10664 lines
347 KiB
Plaintext
10664 lines
347 KiB
Plaintext
\input texinfo
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@c %**start of header
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@setfilename dynare.info
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@documentencoding UTF-8
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@settitle Dynare Reference Manual
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@afourwide
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@dircategory Math
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@direntry
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* Dynare: (dynare). A platform for handling a wide class
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of economic models.
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@end direntry
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@include version.texi
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@c Define some macros
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@macro descriptionhead
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@ifnothtml
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@sp 1
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@end ifnothtml
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@emph{Description}
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||
@end macro
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||
@macro optionshead
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@iftex
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||
@sp 1
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@end iftex
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@emph{Options}
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||
@end macro
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||
|
||
@macro flagshead
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@iftex
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||
@sp 1
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@end iftex
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@emph{Flags}
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@end macro
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@macro examplehead
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@iftex
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@sp 1
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@end iftex
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@emph{Example}
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@end macro
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@macro exampleshead
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@iftex
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@sp 1
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@end iftex
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@emph{Examples}
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||
@end macro
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||
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@macro remarkhead
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@iftex
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@sp 1
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@end iftex
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@noindent @emph{Remark}
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@end macro
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@macro outputhead
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@iftex
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@sp 1
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@end iftex
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@emph{Output}
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||
@end macro
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||
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||
@macro algorithmhead
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@iftex
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@sp 1
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@end iftex
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@emph{Algorithm}
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||
@end macro
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||
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@macro algorithmshead
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@iftex
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@sp 1
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@end iftex
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@emph{Algorithms}
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||
@end macro
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||
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||
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||
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@macro customhead{title}
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@iftex
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@sp 1
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@end iftex
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||
@emph{\title\}
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||
@end macro
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||
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@macro dates
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@code{dates }
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@end macro
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@macro dseries
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@code{dseries }
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@end macro
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@c %**end of header
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@copying
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Copyright @copyright{} 1996-2013, Dynare Team.
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@quotation
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Permission is granted to copy, distribute and/or modify this document
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under the terms of the GNU Free Documentation License, Version 1.3 or
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any later version published by the Free Software Foundation; with no
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Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
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A copy of the license can be found at @uref{http://www.gnu.org/licenses/fdl.txt}.
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@end quotation
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@end copying
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@titlepage
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@title Dynare
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@subtitle Reference Manual, version @value{VERSION}
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@author Stéphane Adjemian
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@author Houtan Bastani
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@author Frédéric Karamé
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@author Michel Juillard
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@author Junior Maih
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@author Ferhat Mihoubi
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@author George Perendia
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@author Johannes Pfeifer
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@author Marco Ratto
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@author Sébastien Villemot
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@page
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@vskip 0pt plus 1filll
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@insertcopying
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@end titlepage
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@contents
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@ifnottex
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@node Top
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@top Dynare
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This is Dynare Reference Manual, version @value{VERSION}.
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@insertcopying
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@end ifnottex
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@menu
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* Introduction::
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* Installation and configuration::
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* Running Dynare::
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* The Model file::
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* The Configuration File::
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* Time Series::
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* Reporting::
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||
* Examples::
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||
* Dynare internal documentation and unitary tests::
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||
* Bibliography::
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* Command and Function Index::
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||
* Variable Index::
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||
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@detailmenu
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||
--- The Detailed Node Listing ---
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||
|
||
Introduction
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||
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* What is Dynare ?::
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* Documentation sources::
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* Citing Dynare in your research::
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||
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Installation and configuration
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||
|
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* Software requirements::
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||
* Installation of Dynare::
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* Configuration::
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||
|
||
Installation of Dynare
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|
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* On Windows::
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* On Debian GNU/Linux and Ubuntu::
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* On Mac OS X::
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* For other systems::
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||
|
||
Configuration
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||
|
||
* For MATLAB::
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||
* For GNU Octave::
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* Some words of warning::
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||
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||
Running Dynare
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* Dynare invocation::
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||
* Dynare hooks::
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* Understanding Preprocessor Error Messages::
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||
|
||
The Model file
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||
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||
* Conventions::
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||
* Variable declarations::
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* Expressions::
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* Parameter initialization::
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* Model declaration::
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* Auxiliary variables::
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||
* Initial and terminal conditions::
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||
* Shocks on exogenous variables::
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* Other general declarations::
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||
* Steady state::
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||
* Getting information about the model::
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* Deterministic simulation::
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||
* Stochastic solution and simulation::
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* Estimation::
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* Forecasting::
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* Optimal policy::
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||
* Sensitivity and identification analysis::
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||
* Markov-switching SBVAR::
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||
* Displaying and saving results::
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||
* Macro-processing language::
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||
* Verbatim inclusion::
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||
* Misc commands::
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||
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||
Expressions
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||
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||
* Parameters and variables::
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||
* Operators::
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||
* Functions::
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||
* A few words of warning in stochastic context::
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||
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Parameters and variables
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||
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||
* Inside the model::
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* Outside the model::
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||
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Functions
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||
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* Built-in Functions::
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* External Functions::
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||
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||
Steady state
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||
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||
* Finding the steady state with Dynare nonlinear solver::
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||
* Using a steady state file::
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||
* Replace some equations during steady state computations::
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Stochastic solution and simulation
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||
* Computing the stochastic solution::
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||
* Typology and ordering of variables::
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||
* First order approximation::
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||
* Second order approximation::
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||
* Third order approximation::
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||
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||
Sensitivity and identification analysis
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||
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||
* Sampling::
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||
* Stability Mapping::
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||
* Reduced Form Mapping::
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||
* RMSE::
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||
* Screening Analysis::
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||
* Identification Analysis::
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||
* Performing Sensitivity and Identification Analysis::
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||
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||
Macro-processing language
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||
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||
* Macro expressions::
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||
* Macro directives::
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||
* Typical usages::
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||
* MATLAB/Octave loops versus macro-processor loops::
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||
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||
Typical usages
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||
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||
* Modularization::
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||
* Indexed sums or products::
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* Multi-country models::
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* Endogeneizing parameters::
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The Configuration File
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* Dynare Configuration::
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* Parallel Configuration::
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Time Series
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* Dates::
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* dseries class::
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||
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Dates
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* dates in a mod file::
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* dates class::
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@end detailmenu
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||
@end menu
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||
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@node Introduction
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@chapter Introduction
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@menu
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* What is Dynare ?::
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||
* Documentation sources::
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||
* Citing Dynare in your research::
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||
@end menu
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||
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@node What is Dynare ?
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@section What is Dynare ?
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Dynare is a software platform for handling a wide class of economic
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models, in particular dynamic stochastic general equilibrium (DSGE)
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and overlapping generations (OLG) models. The models solved by Dynare
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include those relying on the @i{rational expectations} hypothesis, wherein
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agents form their expectations about the future in a way consistent
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with the model. But Dynare is also able to handle models where
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expectations are formed differently: on one extreme, models where
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agents perfectly anticipate the future; on the other extreme, models
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where agents have limited rationality or imperfect knowledge of the
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state of the economy and, hence, form their expectations through a
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learning process. In terms of types of agents, models solved by Dynare
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can incorporate consumers, productive firms, governments, monetary
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authorities, investors and financial intermediaries. Some degree of
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heterogeneity can be achieved by including several distinct classes of
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agents in each of the aforementioned agent categories.
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Dynare offers a user-friendly and intuitive way of describing these
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models. It is able to perform simulations of the model given a
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calibration of the model parameters and is also able to estimate these
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parameters given a dataset. In practice, the user will write a text
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file containing the list of model variables, the dynamic equations
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linking these variables together, the computing tasks to be performed
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and the desired graphical or numerical outputs.
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A large panel of applied mathematics and computer science techniques
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are internally employed by Dynare: multivariate nonlinear solving and
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optimization, matrix factorizations, local functional approximation,
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Kalman filters and smoothers, MCMC techniques for Bayesian estimation,
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graph algorithms, optimal control, @dots{}
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Various public bodies (central banks, ministries of economy and
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finance, international organisations) and some private financial
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institutions use Dynare for performing policy analysis exercises and
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as a support tool for forecasting exercises. In the academic world,
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Dynare is used for research and teaching purposes in postgraduate
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macroeconomics courses.
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||
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||
Dynare is a free software, which means that it can be downloaded free
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of charge, that its source code is freely available, and that it can
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be used for both non-profit and for-profit purposes. Most of the
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||
source files are covered by the GNU General Public Licence (GPL)
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version 3 or later (there are some exceptions to this, see the file
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@file{license.txt} in Dynare distribution). It is available for the
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Windows, Mac and Linux platforms and is fully documented through a
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user guide and a reference manual. Part of Dynare is programmed in
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C++, while the rest is written using the
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@uref{http://www.mathworks.com/products/matlab/, MATLAB} programming
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||
language. The latter implies that commercially-available MATLAB
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software is required in order to run Dynare. However, as an
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||
alternative to MATLAB, Dynare is also able to run on top of
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||
@uref{http://www.octave.org, GNU Octave} (basically a free clone of
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MATLAB): this possibility is particularly interesting for students or
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institutions who cannot afford, or do not want to pay for, MATLAB and
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||
are willing to bear the concomitant performance loss.
