.
@item minimal_solving_periods = @var{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 @code{stack_solve_algo = 5}. Default: @code{1}.
@item datafile = @var{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.
@end table
@outputhead
The simulated endogenous variables are available in global matrix
@code{oo_.endo_simul}.
@end deffn
@anchor{oo_.endo_simul}
@defvr {MATLAB/Octave variable} oo_.endo_simul
This variable stores the result of a deterministic simulation
(computed by @code{simul}) or of a stochastic simulation (computed by
@code{stoch_simul} with the @code{periods} option or by
@code{extended_path}).
The variables are arranged row by row, in order of declaration (as in
@code{M_.endo_names}). Note that this variable also contains initial
and terminal conditions, so it has more columns than the value of
@code{periods} option.
@end defvr
@anchor{oo_.exo_simul}
@defvr {MATLAB/Octave variable} oo_.exo_simul
This variable stores the path of exogenous variables during a
simulation (computed by @code{simul}, @code{stoch_simul} or
@code{extended_path}).
The variables are arranged in columns, in order of declaration (as in
@code{M_.endo_names}). Periods are in rows. Note that this convention
regarding columns and rows is the opposite of the convention for
@code{oo_.endo_simul}!
@end defvr
@node Stochastic solution and simulation
@section 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
@cite{Judd (1996)}, @cite{Collard and Juillard (2001a)}, @cite{Collard
and Juillard (2001b)}, and @cite{Schmitt-Grohé and Uríbe (2004)}). The
details of the Dynare implementation of the first order solution are
given in @cite{Villemot (2011)}. Such a solution is computed using
the @code{stoch_simul} command.
As an alternative, it is possible to compute a simulation to a
stochastic model using the @emph{extended path} method presented by
@cite{Fair and Taylor (1983)}. This method is especially useful when
there are strong nonlinearities or binding constraints. Such a
solution is computed using the @code{extended_path} command.
@menu
* Computing the stochastic solution::
* Typology and ordering of variables::
* First order approximation::
* Second order approximation::
* Third order approximation::
@end menu
@node Computing the stochastic solution
@subsection Computing the stochastic solution
@deffn Command stoch_simul [@var{VARIABLE_NAME}@dots{}];
@deffnx Command stoch_simul (@var{OPTIONS}@dots{}) [@var{VARIABLE_NAME}@dots{}];
@descriptionhead
@code{stoch_simul} solves a stochastic (@i{i.e.} rational
expectations) model, using perturbation techniques.
More precisely, @code{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 @code{varexo} command.
The Taylor approximation is computed around the steady state
(@pxref{Steady state}).
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
@uref{http://www.dynare.org/DynareWiki/IrFs,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
@math{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
@code{shocks} command (@pxref{Shocks on exogenous variables}).
When a list of @var{VARIABLE_NAME} is specified, results are displayed
only for these variables.
The @code{stoch_simul} command with a first order approximation can benefit from the block decomposition of the model (@pxref{block}).
@optionshead
@table @code
@item ar = @var{INTEGER}
@anchor{ar}
Order of autocorrelation coefficients to compute and to print. Default: @code{5}.
@item drop = @var{INTEGER}
Number of points (burnin) dropped at the beginning of simulation before computing the summary statistics. Note that this option does not affect the simulated series stored in @var{oo_.endo_simul} and the workspace. Here, no periods are dropped. Default: @code{100}.
@item hp_filter = @var{DOUBLE}
Uses HP filter with @math{\lambda} = @var{DOUBLE} before computing
moments. Default: no filter.
@item hp_ngrid = @var{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: @code{512}.
@item irf = @var{INTEGER}
@anchor{irf}
Number of periods on which to compute the IRFs. Setting @code{irf=0},
suppresses the plotting of IRF's. Default: @code{40}.
@item irf_shocks = ( @var{VARIABLE_NAME} [[,] @var{VARIABLE_NAME} @dots{}] )
@anchor{irf_shocks}
The exogenous variables for which to compute IRFs. Default: all.
@item relative_irf
Requests the computation of normalized IRFs in percentage of the
standard error of each shock.
@item nocorr
Don't print the correlation matrix (printing them is the default).
@item nofunctions
Don't print the coefficients of the approximated solution (printing
them is the default).
@item nomoments
Don't print moments of the endogenous variables (printing them is the
default).
@item nograph
@anchor{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 @code{graph_format}
option, except if @code{graph_format=none}) and displayed to screen
(unless @code{nodisplay} option is used).
@item nodisplay
@anchor{nodisplay} Do not display the graphs, but still save them to disk
(unless @code{nograph} is used).
@item graph_format = @var{FORMAT}
@itemx graph_format = ( @var{FORMAT}, @var{FORMAT}@dots{} )
@anchor{graph_format}
Specify the file format(s) for graphs saved to disk. Possible values are
@code{eps} (the default), @code{pdf}, @code{fig} and @code{none} (under Octave,
only @code{eps} and @code{none} are available). If the file format is set equal to
@code{none}, the graphs are displayed but not saved to the disk.
@item noprint
Don't print anything. Useful for loops.
@item print
Print results (opposite of @code{noprint}).
@item order = @var{INTEGER}
@anchor{order}
Order of Taylor approximation. Acceptable values are @code{1},
@code{2} and @code{3}. Note that for third order,
@code{k_order_solver} option is implied and only empirical moments are
available (you must provide a value for @code{periods}
option). Default: @code{2} (except after an @code{estimation} command,
in which case the default is the value used for the estimation).
@item k_order_solver
@anchor{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
@code{bytecode} option (@pxref{Model declaration}. Default: disabled
for order 1 and 2, enabled otherwise
@item periods = @var{INTEGER}
@vindex oo_.endo_simul
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 @code{initval} block,
possibly recomputed by @code{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 @code{oo_.endo_simul} (@pxref{oo_.endo_simul}). The simulated
exogenous variables are made available in @code{oo_.exo_simul}
(@pxref{oo_.exo_simul}). Default: @code{0}.
@item qz_criterium = @var{DOUBLE}
Value used to split stable from unstable eigenvalues in reordering the
Generalized Schur decomposition used for solving 1^st order
problems. Default: @code{1.000001} (except when estimating with
@code{lik_init} option equal to @code{1}: the default is
@code{0.999999} in that case; @pxref{Estimation}).
@item qz_zero_threshold = @var{DOUBLE}
Value used to test if a generalized eigenvalue is 0/0 in the generalized
Schur decomposition (in which case the model does not admit a unique
solution). Default: @code{1e-6}.
@item replic = @var{INTEGER}
Number of simulated series used to compute the IRFs. Default: @code{1}
if @code{order}=@code{1}, and @code{50} otherwise.
@item simul_replic = @var{INTEGER}
Number of series to simulate when empirical moments are requested
(@i{i.e.} @code{periods} > 0). Note that if this option is greater
than @code{1}, the additional series will not be used for computing
the empirical moments but will simply be saved in binary form to the
file @file{@var{FILENAME}_simul}. Default: @code{1}.
@item solve_algo = @var{INTEGER}
@xref{solve_algo}, for the possible values and their meaning.
@item aim_solver
@anchor{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
@uref{http://www.federalreserve.gov/Pubs/oss/oss4/aimindex.html,AIM
website} for more details on the algorithm.
@item conditional_variance_decomposition = @var{INTEGER}
@anchor{conditional_variance_decomposition = INTEGER}
See below.
@item conditional_variance_decomposition = [@var{INTEGER1}:@var{INTEGER2}]
See below.
@item conditional_variance_decomposition = [@var{INTEGER1} @var{INTEGER2} @dots{}]
Computes a conditional variance decomposition for the specified
period(s). The periods must be strictly positive. Conditional variances are given by
@math{var(y_{t+k}|t)}. For period 1, the conditional variance
decomposition provides the decomposition of the effects of shocks upon
impact. The results are stored in
@code{oo_.conditional_variance_decomposition}
(@pxref{oo_.conditional_variance_decomposition}). The variance decomposition is only conducted, if theoretical moments are requested, i.e. using the @code{periods=0}-option. In case of @code{order=2}, Dynare provides a second-order accurate approximation to the true second moments based on the linear terms of the second-order solution (see @cite{Kim, Kim, Schaumburg and Sims (2008)}).
@item pruning
Discard higher order terms when iteratively computing simulations of
the solution. At second order, Dynare uses the algorithm of @cite{Kim, Kim, Schaumburg and Sims (2008)}, while at third order its generalization by @cite{Andreasen, Fernández-Villaverde and Rubio-Ramírez (2013)} is used.
@item partial_information
@anchor{partial_information}
Computes the solution of the model under partial information, along
the lines of @cite{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 @code{varobs} command. Note
that if @code{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
@uref{http://www.dynare.org/DynareWiki/PartialInformation}.
@item sylvester = @var{OPTION}
@anchor{sylvester}
Determines the algorithm used to solve the Sylvester equation for block decomposed model. Possible values for @code{@var{OPTION}} are:
@table @code
@item default
Uses the default solver for Sylvester equations (@code{gensylv}) based
on Ondra Kamenik algorithm (see
@uref{http://www.dynare.org/documentation-and-support/dynarepp/sylvester.pdf/at_download/file,the
Dynare Website} for more information).
@item fixed_point
Uses a fixed point algorithm to solve the Sylvester equation (@code{gensylv_fp}). This method is faster than the @code{default} one for large scale models.
@end table
@noindent
Default value is @code{default}
@item sylvester_fixed_point_tol = @var{DOUBLE}
@anchor{sylvester_fixed_point_tol}
It is the convergence criterion used in the fixed point sylvester solver. Its default value is 1e-12.
@item dr = @var{OPTION}
@anchor{dr}
Determines the method used to compute the decision rule. Possible values for @code{@var{OPTION}} are:
@table @code
@item default
Uses the default method to compute the decision rule based on the generalized Schur decomposition
(see @cite{Villemot (2011)} for more information).
@item cycle_reduction
Uses the cycle reduction algorithm to solve the polynomial equation for retrieving the coefficients
associated to the endogenous variables in the decision rule. This method is faster than the @code{default} one for large scale models.
@item logarithmic_reduction
Uses the logarithmic reduction algorithm to solve the polynomial equation for retrieving the coefficients
associated to the endogenous variables in the decision rule. This method is in general slower than the @code{cycle_reduction}.
@end table
@noindent
Default value is @code{default}
@item dr_cycle_reduction_tol = @var{DOUBLE}
@anchor{dr_cycle_reduction_tol}
The convergence criterion used in the cycle reduction algorithm. Its default value is 1e-7.
@item dr_logarithmic_reduction_tol = @var{DOUBLE}
@anchor{dr_logarithmic_reduction_tol}
The convergence criterion used in the logarithmic reduction algorithm. Its default value is 1e-12.
@item dr_logarithmic_reduction_maxiter = @var{INTEGER}
@anchor{dr_logarithmic_reduction_maxiter}
The maximum number of iterations used in the logarithmic reduction algorithm. Its default value is 100.
@end table
@outputhead
This command sets @code{oo_.dr}, @code{oo_.mean}, @code{oo_.var} and
@code{oo_.autocorr}, which are described below.
If option @code{periods} is present, sets @code{oo_.endo_simul}
(@pxref{oo_.endo_simul}), and also saves the simulated variables in
MATLAB/Octave vectors of the global workspace with the same name as
the endogenous variables.
If options @code{irf} is different from zero, sets @code{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).
@customhead{Example 1}
@example
shocks;
var e;
stderr 0.0348;
end;
stoch_simul;
@end example
Performs the simulation of the 2nd order approximation of a model
with a single stochastic shock @code{e}, with a standard error of
0.0348.
@customhead{Example 2}
@example
stoch_simul(irf=60) y k;
@end example
Performs the simulation of a model and displays impulse
response functions on 60 periods for variables @code{y} and @code{k}.
@end deffn
@defvr {MATLAB/Octave variable} oo_.mean
After a run of @code{stoch_simul}, contains the mean of the endogenous
variables. Contains theoretical mean if the @code{periods} option is
not present, and empirical mean otherwise. The variables are arranged
in declaration order.
@end defvr
@defvr {MATLAB/Octave variable} oo_.var
After a run of @code{stoch_simul}, contains the variance-covariance of
the endogenous variables. Contains theoretical variance if the
@code{periods} option is not present (or an approximation thereof for @code{order=2}), and empirical variance
otherwise. The variables are arranged in declaration order.
@end defvr
@anchor{oo_.autocorr}
@defvr {MATLAB/Octave variable} oo_.autocorr
After a run of @code{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 order of
autocorrelation. The option @code{ar} specifies the number of
autocorrelation matrices available. Contains theoretical
autocorrelations if the @code{periods} option is not present (or an approximation thereof for @code{order=2}), and
empirical autocorrelations otherwise.
The element @code{oo_.autocorr@{i@}(k,l)} is equal to the correlation
between @math{y^k_t} and @math{y^l_{t-i}}, where @math{y^k}
(resp. @math{y^l}) is the @math{k}-th (resp. @math{l}-th) endogenous
variable in the declaration order.
Note that if theoretical moments have been requested,
@code{oo_.autocorr@{i@}} is the same than @code{oo_.gamma_y@{i+1@}}.
@end defvr
@defvr {MATLAB/Octave variable} oo_.gamma_y
After a run of @code{stoch_simul}, if theoretical moments have been
requested (@i{i.e.} if the @code{periods} option is not present), this
variable contains a cell array with the following values (where
@code{ar} is the value of the option of the same name):
@table @code
@item oo_.gamma@{1@}
Variance/co-variance matrix.
@item oo_.gamma@{i+1@} (for i=1:ar)
Autocorrelation function. @pxref{oo_.autocorr} for more
details. Beware, this is the @i{autocorrelation} function, not the
@i{autocovariance} function.
@item oo_.gamma@{nar+2@}
Variance decomposition.
@item oo_.gamma@{nar+3@}
If a second order approximation has been requested, contains the
vector of the mean correction terms.
@end table
In case of @code{order=2}, the theoretical second moments are a second order accurate approximation of the true second moments, see @code{conditional_variance_decomposition}.
@end defvr
@defvr {MATLAB/Octave variable} oo_.irfs
After a run of @code{stoch_simul} with option @code{irf} different
from zero, contains the impulse responses, with the following naming
convention: @code{@var{VARIABLE_NAME}_@var{SHOCK_NAME}}.
For example, @code{oo_.irfs.gnp_ea} contains the effect on @code{gnp}
of a one standard deviation shock on @code{ea}.
@end defvr
@vindex oo_.dr
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 @code{oo_.dr} which is described below.
@deffn Command extended_path ;
@deffnx Command extended_path (@var{OPTIONS}@dots{}) ;
@descriptionhead
@code{extended_path} solves a stochastic (@i{i.e.} rational
expectations) model, using the @emph{extended path} method presented by
@cite{Fair and Taylor (1983)}. Time series for the endogenous variables
are generated by assuming that the agents believe that there will no
more shocks in the following periods.
This function first computes a random path for the exogenous variables
(stored in @code{oo_.exo_simul}, @pxref{oo_.exo_simul}) and then
computes the corresponding path for endogenous variables, taking the
steady state as starting point. The result of the simulation is stored
in @code{oo_.endo_simul} (@pxref{oo_.endo_simul}). Note that this
simulation approach does not solve for the policy and transition
equations but for paths for the endogenous variables.
@optionshead
@table @code
@item periods = @var{INTEGER}
The number of periods for which the simulation is to be computed. No
default value, mandatory option.
@item solver_periods = @var{INTEGER}
The number of periods used to compute the solution of the perfect
foresight at every iteration of the algorithm. Default: @code{200}.
@item order = @var{INTEGER}
If @code{order} is greater than 0 Dynare uses a gaussian quadrature to take into account the effects of future uncertainty. If @code{order}=@var{S} then the time series for the endogenous variables
are generated by assuming that the agents believe that there will no more shocks after period @var{t+S}. This is an experimental feature and can be quite slow. Default: @code{0}.
@item hybrid
Use the constant of the second order perturbation reduced form to correct the paths generated by the (stochastic) extended path algorithm.
@end table
@end deffn
@node Typology and ordering of variables
@subsection Typology and ordering of variables
Dynare distinguishes four types of endogenous variables:
@table @emph
@item Purely backward (or purely predetermined) variables
@vindex M_.npred
Those that appear only at current and past period in the model, but
not at future period (@i{i.e.} at @math{t} and @math{t-1} but not
@math{t+1}). The number of such variables is equal to
@code{M_.npred}.
@item Purely forward variables
@vindex M_.nfwrd
Those that appear only at current and future period in the model, but
not at past period (@i{i.e.} at @math{t} and @math{t+1} but not
@math{t-1}). The number of such variables is stored in
@code{M_.nfwrd}.
@item Mixed variables
@vindex M_.nboth
Those that appear at current, past and future period in the model
(@i{i.e.} at @math{t}, @math{t+1} and @math{t-1}). The number of such
variables is stored in @code{M_.nboth}.
@item Static variables
@vindex M_.nstatic
Those that appear only at current, not past and future period in the
model (@i{i.e.} only at @math{t}, not at @math{t+1} or
@math{t-1}). The number of such variables is stored in
@code{M_.nstatic}.
@end table
Note that all endogenous variables fall into one of these four
categories, since after the creation of auxiliary variables
(@pxref{Auxiliary variables}), all endogenous have at most one lead
and one lag. We therefore have the following identity:
@example
M_.npred + M_.both + M_.nfwrd + M_.nstatic = M_.endo_nbr
@end example
Internally, Dynare uses two orderings of the endogenous variables: the
order of declaration (which is reflected in @code{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.
@vindex oo_.dr.order_var
@vindex oo_.dr.inv_order_var
Variable @code{oo_.dr.order_var} maps DR-order to declaration
order, and variable @code{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 @code{oo_.dr_order_var(k)} in
declaration order. Conversely, k-th declared variable is numbered
@code{oo_.dr.inv_order_var(k)} in DR-order.
@vindex M_.nspred
@vindex M_.nsfwrd
@vindex M_.ndynamic
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 @code{M_.nspred = M_.npred + M_.nboth} such
variables. Similarly, one has @code{M_.nsfwrd = M_.nfwrd + M_.nboth},
and @code{M_.ndynamic = M_.nfwrd+M_.nboth+M_.npred}.
@node First order approximation
@subsection First order approximation
The approximation has the form:
@math{y_t = y^s + A y^h_{t-1} + B u_t}
where @math{y^s} is the steady state value of @math{y} and
@math{y^h_t=y_t-y^s}.
The coefficients of the decision rules are stored as follows:
@itemize
@item
@vindex oo_.dr.ys
@math{y^s} is stored in @code{oo_.dr.ys}. The vector rows
correspond to all endogenous in the declaration order.
@item
@vindex oo_.dr.ghx
A is stored in @code{oo_.dr.ghx}. The matrix rows correspond to all
endogenous in DR-order. The matrix columns correspond to state
variables in DR-order.
@item
@vindex oo_.dr.ghu
B is stored @code{oo_.dr.ghu}. The matrix rows correspond to all
endogenous in DR-order. The matrix columns correspond to exogenous
variables in declaration order.
@end itemize
@node Second order approximation
@subsection Second order approximation
The approximation has the form:
@math{y_t = y^s + 0.5 \Delta^2 +
A y^h_{t-1} + B u_t + 0.5 C
(y^h_{t-1}\otimes y^h_{t-1}) + 0.5 D
(u_t \otimes u_t) + E
(y^h_{t-1} \otimes u_t)}
where @math{y^s} is the steady state value of @math{y},
@math{y^h_t=y_t-y^s}, and @math{\Delta^2} 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:
@itemize
@item
@vindex oo_.dr.ghs2
@math{\Delta^2} is stored in @code{oo_.dr.ghs2}. The vector rows
correspond to all endogenous in DR-order.
@item
@vindex oo_.dr.ghxx
@math{C} is stored in @code{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.
@item
@vindex oo_.dr.ghuu
@math{D} is stored in @code{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.
@item
@vindex oo_.dr.ghxu
@math{E} is stored in @code{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).
@end itemize
@node Third order approximation
@subsection Third order approximation
The approximation has the form:
@math{y_t = y^s + G_0 +
G_1 z_t +
G_2 (z_t \otimes z_t) +
G_3 (z_t \otimes z_t \otimes z_t)}
where @math{y^s} is the steady state value of @math{y}, and @math{z_t} is a
vector consisting of the deviation from the steady state of the state
variables (in DR-order) at date @math{t-1} followed by the exogenous variables at
date @math{t} (in declaration order). The vector @math{z_t} is
therefore of size @math{n_z} = @code{M_.nspred +
M_.exo_nbr}.
The coefficients of the decision rules are stored as follows:
@itemize
@item
@vindex oo_.dr.ys
@math{y^s} is stored in @code{oo_.dr.ys}. The vector rows
correspond to all endogenous in the declaration order.
@item
@vindex oo_.dr.g_0
@math{G_0} is stored in @code{oo_.dr.g_0}. The
vector rows correspond to all endogenous in DR-order.
@item
@vindex oo_.dr.g_1
@math{G_1} is stored in @code{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.
@item
@vindex oo_.dr.g_2
@math{G_2} is stored in @code{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{i.e.} symmetric elements are stored only
once, which implies that the matrix has @math{n_z(n_z+1)/2} columns. More
precisely, each column of this matrix corresponds to a pair @math{(i_1, i_2)}
where each index represents an element of @math{z_t} and is therefore between
@math{1} and @math{n_z}. Only non-decreasing pairs are stored, @i{i.e.} those for
which @math{i_1 \leq i_2}. The columns are arranged in the lexicographical order
of non-decreasing pairs. Also note that for those pairs where @math{i_1 \neq
i_2}, since the element is stored only once but appears two times in
the unfolded @math{G_2} matrix, it must be multiplied by 2 when computing the
decision rules.
@item
@vindex oo_.dr.g_3
@math{G_3} is stored in @code{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{i.e.} symmetric elements are stored only
once, which implies that the matrix has @math{n_z(n_z+1)(n_z+2)/6}
columns. More precisely, each column of this matrix corresponds to a
tuple @math{(i_1, i_2, i_3)} where each index represents an element of
@math{z_t} and is therefore between @math{1} and @math{n_z}. Only
non-decreasing tuples are stored, @i{i.e.} those for which @math{i_1
\leq i_2 \leq i_3}. The columns are arranged in the lexicographical
order of non-decreasing tuples. Also note that for tuples that have
three distinct indices (@i{i.e.} @math{i_1 \neq i_2} and @math{i_1
\neq i_3} and @math{i_2 \neq i_3}, since these elements are stored
only once but appears six times in the unfolded @math{G_3} matrix,
they must be multiplied by 6 when computing the decision
rules. Similarly, for those tuples that have two equal indices
(@i{i.e.} of the form @math{(a,a,b)} or @math{(a,b,a)} or
@math{(b,a,a)}), since these elements are stored only once but appears
three times in the unfolded @math{G_3} matrix, they must be multiplied
by 3 when computing the decision rules.
@end itemize
@anchor{oo_.conditional_variance_decomposition}
@defvr {MATLAB/Octave variable} oo_.conditional_variance_decomposition
After a run of @code{stoch_simul} with the
@code{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).
@end defvr
@node Estimation
@section 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 @cite{Ireland (2004)}) and Bayesian
techniques (as in @cite{Rabanal and Rubio-Ramirez (2003)},
@cite{Schorfheide (2000)} or @cite{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 (@pxref{block}).
@deffn Command varobs @var{VARIABLE_NAME}@dots{};
@descriptionhead
This command lists the name of observed endogenous variables for the
estimation procedure. These variables must be available in the data
file (@pxref{estimation_cmd}).
Alternatively, this command is also used in conjunction with the
@code{partial_information} option of @code{stoch_simul}, for declaring
the set of observed variables when solving the model under partial
information.
Only one instance of @code{varobs} is allowed in a model file. If one
needs to declare observed variables in a loop, the macro-processor can
be used as shown in the second example below.
@customhead{Simple example}
@example
varobs C y rr;
@end example
@customhead{Example with a loop}
@example
varobs
@@#for co in countries
GDP_@@@{co@}
@@#endfor
;
@end example
@end deffn
@deffn Block observation_trends ;
@descriptionhead
This block specifies @emph{linear} trends for observed variables as
functions of model parameters.
Each line inside of the block should be of the form:
@example
@var{VARIABLE_NAME}(@var{EXPRESSION});
@end example
In most cases, variables shouldn't be centered when
@code{observation_trends} is used.
@examplehead
@example
observation_trends;
Y (eta);
P (mu/eta);
end;
@end example
@end deffn
@anchor{estimated_params}
@deffn Block estimated_params ;
@descriptionhead
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:
@example
stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME
, INITIAL_VALUE [, LOWER_BOUND, UPPER_BOUND ];
@end example
In a Bayesian estimation, each line follows this syntax:
@example
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 ] ] ];
@end example
The first part of the line consists of one of the three following
alternatives:
@table @code
@item stderr @var{VARIABLE_NAME}
Indicates that the standard error of the exogenous variable
@var{VARIABLE_NAME}, or of the observation error/measurement errors associated with
endogenous observed variable @var{VARIABLE_NAME}, is to be estimated
@item corr @var{VARIABLE_NAME1}, @var{VARIABLE_NAME2}
Indicates that the correlation between the exogenous variables
@var{VARIABLE_NAME1} and @var{VARIABLE_NAME2}, or the correlation of
the observation errors/measurement errors associated with endogenous observed variables
@var{VARIABLE_NAME1} and @var{VARIABLE_NAME2}, is to be estimated. Note that correlations set by previous @code{shocks}-blocks or @code{estimation}-commands are kept at their value set prior to estimation if they are not estimated again subsequently. Thus, the treatment is the same as in the case of deep parameters set during model calibration and not estimated.
@item @var{PARAMETER_NAME}
The name of a model parameter to be estimated
@item DSGE_PRIOR_WEIGHT
@dots{}
@end table
The rest of the line consists of the following fields, some of them
being optional:
@table @code
@item @var{INITIAL_VALUE}
Specifies a starting value for maximum likelihood estimation
@item @var{LOWER_BOUND}
Specifies a lower bound for the parameter value in maximum likelihood estimation
@item @var{UPPER_BOUND}
Specifies an upper bound for the parameter value in maximum likelihood estimation
@item @var{PRIOR_SHAPE}
A keyword specifying the shape of the prior density.
The possible values are: @code{beta_pdf},
@code{gamma_pdf}, @code{normal_pdf},
@code{uniform_pdf}, @code{inv_gamma_pdf},
@code{inv_gamma1_pdf}, @code{inv_gamma2_pdf}. Note
that @code{inv_gamma_pdf} is equivalent to
@code{inv_gamma1_pdf}
@item @var{PRIOR_MEAN}
The mean of the prior distribution
@item @var{PRIOR_STANDARD_ERROR}
The standard error of the prior distribution
@item @var{PRIOR_3RD_PARAMETER}
A third parameter of the prior used for generalized beta distribution,
generalized gamma and for the uniform distribution. Default: @code{0}
@item @var{PRIOR_4TH_PARAMETER}
A fourth parameter of the prior used for generalized beta distribution
and for the uniform distribution. Default: @code{1}
@item @var{SCALE_PARAMETER}
The scale parameter to be used for the jump distribution of the
Metropolis-Hasting algorithm
@end table
Note that @var{INITIAL_VALUE}, @var{LOWER_BOUND}, @var{UPPER_BOUND},
@var{PRIOR_MEAN}, @var{PRIOR_STANDARD_ERROR},
@var{PRIOR_3RD_PARAMETER}, @var{PRIOR_4TH_PARAMETER} and
@var{SCALE_PARAMETER} can be any valid @var{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
@var{SCALE_PARAMETER}, you must specify @var{PRIOR_3RD_PARAMETER} and
@var{PRIOR_4TH_PARAMETER}. Use empty values, if these parameters don't
apply.
@examplehead
The following line:
@example
corr eps_1, eps_2, 0.5, , , beta_pdf, 0, 0.3, -1, 1;
@end example
sets a generalized beta prior for the correlation between @code{eps_1} and
@code{eps_2} with mean 0 and variance 0.3. By setting
@var{PRIOR_3RD_PARAMETER} to -1 and @var{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 @var{LOWER_BOUND} and
@var{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:
@example
corr eps_1, eps_2, 0.5, -0.5, 1, beta_pdf, 0, 0.3, -1, 1;
@end example
sets the same generalized beta distribution as before, but now truncates
this distribution to [-0.5,1] through the use of @var{LOWER_BOUND} and
@var{UPPER_BOUND}. Hence, the prior does not integrate to 1 anymore.
@customhead{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 @code{parameters} statement and to define the transformation,
using a pound sign (#) expression (@pxref{Model declaration}).
@examplehead
@example
parameters bet;
model;
# sig = 1/bet;
c = sig*c(+1)*mpk;
end;
estimated_params;
bet, normal_pdf, 1, 0.05;
end;
@end example
@end deffn
@deffn Block estimated_params_init ;
This block declares numerical initial values for the optimizer when
these ones are different from the prior mean.
Each line has the following syntax:
@example
stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME
, INITIAL_VALUE;
@end example
@xref{estimated_params}, for the meaning and syntax of the various components.
@end deffn
@deffn Block estimated_params_bounds ;
This block declares lower and upper bounds for parameters in maximum
likelihood estimation.
Each line has the following syntax:
@example
stderr VARIABLE_NAME | corr VARIABLE_NAME_1, VARIABLE_NAME_2 | PARAMETER_NAME
, LOWER_BOUND, UPPER_BOUND;
@end example
@xref{estimated_params}, for the meaning and syntax of the various components.
@end deffn
@anchor{estimation_cmd}
@deffn Command estimation [@var{VARIABLE_NAME}@dots{}];
@deffnx Command estimation (@var{OPTIONS}@dots{}) [@var{VARIABLE_NAME}@dots{}];
@descriptionhead
This command runs Bayesian or maximum likelihood estimation.
The following information will be displayed by the command:
@itemize
@item
results from posterior optimization (also for maximum likelihood)
@item
marginal log density
@item
mean and shortest confidence interval from posterior simulation
@item
Metropolis-Hastings convergence graphs that still need to be documented
@item
graphs with prior, posterior and mode
@item
graphs of smoothed shocks, smoothed observation errors, smoothed and historical variables
@end itemize
@algorithmshead
The Monte Carlo Markov Chain (MCMC) univariate diagnostics are generated
by the estimation command if @ref{mh_nblocks} is larger than 1, if
@ref{mh_replic} is larger than 2000, and if option @ref{nodiagnostic} is
not used. As described in section 3 of @cite{Brooks and Gelman (1998)}
the convergence diagnostics are based on comparing pooled and within
MCMC moments (Dynare displays the second and third order moments, and
the length of the Highest Probability Density interval covering 80% of
the posterior distribution). Due to computational reasons, the
multivariate convergence diagnostic does not follow @cite{Brooks and
Gelman (1998)} strictly, but rather applies their idea for univariate
convergence diagnostics to the range of the posterior likelihood
function instead of the individual parameters. The posterior kernel is
used to aggregate the parameters into a scalar statistic whose
convergence is then checked using the @cite{Brooks and Gelman (1998)}
univariate convergence diagnostic.
@optionshead
@table @code
@item datafile = @var{FILENAME}
@anchor{datafile}
The datafile: a @file{.m} file, a @file{.mat} file, a @file{.csv} file, or a
@file{.xls}/@file{.xlsx} file (the latter format is supported under Octave
if the @uref{http://octave.sourceforge.net/io/,io} and
@uref{http://octave.sourceforge.net/java/,java} packages from
Octave-Forge are installed, along with a
@uref{http://www.java.com/download,Java Runtime Environment})
@item xls_sheet = @var{NAME}
@anchor{xls_sheet}
The name of the sheet with the data in an Excel file
@item xls_range = @var{RANGE}
@anchor{xls_range}
The range with the data in an Excel file
@item nobs = @var{INTEGER}
@anchor{nobs}
The number of observations to be used. Default: all observations in
the file
@item nobs = [@var{INTEGER1}:@var{INTEGER2}]
@anchor{nobs1}
Runs a recursive estimation and forecast for samples of size ranging
of @var{INTEGER1} to @var{INTEGER2}. Option @code{forecast} must
also be specified. The forecasts are stored in the
@code{RecursiveForecast} field of the results structure (@pxref{RecursiveForecast}).
@item first_obs = @var{INTEGER}
@anchor{first_obs}
The number of the first observation to be used. Default: @code{1}
@item prefilter = @var{INTEGER}
@anchor{prefilter}
A value of @code{1} means that the estimation procedure will demean
the data. Default: @code{0}, @i{i.e.} no prefiltering
@item presample = @var{INTEGER}
@anchor{presample}
The number of observations to be skipped before evaluating the
likelihood. Default: @code{0}
@item loglinear
@anchor{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
@item plot_priors = @var{INTEGER}
Control the plotting of priors:
@table @code
@item 0
No prior plot
@item 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.
@end table
@noindent
Default value is @code{1}.
@item nograph
@xref{nograph}.
@item nodisplay
@xref{nodisplay}.
@item graph_format = @var{FORMAT}
@itemx graph_format = ( @var{FORMAT}, @var{FORMAT}@dots{} )
@xref{graph_format}.
@item lik_init = @var{INTEGER}
@anchor{lik_init}
Type of initialization of Kalman filter:
@table @code
@item 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
@item 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
@item 3
For nonstationary models: use a diffuse filter (use rather the @code{diffuse_filter} option)
@item 4
The filter is initialized with the fixed point of the Riccati equation
@end table
@noindent
Default value is @code{1}. For advanced use only.
@item lik_algo = @var{INTEGER}
For internal use and testing only.
@item conf_sig = @var{DOUBLE}
@xref{conf_sig}.
@item mh_replic = @var{INTEGER}
@anchor{mh_replic} Number of replications for Metropolis-Hastings
algorithm. For the time being, @code{mh_replic} should be larger than
@code{1200}. Default: @code{20000}
@item sub_draws = @var{INTEGER}
@anchor{sub_draws} number of draws from the Metropolis iterations that
are used to compute posterior distribution of various objects (smoothed
variable, smoothed shocks, forecast, moments, IRF). @code{sub_draws} should be smaller than
the total number of Metropolis draws available. Default:
@code{min(1200,0.25*Total number of draws)}
@item mh_nblocks = @var{INTEGER}
@anchor{mh_nblocks} Number of parallel chains for Metropolis-Hastings algorithm. Default:
@code{2}
@item mh_drop = @var{DOUBLE}
The fraction of initially generated parameter vectors to be dropped
before using posterior simulations. Default: @code{0.5}
@item mh_jscale = @var{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:
@code{0.2}
@item mh_init_scale = @var{DOUBLE}
The scale to be used for drawing the initial value of the
Metropolis-Hastings chain. Default: 2*@code{mh_scale}
@item mh_recover
@anchor{mh_recover} Attempts to recover a Metropolis-Hastings
simulation that crashed prematurely. Shouldn't be used together with
@code{load_mh_file}
@item mh_mode = @var{INTEGER}
@dots{}
@item mode_file = @var{FILENAME}
@anchor{mode_file}
Name of the file containing previous value for the mode. When
computing the mode, Dynare stores the mode (@code{xparam1}) and the
hessian (@code{hh}, only if @code{cova_compute=1}) in a file called
@file{@var{MODEL_FILENAME}_mode.mat}
@item mode_compute = @var{INTEGER} | @var{FUNCTION_NAME}
Specifies the optimizer for the mode computation:
@table @code
@item 0
The mode isn't computed. When @code{mode_file} option is specified, the
mode is simply read from that file.
When @code{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 @code{mode_file}
option is not specified and there is no @code{estimated_params} block,
but the @code{smoother} option is used, it is a roundabout way to
compute the smoothed value of the variables of a model with calibrated parameters.
@item 1
Uses @code{fmincon} optimization routine (available under MATLAB if
the optimization toolbox is installed; not available under Octave)
@item 2
Value no longer used
@item 3
Uses @code{fminunc} optimization routine (available under MATLAB if
the optimization toolbox is installed; available under Octave if the
@uref{http://octave.sourceforge.net/optim/,optim} package from
Octave-Forge is installed)
@item 4
Uses Chris Sims's @code{csminwel}
@item 5
Uses Marco Ratto's @code{newrat}. This value is not compatible with non
linear filters or DSGE-VAR models
@item 6
Uses a Monte-Carlo based optimization routine (see
@uref{http://www.dynare.org/DynareWiki/MonteCarloOptimization,Dynare
wiki} for more details)
@item 7
Uses @code{fminsearch}, a simplex based optimization routine (available
under MATLAB if the optimization toolbox is installed; available under
Octave if the @uref{http://octave.sourceforge.net/optim/,optim}
package from Octave-Forge is installed)
@item 8
Uses Dynare implementation of the Nelder-Mead simplex based optimization
routine (generally more efficient than the MATLAB or Octave implementation
available with @code{mode_compute=7})
@item 9
Uses the CMA-ES (Covariance Matrix Adaptation Evolution Strategy) algorithm, an evolutionary algorithm for difficult non-linear non-convex optimization
@item @var{FUNCTION_NAME}
It is also possible to give a @var{FUNCTION_NAME} to this option,
instead of an @var{INTEGER}. In that case, Dynare takes the return
value of that function as the posterior mode.
@end table
@noindent
Default value is @code{4}.
@item 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
@item mode_check_neighbourhood_size = @var{DOUBLE}
Used in conjunction with option @code{mode_check}, gives the width of
the window around the posterior mode to be displayed on the diagnostic
plots. This width is expressed in percentage deviation. The @code{Inf}
value is allowed, and will trigger a plot over the entire domain
(see also @code{mode_check_symmetric_plots}).
Default: @code{0.5}.
@item mode_check_symmetric_plots = @var{INTEGER}
Used in conjunction with option @code{mode_check}, if set to @code{1},
tells Dynare to ensure that the check plots are symmetric around the
posterior mode. A value of @code{0} allows to have asymmetric plots,
which can be useful if the posterior mode is close to a domain
boundary, or in conjunction with @code{mode_check_neighbourhood_size =
Inf} when the domain in not the entire real line. Default: @code{1}.