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||
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||
The development of Dynare is mainly done at
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@uref{http://www.cepremap.ens.fr, Cepremap} by a core team of
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researchers who devote part of their time to software development.
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||
Currently the development team of Dynare is composed of Stéphane
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Adjemian (Université du Maine, Gains and Cepremap), Houtan Bastani
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(Cepremap), Michel Juillard (Banque de France), Frédéric Karamé
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||
(Université du Maine, Gains and Cepremap), Junior Maih (Norges Bank),
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||
Ferhat Mihoubi (Université Paris-Est Créteil, Epee and Cepremap), George
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Perendia, Johannes Pfeifer (University of Mannheim), Marco Ratto (JRC)
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||
and Sébastien Villemot (Cepremap).
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||
Increasingly, the developer base is expanding, as tools developed by
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researchers outside of Cepremap are integrated into Dynare. Financial
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support is provided by Cepremap, Banque de France and DSGE-net (an
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||
international research network for DSGE modeling). The Dynare project
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||
also received funding through the Seventh Framework Programme for
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Research (FP7) of the European Commission's Socio-economic Sciences
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||
and Humanities (SSH) Program from October 2008 to September 2011 under
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grant agreement SSH-CT-2009-225149.
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||
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||
Interaction between developers and users of Dynare is central to the
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||
project. A @uref{http://www.dynare.org/phpBB3, web forum} is available
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||
for users who have questions about the usage of Dynare or who want to
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report bugs. Training sessions are given through the Dynare Summer
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||
School, which is organized every year and is attended by about 40
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||
people. Finally, priorities in terms of future developments and
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||
features to be added are decided in cooperation with the institutions
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||
providing financial support.
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||
|
||
@node Documentation sources
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||
@section Documentation sources
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||
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||
The present document is the reference manual for Dynare. It documents
|
||
all commands and features in a systematic fashion.
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||
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||
New users should rather begin with Dynare User Guide (@cite{Mancini
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(2007)}), distributed with Dynare and also available from the
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@uref{http://www.dynare.org,official Dynare web site}.
|
||
|
||
Other useful sources of information include the
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||
@uref{http://www.dynare.org,Dynare wiki} and the
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||
@uref{http://www.dynare.org/phpBB3, Dynare forums}.
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||
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||
@node Citing Dynare in your research
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||
@section Citing Dynare in your research
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||
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||
If you would like to refer to Dynare in a research article, the
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recommended way is to cite the present manual, as follows:
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||
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||
@quotation
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||
Stéphane Adjemian, Houtan Bastani, Michel Juillard, Frédéric Karamé,
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Ferhat Mihoubi, George Perendia, Johannes Pfeifer, Marco Ratto and
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||
Sébastien Villemot (2011), ``Dynare: Reference Manual, Version 4,''
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@i{Dynare Working Papers}, 1, CEPREMAP
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||
@end quotation
|
||
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||
Note that citing the Dynare Reference Manual in your research is a
|
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good way to help the Dynare project.
|
||
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||
If you want to give a URL, use the address of the Dynare website:
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||
@uref{http://www.dynare.org}.
|
||
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||
@node Installation and configuration
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||
@chapter Installation and configuration
|
||
|
||
@menu
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||
* Software requirements::
|
||
* Installation of Dynare::
|
||
* Configuration::
|
||
@end menu
|
||
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||
@node Software requirements
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||
@section Software requirements
|
||
|
||
Packaged versions of Dynare are available for Windows XP/Vista/7/8,
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@uref{http://www.debian.org,Debian GNU/Linux},
|
||
@uref{http://www.ubuntu.com/,Ubuntu} and Mac OS X Leopard/Snow
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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
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||
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
|
||
@vindex M_.lead_lag_incidence
|
||
Contains the dynamic model equations. Note that Dynare might introduce auxiliary equations and variables (@pxref{Auxiliary variables}). Outputs are the residuals of the dynamic model equations in the order the equations were declared and the Jacobian of the dynamic model equations. For higher order approximations also the Hessian and the third-order derivates are provided. When computing the Jacobian of the dynamic model, the order of the endogenous variables in the columns is stored in @code{M_.lead_lag_incidence}. The rows of this matrix represent time periods: the first row denotes a lagged (time t-1) variable, the second row a contemporaneous (time t) variable, and the third row a leaded (time t+1) variable. The colums of the matrix represent the endogenous variables in their order of declaration. A zero in the matrix means that this endogenous does not appear in the model in this time period. The value in the @code{M_.lead_lag_incidence} matrix corresponds to the column of that variable in the Jacobian of the dynamic model. Example: Let the second declared variable be @code{c} and the @code{(3,2)} entry of @code{M_.lead_lag_incidence} be @code{15}. Then the @code{15}th column of the Jacobian is the derivative with respect to @code{y(+1)}.
|
||
|
||
@item @var{FILENAME}_static.m
|
||
Contains the long run static model equations. Note that Dynare might introduce auxiliary equations and variables (@pxref{Auxiliary variables}). Outputs are the residuals of the static model equations in the order the equations were declared and the Jacobian of the static equations. Entry @code{(i,j)} of the Jacobian represents the derivative of the @code{i}th static model equation with respect to the @code{j}th model variable in declaration order.
|
||
@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 nograph
|
||
Activate the @code{nograph} option (@pxref{nograph}), so that Dynare will not produce any
|
||
graph
|
||
|
||
@item nointeractive
|
||
Instructs Dynare to not request user input
|
||
|
||
@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}).
|
||
|
||
@item nostrict
|
||
Allows Dynare to issue a warning and continue processing when
|
||
@enumerate
|
||
@item there are more endogenous variables than equations
|
||
@item an undeclared symbol is assigned in @code{initval} or @code{endval}
|
||
@end enumerate
|
||
@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: <<file.mod>>: line A, col B: <<error message>>}
|
||
@item @code{ERROR: <<file.mod>>: line A, cols B-C: <<error message>>}
|
||
@item @code{ERROR: <<file.mod>>: line A, col B - line C, col D: <<error message>>}
|
||
@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:
|
||
<<file.mod>>: 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::
|
||
* Verbatim inclusion::
|
||
* 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.
|
||
|
||
Note that Dynare internally always uses the ``stock at the end of the period''
|
||
concept, even when the model has been entered using the
|
||
@code{predetermined_variables}-command. Thus, when plotting,
|
||
computing or simulating variables, Dynare will follow the convention to
|
||
use variables that are decided in the current period. For example,
|
||
when generating impulse response functions for capital, Dynare
|
||
will plot @code{k}, which is the capital stock decided upon by
|
||
investment today (and which will be used in tomorrow's production function).
|
||
This is the reason that capital is shown to be moving on impact, because
|
||
it is @code{k} and not the predetermined @code{k(-1)} that is displayed.
|
||
It is important to remember that this also affects simulated time
|
||
series and output from smoother routines for predetermined variables.
|
||
Compared to non-predetermined variables they might otherwise appear
|
||
to be falsely shifted to the future by one period.
|
||
@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
|
||
|
||
@anchor{equation_tag_for_conditional_steady_state}
|
||
@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 strictly 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%.
|
||
|
||
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.
|
||
|
||
@item loglinear
|
||
@xref{loglinear}.
|
||
|
||
@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 ordered 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 stylized 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
|
||
|
||
Of course, the shown form of the approximation is only stylized, because it neglects the required different ordering in @math{y^s} and @math{y^h_t}. The precise form of the approximation that shows the way Dynare deals with differences between declaration and DR-order, is
|
||
|
||
@math{y_t(oo\_.dr.order\_var) = y^s(oo\_.dr.order\_var) + A \cdot y_{t-1}(oo\_.dr.order\_var(k2))-y^s(oo\_.dr.order\_var(k2)) + B\cdot u_t}
|
||
|
||
where @math{k2} selects the state variables, @math{y_t} and @math{y^s} are in declaration order and the coefficient matrices are in DR-order. Effectively, all variables on the right hand side are brought into DR order for computations and then assigned to @math{y_t} in declaration order.
|
||
|
||
@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. For the reordering required due to differences in declaration and DR order, see the first order approximation.
|
||
|
||
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 the posterior mode optimizer or the
|
||
maximum likelihood estimation. If unset, defaults to the prior mean.
|
||
|
||
@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) diagnostics are generated
|
||
by the estimation command if @ref{mh_replic} is larger than 2000 and if
|
||
option @ref{nodiagnostic} is not used. If @ref{mh_nblocks} is equal to one,
|
||
the convergence diagnostics of @cite{Geweke (1992,1999)} is computed. It uses a
|
||
chi square test to compare the means of the first and last draws specified by
|
||
@ref{geweke_interval} after discarding the burnin of @ref{mh_drop}. The test is
|
||
computed using variance estimates under the assumption of no serial correlation
|
||
as well as using tapering windows specified in @ref{taper_steps}.
|
||
If @ref{mh_nblocks} is larger than 1, the convergence diagnostics of
|
||
@cite{Brooks and Gelman (1998)} are used instead.