@item prior_trunc = @var{DOUBLE}
@anchor{prior_trunc} Probability of extreme values of the prior
density that is ignored when computing bounds for the
parameters. Default: @code{1e-32}
@item load_mh_file
@anchor{load_mh_file} Tells Dynare to add to previous
Metropolis-Hastings simulations instead of starting from
scratch. Shouldn't be used together with @code{mh_recover}
@item optim = (@var{fmincon options})
Can be used to set options for @code{fmincon}, the optimizing function
of MATLAB Optimization toolbox. Use MATLAB's syntax for these
options. Default:
@code{('display','iter','LargeScale','off','MaxFunEvals',100000,'TolFun',1e-8,'TolX',1e-6)}
@item nodiagnostic
@anchor{nodiagnostic} Does not compute the convergence diagnostics for
Metropolis-Hastings. Default: diagnostics are computed and displayed
@item bayesian_irf
@vindex oo_.PosteriorIRF.dsge
@anchor{bayesian_irf} Triggers the computation of the posterior
distribution of IRFs. The length of the IRFs are controlled by the
@code{irf} option. Results are stored in @code{oo_.PosteriorIRF.dsge}
(see below for a description of this variable)
@item 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, @code{dsge_prior_weight}, must be defined in
the @code{estimated_params} section. NB: The previous method of
declaring @code{dsge_prior_weight} as a parameter and then placing it
in @code{estimated_params} is now deprecated and will be removed in a
future release of Dynare.
@item dsge_var = @var{DOUBLE}
@anchor{dsge_var}
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 @code{dsge_prior_weight} as a parameter
and then calibrating it is now deprecated and will be removed in a
future release of Dynare.
@item dsge_varlag = @var{INTEGER}
@anchor{dsge_varlag} The number of lags used to estimate a DSGE-VAR
model. Default: @code{4}.
@item moments_varendo
@vindex oo_.PosteriorTheoreticalMoments
@anchor{moments_varendo} Triggers the computation of the posterior
distribution of the theoretical moments of the endogenous
variables. Results are stored in
@code{oo_.PosteriorTheoreticalMoments} (see below for a description of
this variable). The number of lags in the autocorrelation function is
controlled by the @code{ar} option.
@item conditional_variance_decomposition = @var{INTEGER}
See below.
@item conditional_variance_decomposition = [@var{INTEGER1}:@var{INTEGER2}]
See below.
@item conditional_variance_decomposition = [@var{INTEGER1} @var{INTEGER2} @dots{}]
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 @math{var(y_{t+k}|t)}. For
period 1, the conditional variance decomposition provides the
decomposition of the effects of shocks upon impact. The results are
stored in
@code{oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition},
but currently there is no output. Note that this option requires the
option @code{moments_varendo} to be specified.
@item filtered_vars
@vindex oo_.FilteredVariables
@anchor{filtered_vars} Triggers the computation of the posterior
distribution of filtered endogenous variables/one-step ahead forecasts, i.e. @math{E_{t}{y_{t+1}}}. Results are
stored in @code{oo_.FilteredVariables} (see below for a description of
this variable)
@item smoother
@vindex oo_.SmoothedVariables
@vindex oo_.SmoothedShocks
@vindex oo_.SmoothedMeasurementErrors
@vindex oo_.UpdatedVariables
@anchor{smoother} Triggers the computation of the posterior distribution
of smoothered endogenous variables and shocks, i.e. the expected value of variables and shocks given the information available in all observations up to the @emph{final} date (@math{E_{T}{y_t}}). Results are stored in
@code{oo_.SmoothedVariables}, @code{oo_.SmoothedShocks} and
@code{oo_.SmoothedMeasurementErrors}. Also triggers the computation of
@code{oo_.UpdatedVariables}, which contains the estimation of the expected value of variables given the information available at the @emph{current} date (@math{E_{t}{y_t}}). See below for a description of all these
variables.
@item forecast = @var{INTEGER}
@vindex oo_.forecast
@anchor{forecast} Computes the posterior distribution of a forecast on
@var{INTEGER} periods after the end of the sample used in
estimation. If no Metropolis-Hastings is computed, the result is
stored in variable @code{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
@code{oo_.PointForecast} and
@code{oo_.MeanForecast}. @xref{Forecasting}, for a description of
these variables.
@item tex
@anchor{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)
@item kalman_algo = @var{INTEGER}
@anchor{kalman_algo}
@table @code
@item 0
Automatically use the Multivariate Kalman Filter for stationary models and the Multivariate Diffuse Kalman Filter for non-stationary models
@item 1
Use the Multivariate Kalman Filter
@item 2
Use the Univariate Kalman Filter
@item 3
Use the Multivariate Diffuse Kalman Filter
@item 4
Use the Univariate Diffuse Kalman Filter
@end table
@noindent
Default value is @code{0}.
@item kalman_tol = @var{DOUBLE}
@anchor{kalman_tol} Numerical tolerance for determining the singularity of the covariance matrix of the prediction errors during the Kalman filter (minimum allowed reciprocal of the matrix condition number). Default value is @code{1e-10}
@item filter_covariance
@anchor{filter_covariance} Saves the series of one step ahead error of
forecast covariance matrices.
@item filter_step_ahead = [@var{INTEGER1}:@var{INTEGER2}]
@anchor{filter_step_ahead}
@vindex oo_.FilteredVariablesKStepAhead
@vindex oo_.FilteredVariablesKStepAheadVariances
Triggers the computation k-step ahead filtered values. Stores results in
@code{oo_.FilteredVariablesKStepAhead} and
@code{oo_.FilteredVariablesKStepAheadVariances}.
@item filter_decomposition
@anchor{filter_decomposition} Triggers the computation of the shock
decomposition of the above k-step ahead filtered values.
@item constant
@dots{}
@item noconstant
@dots{}
@item diffuse_filter
Uses the diffuse Kalman filter (as described in
@cite{Durbin and Koopman (2001)} and @cite{Koopman and Durbin
(2003)}) to estimate models with non-stationary observed variables.
When @code{diffused_filter} is used the @code{lik_init} option of
@code{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 @file{.mod}
file followed by @file{_steadystate}. See @file{fs2000_steadystate.m}
in @file{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).
@item selected_variables_only
Only run the smoother on the variables listed just after the
@code{estimation} command. Default: run the smoother on all the
declared endogenous variables.
@item cova_compute = @var{INTEGER}
When @code{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. Otherwise, if this option is equal to
@code{1}, the covariance matrix is computed and stored in variable
@code{hh} of @file{@var{MODEL_FILENAME}_mode.mat}. Default is @code{1}.
@item solve_algo = @var{INTEGER}
@xref{solve_algo}.
@item order = @var{INTEGER}
Order of approximation, either @code{1} or @code{2}. When equal to
@code{2}, the likelihood is evaluated with a particle filter based on
a second order approximation of the model (see
@cite{Fernandez-Villaverde and Rubio-Ramirez (2005)}). Default is
@code{1}, ie the lilkelihood of the linearized model is evaluated
using a standard Kalman filter.
@item irf = @var{INTEGER}
@xref{irf}. Only used if @ref{bayesian_irf} is passed.
@item irf_shocks = ( @var{VARIABLE_NAME} [[,] @var{VARIABLE_NAME} @dots{}] )
@xref{irf_shocks}. Only used if @ref{bayesian_irf} is passed. Cannot be used
with @ref{dsge_var}.
@item aim_solver
@xref{aim_solver}.
@item sylvester = OPTION
@xref{sylvester}.
@item sylvester_fixed_point_tol = @var{DOUBLE}
@xref{sylvester_fixed_point_tol}.
@item lyapunov = @var{OPTION}
@anchor{lyapunov}
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 @code{@var{OPTION}} are:
@table @code
@item default
Uses the default solver for Lyapunov equations based on Bartels-Stewart algorithm.
@item fixed_point
Uses a fixed point algorithm to solve the Lyapunov equation. This method is faster than the @code{default} one for large scale models, but it could require a large amount of iterations.
@item doubling
Uses a doubling algorithm to solve the Lyapunov equation (@code{disclyap_fast}). This method is faster than the two previous one for large scale models.
@item square_root_solver
Uses a square-root solver for Lyapunov equations
(@code{dlyapchol}). This method is fast for large scale models
(available under MATLAB if the control system toolbox is installed;
available under Octave if the
@uref{http://octave.sourceforge.net/control/,control} package from
Octave-Forge is installed)
@end table
@noindent
Default value is @code{default}
@item lyapunov_fixed_point_tol = @var{DOUBLE}
@anchor{lyapunov_fixed_point_tol}
This is the convergence criterion used in the fixed point lyapunov solver. Its default value is 1e-10.
@item lyapunov_doubling_tol = @var{DOUBLE}
@anchor{lyapunov_doubling_tol}
This is the convergence criterion used in the doubling algorithm to solve the lyapunov equation. Its default value is 1e-16.
@item analytic_derivation
Triggers estimation with analytic gradient. The final hessian is also
computed analytically. Only works for stationary models without
missing observations.
@item ar = @var{INTEGER}
@xref{ar}. Only useful in conjuction with option @code{moments_varendo}.
@item endogenous_prior
Use endogenous priors as in @cite{Christiano, Trabandt and Walentin
(2011)}.
@item use_univariate_filters_if_singularity_is_detected = @var{INTEGER}
Decide whether Dynare should automatically switch to univariate filter
if a singularity is encountered in the likelihood computation (this is
the behaviour if the option is equal to @code{1}). Alternatively, if
the option is equal to @code{0}, Dynare will not automatically change
the filter, but rather use a penalty value for the likelihood when
such a singularity is encountered. Default: @code{1}.
@item qz_zero_threshold = @var{DOUBLE}
Value used to test if a generalized eigenvalue is 0/0 in the generalized
Schur decomposition (in which case the model does not admit a unique
solution). Default: @code{1e-6}.
@end table
@customhead{Note}
If no @code{mh_jscale} parameter is used in estimated_params, the
procedure uses @code{mh_jscale} for all parameters. If
@code{mh_jscale} option isn't set, the procedure uses @code{0.2} for
all parameters.
@outputhead
@vindex M_.params
@vindex M_.Sigma_e
After running @code{estimation}, the parameters @code{M_.params} and
the variance matrix @code{M_.Sigma_e} of the shocks are set to the
mode for maximum likelihood estimation or posterior mode computation
without Metropolis iterations.
After @code{estimation} with Metropolis iterations (option
@code{mh_replic} > 0 or option @code{load_mh_file} set) the parameters
@code{M_.params} and the variance matrix @code{M_.Sigma_e} of the
shocks are set to the posterior mean.
Depending on the options, @code{estimation} stores results in various
fields of the @code{oo_} structure, described below.
@end deffn
In the following variables, we will adopt the following shortcuts for
specific field names:
@table @var
@item MOMENT_NAME
This field can take the following values:
@table @code
@item HPDinf
Lower bound of a 90% HPD interval@footnote{See option @ref{conf_sig}
to change the size of the HPD interval}
@item HPDsup
Upper bound of a 90% HPD interval
@item Mean
Mean of the posterior distribution
@item Median
Median of the posterior distribution
@item Std
Standard deviation of the posterior distribution
@item Variance
Variance of the posterior distribution
@item deciles
Deciles of the distribution.
@item density
Non parametric estimate of the posterior density. First and second
columns are respectively abscissa and ordinate coordinates.
@end table
@item ESTIMATED_OBJECT
This field can take the following values:
@table @code
@item measurement_errors_corr
Correlation between two measurement errors
@item measurement_errors_std
Standard deviation of measurement errors
@item parameters
Parameters
@item shocks_corr
Correlation between two structural shocks
@item shocks_std
Standard deviation of structural shocks
@end table
@end table
@defvr {MATLAB/Octave variable} oo_.MarginalDensity.LaplaceApproximation
Variable set by the @code{estimation} command.
@end defvr
@defvr {MATLAB/Octave variable} oo_.MarginalDensity.ModifiedHarmonicMean
Variable set by the @code{estimation} command, if it is used with
@code{mh_replic > 0} or @code{load_mh_file} option.
@end defvr
@defvr {MATLAB/Octave variable} oo_.FilteredVariables
Variable set by the @code{estimation} command, if it is used with the
@code{filtered_vars} option. Fields are of the form:
@example
@code{oo_.FilteredVariables.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.FilteredVariablesKStepAhead
Variable set by the @code{estimation} command, if it is used with the
@code{filter_step_ahead} option.
@end defvr
@defvr {MATLAB/Octave variable} oo_.FilteredVariablesKStepAheadVariances
Variable set by the @code{estimation} command, if it is used with the
@code{filter_step_ahead} option.
@end defvr
@defvr {MATLAB/Octave variable} oo_.PosteriorIRF.dsge
Variable set by the @code{estimation} command, if it is used with the
@code{bayesian_irf} option. Fields are of the form:
@example
@code{oo_.PosteriorIRF.dsge.@var{MOMENT_NAME}.@var{VARIABLE_NAME}_@var{SHOCK_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.SmoothedMeasurementErrors
Variable set by the @code{estimation} command, if it is used with the
@code{smoother} option. Fields are of the form:
@example
@code{oo_.SmoothedMeasurementErrors.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.SmoothedShocks
Variable set by the @code{estimation} command, if it is used with the
@code{smoother} option. Fields are of the form:
@example
@code{oo_.SmoothedShocks.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.SmoothedVariables
Variable set by the @code{estimation} command, if it is used with the
@code{smoother} option. Fields are of the form:
@example
@code{oo_.SmoothedVariables.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.UpdatedVariables
Variable set by the @code{estimation} command, if it is used with the
@code{smoother} option. Contains the estimation of the expected value of
variables given the information available at the @emph{current}
date. Fields are of the form:
@example
@code{oo_.UpdatedVariables.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.PosteriorTheoreticalMoments
Variable set by the @code{estimation} command, if it is used with the
@code{moments_varendo} option. Fields are of the form:
@example
@code{oo_.PosteriorTheoreticalMoments.dsge.@var{THEORETICAL_MOMENT}.@var{ESTIMATED_OBJECT}.@var{MOMENT_NAME}.@var{VARIABLE_NAME}}
@end example
where @var{THEORETICAL_MOMENT} is one of the following:
@table @code
@item covariance
Variance-covariance of endogenous variables
@item correlation
Auto- and cross-correlation of endogenous variables. Fields are vectors with correlations from 1 up to order @code{options_.ar}
@item VarianceDecomposition
Decomposition of variance@footnote{When the shocks are correlated, it
is the decomposition of orthogonalized shocks via Cholesky
decompostion according to the order of declaration of shocks
(@pxref{Variable declarations})}
@item ConditionalVarianceDecomposition
Only if the @code{conditional_variance_decomposition} option has been
specified
@end table
@end defvr
@defvr {MATLAB/Octave variable} oo_.posterior_density
Variable set by the @code{estimation} command, if it is used with
@code{mh_replic > 0} or @code{load_mh_file} option. Fields are of the form:
@example
@code{oo_.posterior_density.@var{PARAMETER_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.posterior_hpdinf
Variable set by the @code{estimation} command, if it is used with
@code{mh_replic > 0} or @code{load_mh_file} option. Fields are of the form:
@example
@code{oo_.posterior_hpdinf.@var{ESTIMATED_OBJECT}.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.posterior_hpdsup
Variable set by the @code{estimation} command, if it is used with
@code{mh_replic > 0} or @code{load_mh_file} option. Fields are of the form:
@example
@code{oo_.posterior_hpdsup.@var{ESTIMATED_OBJECT}.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.posterior_mean
Variable set by the @code{estimation} command, if it is used with
@code{mh_replic > 0} or @code{load_mh_file} option. Fields are of the form:
@example
@code{oo_.posterior_mean.@var{ESTIMATED_OBJECT}.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.posterior_mode
Variable set by the @code{estimation} command, if it is used with
@code{mh_replic > 0} or @code{load_mh_file} option. Fields are of the form:
@example
@code{oo_.posterior_mode.@var{ESTIMATED_OBJECT}.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.posterior_std
Variable set by the @code{estimation} command, if it is used with
@code{mh_replic > 0} or @code{load_mh_file} option. Fields are of the form:
@example
@code{oo_.posterior_std.@var{ESTIMATED_OBJECT}.@var{VARIABLE_NAME}}
@end example
@end defvr
Here are some examples of generated variables:
@example
oo_.posterior_mode.parameters.alp
oo_.posterior_mean.shocks_std.ex
oo_.posterior_hpdsup.measurement_errors_corr.gdp_conso
@end example
@defvr {MATLAB/Octave variable} oo_.MC_record.Seeds
Variable set by the @code{estimation} command. Stores seeds used in MCMC chains
@end defvr
@defvr {MATLAB/Octave variable} oo_.MC_record.AcceptationRates
Variable set by the @code{estimation} command. Stores acceptation rates of the MCMC chains
@end defvr
@defvr {MATLAB/Octave variable} oo_.MC_record.LastParameters
Variable set by the @code{estimation} command. Stores parameter vector of final MCMC chain draw
@end defvr
@defvr {MATLAB/Octave variable} oo_.MC_record.LastLogPost
Variable set by the @code{estimation} command. Stores log-posterior of final MCMC chain draw
@end defvr
@defvr {MATLAB/Octave variable} oo_.RecursiveForecast
@anchor{RecursiveForecast}
Variable set by the @code{forecast} option of the @code{estimation} command when used with the nobs = [@var{INTEGER1}:@var{INTEGER2}] option (@pxref{nobs1,,nobs}).
Fields are of the form:
@example
@code{oo_.RecursiveForecast.@var{FORECAST_OBJECT}.@var{VARIABLE_NAME}}
@end example
where @var{FORECAST_OBJECT} is one of the following@footnote{See @ref{forecast} for more information}:
@table @code
@item Mean
Mean of the posterior forecast distribution
@item HPDinf/HPDsup
Upper/lower bound of the 90\% HPD interval taking into account only parameter uncertainty
@item HPDTotalinf/HPDTotalsup
Upper/lower bound of the 90\% HPD interval taking into account both parameter and future shock uncertainty
@end table
@var{VARIABLE_NAME} contains a matrix of the following size: number of time periods for which forecasts are requested using the nobs = [@var{INTEGER1}:@var{INTEGER2}] option times the number of forecast horizons requested by the @code{forecast} option. I.e., the row indicates the period at which the forecast is performed and the column the respective k-step ahead forecast. The starting periods are sorted in ascending order, not in declaration order.
@end defvr
@deffn Command model_comparison @var{FILENAME}[(@var{DOUBLE})]@dots{};
@deffnx Command model_comparison (marginal_density = laplace | modifiedharmonicmean) @var{FILENAME}[(@var{DOUBLE})]@dots{};
@descriptionhead
This command computes odds ratios and estimate a posterior density
over a collection of models. The priors over models can be specified
as the @var{DOUBLE} values, otherwise a uniform prior is assumed.
@examplehead
@example
model_comparison my_model(0.7) alt_model(0.3);
@end example
This example attributes a 70% prior over @code{my_model} and 30% prior
over @code{alt_model}.
@end deffn
@deffn Command shock_decomposition [@var{VARIABLE_NAME}]@dots{};
@deffnx Command shock_decomposition (@var{OPTIONS}@dots{}) [@var{VARIABLE_NAME}]@dots{};
@descriptionhead
This command computes and displays shock decomposition according to
the model for a given sample.
Note that this command must come after either @code{estimation} (in case
of an estimated model) or @code{stoch_simul} (in case of a calibrated
model).
@optionshead
@table @code
@item parameter_set = @var{PARAMETER_SET}
Specify the parameter set to use for running the smoother. The
@var{PARAMETER_SET} can take one of the following five values:
@code{calibration}, @code{prior_mode}, @code{prior_mean},
@code{posterior_mode}, @code{posterior_mean},
@code{posterior_median}. Default value: @code{posterior_mean} if
Metropolis has been run, else @code{posterior_mode}.
@item shocks = (@var{VARIABLE_NAME} [@var{VARIABLE_NAME} @dots{}] [ ; @var{VARIABLE_NAME} [@var{VARIABLE_NAME} @dots{}] @dots{}] )
@dots{}
@item labels = ( @var{VARIABLE_NAME} [@var{VARIABLE_NAME} @dots{}] )
@dots{}
@item datafile = @var{FILENAME}
@xref{datafile}. Useful when computing the shock decomposition on a
calibrated model.
@end table
@end deffn
@deffn Command unit_root_vars @var{VARIABLE_NAME}@dots{};
This command is deprecated. Use @code{estimation} option @code{diffuse_filter} instead for estimating a model with non-stationary observed variables or @code{steady} option @code{nocheck} to prevent @code{steady} to check the steady state returned by your steady state file.
@end deffn
Dynare also has the ability to estimate Bayesian VARs:
@deffn Command bvar_density ;
Computes the marginal density of an estimated BVAR model, using
Minnesota priors.
See @file{bvar-a-la-sims.pdf}, which comes with Dynare distribution,
for more information on this command.
@end deffn
Dynare can also run the smoother on a calibrated model:
@deffn Command calib_smoother [@var{VARIABLE_NAME}]@dots{};
@deffnx Command calib_smoother (@var{OPTIONS}@dots{}) [@var{VARIABLE_NAME}]@dots{};
@descriptionhead
This command computes the smoothed variables (and possible the filtered
variables) on a @code{calibrated} model.
A datafile must be provided, and the observable variables declared with
@code{varobs}. The smoother is based on a first-order approximation of
the model.
@vindex oo_.SmoothedVariables
@vindex oo_.SmoothedShocks
@vindex oo_.UpdatedVariables
By default, the command computes the smoothed variables and shocks and stores the
results in @code{oo_.SmoothedVariables} and
@code{oo_.SmoothedShocks}. It also fills @code{oo_.UpdatedVariables}.
@optionshead
@table @code
@item datafile = @var{FILENAME}
@xref{datafile}.
@item filtered_vars
Triggers the computation of filtered variables. @xref{filtered_vars}, for
more details.
@item filter_step_ahead = [@var{INTEGER1}:@var{INTEGER2}]
@xref{filter_step_ahead}.
@end table
@end deffn
@node Forecasting
@section Forecasting
On a calibrated model, forecasting is done using the @code{forecast}
command. On an estimated model, use the @code{forecast} option of
@code{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 @code{conditional_forecast},
@code{conditional_forecast_paths} and @code{plot_conditional_forecast}
for that purpose.
If the model contains strong non-linearities, the conditional forecasts
can be computed using an extended path method with the @code{simulation_type}
option in @code{conditional_forecast} command set to @code{deterministic}.
Because in this case deterministic simulations are carried out,
the nature of the shocks (surprise or perfect foresight) has to be indicated
in the @code{conditional_forecast_paths} block, using the command @code{expectation}
for each endogenous path. The forecasts are plotted using the rplot command.
Finally, it is possible to do forecasting with a Bayesian VAR using
the @code{bvar_forecast} command.
@deffn Command forecast [@var{VARIABLE_NAME}@dots{}];
@deffnx Command forecast (@var{OPTIONS}@dots{}) [@var{VARIABLE_NAME}@dots{}];
@descriptionhead
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.
@code{forecast} must be called after @code{stoch_simul}.
@code{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 @code{conf_sig} to change the level of the
confidence interval.
@optionshead
@table @code
@item periods = @var{INTEGER}
Number of periods of the forecast. Default: @code{40}
@item conf_sig = @var{DOUBLE}
@anchor{conf_sig} Level of significance for confidence
interval. Default: @code{0.90}
@item nograph
@xref{nograph}.
@item nodisplay
@xref{nodisplay}.
@item graph_format = @var{FORMAT}
@itemx graph_format = ( @var{FORMAT}, @var{FORMAT}@dots{} )
@xref{graph_format}.
@end table
@customhead{Initial Values}
@code{forecast} computes the forecast taking as initial values the values specified in @code{histval} (@pxref{Initial and terminal conditions,histval}). When no @code{histval} block is present, the initial values are the one stated in @code{initval}. When @code{initval} is followed by command @code{steady}, the initial values are the steady state (@pxref{Steady state,steady}).
@outputhead
The results are stored in @code{oo_.forecast}, which is described below.
@examplehead
@example
varexo_det tau;
varexo e;
@dots{}
shocks;
var e; stderr 0.01;
var tau;
periods 1:9;
values -0.15;
end;
stoch_simul(irf=0);
forecast;
@end example
@end deffn
@defvr {MATLAB/Octave variable} oo_.forecast
Variable set by the @code{forecast} command, or by the
@code{estimation} command if used with the @code{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:
@example
@code{oo_.forecast.@var{FORECAST_MOMENT}.@var{VARIABLE_NAME}}
@end example
where @var{FORECAST_MOMENT} is one of the following:
@table @code
@item HPDinf
Lower bound of a 90% HPD interval@footnote{See option @ref{conf_sig}
to change the size of the HPD interval} of forecast due to parameter
uncertainty
@item HPDsup
Lower bound of a 90% HPD interval due to parameter uncertainty
@item HPDTotalinf
Lower bound of a 90% HPD interval of forecast due to parameter
uncertainty and future shocks (only with the @code{estimation} command)
@item HPDTotalsup
Lower bound of a 90% HPD interval due to parameter uncertainty and
future shocks (only with the @code{estimation} command)
@item Mean
Mean of the posterior distribution of forecasts
@item Median
Median of the posterior distribution of forecasts
@item Std
Standard deviation of the posterior distribution of forecasts
@end table
@end defvr
@defvr {MATLAB/Octave variable} oo_.PointForecast
Set by the @code{estimation} command, if it is used with the
@code{forecast} option and if either @code{mh_replic > 0} or
@code{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:
@example
@code{oo_.PointForecast.@var{MOMENT_NAME}.@var{VARIABLE_NAME}}
@end example
@end defvr
@defvr {MATLAB/Octave variable} oo_.MeanForecast
Set by the @code{estimation} command, if it is used with the
@code{forecast} option and if either @code{mh_replic > 0} or
@code{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:
@example
@code{oo_.MeanForecast.@var{MOMENT_NAME}.@var{VARIABLE_NAME}}
@end example
@end defvr
@deffn Command conditional_forecast (@var{OPTIONS}@dots{}) [@var{VARIABLE_NAME}@dots{}];
@descriptionhead
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 @code{conditional_forecast_paths} block to give the list of
constrained endogenous, and their constrained future path.
If an extended path method is applied on the original dsge model,
the nature of the expectation on the constrained endogenous has to be
specified using expectation command. Option
@code{controlled_varexo} is used to specify the structural shocks
which will be matched to generate the constrained path.
Use @code{plot_conditional_forecast} to graph the results.
@optionshead
@table @code
@item parameter_set = @code{calibration} | @code{prior_mode} | @code{prior_mean} | @code{posterior_mode} | @code{posterior_mean} | @code{posterior_median}
Specify the parameter set to use for the forecasting. No default
value, mandatory option.
@item controlled_varexo = (@var{VARIABLE_NAME}@dots{})
Specify the exogenous variables to use as control variables. No
default value, mandatory option.
@item periods = @var{INTEGER}
Number of periods of the forecast. Default: @code{40}. @code{periods}
cannot be less than the number of constrained periods.
@item replic = @var{INTEGER}
Number of simulations. Default: @code{5000}.
@item conf_sig = @var{DOUBLE}
Level of significance for confidence interval. Default: @code{0.80}
@item simulation_type = @code{stochastic} | @code{deterministic}
Indicates the nature of simulations used to compute the conditional forecast.
The default value @code{stochastic} is used, when simulations are computed
using the reduced form representation of the DSGE model.
If the model has to be simulated using extended path method on the original
DSGE model, @code{simulation_type} has to be set equal to @code{deterministic}.
@end table
@examplehead
@example
var y a
varexo e u;
@dots{}
estimation(@dots{});
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 = 3000);
plot_conditional_forecast(periods = 10) a y;
@end example
@examplehead
@example
/* conditional forecast using extended path method
with perfect foresight on r path*/
var y r
varexo e u;
@dots{}
conditional_forecast_paths;
var y;
periods 1:3, 4:5;
values 2, 5;
var r
periods 1:5;
values 3;
expectation perfect_foresight;
end;
conditional_forecast(parameter_set = calibration, controlled_varexo = (e, u), simulation_type=deterministic);
rplot a;
rplot y;
@end example
@end deffn
@deffn Block conditional_forecast_paths ;
Describes the path of constrained endogenous, before calling
@code{conditional_forecast}. The syntax is similar to deterministic
shocks in @code{shocks}, see @code{conditional_forecast} for an
example.
The syntax of the block is the same than the deterministic shocks in
the @code{shocks} blocks (@pxref{Shocks on exogenous variables}).
If the conditional forecast is carried out using the extended path method
on the original DSGE model, the nature of the expectation have to be specified
for each endogenous path, using the @code{expectation} = @code{surprise} | @code{perfect_foresight}.
By default, @code{expectation} is equal to @code{surprise}.
@end deffn
@deffn Command plot_conditional_forecast [@var{VARIABLE_NAME}@dots{}];
@deffnx Command plot_conditional_forecast (periods = @var{INTEGER}) [@var{VARIABLE_NAME}@dots{}];
@descriptionhead
Plots the conditional (plain lines) and unconditional (dashed lines) forecasts.
To be used after @code{conditional_forecast}.
@optionshead
@table @code
@item periods = @var{INTEGER}
Number of periods to be plotted. Default: equal to @code{periods} in
@code{conditional_forecast}. The number of periods declared in
@code{plot_conditional_forecast} cannot be greater than the one
declared in @code{conditional_forecast}.
@end table
@end deffn
@deffn Command bvar_forecast ;
This command computes (out-of-sample) forecasts for an estimated BVAR
model, using Minnesota priors.
See @file{bvar-a-la-sims.pdf}, which comes with Dynare distribution,
for more information on this command.
@end deffn
@node Optimal policy
@section Optimal policy
Dynare has tools to compute optimal policies for various types of
objectives. You can either solve for optimal policy under commitment
with @code{ramsey_policy}, for optimal policy under discretion with
@code{discretionary_policy} or for optimal simple rule with
@code{osr}.
@anchor{osr}
@deffn Command osr [@var{VARIABLE_NAME}@dots{}];
@deffnx Command osr (@var{OPTIONS}@dots{}) [@var{VARIABLE_NAME}@dots{}];
@descriptionhead
This command computes optimal simple policy rules for
linear-quadratic problems of the form:
@quotation
@math{\max_\gamma E(y'_tWy_t)}
@end quotation
such that:
@quotation
@math{A_1 E_ty_{t+1}+A_2 y_t+ A_3 y_{t-1}+C e_t=0}
@end quotation
where:
@itemize
@item
@math{\gamma} are parameters to be optimized. They must be elements of matrices
@math{A_1}, @math{A_2}, @math{A_3};
@item
@math{y} are the endogenous variables;
@item
@math{e} are the exogenous stochastic shocks;
@end itemize
The parameters to be optimized must be listed with @code{osr_params}.
The quadratic objectives must be listed with @code{optim_weights}.
This problem is solved using a numerical optimizer.
@optionshead
This command accept the same options than @code{stoch_simul}
(@pxref{Computing the stochastic solution}).
The value of the objective is stored in the variable
@code{oo_.osr.objective_function}, which is described below.
@end deffn
@anchor{osr_params}
@deffn Command osr_params @var{PARAMETER_NAME}@dots{};
This command declares parameters to be optimized by @code{osr}.
@end deffn
@anchor{optim_weights}
@deffn Block optim_weights ;
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 @code{osr}.
An element of the diagonal of the weight matrix is given by a line of
the form:
@example
@var{VARIABLE_NAME} @var{EXPRESSION};
@end example
An off-the-diagonal element of the weight matrix is given by a line of
the form:
@example
@var{VARIABLE_NAME}, @var{VARIABLE_NAME} @var{EXPRESSION};
@end example
@end deffn
@defvr {MATLAB/Octave variable} oo_.osr.objective_function
After an execution of the @code{osr} command, this variable contains
the value of the objective under optimal policy.
@end defvr
@deffn Command ramsey_policy [@var{VARIABLE_NAME}@dots{}];
@deffnx Command ramsey_policy (@var{OPTIONS}@dots{}) [@var{VARIABLE_NAME}@dots{}];
@descriptionhead
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 @code{planner_objective} command.
@xref{Auxiliary
variables}, for an explanation of how this operator is handled
internally and how this affects the output.
@optionshead
This command accepts all options of @code{stoch_simul}, plus:
@table @code
@item planner_discount = @var{EXPRESSION}
Declares the discount factor of the central planner. Default: @code{1.0}
@item instruments = (@var{VARIABLE_NAME},@dots{})
Declares instrument variables for the computation of the steady state
under optimal policy. Requires a @code{steady_state_model} block or a
@code{@dots{}_steadystate.m} file. See below.
@end table
Note that only first order approximation is available (@i{i.e.}
@code{order=1} must be specified).
@outputhead
This command generates all the output variables of @code{stoch_simul}.
@vindex oo_.planner_objective_value
In addition, it stores the value of planner objective function under
Ramsey policy in @code{oo_.planner_objective_value}.
@customhead{Steady 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 @code{initval} for the
endogenous variables.
It greatly facilitates the computation, if the user provides an
analytical solution for the steady state (in @code{steady_state_model}
block or in a @code{@dots{}_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 @code{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. A typical
example is choosing inflation or nominal interest rate as an
instrument.
@end deffn
@anchor{discretionary_policy}
@deffn Command discretionary_policy [@var{VARIABLE_NAME}@dots{}];
@deffnx Command discretionary_policy (@var{OPTIONS}@dots{}) [@var{VARIABLE_NAME}@dots{}];
@descriptionhead
This command computes an approximation of the optimal policy under
discretion. The algorithm implemented is essentially an LQ solver, and
is described by @cite{Dennis (2007)}.
You should ensure that your model is linear and your objective is
quadratic. Also, you should set the @code{linear} option of the
@code{model} block.
@optionshead
This command accepts the same options than @code{ramsey_policy}, plus:
@table @code
@item discretionary_tol = @var{NON-NEGATIVE DOUBLE}
Sets the tolerance level used to assess convergence of the solution
algorithm. Default: @code{1e-7}.
@item solve_maxit = @var{INTEGER}
Maximum number of iterations. Default: @code{3000}.
@end table
@end deffn
@anchor{planner_objective}
@deffn Command planner_objective @var{MODEL_EXPRESSION};
This command declares the policy maker objective, for use with
@code{ramsey_policy} or @code{discretionary_policy}.
You need to give the one-period objective, not the discounted lifetime
objective. The discount factor is given by the @code{planner_discount}
option of @code{ramsey_policy} and @code{discretionary_policy}.
With @code{ramsey_policy}, you are not limited to quadratic
objectives: you can give any arbitrary nonlinear expression.
With @code{discretionary_policy}, the objective function must be quadratic.
@end deffn
@node Sensitivity and identification analysis
@section 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:
@enumerate
@item
What is the domain of structural coefficients assuring the stability and determinacy
of a DSGE model?
@item
Which parameters mostly drive the fit of, @i{e.g.}, GDP and which the fit of inflation?
Is there any conflict between the optimal fit of one observed series versus another?
@item
How to represent in a direct, albeit approximated, form the relationship between
structural parameters and the reduced form of a rational expectations model?
@end enumerate
The discussion of the methodologies and their application is described in
@cite{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 set up.
Sensitivity analysis results are saved locally in @code{/GSA},
where @code{.mod} is the name of the DYNARE model file.
@menu
* Sampling::
* Stability Mapping::
* Reduced Form Mapping::
* RMSE::
* Screening Analysis::
* Identification Analysis::
* Performing Sensitivity and Identification Analysis::
@end menu
@node Sampling
@subsection Sampling
The following binary files are produced:
@itemize
@item
@code{_prior.mat}: this file stores information about the analyses
performed sampling from the prior ranges, @i{i.e.} @code{pprior=1} and @code{ppost=0};
@item
@code{_mc.mat}: this file stores information about the analyses performed
sampling from multivariate normal, @i{i.e.} @code{pprior=0} and @code{ppost=0};
@item
@code{_post.mat}: this file stores information about analyses performed
using the Metropolis posterior sample, @i{i.e.} @code{ppost=1}.
@end itemize
@node Stability Mapping
@subsection Stability Mapping
Figure files produced are of the form @code{_prior_*.fig} and store results
for stability mapping from prior Monte-Carlo samples:
@itemize
@item
@code{_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;
@item
@code{_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;
@item
@code{_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;
@item
@code{_prior_stable_corr_*.fig}: plots of bivariate projections
of the sample fulfilling Blanchard-Kahn conditions;
@item
@code{_prior_indeterm_corr_*.fig}: plots of bivariate projections
of the sample producing indeterminacy;
@item
@code{_prior_unstable_corr_*.fig}: plots of bivariate projections
of the sample producing instability;
@item
@code{_prior_unacceptable_corr_*.fig}: plots of bivariate projections
of the sample producing unacceptable solutions, @i{i.e.} either
instability or indeterminacy or the solution could not be found (@i{e.g.}
the steady state solution could not be found by the solver).
@end itemize
Similar conventions apply for @code{_mc_*.fig} files, obtained when
samples from multivariate normal are used.
@node Reduced Form Mapping
@subsection Reduced Form Mapping
The mapping of the reduced form solution forces the use of samples from
prior ranges or prior distributions, @i{i.e.}: @code{pprior=1} and @code{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:
@itemize
@item
@code{_redform__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
(@code{namendo}) versus lagged endogenous variables (@code{namlagendo}); suffix
@code{log} indicates the results for log-transformed entries;
@item
@code{_redform__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
(@code{namendo}) versus exogenous variables (@code{namexo}); suffix @code{log}
indicates the results for log-transformed entries;
@item
@code{_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.
@end itemize
Detailed results of the analyses are shown in the subfolder @code{/GSA/redform_stab},
where the detailed results of the estimation of the single functional relationships
between parameters @math{\theta} and reduced form coefficient are stored in separate directories
named as:
@itemize
@item
@code{_vs_}: for the entries of the transition matrix;
@item
@code{_vs_}: for entries of the matrix of the shocks.
@end itemize
Moreover, analyses for log-transformed entries are denoted with the following
suffixes (@math{y} denotes the generic reduced form coefficient):
@itemize
@item
@code{log}: @math{y^* = \log(y)};
@item
@code{minuslog}: @math{y^* = \log(-y)};
@item
@code{logsquared}: @math{y^* = \log(y^2)} for symmetric fat tails;
@item
@code{logskew}: @math{y^* = \log(|y + \lambda|)} for asymmetric fat tails.