|
||
As described in section 3 of @cite{Brooks and Gelman (1998)} the univariate
|
||
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. These first observations are used as a training sample. 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}
|
||
@anchor{mh_drop}
|
||
The fraction of initially generated parameter vectors to be dropped as a burnin before using posterior simulations. Default: @code{0.5}
|
||
|
||
@item mh_jscale = @var{DOUBLE}
|
||
@anchor{mh_jscale}
|
||
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}
|
||
@anchor{mode_compute}
|
||
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 10
|
||
Uses the simpsa algorithm, based on the combination of the non-linear simplex and simulated annealing algorithms and proposed by
|
||
@cite{Cardoso, Salcedo and Feyo de Azevedo (1996)}.
|
||
|
||
@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 mcmc_jumping_covariance = hessian|prior_variance|identity_matrix|@var{FILENAME}
|
||
Tells Dynare which covariance to use for the proposal density of the MCMC sampler. @code{mcmc_jumping_covariance} can be one of the following:
|
||
|
||
@table @code
|
||
@item hessian
|
||
Uses the Hessian matrix computed at the mode.
|
||
|
||
@item prior_variance
|
||
Uses the prior variances. No infinite prior variances are allowed in this case.
|
||
|
||
@item identity_matrix
|
||
Uses an identity matrix.
|
||
|
||
@item @var{FILENAME}
|
||
Loads an arbitrary user-specified covariance matrix from @code{@var{FILENAME}.mat}. The covariance matrix must be saved in a variable named @code{jumping_covariance}, must be square, positive definite, and have the same dimension as the number of estimated parameters.
|
||
|
||
@end table
|
||
@noindent
|
||
Note that the covariance matrices are still scaled with @ref{mh_jscale}. Default value is @code{hessian}.
|
||
|
||
@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 mode_check_number_of_points = @var{INTEGER}
|
||
Number of points around the posterior mode where the posterior kernel is evaluated (for each parameter). Default is @code{20}
|
||
|
||
@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{NAME}, @var{VALUE}, ...)
|
||
A list of @var{NAME} and @var{VALUE} pairs. Can be used to set options for the optimization routines. The set of available options depends on the selected optimization routine (ie on the value of option @ref{mode_compute}):
|
||
|
||
@table @code
|
||
|
||
@item 1, 3, 7
|
||
Available options are given in the documentation of the MATLAB optimization toolbox or in Octave's documentation.
|
||
|
||
@item 4
|
||
Available options are:
|
||
|
||
@table @code
|
||
|
||
@item 'MaxIter'
|
||
Maximum number of iterations. Default: @code{1000}
|
||
|
||
@item 'NumgradAlgorithm'
|
||
Possible values are @code{2}, @code{3} and @code{5} respectively corresponding to the two, three and five points formula used to compute the gradient of the objective function (see @cite{Abramowitz and Stegun (1964)}). Values @code{13} and @code{15} are more experimental. If perturbations on the right and the left increase the value of the objective function (we minimize this function) then we force the corresponding element of the gradient to be zero. The idea is to temporarly reduce the size of the optimization problem. Default: @code{2}.
|
||
|
||
@item 'NumgradEpsilon'
|
||
Size of the perturbation used to compute numerically the gradient of the objective function. Default: @code{1e-6}
|
||
|
||
@item 'TolFun'
|
||
Stopping criteria. Default: @code{1e-7}
|
||
|
||
@item 'InitialInverseHessian'
|
||
Initial approximation for the inverse of the Hessian matrix of the posterior kernel (or likelihood). Obviously this approximation has to be a square, positive definite and symmetric matrix. Default: @code{'1e-4*eye(nx)'}, where @code{nx} is the number of parameters to be estimated.
|
||
|
||
@end table
|
||
|
||
@item 6
|
||
Available options are:
|
||
|
||
@table @code
|
||
|
||
@item 'NumberOfMh'
|
||
Number of MCMC run sequentially. Default: @code{3}
|
||
|
||
@item 'ncov-mh'
|
||
Number of iterations used for updating the covariance matrix of the jumping distribution. Default: @code{20000}
|
||
|
||
@item 'nscale-mh'
|
||
Maximum number of iterations used for adjusting the scale parameter of the jumping distribution. @code{200000}
|
||
|
||
@item 'nclimb'
|
||
Number of iterations in the last MCMC (climbing mode).
|
||
|
||
@item 'InitialCovarianceMatrix'
|
||
Initial covariance matrix of the jumping distribution. Default is @code{'previous'} if option @code{mode_file} is used, @code{'prior'} otherwise.
|
||
|
||
@item 'AcceptanceRateTarget'
|
||
A real number between zero and one. The scale parameter of the jumping distribution is adjusted so that the effective acceptance rate matches the value of option @code{'AcceptanceRateTarget'}. Default: @code{1.0/3.0}
|
||
|
||
@end table
|
||
|
||
@item 8
|
||
Available options are:
|
||
|
||
@table @code
|
||
|
||
@item 'MaxIter'
|
||
Maximum number of iterations. Default: @code{5000}
|
||
|
||
@item 'MaxFunEvals'
|
||
Maximum number of objective function evaluations. No default.
|
||
|
||
@item 'MaxFunvEvalFactor'
|
||
Set @code{MaxFunvEvals} equal to @code{MaxFunvEvalFactor} times the number of estimated parameters. Default: @code{500}.
|
||
|
||
@item 'TolFun'
|
||
Tolerance parameter (w.r.t the objective function). Default: @code{1e-4}
|
||
|
||
@item 'TolX'
|
||
Tolerance parameter (w.r.t the instruments). Default: @code{1e-4}
|
||
|
||
@item 'InitialSimplexSize'
|
||
|
||
Initial size of the simplex, expressed as percentage deviation from the provided initial guess in each direction. Default: @code{.05}
|
||
|
||
@end table
|
||
|
||
@item 9
|
||
Available options are:
|
||
|
||
@table @code
|
||
|
||
@item 'MaxIter'
|
||
Maximum number of iterations.
|
||
|
||
@item 'MaxFunEvals'
|
||
Maximum number of objective function evaluations. Default: @code{Inf}.
|
||
|
||
@item 'TolFun'
|
||
Tolerance parameter (w.r.t the objective function). Default: @code{1e-7}
|
||
|
||
@item 'TolX'
|
||
Tolerance parameter (w.r.t the instruments). Default: @code{1e-7}
|
||
|
||
@end table
|
||
|
||
@item 10
|
||
Available options are:
|
||
|
||
@table @code
|
||
|
||
@item 'MaxIter'
|
||
Maximum number of iterations. Default: @code{5000}
|
||
|
||
@item 'MaxFunvEvals'
|
||
Maximum number of objective function evaluations. No default.
|
||
|
||
@item 'TolFun'
|
||
Tolerance parameter (w.r.t the objective function). Default: @code{1e-4}
|
||
|
||
@item 'TolX'
|
||
Tolerance parameter (w.r.t the instruments). Default: @code{1e-4}
|
||
|
||
@item 'EndTemperature'
|
||
Terminal condition w.r.t the temperature. When the temperature reaches @code{EndTemperature}, the temperature is set to zero and the algorithm falls back into a standard simplex algorithm. Default: @code{.1}
|
||
|
||
@end table
|
||
|
||
@end table
|
||
|
||
@customhead{Example 1}
|
||
To change the defaults of csminwel (@code{mode_compute=4}):
|
||
|
||
@code{estimation(..., mode_compute=4, optim=('NumgradAlgorithm',3,'TolFun',1e-5), ...);}
|
||
|
||
|
||
@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{diffuse_filter} is used the @code{lik_init} option of
|
||
@code{estimation} has no effect.
|
||
|
||
When there are nonstationary exogenous variables in a model, there is no unique deterministic steady state. For instance, if productivity is a pure random walk:
|
||
|
||
@math{a_t = a_{t-1} + e_t}
|
||
|
||
any value of @math{\bar a} of @math{a} is a deterministic steady state for productivity. Consequently, the model admits an infinity of steady states. In this situation, the user must help Dynare in selecting one steady state, except if zero is a trivial model's steady state, which happens when the @code{linear} option is used in the model declaration. The user can either provide the steady state to Dynare using a @code{steady_state_model} block (or writing a steady state file) if a closed form solution is available, @pxref{steady_state_model}, or specify some constraints on the steady state, @pxref{equation_tag_for_conditional_steady_state}, so that Dynare computes the steady state conditionally on some predefined levels for the non stationary variables. In both cases, the idea is to use dummy values for the steady state level of the exogenous non stationary variables.
|
||
|
||
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}.
|
||
|
||
@item taper_steps = [@var{INTEGER1} @var{INTEGER2} @dots{}]
|
||
@anchor{taper_steps}
|
||
Percent tapering used for the spectral window in the @cite{Geweke (1992,1999)}
|
||
convergence diagnostics (requires @ref{mh_nblocks}=1). The tapering is used to
|
||
take the serial correlation of the posterior draws into account. Default: @code{[4 8 15]}.
|
||
|
||
@item geweke_interval = [@var{DOUBLE} @var{DOUBLE}]
|
||
@anchor{geweke_interval}
|
||
Percentage of MCMC draws at the beginning and end of the MCMC chain taken
|
||
to compute the @cite{Geweke (1992,1999)} convergence diagnostics (requires @ref{mh_nblocks}=1)
|
||
after discarding the first @ref{mh_drop} percent of draws as a burnin. Default: @code{[0.2 0.5]}.