@end itemize
The optimal type of transformation is automatically selected without the
need of user intervention.
@node RMSE
@subsection RMSE
The RMSE analysis can be performed with different types of sampling options:
@enumerate
@item
When @code{pprior=1} and @code{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;
@item
When @code{pprior=0} and @code{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{i.e.} no Bayesian estimation);
@item
When @code{ppost=1} the toolbox analyzes the RMSEs for the posterior sample
obtained by Dynare's Metropolis procedure.
@end enumerate
The use of cases 2 and 3 requires an estimation step beforehand. To
facilitate the sensitivity analysis after estimation, the @code{dynare_sensitivity}
command also allows you to indicate some options of the @code{estimation}
command. These are:
@itemize @bullet
@item @code{datafile}
@item @code{nobs}
@item @code{first_obs}
@item @code{prefilter}
@item @code{presample}
@item @code{nograph}
@item @code{nodisplay}
@item @code{graph_format}
@item @code{conf_sig}
@item @code{loglinear}
@item @code{mode_file}
@end itemize
Binary files produced my RMSE analysis are:
@itemize
@item
@code{_prior_*.mat}: these files store the filtered and smoothed
variables for the prior Monte-Carlo sample, generated when doing RMSE analysis
(@code{pprior=1} and @code{ppost=0});
@item
@code{_mc_*.mat}: these files store the filtered and smoothed variables
for the multivariate normal Monte-Carlo sample, generated when doing
RMSE analysis (@code{pprior=0} and @code{ppost=0}).
@end itemize
Figure files @code{_rmse_*.fig} store results for the RMSE analysis.
@itemize
@item
@code{_rmse_prior*.fig}: save results for the analysis using prior
Monte-Carlo samples;
@item
@code{_rmse_mc*.fig}: save results for the analysis using multivariate
normal Monte-Carlo samples;
@item
@code{_rmse_post*.fig}: save results for the analysis using Metropolis
posterior samples.
@end itemize
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):
@itemize
@item
@code{_rmse_prior_*.fig}: for each parameter, plots the cdfs
corresponding to the best 10% RMSEs of each observed series;
@item
@code{_rmse_prior_dens_*.fig}: for each parameter, plots the
pdfs corresponding to the best 10% RMESs of each observed series;
@item
@code{_rmse_prior__corr_*.fig}: for
each observed series plots the bi-dimensional projections of samples
with the best 10% RMSEs, when the correlation is significant;
@item
@code{_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;
@item
@code{_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;
@item
@code{_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;
@item
@code{_rmse_prior_lik_SA_*.fig}: when @code{lik_only=1}, this shows
the Smirnov tests for the filtering of the best 10% log-likelihood values;
@item
@code{_rmse_prior_post_SA_*.fig}: when @code{lik_only=1}, this shows
the Smirnov test for the filtering of the best 10% log-posterior values.
@end itemize
@node Screening Analysis
@subsection Screening Analysis
Screening analysis does not require any additional options with respect to
those listed in @ref{Sampling Options}. 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 @code{/GSA/SCREEN}. The data file @code{_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:
@itemize
@item
@code{_redform__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
(@code{namendo}) versus lagged endogenous variables (@code{namlagendo});
@item
@code{_redform__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
(@code{namendo}) versus exogenous variables (@code{namexo});
@item
@code{_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.
@end itemize
@node Identification Analysis
@subsection Identification Analysis
Setting the option @code{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
@code{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 @code{morris=2},
which implements @cite{Iskrev (2010)} identification analysis.
For example, the placing @code{identification; dynare_sensitivity(identification=1, morris=2);}
in the Dynare model file trigger identification analysis using analytic derivatives
@cite{Iskrev (2010)}, jointly with the mapping of the acceptable region.
The identification analysis with derivatives can also be triggered by the
commands @code{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.
@node Performing Sensitivity and Identification Analysis
@subsection Performing Sensitivity and Identification Analysis
@deffn Command dynare_sensitivity ;
@deffnx Command dynare_sensitivity (@var{OPTIONS}@dots{});
@descriptionhead
This command triggers sensitivity analysis on a DSGE model.
@optionshead
@customhead{Sampling Options}
@anchor{Sampling Options}
@table @code
@item nsam = @var{INTEGER}
Size of the Monte-Carlo sample. Default: @code{2048}
@item ilptau = @var{INTEGER}
If equal to @code{1}, use @math{LP_\tau} quasi-Monte-Carlo.
If equal to @code{0}, use LHS Monte-Carlo. Default: @code{1}
@item pprior = @var{INTEGER}
If equal to @code{1}, sample from the prior distributions.
If equal to @code{0}, sample from the multivariate normal @math{N(\bar{\theta},\Sigma)},
where @math{\bar{\theta}} is the posterior mode and @math{\Sigma=H^{-1}}, @math{H}
is the Hessian at the mode. Default: @code{1}
@item prior_range = @var{INTEGER}
If equal to @code{1}, sample uniformly from prior ranges.
If equal to @code{0}, sample from prior distributions. Default: @code{1}
@item morris = @var{INTEGER}
@anchor{morris}
If equal to @code{0}, ANOVA mapping (Type I error)
If equal to @code{1}, Screening analysis (Type II error)
If equal to @code{2}, Analytic derivatives (similar to Type II error, only valid when
@code{identification=1}).Default: @code{1} when @code{identification=1}, @code{0} otherwise
@item morris_nliv = @var{INTEGER}
@anchor{morris_nliv}
Number of levels in Morris design. Default: @code{6}
@item morris_ntra = @var{INTEGER}
@anchor{morris_ntra}
Number trajectories in Morris design. Default: @code{20}
@item ppost = @var{INTEGER}
If equal to @code{1}, use Metropolis posterior sample.
If equal to @code{0}, do not use Metropolis posterior sample. NB: This
overrides any other sampling option. Default: @code{0}
@item neighborhood_width = @var{DOUBLE}
When @code{pprior=0} and @code{ppost=0}, allows for the sampling of
parameters around the value specified in the @code{mode_file}, in the range
@code{xparam1}@math{\pm\left|@code{xparam1}\times@code{neighborhood_width}\right|}. Default: @code{0}
@end table
@customhead{Stability Mapping Options}
@table @code
@item stab = @var{INTEGER}
If equal to @code{1}, perform stability mapping.
If equal to @code{0}, do not perform stability mapping. Default: @code{1}
@item load_stab = @var{INTEGER}
If equal to @code{1}, load a previously created sample.
If equal to @code{0}, generate a new sample. Default: @code{0}
@item alpha2_stab = @var{DOUBLE}
Critical value for correlations @math{\rho} in filtered samples:
plot couples of parmaters with @math{\left|\rho\right|>} @code{alpha2_stab}.
Default: @code{0.3}
@item ksstat = @var{DOUBLE}
Critical value for Smirnov statistics @math{d}: plot parameters with
@math{d>} @code{ksstat}. Default: @code{0.1}
@item pvalue_ks = @var{DOUBLE}
The threshold @math{pvalue} for significant Kolmogorov-Smirnov test (@i{i.e.} plot parameters with
@math{pvalue<} @code{pvalue_ks}). Default: @code{0.001}
@item pvalue_corr = @var{DOUBLE}
The threshold @math{pvalue} for significant correlation in filtered samples
(@i{i.e.} plot bivariate samples when @math{pvalue<} @code{pvalue_corr}). Default: @code{0.001}
@end table
@customhead{Reduced Form Mapping Options}
@table @code
@item redform = @var{INTEGER}
If equal to @code{1}, prepare Monte-Carlo sample of reduced form matrices.
If equal to @code{0}, do not prepare Monte-Carlo sample of reduced form matrices. Default: @code{0}
@item load_redform = @var{INTEGER}
If equal to @code{1}, load previously estimated mapping.
If equal to @code{0}, estimate the mapping of the reduced form model. Default: @code{0}
@item logtrans_redform = @var{INTEGER}
If equal to @code{1}, use log-transformed entries.
If equal to @code{0}, use raw entries. Default: @code{0}
@item threshold_redform = [@var{DOUBLE} @var{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: @code{empty}
@item ksstat_redform = @var{DOUBLE}
Critical value for Smirnov statistics @math{d} when reduced form entries
are filtered. Default: @code{0.1}
@item alpha2_redform = @var{DOUBLE}
Critical value for correlations @math{\rho} when reduced form entries
are filtered. Default: @code{0.3}
@item namendo = (@var{VARIABLE_NAME}@dots{})
List of endogenous variables. `@code{:}' indicates all endogenous variables.
Default: @code{empty}
@item namlagendo = (@var{VARIABLE_NAME}@dots{})
List of lagged endogenous variables. `@code{:}' indicates all lagged endogenous variables.
Analyze entries @code{[namendo}@math{\times}@code{namlagendo]} Default: @code{empty}
@item namexo = (@var{VARIABLE_NAME}@dots{})
List of exogenous variables. `@code{:}' indicates all exogenous variables.
Analyze entries @code{[namendo}@math{\times}@code{namexo]}. Default: @code{empty}
@end table
@customhead{RMSE Options}
@table @code
@item rmse = @var{INTEGER}
If equal to @code{1}, perform RMSE analysis.
If equal to @code{0}, do not perform RMSE analysis. Default: @code{0}
@item load_rmse = @var{INTEGER}
If equal to @code{1}, load previous RMSE analysis.
If equal to @code{0}, make a new RMSE analysis. Default: @code{0}
@item lik_only = @var{INTEGER}
If equal to @code{1}, compute only likelihood and posterior.
If equal to @code{0}, compute RMSE's for all observed series. Default: @code{0}
@item var_rmse = (@var{VARIABLE_NAME}@dots{})
List of observed series to be considered. `@code{:}' indicates all observed
variables. Default: @code{varobs}
@item pfilt_rmse = @var{DOUBLE}
Filtering threshold for RMSE's. Default: @code{0.1}
@item istart_rmse = @var{INTEGER}
Value at which to start computing RMSE's (use @code{2} to avoid big intitial
error). Default: @code{presample+1}
@item alpha_rmse = @var{DOUBLE}
Critical value for Smirnov statistics @math{d}: plot parameters with
@math{d>} @code{alpha_rmse}. Default: @code{0.002}
@item alpha2_rmse = @var{DOUBLE}
Critical value for correlation @math{\rho}: plot couples of parmaters with
@math{\left|\rho\right|=} @code{alpha2_rmse}. Default: @code{1.0}
@item datafile = @var{FILENAME}
@xref{datafile}.
@item nobs = @var{INTEGER}
@item nobs = [@var{INTEGER1}:@var{INTEGER2}]
@xref{nobs}.
@item first_obs = @var{INTEGER}
@xref{first_obs}.
@item prefilter = @var{INTEGER}
@xref{prefilter}.
@item presample = @var{INTEGER}
@xref{presample}.
@item nograph
@xref{nograph}.
@item nodisplay
@xref{nodisplay}.
@item graph_format = @var{FORMAT}
@itemx graph_format = ( @var{FORMAT}, @var{FORMAT}@dots{} )
@xref{graph_format}.
@item conf_sig = @var{DOUBLE}
@xref{conf_sig}.
@item loglinear
@xref{loglinear}.
@item mode_file = @var{FILENAME}
@xref{mode_file}.
@item kalman_algo = @var{INTEGER}
@xref{kalman_algo}.
@end table
@customhead{Identification Analysis Options}
@table @code
@item identification = @var{INTEGER}
If equal to @code{1}, performs identification anlysis (forcing @code{redform=0} and @code{morris=1})
If equal to @code{0}, no identification analysis. Default: @code{0}
@item morris = @var{INTEGER}
@xref{morris}.
@item morris_nliv = @var{INTEGER}
@xref{morris_nliv}.
@item morris_ntra = @var{INTEGER}
@xref{morris_ntra}.
@item load_ident_files = @var{INTEGER}
Loads previously performed identification analysis. Default: @code{0}
@item useautocorr = @var{INTEGER}
Use autocorrelation matrices in place of autocovariance matrices in moments
for identification analysis. Default: @code{0}
@item ar = @var{INTEGER}
Maximum number of lags for moments in identification analysis. Default: @code{1}
@item lik_init = @var{INTEGER}
@xref{lik_init}.
@end table
@end deffn
@deffn Command identification ;
@deffnx Command identification (@var{OPTIONS}@dots{});
@descriptionhead
This command triggers identification analysis.
@optionshead
@table @code
@item ar = @var{INTEGER}
Number of lags of computed autocorrelations (theoretical moments). Default: @code{1}
@item useautocorr = @var{INTEGER}
If equal to @code{1}, compute derivatives of autocorrelation. If equal
to @code{0}, compute derivatives of autocovariances. Default: @code{0}
@item load_ident_files = @var{INTEGER}
If equal to @code{1}, allow Dynare to load previously
computed analyzes. Default: @code{0}
@item prior_mc = @var{INTEGER}
Size of Monte-Carlo sample. Default: @code{1}
@item prior_range = @var{INTEGER}
Triggers uniform sample within the range implied by the prior specifications (when
@code{prior_mc>1}). Default: @code{0}
@item advanced = @var{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 @code{max_dim_cova_group}. Default: @code{0}
@item max_dim_cova_group = @var{INTEGER}
In the brute force search (performed when @code{advanced=1}) this option sets the maximum dimension of groups
of parameters that best reproduce the behavior of each single model parameter. Default: @code{2}
@item periods = @var{INTEGER}
When the analytic Hessian is not available (@i{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: @code{300}
@item replic = @var{INTEGER}
When the analytic Hessian is not available, this triggers the number of replicas
to compute Simulated Moments Uncertainty. Default: @code{100}
@item gsa_sample_file = @var{INTEGER}
If equal to @code{0}, do not use sample file.
If equal to @code{1}, triggers gsa prior sample.
If equal to @code{2}, triggers gsa Monte-Carlo sample (@i{i.e.} loads a sample corresponding to
@code{pprior=0} and @code{ppost=0} in the @code{dynare_sensitivity} options). Default: @code{0}
@item gsa_sample_file = @var{FILENAME}
Uses the provided path to a specific user defined sample file. Default: @code{0}
@item parameter_set = @code{calibration} | @code{prior_mode} | @code{prior_mean} | @code{posterior_mode} | @code{posterior_mean} | @code{posterior_median}
Specify the parameter set to use. Default: @code{prior_mean}
@item lik_init = @var{INTEGER}
@xref{lik_init}.
@item kalman_algo = @var{INTEGER}
@xref{kalman_algo}.
@item nograph
@xref{nograph}.
@item nodisplay
@xref{nodisplay}.
@item graph_format = @var{FORMAT}
@itemx graph_format = ( @var{FORMAT}, @var{FORMAT}@dots{} )
@xref{graph_format}.
@end table
@end deffn
@node Markov-switching SBVAR
@section Markov-switching SBVAR
Given a list of variables, observed variables and a data file, Dynare
can be used to solve a Markov-switching SBVAR model according to
@cite{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 @code{.mod} file. The default is to use
@code{} to tag the input (output) files used (produced) by the
program. Thus, to call any command more than once within a
@code{.mod} file, you must use the @code{*_tag} options
described below.
@anchor{markov_switching}
@deffn Command markov_switching (@var{OPTIONS}@dots{});
@descriptionhead
Declares the Markov state variable information of a Markov-switching
SBVAR model.
@optionshead
@table @code
@item chain = @var{INTEGER}
@anchor{ms_chain} The Markov chain. Default: @code{none}
@item state = @var{INTEGER}
This state has duration equal to @code{duration}. Exactly one of
@code{state} and @code{number_of_states} must be passed. Default:
@code{none}
@item number_of_states = @var{INTEGER}
Total number of states. Implies that all states have the same
duration. Exactly one of @code{state} and @code{number_of_states} must
be passed. Default: @code{none}
@item duration = @var{DOUBLE} | @code{inf}
The duration of the state or states. Default: @code{none}
@end table
@end deffn
@anchor{svar}
@deffn Command svar (@var{OPTIONS}@dots{});
@descriptionhead
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.
@optionshead
@table @code
@item coefficients
Specifies that only the slope and intercept in the given equations are
controlled by the given chain. One, but not both, of
@code{coefficients} or @code{variances} must appear. Default:
@code{none}
@item variances
Specifies that only variances in the given equations are controlled by
the given chain. One, but not both, of @code{coefficients} or
@code{variances} must appear. Default: @code{none}
@item equations
Defines the equation controlled by the given chain. If not specificed,
then all equations are controlled by @code{chain}. Default: @code{none}
@item chain = @var{INTEGER}
Specifies a Markov chain defined by @ref{markov_switching}. Default:
@code{none}
@end table
@end deffn
@anchor{ms_estimation}
@deffn Command ms_estimation (@var{OPTIONS}@dots{});
@descriptionhead
Triggers the creation of an initialization file for, and the estimation
of, a Markov-switching SBVAR model. At the end of the run, the
@math{A^0}, @math{A^+}, @math{Q} and @math{\zeta} matrices are contained
in the @code{oo_.ms} structure.
@optionshead
@customhead{General Options}
@table @code
@item file_tag = @var{FILENAME}
The portion of the filename associated with this run. This will create
the model initialization file, @code{init_.dat}. Default:
@code{}
@item output_file_tag = @var{FILENAME}
The portion of the output filename that will be assigned to this run.
This will create, among other files,
@code{est_final_.out},
@code{est_intermediate_.out}. Default:
@code{}
@item no_create_init
Do not create an initialization file for the model. Passing this option
will cause the @i{Initialization Options} to be ignored. Further, the
model will be generated from the output files associated with the
previous estimation run (@i{i.e.} @code{est_final_.out},
@code{est_intermediate_.out} or @code{init_.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:
@code{off} (@i{i.e.} create initialization file)
@end table
@customhead{Initialization Options}
@table @code
@item coefficients_prior_hyperparameters = [@var{DOUBLE1} @var{DOUBLE2} @var{DOUBLE3} @var{DOUBLE4} @var{DOUBLE5} @var{DOUBLE6}]
Sets the hyper parameters for the model. The six elements of the
argument vector have the following interpretations:
@table @code
@item Position
@code{Interpretation}
@item 1
Overall tightness for @math{A^0} and @math{A^+}
@item 2
Relative tightness for @math{A^+}
@item 3
Relative tightness for the constant term
@item 4
Tightness on lag decay (range: 1.2 - 1.5); a faster decay produces
better inflation process
@item 5
Weight on nvar sums of coeffs dummy observations (unit roots)
@item 6
Weight on single dummy initial observation including constant
@end table
Default: @code{[1.0 1.0 0.1 1.2 1.0 1.0]}
@item freq = @var{INTEGER} | @code{monthly} | @code{quarterly} | @code{yearly}
Frequency of the data (@i{e.g.} @code{monthly}, @code{12}). Default:
@code{4}
@item initial_year = @var{INTEGER}
The first year of data. Default: @code{none}
@item initial_subperiod = @var{INTEGER}
The first period of data (@i{i.e.} for quarterly data, an integer in
[@code{1,4}]). Default: @code{1}
@item final_year = @var{INTEGER}
The last year of data. Default: Set to encompass entire dataset
@item final_subperiod = @var{INTEGER}
The final period of data (@i{i.e.} for monthly data, an integer in
[@code{1,12}]. Default: Set to encompass entire dataset
@item datafile = @var{FILENAME}
@xref{datafile}.