|
||
|
||
@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
|
||
|
||
@defvr {MATLAB/Octave variable} oo_.convergence.geweke
|
||
@anchor{convergence.geweke}
|
||
Variable set by the convergence diagnostics of the @code{estimation} command when used with @ref{mh_nblocks}=1 option (@pxref{mh_nblocks}).
|
||
|
||
Fields are of the form:
|
||
@example
|
||
@code{oo_.convergence.geweke.@var{VARIABLE_NAME}.@var{DIAGNOSTIC_OBJECT}}
|
||
@end example
|
||
where @var{DIAGNOSTIC_OBJECT} is one of the following:
|
||
|
||
@table @code
|
||
|
||
@item posteriormean
|
||
Mean of the posterior parameter distribution
|
||
|
||
@item posteriorstd
|
||
Standard deviation of the posterior parameter distribution
|
||
|
||
@item nse_iid
|
||
Numerical standard error (NSE) under the assumption of iid draws
|
||
|
||
@item rne_iid
|
||
Relative numerical efficiency (RNE) under the assumption of iid draws
|
||
|
||
@item nse_x
|
||
Numerical standard error (NSE) when using an x% taper
|
||
|
||
@item rne_x
|
||
Relative numerical efficiency (RNE) when using an x% taper
|
||
|
||
@item pooled_mean
|
||
Mean of the parameter when pooling the beginning and end parts of the chain
|
||
specified in @ref{geweke_interval} and weighting them with their relative precision.
|
||
It is a vector containing the results under the iid assumption followed by the ones
|
||
using the @ref{taper_steps} (@pxref{taper_steps}).
|
||
|
||
@item pooled_nse
|
||
NSE of the parameter when pooling the beginning and end parts of the chain and weighting them with their relative precision. See @code{pooled_mean}
|
||
|
||
@item prob_chi2_test
|
||
p-value of a chi squared test for equality of means in the beginning and the end
|
||
of the MCMC chain. See @code{pooled_mean}. A value above 0.05 indicates that
|
||
the null hypothesis of equal means and thus convergence cannot be rejected
|
||
at the 5 percent level. Differing values along the @ref{taper_steps} signal
|
||
the presence of significant autocorrelation in draws. In this case, the
|
||
estimates using a higher tapering are usually more reliable.
|
||
|
||
@end table
|
||
@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 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
|
||
|
||
@outputhead
|
||
|
||
The results are not stored in the @code{oo_} structure but in a separate structure @code{forecasts} saved to the harddisk into a file called @code{conditional_forecasts.mat}.
|
||
|
||
@defvr {MATLAB/Octave variable} forecasts.cond
|
||
Variable set by the @code{conditional_forecast} command. It stores the conditional forecasts. Fields are @code{periods+1} by 1 vectors storing the steady state (time 0) and the subsequent @code{periods} forecasts periods. Fields are of the form:
|
||
@example
|
||
@code{forecasts.cond.@var{FORECAST_MOMENT}.@var{VARIABLE_NAME}}
|
||
@end example
|
||
where @var{FORECAST_MOMENT} is one of the following:
|
||
|
||
@table @code
|
||
|
||
@item Mean
|
||
Mean of the conditional forecast distribution.
|
||
|
||
@item ci
|
||
Confidence interval of the conditional forecast distribution. The size corresponds to @code{conf_sig}.
|
||
@end table
|
||
|
||
@end defvr
|
||
|
||
@defvr {MATLAB/Octave variable} forecasts.uncond
|
||
Variable set by the @code{conditional_forecast} command. It stores the unconditional forecasts. Fields are of the form:
|
||
@example
|
||
@code{forecasts.uncond.@var{FORECAST_MOMENT}.@var{VARIABLE_NAME}}
|
||
@end example
|
||
@end defvr
|
||
|
||
@defvr {MATLAB/Octave variable} forecasts.instruments
|
||
Variable set by the @code{conditional_forecast} command. Stores the names of the exogenous instruments.
|
||
@end defvr
|
||
|
||
@defvr {MATLAB/Octave variable} forecasts.controlled_variables
|
||
Variable set by the @code{conditional_forecast} command. Stores the position of the constrained endogenous variables in declaration order.
|
||
@end defvr
|
||
|
||
@defvr {MATLAB/Octave variable} forecasts.graphs
|
||
Variable set by the @code{conditional_forecast} command. Stores the information for generating the conditional forecast plots.
|
||
@end defvr
|
||
|
||
|
||
@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 the numerical optimizer @code{csminwel} of Chris Sims.
|
||
|
||
@optionshead
|
||
|
||
This command accepts the same options as @code{stoch_simul}
|
||
(@pxref{Computing the stochastic solution}) plus
|
||
|
||
@table @code
|
||
|
||
@item maxit = @var{INTEGER}
|
||
Determines the maximum number of iterations used in the non-linear solver. Default: @code{1000}
|
||
|
||
@item tolf = @var{DOUBLE}
|
||
Convergence criterion for termination based on the function value. Iteration will
|
||
cease when it proves impossible to improve the function value by more than tolf. Default: @code{1e-7}
|
||
@end table
|
||
|
||
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 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{<mod_file>/GSA},
|
||
where @code{<mod_file>.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{<mod_file>_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{<mod_file>_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{<mod_file>_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{<mod_file>_prior_*.fig} and store results
|
||
for stability mapping from prior Monte-Carlo samples:
|
||
@itemize
|
||
@item
|
||
@code{<mod_file>_prior_stab_SA_*.fig}: plots of the Smirnov test analyses
|
||
confronting the cdf of the sample fulfilling Blanchard-Kahn conditions
|
||
with the cdf of the rest of the sample;
|
||
|
||
@item
|
||
@code{<mod_file>_prior_stab_indet_SA_*.fig}: plots of the Smirnov test
|
||
analyses confronting the cdf of the sample producing indeterminacy
|
||
with the cdf of the original prior sample;
|
||
|
||
@item
|
||
@code{<mod_file>_prior_stab_unst_SA_*.fig}: plots of the Smirnov test
|
||
analyses confronting the cdf of the sample producing unstable (explosive
|
||
roots) behavior with the cdf of the original prior sample;
|
||
|
||
@item
|
||
@code{<mod_file>_prior_stable_corr_*.fig}: plots of bivariate projections
|
||
of the sample fulfilling Blanchard-Kahn conditions;
|
||
|
||
@item
|
||
@code{<mod_file>_prior_indeterm_corr_*.fig}: plots of bivariate projections
|
||
of the sample producing indeterminacy;
|
||
|
||
@item
|
||
@code{<mod_file>_prior_unstable_corr_*.fig}: plots of bivariate projections
|
||
of the sample producing instability;
|
||
|
||
@item
|
||
@code{<mod_file>_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{<mod_file>_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{<mod_file>_redform_<endo name>_vs_lags_*.fig}: shows bar charts
|
||
of the sensitivity indices for the ten most important parameters driving
|
||
the reduced form coefficients of the selected endogenous variables
|
||
(@code{namendo}) versus lagged endogenous variables (@code{namlagendo}); suffix
|
||
@code{log} indicates the results for log-transformed entries;
|
||
|
||
@item
|
||
@code{<mod_file>_redform_<endo name>_vs_shocks_*.fig}: shows bar charts
|
||
of the sensitivity indices for the ten most important parameters driving
|
||
the reduced form coefficients of the selected endogenous variables
|
||
(@code{namendo}) versus exogenous variables (@code{namexo}); suffix @code{log}
|
||
indicates the results for log-transformed entries;
|
||
|
||
@item
|
||
@code{<mod_file>_redform_GSA(_log).fig}: shows bar chart of all sensitivity
|
||
indices for each parameter: this allows one to notice parameters that
|
||
have a minor effect for any of the reduced form coefficients.
|
||
@end itemize
|
||
|
||
Detailed results of the analyses are shown in the subfolder @code{<mod_file>/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{<namendo>_vs_<namlagendo>}: for the entries of the transition matrix;
|
||
|
||
@item
|
||
@code{<namendo>_vs_<namexo>}: 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{<mod_file>_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{<mode_file>_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{<mod_file>_rmse_*.fig} store results for the RMSE analysis.
|
||
|
||
@itemize
|
||
@item
|
||
@code{<mod_file>_rmse_prior*.fig}: save results for the analysis using prior
|
||
Monte-Carlo samples;
|
||
|
||
@item
|
||
@code{<mod_file>_rmse_mc*.fig}: save results for the analysis using multivariate
|
||
normal Monte-Carlo samples;
|
||
|
||
@item
|
||
@code{<mod_file>_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{<mod_file>_rmse_prior_*.fig}: for each parameter, plots the cdfs
|
||
corresponding to the best 10% RMSEs of each observed series;
|
||
|
||
@item
|
||
@code{<mod_file>_rmse_prior_dens_*.fig}: for each parameter, plots the
|
||
pdfs corresponding to the best 10% RMESs of each observed series;
|
||
|
||
@item
|
||
@code{<mod_file>_rmse_prior_<name of observedseries>_corr_*.fig}: for
|
||
each observed series plots the bi-dimensional projections of samples
|
||
with the best 10% RMSEs, when the correlation is significant;
|
||
|
||
@item
|
||
@code{<mod_file>_rmse_prior_lnlik*.fig}: for each observed series, plots
|
||
in red the cdf of the log-likelihood corresponding to the best 10%
|
||
RMSEs, in green the cdf of the rest of the sample and in blue the
|
||
cdf of the full sample; this allows one to see the presence of some
|
||
idiosyncratic behavior;
|
||
|
||
@item
|
||
@code{<mod_file>_rmse_prior_lnpost*.fig}: for each observed series, plots
|
||
in red the cdf of the log-posterior corresponding to the best 10% RMSEs,
|
||
in green the cdf of the rest of the sample and in blue the cdf of the full
|
||
sample; this allows one to see idiosyncratic behavior;
|
||
|
||
@item
|
||
@code{<mod_file>_rmse_prior_lnprior*.fig}: for each observed series, plots
|
||
in red the cdf of the log-prior corresponding to the best 10% RMSEs,
|
||
in green the cdf of the rest of the sample and in blue the cdf of the full
|
||
sample; this allows one to see idiosyncratic behavior;
|
||
|
||
@item
|
||
@code{<mod_file>_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{<mod_file>_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{<mod_file>/GSA/SCREEN}. The data file @code{<mod_file>_prior} stores
|
||
all the information of the analysis (Morris sample, reduced form coefficients,
|
||
etc.).
|
||
|
||
Screening analysis merely concerns reduced form coefficients. Similar
|
||
synthetic bar charts as for the reduced form analysis with Monte-Carlo samples are
|
||
saved:
|
||
@itemize
|
||
@item
|
||
@code{<mod_file>_redform_<endo name>_vs_lags_*.fig}: shows bar charts
|
||
of the elementary effect tests for the ten most important parameters
|
||
driving the reduced form coefficients of the selected endogenous variables
|
||
(@code{namendo}) versus lagged endogenous variables (@code{namlagendo});
|
||
|
||
@item
|
||
@code{<mod_file>_redform_<endo name>_vs_shocks_*.fig}: shows bar charts
|
||
of the elementary effect tests for the ten most important parameters
|
||
driving the reduced form coefficients of the selected endogenous variables
|
||
(@code{namendo}) versus exogenous variables (@code{namexo});
|
||
|
||
@item
|
||
@code{<mod_file>_redform_screen.fig}: shows bar chart of all elementary
|
||
effect tests for each parameter: this allows one to identify parameters that
|
||
have a minor effect for any of the reduced form coefficients.
|
||
@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>.mod} file. The default is to use
|
||
@code{<mod_file>} to tag the input (output) files used (produced) by the
|
||
program. Thus, to call any command more than once within a
|
||
@code{<mod_file>.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
|
||
|
||
|
||
@deffn Command sbvar (@var{OPTIONS}@dots{});
|
||
@descriptionhead
|
||
|
||
To be documented. For now, see the wiki: @uref{http://www.dynare.org/DynareWiki/SbvarOptions}
|
||
|
||
@optionshead
|
||
|
||
@table @code
|
||
|
||
@item datafile
|
||
@item freq
|
||
@item initial_year
|
||
@item initial_subperiod
|
||
@item final_year
|
||
@item final_subperiod
|
||
@item data
|
||
@item vlist
|
||
@item vlistlog
|
||
@item vlistper
|
||
@item restriction_fname
|
||
@item nlags
|
||
@item cross_restrictions
|
||
@item contemp_reduced_form
|
||
@item real_pseudo_forecast
|
||
@item no_bayesian_prior
|
||
@item dummy_obs
|
||
@item nstates
|
||
@item indxscalesstates
|
||
@item alpha
|
||
@item beta
|
||
@item gsig2_lmdm
|
||
@item q_diag
|
||
@item flat_prior
|
||
@item ncsk
|
||
@item nstd
|
||
@item ninv
|
||
@item indxparr
|
||
@item indxovr
|
||
@item aband
|
||
@item indxap
|
||
@item apband
|
||
@item indximf
|
||
@item indxfore
|
||
@item foreband
|
||
@item indxgforhat
|
||
@item indxgimfhat
|
||
@item indxestima
|
||
@item indxgdls
|
||
@item eq_ms
|
||
@item cms
|
||
@item ncms
|
||
@item eq_cms
|
||
@item tlindx
|
||
@item tlnumber
|
||
@item cnum
|
||
@item forecast
|
||
@item coefficients_prior_hyperparameters
|
||
|
||
@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_<file_tag>.dat}. Default:
|
||
@code{<mod_file>}
|
||
|
||
@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_<output_file_tag>.out},
|
||
@code{est_intermediate_<output_file_tag>.out}. Default:
|
||
@code{<file_tag>}
|
||
|
||
@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_<file_tag>.out},
|
||
@code{est_intermediate_<file_tag>.out} or @code{init_<file_tag>.dat},
|
||
searched for in sequential order). This functionality can be useful for
|
||
continuing a previous estimation run to ensure convergence was reached
|
||
or for reusing an initialization file. NB: If this option is not passed,
|
||
the files from the previous estimation run will be overwritten. Default:
|
||
@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{<mod_file>}
|
||
|
||
@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{<file_tag>}
|
||
|
||
@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}
|
||
|
||
@item save_draws
|
||
Save all elements of @math{A^0}, @math{A^+}, @math{\xi}, and the
|
||
transition matrix to a file named @code{draws_<<file_tag>>.out} with
|
||
each draw on a separate line. A file that describes how these matrices
|
||
are laid out is contained in
|
||
@code{draws_header_<<file_tag>>.out}. Default: @code{off}
|
||
|
||
@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{<file_tag>}
|
||
|
||
@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{<output_file_tag/Output/Probabilities>}.
|
||
|
||
@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{<output_file_tag/Output/IRF>}, while data files are contained in
|
||
@code{<output_file_tag/IRF>}.
|
||
|
||
@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{<output_file_tag/Output/Forecast>},
|
||
while data files are contained in @code{<output_file_tag/Forecast>}.
|
||
|
||
@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{<output_file_tag/Output/Variance_Decomposition>}, while data files
|
||
are contained in @code{<output_file_tag/Variance_Decomposition>}.
|
||
|
||
@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})
|
||
@item
|
||
getting the length of an array: @code{length} operator (for example:
|
||
@code{length(["a", "b", "c"])} returns @code{3} and, hence,
|
||
@code{1:length(["a", "b", "c"])} is equivalent to integer array
|
||
@code{[1,2,3]})
|
||
@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 Verbatim inclusion
|
||
@section Verbatim inclusion
|
||
|
||
Pass everything contained within the @code{verbatim} block to the @code{<mod_file>.m} file.
|
||
|
||
@deffn Block verbatim ;
|
||
|
||
@descriptionhead
|
||
|
||
By default, whenever Dynare encounters code that is not understood by the parser, it is directly passed to the preprocessor output.
|
||
|
||
In order to force this behavior you can use the @code{verbatim} block. This is useful when the code you want passed to the @code{<mod_file>.m} file contains tokens recognized by the Dynare preprocessor.
|
||
|
||
@examplehead
|
||
|
||
@example
|
||
verbatim;
|
||
% Anything contained in this block will be passed
|
||
% directly to the <modfile>.m file, including comments
|
||
var = 1;
|
||
end;
|
||
@end example
|
||
|
||
@end deffn
|
||
|
||
@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
|
||
|
||
@menu
|
||
* Dates::
|
||
* dseries class::
|
||
@end menu
|
||
|
||
|
||
Dynare provides a Matlab/Octave class for handling time series data, which is
|
||
based on a class for handling dates. Dynare also provides a new type for
|
||
dates, so that the basic user do not have to worry about class and
|
||
methods for dates. Below, you will first find the class and methods
|
||
used for creating and dealing with dates and then the class used for
|
||
using time series.
|
||
|
||
@node Dates
|
||
@section Dates
|
||
|
||
@menu
|
||
* dates in a mod file::
|
||
* dates class::
|
||
@end menu
|
||
|
||
@node dates in a mod file
|
||
@subsection dates in a mod file
|
||
|
||
Dynare understands dates in a mod file. Users can declare annual,
|
||
quaterly, monthly or weekly dates using the following syntax:
|
||
@example
|
||
1990Y
|
||
1990Q3
|
||
1990M11
|
||
1990W49
|
||
@end example
|
||
@noindent Behind the scene, the dynare's preprocessor translates these expressions
|
||
into instantiations of the Matlab/Octave's class @dates described
|
||
below. Basic operations can be performed on dates:
|
||
@table @strong
|
||
|
||
@item plus binary operator (@code{+})
|
||
|
||
An integer scalar, interpreted as a number of periods, can be added to a date. For instance, if @code{a = 1950Q1} then
|
||
@code{b = 1951Q2} and @code{b = a + 5} are identical.
|
||
|
||
@item plus unary operator (@code{+})
|
||
|
||
Increments a date by one period. @code{+1950Q1} is identical to @code{1950Q2}, @code{++++1950Q1} is identical to @code{1951Q1}.
|
||
|
||
@item minus binary operator (@code{-})
|
||
|
||
The difference between two dates is a number of periods. For instance if @code{1951Q2-1950Q1} is equal to @code{5} (quarters).