@item xls_sheet = @var{NAME}
@xref{xls_sheet}.
@item xls_range = @var{RANGE}
@xref{xls_range}.
@item nlags = @var{INTEGER}
The number of lags in the model. Default: @code{1}
@item cross_restrictions
Use cross @math{A^0} and @math{A^+} restrictions. Default: @code{off}
@item contemp_reduced_form
Use contemporaneous recursive reduced form. Default: @code{off}
@item no_bayesian_prior
Do not use bayesian prior. Default: @code{off} (@i{i.e.} use bayesian
prior)
@item alpha = @var{INTEGER}
Alpha value for squared time-varying structural shock lambda. Default:
@code{1}
@item beta = @var{INTEGER}
Beta value for squared time-varying structural shock lambda. Default:
@code{1}
@item gsig2_lmdm = @var{INTEGER}
The variance for each independent @math{\lambda} parameter under
@code{SimsZha} restrictions. Default: @code{50^2}
@item specification = @code{sims_zha} | @code{none}
This controls how restrictions are imposed to reduce the number of
parameters. Default: @code{Random Walk}
@end table
@customhead{Estimation Options}
@table @code
@item convergence_starting_value = @var{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: @code{1e-3}
@item convergence_ending_value = @var{DOUBLE}
The convergence criterion ending value. Values much smaller than square
root machine epsilon are probably overkill. Default: @code{1e-6}
@item convergence_increment_value = @var{DOUBLE}
Determines how quickly the convergence criterion moves from the starting
value to the ending value. Default: @code{0.1}
@item max_iterations_starting_value = @var{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: @code{50}
@item max_iterations_increment_value = @var{DOUBLE}
Determines how quickly the maximum number of iterations is
increased. Default: @code{2}
@item max_block_iterations = @var{INTEGER}
@anchor{max_block_iterations} 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: @code{100}
@item max_repeated_optimization_runs = @var{INTEGER}
The entire process described by @ref{max_block_iterations} is repeated
until improvement has stopped. This is the maximum number of times the
process is allowed to repeat. Set this to @code{0} to not allow
repetitions. Default: @code{10}
@item function_convergence_criterion = @var{DOUBLE}
The convergence criterion for the objective function when
@code{max_repeated_optimizations_runs} is positive. Default: @code{0.1}
@item parameter_convergence_criterion = @var{DOUBLE}
The convergence criterion for parameter values when
@code{max_repeated_optimizations_runs} is positive. Default: @code{0.1}
@item number_of_large_perturbations = @var{INTEGER}
The entire process described by @ref{max_block_iterations} is repeated
with random starting values drawn from the posterior. This specifies the
number of random starting values used. Set this to @code{0} to not use
random starting values. A larger number should be specified to ensure
that the entire parameter space has been covererd. Default: @code{5}
@item number_of_small_perturbations = @var{INTEGER}
The number of small perturbations to make after the large perturbations
have stopped improving. Setting this number much above @code{10} is
probably overkill. Default: @code{5}
@item number_of_posterior_draws_after_perturbation = @var{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: @code{1}
@item max_number_of_stages = @var{INTEGER}
The small and large perturbation are repeated until improvement has
stopped. This specifices the maximum number of stages allowed. Default:
@code{20}
@item random_function_convergence_criterion = @var{DOUBLE}
The convergence criterion for the objective function when
@code{number_of_large_perturbations} is positive. Default: @code{0.1}
@item random_parameter_convergence_criterion = @var{DOUBLE}
The convergence criterion for parameter values when
@code{number_of_large_perturbations} is positive. Default: @code{0.1}
@end table
@end deffn
@examplehead
@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);
@end example
@anchor{ms_simulation}
@deffn Command ms_simulation ;
@deffnx Command ms_simulation (@var{OPTIONS}@dots{});
@descriptionhead
Simulates a Markov-switching SBVAR model.
@optionshead
@table @code
@item file_tag = @var{FILENAME}
@anchor{file_tag} The portion of the filename associated with the
@code{ms_estimation} run. Default: @code{}
@item output_file_tag = @var{FILENAME}
@anchor{output_file_tag} The portion of the output filename that will be
assigned to this run. Default: @code{}
@item mh_replic = @var{INTEGER}
The number of draws to save. Default: @code{10,000}
@item drop = @var{INTEGER}
The number of burn-in draws. Default:
@code{0.1*mh_replic*thinning_factor}
@item thinning_factor = @var{INTEGER}
The total number of draws is equal to
@code{thinning_factor*mh_replic+drop}. Default: @code{1}
@item adaptive_mh_draws = @var{INTEGER}
Tuning period for Metropolis-Hasting draws. Default: @code{30,000}
@end table
@end deffn
@examplehead
@example
ms_simulation(file_tag=second_run);
ms_simulation(file_tag=third_run, mh_replic=5000, thinning_factor=3);
@end example
@anchor{ms_compute_mdd}
@deffn Command ms_compute_mdd ;
@deffnx Command ms_compute_mdd (@var{OPTIONS}@dots{});
@descriptionhead
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 @code{oo_.ms} structure.
@optionshead
@table @code
@item file_tag = @var{FILENAME}
@xref{file_tag}.
@item output_file_tag = @var{FILENAME}
@xref{output_file_tag}.
@item simulation_file_tag = @var{FILENAME}
@anchor{simulation_file_tag} The portion of the filename associated with
the simulation run. Defualt: @code{}
@item proposal_type = @var{INTEGER}
The proposal type:
@table @code
@item 1
Gaussian
@item 2
Power
@item 3
Truncated Power
@item 4
Step
@item 5
Truncated Gaussian
@end table
Default: @code{3}
@item proposal_lower_bound = @var{DOUBLE}
The lower cutoff in terms of probability. Not used for
@code{proposal_type} in [@code{1,2}]. Required for all other proposal
types. Default: @code{0.1}
@item proposal_upper_bound = @var{DOUBLE}
The upper cutoff in terms of probability. Not used for
@code{proposal_type} equal to @code{1}. Required for all other proposal
types. Default: @code{0.9}
@item mdd_proposal_draws = @var{INTEGER}
The number of proposal draws. Default: @code{100,000}
@item mdd_use_mean_center
Use the posterior mean as center. Default: @code{off}
@end table
@end deffn
@anchor{ms_compute_probabilities}
@deffn Command ms_compute_probabilities ;
@deffnx Command ms_compute_probabilities (@var{OPTIONS}@dots{});
@descriptionhead
Computes smoothed regime probabilities of a Markov-switching SBVAR
model. Output @code{.eps} files are contained in
@code{}.
@optionshead
@table @code
@item file_tag = @var{FILENAME}
@xref{file_tag}.
@item output_file_tag = @var{FILENAME}
@xref{output_file_tag}.
@item filtered_probabilities
Filtered probabilities are computed instead of smoothed. Default:
@code{off}
@item real_time_smoothed
Smoothed probabilities are computed based on time @code{t} information
for @math{0\le t\le nobs}. Default: @code{off}
@end table
@end deffn
@anchor{ms_irf}
@deffn Command ms_irf ;
@deffnx Command ms_irf (@var{OPTIONS}@dots{});
@descriptionhead
Computes impulse response functions for a Markov-switching SBVAR
model. Output @code{.eps} files are contained in
@code{}, while data files are contained in
@code{}.
@optionshead
@table @code
@item file_tag = @var{FILENAME}
@xref{file_tag}.
@item output_file_tag = @var{FILENAME}
@xref{output_file_tag}.
@item simulation_file_tag = @var{FILENAME}
@xref{simulation_file_tag}.
@item horizon = @var{INTEGER}
@anchor{horizon} The forecast horizon. Default: @code{12}
@item filtered_probabilities
@anchor{filtered_probabilities} Uses filtered probabilities at the end
of the sample as initial conditions for regime probabilities. Only one
of @code{filtered_probabilities}, @code{regime} and @code{regimes} may
be passed. Default: @code{off}
@item error_band_percentiles = [@var{DOUBLE1} @dots{}]
@anchor{error_band_percentiles} The percentiles to compute. Default:
@code{[0.16 0.50 0.84]}. If @code{median} is passed, the default
is @code{[0.5]}
@item shock_draws = @var{INTEGER}
@anchor{shock_draws} The number of regime paths to draw. Default:
@code{10,000}
@item shocks_per_parameter = @var{INTEGER}
@anchor{shocks_per_parameter} The number of regime paths to draw under
parameter uncertainty. Default: @code{10}
@item thinning_factor = @var{INTEGER}
@anchor{thinning_factor} Only @math{1/@code{thinning_factor}} of the
draws in posterior draws file are used. Default: @code{1}
@item free_parameters = @var{NUMERICAL_VECTOR}
@anchor{free_parameters} A vector of free parameters to initialize theta
of the model. Default: use estimated parameters
@item parameter_uncertainty
@anchor{parameter_uncertainty} Calculate IRFs under parameter
uncertainty. Requires that @command{ms_simulation} has been
run. Default: @code{off}
@item regime = @var{INTEGER}
@anchor{regime} Given the data and model parameters, what is the ergodic
probability of being in the specified regime. Only one of
@code{filtered_probabilities}, @code{regime} and @code{regimes} may be
passed. Default: @code{off}
@item regimes
@anchor{regimes} Describes the evolution of regimes. Only one of
@code{filtered_probabilities}, @code{regime} and @code{regimes} may be
passed. Default: @code{off}
@item median
@anchor{median} A shortcut to setting
@code{error_band_percentiles=[0.5]}. Default: @code{off}
@end table
@end deffn
@anchor{ms_forecast}
@deffn Command ms_forecast ;
@deffnx Command ms_forecast (@var{OPTIONS}@dots{});
@descriptionhead
Generates forecasts for a Markov-switching SBVAR model. Output
@code{.eps} files are contained in @code{},
while data files are contained in @code{}.
@optionshead
@table @code
@item file_tag = @var{FILENAME}
@xref{file_tag}.
@item output_file_tag = @var{FILENAME}
@xref{output_file_tag}.
@item simulation_file_tag = @var{FILENAME}
@xref{simulation_file_tag}.
@item data_obs_nbr = @var{INTEGER}
The number of data points included in the output. Default: @code{0}
@item error_band_percentiles = [@var{DOUBLE1} @dots{}]
@xref{error_band_percentiles}.
@item shock_draws = @var{INTEGER}
@xref{shock_draws}.
@item shocks_per_parameter = @var{INTEGER}
@xref{shocks_per_parameter}.
@item thinning_factor = @var{INTEGER}
@xref{thinning_factor}.
@item free_parameters = @var{NUMERICAL_VECTOR}
@xref{free_parameters}.
@item parameter_uncertainty
@xref{parameter_uncertainty}.
@item regime = @var{INTEGER}
@xref{regime}.
@item regimes
@xref{regimes}.
@item median
@xref{median}.
@end table
@end deffn
@anchor{ms_variance_decomposition}
@deffn Command ms_variance_decomposition ;
@deffnx Command ms_variance_decomposition (@var{OPTIONS}@dots{});
@descriptionhead
Computes the variance decomposition for a Markov-switching SBVAR
model. Output @code{.eps} files are contained in
@code{}, while data files
are contained in @code{}.
@optionshead
@table @code
@item file_tag = @var{FILENAME}
@xref{file_tag}.
@item output_file_tag = @var{FILENAME}
@xref{output_file_tag}.
@item simulation_file_tag = @var{FILENAME}
@xref{simulation_file_tag}.
@item horizon = @var{INTEGER}
@xref{horizon}.
@item filtered_probabilities
@xref{filtered_probabilities}.
@item no_error_bands
Do not output percentile error bands (@i{i.e.} compute mean). Default:
@code{off} (@i{i.e.} output error bands)
@item error_band_percentiles = [@var{DOUBLE1} @dots{}]
@xref{error_band_percentiles}.
@item shock_draws = @var{INTEGER}
@xref{shock_draws}.
@item shocks_per_parameter = @var{INTEGER}
@xref{shocks_per_parameter}.
@item thinning_factor = @var{INTEGER}
@xref{thinning_factor}.
@item free_parameters = @var{NUMERICAL_VECTOR}
@xref{free_parameters}.
@item parameter_uncertainty
@xref{parameter_uncertainty}.
@item regime = @var{INTEGER}
@xref{regime}.
@item regimes
@xref{regimes}.
@end table
@end deffn
@node Displaying and saving results
@section Displaying and saving results
Dynare has comments to plot the results of a simulation and to save the results.
@deffn Command rplot @var{VARIABLE_NAME}@dots{};
Plots the simulated path of one or several variables, as stored in
@var{oo_.endo_simul} by either @var{simul} (@pxref{Deterministic
simulation}) or @var{stoch_simul} with
option @var{periods} (@pxref{Computing the stochastic solution}). The
variables are plotted in levels.
@end deffn
@deffn Command dynatype (@var{FILENAME}) [@var{VARIABLE_NAME}@dots{}];
This command prints the listed variables in a text file named
@var{FILENAME}. If no @var{VARIABLE_NAME} is listed, all endogenous
variables are printed.
@end deffn
@deffn Command dynasave (@var{FILENAME}) [@var{VARIABLE_NAME}@dots{}];
This command saves the listed variables in a binary file named
@var{FILENAME}. If no @var{VARIABLE_NAME} are listed, all endogenous
variables are saved.
In MATLAB or Octave, variables saved with the @code{dynasave} command
can be retrieved by the command:
@example
load -mat @var{FILENAME}
@end example
@end deffn
@node Macro-processing language
@section Macro-processing language
It is possible to use ``macro'' commands in the @file{.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@dots{}
The Dynare macro-language provides a new set of @emph{macro-commands}
which can be inserted inside @file{.mod} files. It features:
@itemize
@item
file inclusion
@item
loops (@code{for} structure)
@item
conditional inclusion (@code{if/then/else} structures)
@item
expression substitution
@end itemize
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 @file{.mod}
file with macros into a @file{.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
@emph{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 @code{savemacro} option of the
@code{dynare} command (@pxref{Dynare invocation}).
The macro-processor is invoked by placing @emph{macro directives} in
the @file{.mod} file. Directives begin with an at-sign followed by a
pound sign (@code{@@#}). 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 (@code{\\}) at the end
of the line indicates that the directive is continued on the next
line. The main directives are:
@itemize
@item
@code{@@#include}, for file inclusion,
@item
@code{@@#define}, for defining a macro-processor variable,
@item
@code{@@#if}, @code{@@#ifdef}, @code{@@#ifndef}, @code{@@#else},
@code{@@#endif} for conditional statements,
@item
@code{@@#for}, @code{@@#endfor} for constructing loops.
@end itemize
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 @code{@@#define} directive, and can be of four
types: integer, character string, array of integers, array of
strings.
@menu
* Macro expressions::
* Macro directives::
* Typical usages::
* MATLAB/Octave loops versus macro-processor loops::
@end menu
@node Macro expressions
@subsection 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 @strong{double} quotes
(like @code{"name"}). Arrays are enclosed within brackets, and their
elements are separated by commas (like @code{[1,2,3]} or @code{["US",
"EA"]}).
Note that there is no boolean type: @emph{false} is
represented by integer zero and @emph{true} is any non-null integer.
The following operators can be used on integers:
@itemize
@item
arithmetic operators: @code{+}, @code{-}, @code{*}, @code{/}
@item
comparison operators: @code{<}, @code{>}, @code{<=}, @code{>=},
@code{==}, @code{!=}
@item
logical operators: @code{&&}, @code{||}, @code{!}
@item
integer ranges, using the following syntax:
@code{@var{INTEGER1}:@var{INTEGER2}} (for example, @code{1:4} is
equivalent to integer array @code{[1,2,3,4]})
@end itemize
The following operators can be used on strings:
@itemize
@item
comparison operators: @code{==}, @code{!=}
@item
concatenation of two strings: @code{+}
@item
extraction of substrings: if @code{@var{s}} is a string, then
@code{@var{s}[3]} is a string containing only the third character of
@code{@var{s}}, and @code{@var{s}[4:6]} contains the characters from
4th to 6th
@end itemize
The following operators can be used on arrays:
@itemize
@item
dereferencing: if @code{@var{v}} is an array, then @code{@var{v}[2]} is its 2nd element
@item
concatenation of two arrays: @code{+}
@item
difference @code{-}: returns the first operand from which the elements
of the second operand have been removed
@item
extraction of sub-arrays: @i{e.g.} @code{@var{v}[4:6]}
@item
testing membership of an array: @code{in} operator (for example:
@code{"b" in ["a", "b", "c"]} returns @code{1})
@end itemize
Macro-expressions can be used at two places:
@itemize
@item
inside macro directives, directly;
@item
in the body of the @code{.mod} file, between an at-sign and curly
braces (like @code{@@@{@var{expr}@}}): the macro processor will
substitute the expression with its value.
@end itemize
In the following, @var{MACRO_EXPRESSION} designates an expression
constructed as explained above.
@node Macro directives
@subsection Macro directives
@deffn {Macro directive} @@#include "@var{FILENAME}"
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{i.e.} to include a file from an included file).
@examplehead
@example
@@#include "modelcomponent.mod"
@end example
@end deffn
@deffn {Macro directive} @@#define @var{MACRO_VARIABLE} = @var{MACRO_EXPRESSION}
Defines a macro-variable.
@customhead{Example 1}
@example
@@#define x = 5 // Integer
@@#define y = "US" // String
@@#define v = [ 1, 2, 4 ] // Integer array
@@#define w = [ "US", "EA" ] // String array
@@#define z = 3 + v[2] // Equals 5
@@#define t = ("US" in w) // Equals 1 (true)
@end example
@customhead{Example 2}
@example
@@#define x = [ "B", "C" ]
@@#define i = 2
model;
A = @@@{x[i]@};
end;
@end example
is strictly equivalent to:
@example
model;
A = C;
end;
@end example
@end deffn
@deffn {Macro directive} @@#if @var{MACRO_EXPRESSION}
@deffnx {Macro directive} @@#ifdef @var{MACRO_VARIABLE}
@deffnx {Macro directive} @@#ifndef @var{MACRO_VARIABLE}
@deffnx {Macro directive} @@#else
@deffnx {Macro directive} @@#endif
Conditional inclusion of some part of the @file{.mod} file.
The lines between @code{@@#if}, @code{@@#ifdef} or @code{@@#ifndef} and the next
@code{@@#else} or @code{@@#endif} is executed only if the condition
evaluates to a non-null integer. The @code{@@#else} branch is optional
and, if present, is only evaluated if the condition evaluates to
@code{0}.
@examplehead
Choose between two alternative monetary policy rules using a macro-variable:
@example
@@#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;
@end example
@examplehead
Choose between two alternative monetary policy rules using a
macro-variable. As @code{linear_mon_pol} was not previously defined in
this example, the second equation will be chosen:
@example
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;
@end example
Choose between two alternative monetary policy rules using a
macro-variable. As @code{linear_mon_pol} was not previously defined in
this example, the first equation will be chosen:
@example
model;
@@#ifndef 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;
@end example
@end deffn
@deffn {Macro directive} @@#for @var{MACRO_VARIABLE} in @var{MACRO_EXPRESSION}
@deffnx {Macro directive} @@#endfor
Loop construction for replicating portions of the @file{.mod} file.