|
||
|
||
@item minus unary operator (@code{-})
|
||
|
||
Substracts one period to a date. @code{-1950Q1} is identical to @code{1949Q4}. The unary minus operator is the reciprocal of the unary plus operator, @code{+-1950Q1} is identical to @code{1950Q1}.
|
||
|
||
@item colon operator (@code{:})
|
||
|
||
Can be used to create a range of dates. For instance, @code{r = 1950Q1:1951Q1} creates a @dates object with five elements: @code{1950Q1}, @code{1950Q2}, @code{1950Q3}, @code{1950Q4} and @code{1951Q1}. By default the increment between each element is one period. This default can be changed using, for instance, the following instruction: @code{1950Q1:2:1951Q1} which will instantiate a @dates object with three elements: @code{1950Q1}, @code{1950Q3} and @code{1951Q1}.
|
||
|
||
@item horzcat operator (@code{[,]})
|
||
|
||
Concatenates @dates objects without removing repetitions. For instance @code{[1950Q1, 1950Q2]} is a a @dates object with two elements (@code{1950Q1} and @code{1950Q2}).
|
||
|
||
@item vertcat operator (@code{[;]})
|
||
|
||
Same as @code{horzcat} operator.
|
||
|
||
@item eq operator (equal, @code{==})
|
||
|
||
Tests if two @dates objects are equal. @code{+1950Q1==1950Q2} returns @code{1}, @code{1950Q1==1950Q2} returns @code{0}. If the compared objects have both @code{n>1} elements, the @code{eq} operator returns a column vector, @code{n} by @code{1}, of zeros and ones.
|
||
|
||
@item ne operator (not equal, @code{~=})
|
||
|
||
Tests if two @dates objects are not equal. @code{+1950Q1==1950Q2} returns @code{0}, @code{1950Q1==1950Q2} returns @code{1}. If the compared objects have both @code{n>1} elements, the @code{ne} operator returns a column vector, @code{n} by @code{1}, of zeros and ones.
|
||
|
||
@item lt operator (less than, @code{<})
|
||
|
||
Tests if a @dates object preceeds another @dates object. For instance, @code{1950Q1<1950Q3} returns @code{1}. If the compared objects have both @code{n>1} elements, the @code{lt} operator returns a column vector, @code{n} by @code{1}, of zeros and ones.
|
||
|
||
@item gt operator (greater than, @code{>})
|
||
|
||
Tests if a @dates object follows another @dates object. For instance, @code{1950Q1>1950Q3} returns @code{0}. If the compared objects have both @code{n>1} elements, the @code{gt} operator returns a column vector, @code{n} by @code{1}, of zeros and ones.
|
||
|
||
@item le operator (less or equal, @code{<=})
|
||
|
||
Tests if a @dates object preceeds another @dates object or is equal to this object. For instance, @code{1950Q1<=1950Q3} returns @code{1}. If the compared objects have both @code{n>1} elements, the @code{le} operator returns a column vector, @code{n} by @code{1}, of zeros and ones.
|
||
|
||
@item ge operator (greater or equal, @code{>=})
|
||
|
||
Tests if a @dates object follows another @dates object or is equal to this object. For instance, @code{1950Q1>=1950Q3} returns @code{0}. If the compared objects have both @code{n>1} elements, the @code{ge} operator returns a column vector, @code{n} by @code{1}, of zeros and ones.
|
||
|
||
@end table
|
||
|
||
@noindent One can select an element, or some elements, in a @dates object as he would extract some elements from a vector in Matlab/Octave. Let @code{a = 1950Q1:1951Q1} be a @dates object, then @code{a(1)==1950Q1} returns @code{1}, @code{a(end)==1951Q1} returns @code{1} and @code{a(end-1:end)} selects the two last elements of @code{a} (by instantiating the @dates object @code{[1950Q4, 1951Q1]}).
|
||
|
||
@node dates class
|
||
@subsection dates class
|
||
|
||
The @dates class has three members:
|
||
@table @code
|
||
@anchor{dates class members}
|
||
|
||
@item freq
|
||
an integer equal to 1, 4, 12 or 52 (resp. for annual, quaterly, monthly
|
||
or weekly dates).
|
||
|
||
@item ndat
|
||
an integer scalar, the number of declared dates in the object.
|
||
|
||
@item time
|
||
a @code{ndat}*2 array of integers, the years are stored in the first
|
||
column, the subperiods (1 for annual dates, 1-4 for quaterly dates, 1-12
|
||
for monthly dates and 1-52 for weekly dates) are stored in the second
|
||
column.
|
||
|
||
@end table
|
||
@noindent Each member is private, one can display the content of a member but cannot change its value:
|
||
@example
|
||
>> d = dates('2009Q2');
|
||
>> d.time
|
||
|
||
ans =
|
||
|
||
2009 2
|
||
|
||
>>
|
||
@end example
|
||
|
||
@noindent Note that it is not possible to mix frequencies in a @dates object: all the elements must have common frequency. The @dates class has five constructors:
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dates} dates ()
|
||
@deftypefnx {dates} dates (@code{FREQ})
|
||
|
||
Returns an empty @dates object with a given frequency (if the constructor is called with one input argument). @code{FREQ} is a character equal to 'Y' or 'A' for annual dates, 'Q' for quaterly dates, 'M' for monthly dates or 'W' for weekly dates. Note that @code{FREQ} is not case sensitive, so that, for instance, 'q' is also allowed for quaterly dates. The frequency can also be set with an integer scalar equal to 1 (annual), 4 (quaterly), 12 (monthly) or 52 (weekly). The instantiation of empty objects can be used to rename the @dates class. For instance, if one only works with quaterly dates, he can create @code{qq} as:
|
||
@example
|
||
qq = dates('Q')
|
||
@end example
|
||
and a @dates object holding the date @code{2009Q2}:
|
||
@example
|
||
d0 = dates(2009,2);
|
||
@end example
|
||
@noindent which is much simpler if @dates objects have to be defined programatically.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dates} dates (@code{STRING})
|
||
@deftypefnx {dates} dates (@code{STRING}, @code{STRING}, ...)
|
||
|
||
Returns a @dates object that represents a date as given by the string @code{STRING}. This string has to be interpretable as a date (only strings of the following forms are admitted: @code{'1990Y'}, @code{'1990A'}, @code{'1990Q1'}, @code{'1990M2'}, @code{'1990W5'}), the routine @code{isdate} can be used to test if a string is interpretable as a date. If more than one argument is provided, they should all be dates represented as strings, the resulting @dates object contains as many elements as arguments to the constructor.
|
||
|
||
@end deftypefn
|
||
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dates} dates (@code{DATES})
|
||
@deftypefnx {dates} dates (@code{DATES}, @code{DATES}, ...)
|
||
|
||
Returns a copy of the @dates object @code{DATES} passed as input arguments. If more than one argument is provided, they should all be @dates objects. The number of elements in the instantiated @dates object is equal to the sum of the elements in the @dates passed as arguments to the constructor.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dates} dates (@code{FREQ}, @code{YEAR}, @code{SUBPERIOD})
|
||
|
||
where @code{FREQ} is a single character ('Y', 'A', 'Q', 'M', 'W') or integer (1, 4, 12 or 52) specifying the frequency, @code{YEAR} and @code{SUBPERIOD} are @code{n*1} vectors of integers. Returns a @dates object with @code{n} elements. If @code{FREQ} is equal to @code{'Y', 'A'} or @code{1}, the third argument is not needed (because @code{SUBPERIOD} is necessarly a vector of ones in this case).
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@exampleshead
|
||
@example
|
||
do1 = dates('1950Q1');
|
||
do2 = dates('1950Q2','1950Q3');
|
||
do3 = dates(do1,do2);
|
||
do4 = dates('Q',1950, 1);
|
||
@end example
|
||
|
||
@sp 1
|
||
|
||
A list of the available methods, by alphabetical order, is given below. Note that the Matlab/Octave classes do not allow in place modifications: when a method is applied to an object a new object is instantiated. For instance, to apply the method @code{multiplybytwo} to an object @code{X} we write:
|
||
@example
|
||
Y = X.multiplybytwo()
|
||
@end example
|
||
or equivalently:
|
||
@example
|
||
Y = multiplybytwo(X)
|
||
@end example
|
||
the object @code{X} is left unchanged, and the object @code{Y} is a modified copy of @code{X}.