Note that this construct can enclose variable/parameters declaration,
computational tasks, but not a model declaration.
@examplehead
@example
model;
@@#for country in [ "home", "foreign" ]
GDP_@@@{country@} = A * K_@@@{country@}^a * L_@@@{country@}^(1-a);
@@#endfor
end;
@end example
is equivalent to:
@example
model;
GDP_home = A * K_home^a * L_home^(1-a);
GDP_foreign = A * K_foreign^a * L_foreign^(1-a);
end;
@end example
@end deffn
@deffn {Macro directive} @@#echo @var{MACRO_EXPRESSION}
Asks the preprocessor to display some message on standard output. The
argument must evaluate to a string.
@end deffn
@deffn {Macro directive} @@#error @var{MACRO_EXPRESSION}
Asks the preprocessor to display some error message on standard output
and to abort. The argument must evaluate to a string.
@end deffn
@node Typical usages
@subsection Typical usages
@menu
* Modularization::
* Indexed sums or products::
* Multi-country models::
* Endogeneizing parameters::
@end menu
@node Modularization
@subsubsection Modularization
The @code{@@#include} directive can be used to split @file{.mod} files
into several modular components.
Example setup:
@table @file
@item modeldesc.mod
Contains variable declarations, model equations and shocks declarations
@item simul.mod
Includes @file{modeldesc.mod}, calibrates parameters and runs
stochastic simulations
@item estim.mod
Includes @file{modeldesc.mod}, declares priors on parameters and runs
bayesian estimation
@end table
Dynare can be called on @file{simul.mod} and @file{estim.mod}, but it
makes no sense to run it on @file{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).
@node Indexed sums or products
@subsubsection Indexed sums or products
The following example shows how to construct a moving average:
@example
@@#define window = 2
var x MA_x;
...
model;
...
MA_x = 1/@@@{2*window+1@}*(
@@#for i in -window:window
+x(@@@{i@})
@@#endfor
);
...
end;
@end example
After macro-processing, this is equivalent to:
@example
var x MA_x;
...
model;
...
MA_x = 1/5*(
+x(-2)
+x(-1)
+x(0)
+x(1)
+x(2)
);
...
end;
@end example
@node Multi-country models
@subsubsection Multi-country models
Here is a skeleton example for a multi-country model:
@example
@@#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;
@end example
@node Endogeneizing parameters
@subsubsection 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:
@math{y = \left(\alpha^{1/\xi} \ell^{1-1/\xi}+(1-\alpha)^{1/\xi}k^{1-1/\xi}\right)^{\xi/(\xi-1)}}
The labor share in GDP is defined as:
@code{lab_rat} @math{= (w \ell)/(p y)}
In the model, @math{\alpha} is a (share) parameter, and
@code{lab_rat} is an endogenous variable.
It is clear that calibrating @math{\alpha} is not straigthforward; but
on the contrary, we have real world data for @code{lab_rat}, and
it is clear that these two variables are economically linked.
The solution is to use a method called @emph{variable flipping}, which
consist in changing the way of computing the steady state. During this
computation, @math{\alpha} will be made an endogenous variable and
@code{lab_rat} will be made a parameter. An economically relevant
value will be calibrated for @code{lab_rat}, and the solution
algorithm will deduce the implied value for @math{\alpha}.
An implementation could consist of the following files:
@table @file
@item modeqs.mod
This file contains variable declarations and model equations. The code
for the declaration of @math{\alpha} and @code{lab_rat} would look like:
@example
@@#if steady
var alpha;
parameter lab_rat;
@@#else
parameter alpha;
var lab_rat;
@@#endif
@end example
@item steady.mod
This file computes the steady state. It begins with:
@example
@@#define steady = 1
@@#include "modeqs.mod"
@end example
Then it initializes parameters (including @code{lab_rat}, excluding
@math{\alpha}, computes the steady state (using guess values for
endogenous, including @math{\alpha}, then saves values of parameters
and endogenous at steady state in a file, using the
@code{save_params_and_steady_state} command.
@item simul.mod
This file computes the simulation. It begins with:
@example
@@#define steady = 0
@@#include "modeqs.mod"
@end example
Then it loads values of parameters and endogenous at steady state from
file, using the @code{load_params_and_steady_state} command, and
computes the simulations.
@end table
@node MATLAB/Octave loops versus macro-processor loops
@subsection MATLAB/Octave loops versus macro-processor loops
Suppose you have a model with a parameter @math{\rho}, and you want to make
simulations for three values: @math{\rho = 0.8, 0.9, 1}. There are
several ways of doing this:
@table @asis
@item With a MATLAB/Octave loop
@example
rhos = [ 0.8, 0.9, 1];
for i = 1:length(rhos)
rho = rhos(i);
stoch_simul(order=1);
end
@end example
Here the loop is not unrolled, MATLAB/Octave manages the iterations.
This is interesting when there are a lot of iterations.
@item With a macro-processor loop (case 1)
@example
rhos = [ 0.8, 0.9, 1];
@@#for i in 1:3
rho = rhos(@@@{i@});
stoch_simul(order=1);
@@#endfor
@end example
This is very similar to previous example, except that the loop is
unrolled. The macro-processor manages the loop index but not the data
array (@code{rhos}).
@item With a macro-processor loop (case 2)
@example
@@#for rho_val in [ "0.8", "0.9", "1"]
rho = @@@{rho_val@};
stoch_simul(order=1);
@@#endfor
@end example
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.
@end table
@node Misc commands
@section Misc commands
@deffn Command set_dynare_seed (@var{INTEGER})
@deffnx Command set_dynare_seed ('default')
@deffnx Command set_dynare_seed ('clock')
@deffnx Command set_dynare_seed ('reset')
@deffnx Command set_dynare_seed ('@var{ALGORITHM}', @var{INTEGER})
Sets the seed used for random number generation. It is possible to set
a given integer value, to use a default value, or to use the clock (by
using the latter, one will therefore get different results across
different Dynare runs). The @code{reset} option serves to reset the
seed to the value set by the last @code{set_dynare_seed} command. On
MATLAB 7.8 or above, it is also possible to choose a specific
algorithm for random number generation; accepted values are
@code{mcg16807}, @code{mlfg6331_64}, @code{mrg32k3a}, @code{mt19937ar}
(the default), @code{shr3cong} and @code{swb2712}.
@end deffn
@deffn Command save_params_and_steady_state (@var{FILENAME});
For all parameters, endogenous and exogenous variables, stores
their value in a text file, using a simple name/value associative table.
@itemize
@item
for parameters, the value is taken from the last parameter
initialization
@item
for exogenous, the value is taken from the last initval block
@item
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)
@end itemize
Note that no variable type is stored in the file, so that the values
can be reloaded with @code{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 @file{.mod} file which computes the
steady state and saves the result of the computation at the end of the
file, using @code{save_params_and_steady_state}.
In a second file designed to perform the actual simulations, you would
use @code{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 @file{.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 @code{var} and
@code{parameters} statements.
Also note that you can take advantage of the @code{@@#include}
directive to share the model equations between the two files
(@pxref{Macro-processing language}).
@end deffn
@anchor{load_params_and_steady_state}
@deffn Command load_params_and_steady_state (@var{FILENAME});
For all parameters, endogenous and exogenous variables, loads
their value from a file created with @code{save_params_and_steady_state}.
@itemize
@item
for parameters, their value will be initialized as if they
had been calibrated in the @file{.mod} file
@item
for endogenous and exogenous, their value will be initialized
as they would have been from an initval block
@end itemize
This function is used in conjunction with
@code{save_params_and_steady_state}; see the documentation of that
function for more information.
@end deffn
@anchor{dynare_version}
@deffn {MATLAB/Octave command} dynare_version ;
Output the version of Dynare that is currently being used (@i{i.e.}
the one that is highest on the MATLAB/Octave path).
@end deffn
@node The Configuration File
@chapter 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 @file{$HOME/.dynare}, while on Windows it is
@file{%APPDATA%\dynare.ini} (typically @file{C:\Documents and
Settings\@var{USERNAME}\Application Data\dynare.ini} under Windows XP,
or @file{C:\Users\@var{USERNAME}\AppData\dynare.ini} under Windows
Vista/7/8). You can specify a non standard location using the
@code{conffile} option of the @code{dynare} command (@pxref{Dynare
invocation}).
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:
@example
[command0]
option0 = choice0
option1 = choice1
[command1]
option0 = choice0
option1 = choice1
@end example
The configuration file follows a few conventions (self-explanatory
conventions such as @var{USER_NAME} have been excluded for concision):
@table @var
@item COMPUTER_NAME
Indicates the valid name of a server (@i{e.g.} @code{localhost},
@code{server.cepremap.org}) or an IP address.
@item DRIVE_NAME
Indicates a valid drive name in Windows, without the trailing colon (@i{e.g.} @code{C}).
@item PATH
Indicates a valid path in the underlying operating system (@i{e.g.}
@code{/home/user/dynare/matlab/}).
@item PATH_AND_FILE
Indicates a valid path to a file in the underlying operating system
(@i{e.g.} @code{/usr/local/MATLAB/R2010b/bin/matlab}).
@item BOOLEAN
Is @code{true} or @code{false}.
@end table
@menu
* Dynare Configuration::
* Parallel Configuration::
@end menu
@node Dynare Configuration
@section Dynare Configuration
This section explains how to configure Dynare for general
processing. Currently, there is only one option available.
@deffn {Configuration block} [hooks]
@descriptionhead
The @code{[hooks]} block can be used to specify configuration options
that will be used when running dynare.
@optionshead
@table @code
@item GlobalInitFile = @var{PATH_AND_FILE}
The location of the global initialization file to be run at the end of
@code{global_initialization.m}
@end table
@examplehead
@example
[hooks]
GlobalInitFile = /home/usern/dynare/myInitFile.m
@end example
@end deffn
@node Parallel Configuration
@section 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:
@itemize
@item
the Metropolis-Hastings algorithm;
@item
the Metropolis-Hastings diagnostics;
@item
the posterior IRFs;
@item
the prior and posterior statistics;
@item
some plotting routines.
@end itemize
Note that creating the configuration file is not enough in order to
trigger parallelization of the computations: you also need to specify
the @code{parallel} option to the @code{dynare} command. For more
details, and for other options related to the parallelization engine,
see @pxref{Dynare invocation}.
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):
@table @asis
@item For a Windows grid
@itemize
@item
a standard Windows network (SMB) must be in place;
@item
@uref{http://technet.microsoft.com/en-us/sysinternals/bb896649.aspx,
PsTools} must be installed in the path of the master Windows machine;
@item
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.
@end itemize
@item For a UNIX grid
@itemize
@item
SSH must be installed on the master and on the slave machines;
@item
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
@end itemize
@end table
We now turn to the description of the configuration directives:
@deffn {Configuration block} [cluster]
@descriptionhead
When working in parallel, @code{[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.
@optionshead
@table @code
@item Name = @var{CLUSTER_NAME}
The reference name of this cluster.
@item Members = @var{NODE_NAME}[(@var{WEIGHT})] @var{NODE_NAME}[(@var{WEIGHT})] @dots{}
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 (@i{e.g.}
@code{n1(2) n2(1) n3(3)}, means that @code{n1} is two times more
powerful than @code{n2} whereas @code{n3} is three times more powerful
than @code{n2}). Each node is separated by at least one space and the
weights are in parenthesis with no spaces separating them from their
node.
@end table
@examplehead
@example
[cluster]
Name = c1
Members = n1 n2 n3
[cluster]
Name = c2
Members = n1(4) n2 n3
@end example
@end deffn
@deffn {Configuration block} [node]
@descriptionhead
When working in parallel, @code{[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.
@optionshead
@table @code
@item Name = @var{NODE_NAME}
The reference name of this node.
@item CPUnbr = @var{INTEGER} | [@var{INTEGER}:@var{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.
@item ComputerName = @var{COMPUTER_NAME}
The name or IP address of the node. If you want to run locally, use
@code{localhost} (case-sensitive).
@item Port = @var{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).
@item UserName = @var{USER_NAME}
The username used to log into a remote system. Required for remote
runs on all platforms.
@item Password = @var{PASSWORD}
The password used to log into the remote system. Required for remote
runs originating from Windows.
@item RemoteDrive = @var{DRIVE_NAME}
The drive to be used for remote computation. Required for remote runs
originating from Windows.
@item RemoteDirectory = @var{PATH}
The directory to be used for remote computation. Required for remote
runs on all platforms.
@item DynarePath = @var{PATH}
The path to the @file{matlab} subdirectory within the Dynare
installation directory. The default is the empty string.
@item MatlabOctavePath = @var{PATH_AND_FILE}
The path to the MATLAB or Octave executable. The default value is
@code{matlab}.
@item SingleCompThread = @var{BOOLEAN}
Whether or not to disable MATLAB's native multithreading. The default
value is @code{true}. Option meaningless under Octave.
@item OperatingSystem = @var{OPERATING_SYSTEM}
The operating system associated with a node. Only necessary when
creating a cluster with nodes from different operating systems.
Possible values are @code{unix} or @code{windows}. There is no default
value.
@end table
@examplehead
@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
@end example
@end deffn
@node Time Series
@chapter Time Series
Dynare provides a Matlab class for handling time series data, which is
based on classes for handling dates. Below, you will first find the
classes and methods used for creating and dealing with dates and then
the class used for using time series.
@section dynDate
@deftypefn {dynDate} dynDate (@code{INTEGER})
@deftypefnx {dynDate} dynDate (@code{STRING})
@deftypefnx {dynDate} dynDate (@var{NUMERICAL_VECTOR}, @code{INTEGER})
Returns a @code{dynDate} object that represents a date.
If the value passed is an @code{INTEGER}, return a date of annual
frequency.
If the value passed is a @code{STRING}, it should be passed in one of
the following formats: @code{`1999'} for an annual date,
@code{`1999q4'} for a quarterly date, @code{`1999m12'} for a monthly
date, and @code{`1999w52'} for a weekly date.
If the value passed is a @code{NUMERICAL_VECTOR} it should be a vector
of size @code{2}. The format should be: @code{[year period]}. In this
case, you must pass a second argument to the @code{dynDate} consructor
indicating the freqency of the date as an @code{INTEGER}. This
argument can take the following possible values: @code{1} for annual,
@code{4} for quarterly, @code{12} for monthly and @code{52} for
weekly.
@examplehead
An example of various ways to create a @code{dynDate} object:
@example
do1 = dynDate(`1999'); % 1999
do2 = dynDate(`Q'); % NaNqNan
do3 = dynDate([1999 2], 12); % 1999m2
@end example
@end deftypefn
@section dynDates
@deftypefn {dynDates} dynDates (@code{STRING} [, @code{STRING} @dots{}])
Returns a @code{dynDates} object that represents a list of dates.
Providing a @code{STRING} argument populates the object with the date
represented by said @code{STRING}. If more than one argument is
provided, they should all be dates represented as @code{STRINGS}.
@examplehead
An example of various ways to create a @code{dynDates} object:
@example
do1 = dynDates(`1999', `2000', `2001', `2002');
do2 = dynDates(`1999', `2003', `2002');
do3 = dynDate(`1999Q2'):dynDate(`2000Q3');
@end example
Here, @code{do1} and @code{do2} contain the dates specified in the
order specified. @code{do3} contains a quarterly list of all dates
between @code{1999q2} and @code{2000q3} inclusive.
@end deftypefn
@section dynSeries
@deftypefn {dynSeries} dynSeries (@code{dynDate})
@deftypefnx {dynSeries} dynSeries (@code{FILENAME})
@deftypefnx {dynSeries} dynSeries (@code{DOUBLE_MATRIX}, @code{dynDate}, @code{CELLSTR}, @code{CELLSTR})
@deftypefnx {dynSeries} dynSeries (@code{DOUBLE_MATRIX}, @code{STRING}, @code{CELLSTR}, @code{CELLSTR})
Returns a @code{dynSeries} object that represents one or more time
series.
If a @code{dynDate} argument is provided, instantiate an empty
@code{dynSeries} with an inital date equal to the input argument.
If a @code{FILENAME} is passed as input, a @code{dynSeries} object
will be created from the named file. Valid file types are @file{.m}
file, @file{.mat} file, and @file{.csv}.
If the data is not read from a file, it can be provided via a
@math{T}x@math{N} matrix as the first argument to @code{dynSeries}, with
@math{T} representing the number of observations on @math{N}
variables. The second argument in such a calling sequence can be
either a @code{dynDate} representing the period of the first
observation or a @code{STRING} which would be used to instantiate a
@code{dynDate}. The third argument is a @code{CELLSTR} of size
@math{N} with one entry for each variable name. The final argument is
a @code{CELLSTR} of size @math{N} composed of the @LaTeX{} names
associated with the variables. Input arguments three and four are
optional.
@examplehead
An example of various ways to create a @code{dynSeries} object:
@example
do1 = dynSeries(dynDate(1999));
do2 = dynSeries(`filename.csv');
do3 = dynSeries([1; 2; 3], dynDate(1999), @{`var123'@}, @{`var_@{123@}'@});
@end example
@end deftypefn
@node Reporting
@chapter Reporting
Dynare provides a simple interface for creating @LaTeX{} reports,
comprised of @LaTeX{} tables and TikZ graphs. You can use the report as
created through Dynare or pick out the pieces you want for inclusion
in your own paper.
Reports are created and modified by calling methods on class
objects. The objects are hierarchichal, with the following order (from
highest to lowest): @code{Report, Page, Section, Graph/Table/Vspace,
Series}. For simplicity of syntax, we abstract away from these
classes, allowing you to operate directly on a @code{Report} object,
while maintaining the names of these classes in the @code{Report}
Class methods you will use.
The report is created sequentially, command by command, hence the
order of the commands matters. When an object of a certain hierarchy
is inserted, all methods will function on that object until an object
of equal or greater hierarchy is added. Hence, once you add a
@code{Page} to the report, every time you add a @code{Section} object,
it will be added to this @code{Page} until another @code{Page} is
added to the report (via @ref{addPage}). This will become more clear
with the example at the end of the section.
Options to the methods are passed differently than those to Dynare
commands. They take the form of named options to Matlab functions
where the arguments come in pairs (@i{e.g.}
@code{function_name(`option_1_name', `option_1_value',
`option_2_name', `option_2_value', ...)}, where @code{option_X_name}
is the name of the option while @code{option_X_value} is the value
assigned to that option). The ordering of the option pairs matters
only in the unusual case when an option is provided twice (probably
erroneously). In this case, the last value passed is the one that is
used.
Below, you will see a list of methods available for the Report class and
a clarifying example.
@defmethod Report report compiler, showDate, filename, margin, marginUnit, orientation, paper, title
Instantiates a @code{Report} object.