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dates} {@var{B} = } append (@var{A}, @var{a})
|
||
|
||
Appends @dates object @var{a}, or a string that can be interpreted as a date, to the @dates object @var{A}. If @code{a} is a @dates object it is assumed that it has no more than one element.
|
||
|
||
@examplehead
|
||
@example
|
||
>> D = dates('1950Q1','1950Q2');
|
||
>> d = dates('1950Q3');
|
||
>> E = D.append(d);
|
||
>> F = D.append('1950Q3')
|
||
>> isequal(E,F)
|
||
|
||
ans =
|
||
|
||
1
|
||
>> F
|
||
F = <dates: 1950Q1, 1950Q2, 1950Q3>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dates} {@var{C} = } colon (@var{A}, @var{B})
|
||
@deftypefnx {dates} {@var{C} = } colon (@var{A}, @var{i}, @var{B})
|
||
|
||
Overloads the Matlab/Octave colon (:) operator. @var{A} and @var{B} are @dates objects. The optional increment @var{i} is a scalar integer (default value is @code{i=1}). This method returns a @dates object and can be used to create ranges of dates.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1');
|
||
>> B = dates('1951Q2');
|
||
>> C = A:B
|
||
C = <dates: 1950Q1, 1950Q2, 1950Q3, 1950Q4, 1951Q1>
|
||
>> D = A:2:B
|
||
D = <dates: 1950Q1, 1950Q3, 1951Q1>
|
||
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{B} = } double (@var{A})
|
||
|
||
Overloads the Matlab/Octave @code{double} function. @var{A} is a @dates object. The method returns a floating point representation of a @dates object, the integer and fractional parts respectively corresponding to the year and the subperiod. The fractional part is the subperiod number minus one divided by the frequency (@code{1}, @code{4}, @code{12} or @code{52}).
|
||
|
||
|
||
@examplehead
|
||
@example
|
||
>> a = dates('1950Q1'):dates('1950Q4');
|
||
>> a.double()
|
||
|
||
ans =
|
||
|
||
1950.00
|
||
1950.25
|
||
1950.50
|
||
1950.75
|
||
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} eq (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{eq} (equal, @code{==}) operator. @dates objects @var{A} and @var{B} must have the same number of elements (say, @code{n}). The returned argument is a @code{n} by @code{1} vector of zeros and ones. The i-th element of @var{C} is equal to @code{1} if and only if the dates @code{A(i)} and @code{B(i)} are the same.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1','1951Q2');
|
||
>> B = dates('1950Q1','1950Q2');
|
||
>> A==B
|
||
|
||
ans =
|
||
|
||
1
|
||
0
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} ge (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{ge} (greater or equal, @code{>=}) operator. @dates objects @var{A} and @var{B} must have the same number of elements (say, @code{n}). The returned argument is a @code{n} by @code{1} vector of zeros and ones. The i-th element of @var{C} is equal to @code{1} if and only if the date @code{A(i)} is posterior or equal to the date @code{B(i)}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1','1951Q2');
|
||
>> B = dates('1950Q1','1950Q2');
|
||
>> A>=B
|
||
|
||
ans =
|
||
|
||
1
|
||
1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} gt (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{gt} (greater than, @code{>=}) operator. @dates objects @var{A} and @var{B} must have the same number of elements (say, @code{n}). The returned argument is a @code{n} by @code{1} vector of zeros and ones. The i-th element of @var{C} is equal to @code{1} if and only if the date @code{A(i)} is posterior to the date @code{B(i)}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1','1951Q2');
|
||
>> B = dates('1950Q1','1950Q2');
|
||
>> A>B
|
||
|
||
ans =
|
||
|
||
0
|
||
1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{D} =} horzcat (@var{A}, @var{B}, @var{C}, ...)
|
||
|
||
Overloads the Matlab/Octave @code{horzcat} operator. All the input arguments must be @dates objects. The returned argument is a @dates object gathering all the dates given in the input arguments (repetitions are not removed).
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1');
|
||
>> B = dates('1950Q2');
|
||
>> C = [A, B];
|
||
>> C
|
||
C = <dates: 1950Q1, 1950Q2>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} intersect (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{intersect} function. All the input arguments must be @dates objects. The returned argument is a @dates object gathering all the common dates given in the input arguments. If @var{A} and @var{B} are disjoint @dates objects, the function returns an empty @dates object. Returned dates in @dates object @var{C} are sorted by increasing order.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1'):dates('1951Q4');
|
||
>> B = dates('1951Q1'):dates('1951Q4');
|
||
>> C = intersect(A, B);
|
||
>> C
|
||
C = <dates: 1951Q1, 1951Q2, 1951Q3, 1951Q4>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{B} =} isempty (@var{A})
|
||
|
||
Overloads the Matlab/Octave isempty function for @dates object.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1'):dates('1951Q4');
|
||
>> A.isempty()
|
||
|
||
ans =
|
||
|
||
0
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} isequal (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{isequal} function for @dates objects.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1'):dates('1951Q4');
|
||
>> isequal(A,A)
|
||
|
||
ans =
|
||
|
||
1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} le (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{le} (less or equal, @code{<=}) operator. @dates objects @var{A} and @var{B} must have the same number of elements (say, @code{n}). The returned argument is a @code{n} by @code{1} vector of zeros and ones. The i-th element of @var{C} is equal to @code{1} if and only if the date @code{A(i)} is not posterior to the date @code{B(i)}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1','1951Q2');
|
||
>> B = dates('1950Q1','1950Q2');
|
||
>> A<=B
|
||
|
||
ans =
|
||
|
||
1
|
||
0
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{B} =} length (@var{A})
|
||
|
||
Overloads the Matlab/Octave @code{length} function. Returns the number of dates in @dates object @var{A} (@var{B} is a scalar integer).
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1','1951Q2');
|
||
>> A.length()
|
||
|
||
ans =
|
||
|
||
2
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} lt (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{lt} (less than, @code{<=}) operator. @dates objects @var{A} and @var{B} must have the same number of elements (say, @code{n}). The returned argument is a @code{n} by @code{1} vector of zeros and ones. The i-th element of @var{C} is equal to @code{1} if and only if the date @code{A(i)} preceeds the date @code{B(i)}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = dates('1950Q1','1951Q2');
|
||
>> B = dates('1950Q1','1950Q2');
|
||
>> A<B
|
||
|
||
ans =
|
||
|
||
0
|
||
0
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{D} =} max (@var{A}, @var{B}, @var{C}, ...)
|
||
|
||
Overloads the Matlab/Octave @code{max} function. All input arguments must be @dates objects. The function returns a single element @dates object containing the greatest date.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = @{dates('1950Q2'), dates('1953Q4','1876Q2'), dates('1794Q3')@};
|
||
>> max(A@{:@})
|
||
ans = <dates: 1953Q4>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{D} =} min (@var{A}, @var{B}, @var{C}, ...)
|
||
|
||
Overloads the Matlab/Octave @code{min} function. All input arguments must be @dates objects. The function returns a single element @dates object containing the smallest date.
|
||
|
||
@examplehead
|
||
@example
|
||
>> A = @{dates('1950Q2'), dates('1953Q4','1876Q2'), dates('1794Q3')@};
|
||
>> min(A@{:@})
|
||
ans = <dates: 1794Q3>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} minus (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{minus} operator (@code{-}). If both input arguments are @dates objects, then number of periods between @var{A} and @var{B} is returned (so that @code{A+C=B}). If @var{B} is a vector of integers, the @code{minus} operator shifts the @dates object by @var{B} periods backward.
|
||
|
||
@examplehead
|
||
@example
|
||
>> d1 = dates('1950Q1','1950Q2','1960Q1');
|
||
>> d2 = dates('1950Q3','1950Q4','1960Q1');
|
||
>> ee = d2-d1
|
||
|
||
ee =
|
||
|
||
2
|
||
2
|
||
0
|
||
|
||
>> d1-(-ee)
|
||
ans = <dates: 1950Q3, 1950Q4, 1960Q1>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} plus (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{plus} operator (@code{+}). If both input arguments are @dates objects, then the method combines A and B without removing repetitions. If @var{B} is a vector of integers, the @code{plus} operator shifts the @dates object by @var{B} periods forward.
|
||
|
||
@examplehead
|
||
@example
|
||
>> d1 = dates('1950Q1','1950Q2')+dates('1960Q1');
|
||
>> d2 = (dates('1950Q1','1950Q2')+2)+dates('1960Q1');
|
||
>> ee = d2-d1;
|
||
|
||
ee =
|
||
|
||
2
|
||
2
|
||
0
|
||
|
||
>> d1+ee
|
||
ans = <dates: 1950Q3, 1950Q4, 1960Q1>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{C} =} pop (@var{A})
|
||
@deftypefnx{dates} {@var{C} =} pop (@var{A},@var{B})
|
||
|
||
Pop method for @dates class. If only one input is provided, the method removes the last element of a @dates object. If a second input argument is provided, a scalar integer between @code{1} and @code{A.length()}, the method removes element number @var{B} from @dates object @var{A}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> d1 = dates('1950Q1','1950Q2');
|
||
>> d1.pop()
|
||
ans = <dates: 1950Q1>
|
||
|
||
>> d1.pop(1)
|
||
ans = <dates: 1950Q2>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{B} =} sort (@var{A})
|
||
|
||
Sort method for @dates objects. Returns a @dates object with elements sorted by increasing order.
|
||
|
||
@examplehead
|
||
@example
|
||
>> dd = dates('1945Q3','1938Q4','1789Q3');
|
||
>> dd.sort()
|
||
ans = <dates: 1789Q3, 1938Q4, 1945Q3>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{B} =} uminus (@var{A})
|
||
|
||
Overloads the Matlab/Octave unary minus operator. Returns a @dates object with elements shifted one period backward.