@optionshead
@table @code
@anchor{compiler}
@item compiler, @var{FILENAME}
The full path to the @LaTeX{} compiler on your system. If this option
is not provided, Dynare will try to find the appropriate program to
compile @LaTeX{} on your system. Default is system dependent: Windows:
?, Mac OS X: @code{/usr/texbin/pdflatex}, Linux: the result of
@code{which pdflatex}
@item showDate, @code{BOOLEAN}
Display the date and time when the report was compiled. Default:
@code{true}
@anchor{filename}
@item filename, @var{FILENAME}
The filename to use when saving this report. Default:
@code{report.tex}
@item margin, @var{DOUBLE}
The margin size. Default: @code{2.5}
@item marginUnit, `cm' | `in'
Units associated with the margin. Default: @code{`cm'}
@anchor{orientation}
@item orientation, `landscape' | `portrait'
Paper orientation: Default: @code{`portrait'}
@anchor{paper}
@item paper, `a4' | `letter'
Paper size. Default: @code{`a4'}
@item title, @code{STRING}
Report Title. Default: @code{none}
@end table
@end defmethod
@anchor{addPage}
@defmethod Report addPage footnote, orientation, paper, title, titleFormat
Adds a @code{Page} to the @code{Report}.
@optionshead
@table @code
@item footnote, @code{STRING}
A footnote to be included at the bottom of this page. Default: @code{none}
@item orientation, `landscape' | `portrait'
@xref{orientation}.
@item paper, `a4' | `letter'
@xref{paper}.
@anchor{title}
@item title, @code{STRING} | @code{CELL_ARRAY_STRINGS}
With one entry (a @code{STRING}), the title of the page. With more
than one entry (a @code{CELL_ARRAY_STRINGS}), the title and subtitle(s)
of the page. Default: @code{none}
@anchor{titleFormat}
@item titleFormat, @code{STRING} | @code{CELL_ARRAY_STRINGS}
A string representing the @LaTeX{} markup to use on the
@ref{title}. The number of cell array entries must be equal to that of
the @ref{title} option. Default: @code{none}
@end table
@end defmethod
@defmethod Report addSection cols, height
Adds a @code{Section} to a @code{Page}.
@optionshead
@table @code
@item cols, @code{INTEGER}
The number of columns in the section. Default: @code{1}
@item height, @code{STRING}
A string to be used with the @code{\sectionheight} @LaTeX{}
command. Default: @code{`!'}
@end table
@end defmethod
@defmethod Report addGraph data, figname, showGrid, showLegend, showLegendBox, legendLocation, legendOrientation, legendFontSize, seriesToUse, shade, shadeColor, shadeOpacity, title, xlabel, ylabel, xrange, yrange, showZeroline
Adds a @code{Graph} to a @code{Section}.
@optionshead
@table @code
@anchor{data}
@item data, @code{dynSeries}
The @code{dynSeries} that provides the data for the graph. Default:
@code{none}
@item figname, @code{STRING}
The name to use when saving this figure. Default: @code{[tempname
`.tex']}
@item showGrid, @code{BOOLEAN}
Whether or not to display the minor grid on the graph. Default:
@code{true}
@item showLegend, @code{BOOLEAN}
Whether or not to display the legend. Default: @code{false}
@item showLegendBox, @code{BOOLEAN}
Whether or not to display a box around the legend. Default:
@code{false}
@item legendLocation, `North' | `South' | `East' | `West' | `NorthEast' | `SouthEast' | `NorthWest' | `SouthWest' | `NorthOutside' | `SouthOutside' | `EastOutside' | `WestOutside' | `NorthEastOutside' | `SouthEastOutside' | `NorthWestOutside' | `SouthWestOutside' | `Best' | `BestOutside'
Where to place the legend in the graph. NB: some of these are not
available under Octave. Default: @code{`SouthEast'}
@item legendOrientation, `vertical' | `horizontal'
Orientation of the legend. Default: @code{`horizontal'}
@item legendFontSize, @code{DOUBLE}
The font size for legend entries. Default: @code{8}
@anchor{seriesToUse}
@item seriesToUse, @code{CELL_ARRAY_STRINGS}
The names of the series contained in the @code{dynSeries} provided to
the @ref{data} option. If empty, use all series provided to
@ref{data} option. Default: @code{empty}
@item shade, @code{dynDates}
The date range showing the portion of the graph that should be
shaded. Default: @code{none}
@item shadeColor, @code{MATLAB_COLOR_NAME}
The color to use in the shaded portion of the graph. Default:
@code{`green'}
@item shadeOpacity, @code{DOUBLE}
The opacity of the shaded area, must be in @math{[0,1]}. Default: @code{.2}
@item title, @code{STRING}
Title for the graph. Default: @code{none}
@item xlabel, @code{STRING}
The x-axis label. Default: @code{none}
@item ylabel, @code{STRING}
The y-axis label. Default: @code{none}
@item xrange, @code{dynDates}
The boundary on the x-axis to display in the graph. Default: all
@item yrange, @code{NUMERICAL_VECTOR}
The boundary on the y-axis to display in the graph, represented as a
@code{NUMERICAL_VECTOR} of size @math{2}, with the first entry less
than the second entry. Default: all
@item showZeroline, @code{BOOLEAN}
Display a solid black line at @math{y = 0}. Default: @code{false}
@end table
@end defmethod
@defmethod Report addTable data, showHlines, precision, range, seriesToUse, title, titleSize, vlineAfter, showVlines
Adds a @code{Table} to a @code{Section}.
@optionshead
@table @code
@item data, @code{dynSeries}
@xref{data}.
@item showHlines, @code{BOOLEAN}
Whether or not to show horizontal lines separating the rows. Default: @code{false}
@item precision, @code{INTEGER}
The number of decimal places to report in the table data. Default: @code{1}
@item range, @code{dynDates}
The date range of the data to be displayed. Default: @code{all}
@item seriesToUse, @code{CELL_ARRAY_STRINGS}
@xref{seriesToUse}.
@item title, @code{STRING}
Title for the table. Default: @code{none}
@item titleSize, @code{STRING}
@LaTeX{} string representing the size of the table title. Default: @code{large}
@item vlineAfter, @code{dynDate}
Show a vertical line after the specified date. Default: @code{empty}
@item showVlines, @code{BOOLEAN}
Whether or not to show vertical lines separating the columns. Default: @code{false}
@end table
@end defmethod
@anchor{addSeries}
@defmethod Report addSeries data, graphLineColor, graphLineStyle, graphLineWidth, graphMarker, graphMarkerEdgeColor, graphMarkerFaceColor, graphMarkerSize, tableShowMarkers, tableAlignRight, tableNegColor, tablePosColor
Adds a @code{Series} to a @code{Graph} or a @code{Table}.
@optionshead
@table @code
@item data, @code{dynSeries}
@xref{data}.
@item graphLineColor, @code{MATLAB_COLOR}
Color to use for the series in a graph. Default: @code{`k'}
@item graphLineStyle, @code{`none'} | @code{`-'} | @code{`--'} | @code{`:'} | @code{`-.'}
Line style for this series in a graph. Default: @code{'-'}
@item graphLineWidth @code{DOUBLE}
Line width for this series in a graph. Default: @code{0.5}
@item graphMarker, @code{`+'} | @code{`o'} | @code{`*'} | @code{`.'} | @code{`x'} | @code{`s'} | @code{`square'} | @code{`d'} | @code{`diamond'} | @code{`^'} | @code{`v'} | @code{`>'} | @code{`<'} | @code{`p'} | @code{`pentagram'} | @code{`h'} | @code{`hexagram'} | @code{`none'}
The Marker to use on this series in a graph. Default: @code{none}
@item graphMarkerEdgeColor, @code{MATLAB_COLOR}
The edge color of the graph marker. Default: @code{`auto'}
@item graphMarkerFaceColor, @code{MATLAB_COLOR}
The face color of the graph marker. Default: @code{`auto'}
@item graphMarkerSize, @code{DOUBLE}
The size of the graph marker. Default: @code{6}
@item tableShowMarkers, @code{BOOLEAN}
In a Table, if @code{true}, surround each cell with brackets and color
it according to @ref{tableNegColor} and @ref{tablePosColor}. No effect
for graphs. Default: @code{false}
@item tableAlignRight, @code{BOOLEAN}
Whether or not to align the series name to the right of the
cell. Default: @code{false}
@item tableMarkerLimit, @code{DOUBLE}
For values less than @math{-1*@code{tableMarkerLimit}}, mark the cell
with the color denoted by @ref{tableNegColor}. For those greater than
@code{tableMarkerLimit}, mark the cell with the color denoted by
@ref{tablePosColor}. Default: @code{1e-4}
@anchor{tableNegColor}
@item tableNegColor, @code{LATEX_COLOR}
The color to use when marking Table data that is less than
zero. Default: @code{`red'}
@anchor{tablePosColor}
@item tablePosColor, @code{LATEX_COLOR}
The color to use when marking Table data that is greater than
zero. Default: @code{`blue'}
@end table
@end defmethod
@defmethod Report addVspace hline, number
Adds a @code{Vspace} (vertical space) to a @code{Section}.
@optionshead
@table @code
@item hline, @code{INTEGER}
The number of horizontal lines to be inserted. Default: @code{0}
@item number, @code{INTEGER}
The number of new lines to be inserted. Default: @code{1}
@end table
@end defmethod
@anchor{write}
@defmethod Report write
Writes the @LaTeX{} representation of this @code{Report}, saving it to
the file specified by @ref{filename}.
@end defmethod
@defmethod Report compile compiler
Compiles the report written by @ref{write} into a @code{pdf} file. If
the report has not already been written (determined by the existence
of the file specified by @ref{filename}, @ref{write} is called.
optionshead
@table @code
@item compiler, @code{FILENAME}
Like @ref{compiler}, except will not overwrite the value of
@code{compiler} contained in the report object. Hence, passing the
value here is useful for using different @LaTeX{} compilers or just
for passing the value at the last minute.
@end table
@end defmethod
@examplehead
The following code creates a one page report. The first part of the
page contains two graphs displayed across two columns and one
row. The bottom of the page displays a centered table.
@example
%% Create dynSeries
dsq = dynSeries(`quarterly.csv');
dsa = dynSeries(`annual.csv');
dsca = dynSeries(`annual_control.csv');
%% Report
rep = report();
%% Page 1
rep = rep.addPage(`title', `My Page Title', `titleFormat', `\large\bfseries');
% Section 1
rep = rep.addSection(`cols', 2);
rep = rep.addGraph(`title', `Graph (1,1)', `showLegend', true, ...
`xrange', dynDate(`2007q1'):dynDate(`2013q4'), ...
`shade', dynDate(`2012q2'):dynDate(`2013q4'));
rep = rep.addSeries(`data', dsq@{`SERIES1'@}, `color', `b', ...
`graphLineWidth', 1);
rep = rep.addSeries(`data', dsq@{`SERIES2'@}, `color', `g', ...
`graphLineStyle', '--', `graphLineWidth', 1.5);
rep = rep.addGraph(`title', `Graph (1,2)', `showLegend', true, ...
`xrange', dynDate(`2007q1'):dynDate(`2013q4'), ...
`shade', dynDate(`2012q2'):dynDate(`2013q4'));
rep = rep.addSeries(`data', dsq@{`SERIES3'@}, `color', `b', ...
`graphLineWidth', 1);
rep = rep.addSeries(`data', dsq@{`SERIES4'@}, `color', `g', ...
`graphLineStyle', '--', `graphLineWidth', 1.5);
% Section 2
rep = rep.addSection();
rep = rep.addTable(`title', `Table 1', ...
`range', dynDate(`2012'):dynDate(`2014'));
shortNames = @{`US', `EU'@};
longNames = @{`United States', `Euro Area'@};
for i=1:length(shortNames)
rep = rep.addSeries(`data', dsa@{[`GDP_' shortNames@{i@}]@});
delta = dsa@{[`GDP_' shortNames@{i@}]@}-dsca@{[`GDP_' shortNames@{i@}]@};
delta = delta.tex_rename(`$\Delta$');
rep = rep.addSeries(`data', delta, ...
`tableShowMarkers', true, ...
`tableAlignRight', true);
end
%% Write & Compile Report
rep.write();
rep.compile();
@end example
@node Examples
@chapter Examples
Dynare comes with a database of example @file{.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
@file{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.
@table @file
@item ramst.mod
An elementary real business cycle (RBC) model, simulated in a
deterministic setup.
@item example1.mod
@itemx example2.mod
Two examples of a small RBC model in a stochastic setup, presented in
@cite{Collard (2001)} (see the file @file{guide.pdf} which comes with
Dynare).
@item fs2000.mod
A cash in advance model, estimated by @cite{Schorfheide (2000)}.
@item fs2000_nonstationary.mod
The same model than @file{fs2000.mod}, but written in non-stationary
form. Detrending of the equations is done by Dynare.
@item bkk.mod
Multi-country RBC model with time to build, presented in @cite{Backus,
Kehoe and Kydland (1992)}.
@item agtrend.mod
Small open economy RBC model with shocks to the growth trend, presented
in @cite{Aguiar and Gopinath (2004)}.
@end table
@node Dynare internal documentation and unitary tests
@chapter Dynare internal documentation and unitary tests
One can obtain internal documentation of matlab/octave's routines or perform unitary tests
using the @code{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.
@deffn {MATLAB/Octave command} internals @var{FLAG} @var{ROUTINENAME}[.m]
@descriptionhead
Depending on the @var{FLAG} this command prints internal documentation of a matlab/octave
routine or triggers unitary tests associated to this routine.
@flagshead
@table @code
@item --info
Prints on screen the internal documentation of @var{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 @var{ROUTINENAME} has to be provided.
@item --test
Performs the unitary test associated to @var{ROUTINENAME} (if this routine exists and if the matalab/octave m
file has unitary test sections).
@end table
@examplehead
@example
internals --info particle/local_state_iteration
internals --test particle/local_state_iteration
@end example
@end deffn
@node Bibliography
@chapter Bibliography
@itemize
@item
Aguiar, Mark and Gopinath, Gita (2004): ``Emerging Market Business
Cycles: The Cycle is the Trend,'' @i{NBER Working Paper}, 10734
@item
Andreasen, Martin M., Fernández-Villaverde, Jesús and Juan Rubio-Ramírez (2013): ``The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications,'' @i{NBER Working Paper}, 18983
@item
Backus, David K., Patrick J. Kehoe, and Finn E. Kydland (1992):
``International Real Business Cycles,'' @i{Journal of Political
Economy}, 100(4), 745--775
@item
Boucekkine, Raouf (1995): ``An alternative methodology for solving
nonlinear forward-looking models,'' @i{Journal of Economic Dynamics
and Control}, 19, 711--734
@item
Brooks, Stephen P., and Andrew Gelman (1998): ``General methods for
monitoring convergence of iterative simulations,'' @i{Journal of
computational and graphical statistics}, 7, pp. 434--455
@item
Collard, Fabrice (2001): ``Stochastic simulations with Dynare: A practical guide''
@item
Collard, Fabrice and Michel Juillard (2001a): ``Accuracy of stochastic
perturbation methods: The case of asset pricing models,'' @i{Journal
of Economic Dynamics and Control}, 25, 979--999
@item
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,'' @i{Computational
Economics}, 17, 125--139
@item
Christiano, Lawrence J., Mathias Trabandt and Karl Walentin (2011):
``Introducing financial frictions and unemployment into a small open
economy model,'' @i{Journal of Economic Dynamics and Control}, 35(12),
1999--2041
@item
Dennis, Richard (2007): ``Optimal Policy In Rational Expectations
Models: New Solution Algorithms,'' @i{Macroeconomic Dynamics}, 11(1),
31--55
@item
Durbin, J. and S. J. Koopman (2001), @i{Time Series Analysis by State
Space Methods}, Oxford University Press
@item
Fair, Ray and John Taylor (1983): ``Solution and Maximum Likelihood
Estimation of Dynamic Nonlinear Rational Expectation Models,''
@i{Econometrica}, 51, 1169--1185
@item
Fernández-Villaverde, Jesús and Juan Rubio-Ramírez (2004): ``Comparing
Dynamic Equilibrium Economies to Data: A Bayesian Approach,''
@i{Journal of Econometrics}, 123, 153--187
@item
Fernández-Villaverde, Jesús and Juan Rubio-Ramírez (2005): ``Estimating
Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood,''
@i{Journal of Applied Econometrics}, 20, 891--910
@item
Ireland, Peter (2004): ``A Method for Taking Models to the Data,''
@i{Journal of Economic Dynamics and Control}, 28, 1205--26
@item
Iskrev, Nikolay (2010): ``Local identification in DSGE models,''
@i{Journal of Monetary Economics}, 57(2), 189--202
@item
Judd, Kenneth (1996): ``Approximation, Perturbation, and Projection
Methods in Economic Analysis'', in @i{Handbook of Computational
Economics}, ed. by Hans Amman, David Kendrick, and John Rust, North
Holland Press, 511--585
@item
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, @i{Couverture Orange}, 9602
@item
Kim, Jinill, Sunghyun Kim, Ernst Schaumburg, and Christopher A. Sims
(2008): ``Calculating and using second-order accurate solutions of
discrete time dynamic equilibrium models,'' @i{Journal of Economic
Dynamics and Control}, 32(11), 3397--3414
@item
Koopman, S. J. and J. Durbin (2003): ``Filtering and Smoothing of
State Vector for Diffuse State Space Models,'' @i{Journal of Time
Series Analysis}, 24(1), 85--98
@item
Laffargue, Jean-Pierre (1990): ``Résolution d'un modèle
macroéconomique avec anticipations rationnelles'', @i{Annales
d'Économie et Statistique}, 17, 97--119
@item
Lubik, Thomas and Frank Schorfheide (2007): ``Do Central Banks Respond
to Exchange Rate Movements? A Structural Investigation,'' @i{Journal
of Monetary Economics}, 54(4), 1069--1087
@item
Mancini-Griffoli, Tommaso (2007): ``Dynare User Guide: An introduction
to the solution and estimation of DSGE models''
@item
Pearlman, Joseph, David Currie, and Paul Levine (1986): ``Rational
expectations models with partial information,'' @i{Economic
Modelling}, 3(2), 90--105
@item
Rabanal, Pau and Juan Rubio-Ramirez (2003): ``Comparing New Keynesian
Models of the Business Cycle: A Bayesian Approach,'' Federal Reserve
of Atlanta, @i{Working Paper Series}, 2003-30.
@item
Ratto, Marco (2008): ``Analysing DSGE models with global sensitivity
analysis'', @i{Computational Economics}, 31, 115--139
@item
Schorfheide, Frank (2000): ``Loss Function-based evaluation of DSGE
models,'' @i{Journal of Applied Econometrics}, 15(6), 645--670
@item
Schmitt-Grohé, Stephanie and Martin Uríbe (2004): ``Solving Dynamic
General Equilibrium Models Using a Second-Order Approximation to the
Policy Function,'' @i{Journal of Economic Dynamics and Control},
28(4), 755--775
@item
Sims, Christopher A., Daniel F. Waggoner and Tao Zha (2008): ``Methods for
inference in large multiple-equation Markov-switching models,''
@i{Journal of Econometrics}, 146, 255--274
@item
Smets, Frank and Rafael Wouters (2003): ``An Estimated Dynamic
Stochastic General Equilibrium Model of the Euro Area,'' @i{Journal of
the European Economic Association}, 1(5), 1123--1175
@item
Villemot, Sébastien (2011): ``Solving rational expectations models at
first order: what Dynare does,'' @i{Dynare Working Papers}, 2,
CEPREMAP
@end itemize
@node Command and Function Index
@unnumbered Command and Function Index
@printindex fn
@node Variable Index
@unnumbered Variable Index
@printindex vr
@bye