|
||
|
||
@examplehead
|
||
@example
|
||
>> dd = dates('1945Q3','1938Q4','1973Q1');
|
||
>> -dd
|
||
ans = <dates: 1945Q2, 1938Q3, 1972Q4>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{D} =} union (@var{A}, @var{B}, @var{C}, ...)
|
||
|
||
Overloads the Matlab/Octave @code{union} function. Returns a @dates object with elements sorted by increasing order (repetitions are removed, to keep the repetitions use the @code{horzcat} or @code{plus} operators).
|
||
|
||
@examplehead
|
||
@example
|
||
>> d1 = dates('1945Q3','1973Q1','1938Q4');
|
||
>> d2 = dates('1973Q1','1976Q1');
|
||
>> union(d1,d2)
|
||
ans = <dates: 1938Q4, 1945Q3, 1973Q1, 1976Q1>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{B} =} unique (@var{A})
|
||
|
||
Overloads the Matlab/Octave @code{unique} function. Returns a @dates object with repetitions removed (only the last occurence of a date is kept).
|
||
|
||
@examplehead
|
||
@example
|
||
>> d1 = dates('1945Q3','1973Q1','1945Q3');
|
||
>> d1.unique()
|
||
ans = <dates: 1973Q1, 1945Q3>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dates} {@var{B} =} uplus (@var{A})
|
||
|
||
Overloads the Matlab/Octave unary plus operator. Returns a @dates object with elements shifted one period ahead.
|
||
|
||
@examplehead
|
||
@example
|
||
>> dd = dates('1945Q3','1938Q4','1973Q1');
|
||
>> +dd
|
||
ans = <dates: 1945Q4, 1939Q1, 1973Q2>
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
|
||
@node dseries class
|
||
@section dseries class
|
||
|
||
The Matlab/Octave @dseries class handles time series data. As any Matlab/Octave statements, this class can be used in a Dynare's mod file. A @dseries object has eight members:
|
||
|
||
@table @code
|
||
@anchor{dseries class members}
|
||
|
||
@item nobs
|
||
A scalar integer, the number of observations.
|
||
|
||
@item vobs
|
||
A scalar integer, the number of variables.
|
||
|
||
@item name
|
||
A cell of strings, the names of the variables.
|
||
|
||
@item tex
|
||
A cell of strings, the tex names of the variables.
|
||
|
||
@item freq
|
||
A scalar integer equal to 1, 4, 12 or 52, the frequency of the dataset.
|
||
|
||
@item init
|
||
A single element @dates object, the initial date of the sample.
|
||
|
||
@item dates
|
||
A @dates object with @code{nobs} element, the dates of the sample.
|
||
|
||
@item data
|
||
A @code{nobs} by @code{vobs} array of doubles, the data.
|
||
|
||
@end table
|
||
|
||
@noindent The following constructors are available:
|
||
|
||
@deftypefn {dseries} dseries ()
|
||
@deftypefnx {dseries} dseries (@var{INITIAL_DATE})
|
||
|
||
Instantiates an empty @dseries object, with, if defined, an initial date given by the single element @dates object @var{INITIAL_DATE} (the frequency is then set accordingly).
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} dseries (@var{FILENAME})
|
||
|
||
Instantiates and populates a @dseries object with a data file specified by @var{FILENAME}, a string passed as input. Valid file types are @file{.m} file, @file{.mat} file, @file{.csv} file, and @file{.xls} file. A typical @file{.m} file will have the following form:
|
||
|
||
@example
|
||
INIT__ = '1994Q3';
|
||
NAMES__ = @{'azert';'yuiop'@};
|
||
TEX__ = @{'azert';'yuiop'@};
|
||
|
||
azert = randn(100,1);
|
||
yuiop = randn(100,1);
|
||
@end example
|
||
|
||
If a @file{.mat} file is used instead, it should provide the same informations. Note that the @code{INIT__} variable can be either a @dates object or a string which could be used to instantiate the same @dates object.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} dseries (@var{DATA_MATRIX}, @var{INITIAL_DATE}, @var{LIST_OF_NAMES}, @var{LIST_OF_TEX_NAMES})
|
||
|
||
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{dseries}' constructor, with @math{T} representing the number of observations on @math{N} variables. The second argument, @var{INITIAL_DATE}, can be either a @dates object representing the period of the first observation or a string which would be used to instantiate a @dates object. The third argument, @var{LIST_OF_NAMES}, is a @math{N} by @math{1} cell of strings with one entry for each variable name. The final argument, @var{LIST_OF_TEX_NAMES}, is a @math{N} by @math{1} cell of strings composed of the @LaTeX{} names associated with the variables. Input arguments two, three and four are optional. The default value for @var{INITIAL_DATE} is @code{1Y}.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@exampleshead
|
||
|
||
Various ways to create a @code{dseries} object:
|
||
|
||
@sp 1
|
||
|
||
@example In a mod file:
|
||
do1 = dseries(1999Q3);
|
||
do2 = dseries(`filename.csv');
|
||
do3 = dseries([1; 2; 3], 1999Q3, @{`var123'@}, @{`var_@{123@}'@});
|
||
@end example
|
||
|
||
@sp 1
|
||
|
||
@example In a Matlab/Octave script:
|
||
>> do1 = dseries(dates('1999Q3'));
|
||
>> do2 = dseries(`filename.csv');
|
||
>> do3 = dseries([1; 2; 3], dates('1999Q3'), @{`var123'@}, @{`var_@{123@}'@});
|
||
@end example
|
||
|
||
@sp 1
|
||
|
||
A list of the available methods, by alphabetical order, is given below.
|
||
|
||
@deftypefn {dseries} {[@var{A}, @var{B}] = } align (@var{A}, @var{B})
|
||
|
||
If @dseries objects @var{A} and @var{B} are defined on different time ranges, this function extends @var{A} and/or @var{B} with NaNs so that they are defined on the same time range. Note that both @dseries objects must have the same frequency.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(rand(5,1),dates('2000Q1')); % 2000Q1 -> 2001Q1
|
||
>> ts1 = dseries(rand(3,1),dates('2000Q4')); % 2000Q4 -> 2001Q2
|
||
>> [ts0, ts1] = align(ts0, ts1); % 2000Q1 -> 2001Q2
|
||
>> ts0
|
||
|
||
ts0 is a dseries object:
|
||
|
||
| Variable_1
|
||
2000Q1 | 0.81472
|
||
2000Q2 | 0.90579
|
||
2000Q3 | 0.12699
|
||
2000Q4 | 0.91338
|
||
2001Q1 | 0.63236
|
||
2001Q2 | NaN
|
||
|
||
>> ts1
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| Variable_1
|
||
2000Q1 | NaN
|
||
2000Q2 | NaN
|
||
2000Q3 | NaN
|
||
2000Q4 | 0.66653
|
||
2001Q1 | 0.17813
|
||
2001Q2 | 0.12801
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {@var{B} = } baxter_king_filter (@var{A}, @var{hf}, @var{lf}, @var{K})
|
||
|
||
Implementation of Baxter and King (1999) band pass filter for @dseries objects. This filter isolates business cycle fluctuations with a period of length ranging between @var{hf} (high frequency) to @var{lf} (low frequency) using a symetric moving average smoother with @math{2K+1} points, so that K observations at the beginning and at the end of the sample are lost in the computation of the filter.
|
||
|
||
@examplehead
|
||
@example
|
||
% Simulate a component model (stochastic trend, deterministic trend, and a
|
||
% stationary autoregressive process).
|
||
e = .2*randn(200,1);
|
||
u = randn(200,1);
|
||
stochastic_trend = cumsum(e);
|
||
deterministic_trend = .1*transpose(1:200);
|
||
x = zeros(200,1);
|
||
for i=2:200
|
||
x(i) = .75*x(i-1) + e(i);
|
||
end
|
||
y = x + stochastic_trend + deterministic_trend;
|
||
|
||
% Instantiates time series objects.
|
||
ts0 = dseries(y,'1950Q1');
|
||
ts1 = dseries(x,'1950Q1'); % stationary component.
|
||
|
||
% Apply the Baxter-King filter.
|
||
ts2 = ts0.baxter_king_filter();
|
||
|
||
% Plot the filtered time series.
|
||
plot(ts1(ts2.dates).data,'-k'); % Plot of the stationary component.
|
||
hold on
|
||
plot(ts2.data,'--r'); % Plot of the filtered y.
|
||
hold off
|
||
axis tight
|
||
id = get(gca,'XTick');
|
||
set(gca,'XTickLabel',strings(ts.dates(id)));
|
||
@end example
|
||
|
||
@iftex
|
||
@sp 1
|
||
The previous code should produce something like:
|
||
@center
|
||
@image{dynare.plots/BaxterKingFilter,11.32cm,7cm}
|
||
@end iftex
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {[@var{error_flag}, @var{message} ] = } check (@var{A})
|
||
|
||
Sanity check of @dseries object @var{A}. Returns @math{1} if there is an error, @math{0} otherwise. The second output argument is a string giving brief informations about the error.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {@var{B} = } cumsum (@var{A}[, @var{d}[, @var{v}]])
|
||
|
||
Overloads the Matlab/Octave @code{cumsum} function for @dseries objects. The cumulated sum cannot be computed if the variables in @dseries object @var{A} have @code{NaN}s. If a @dates object @var{d} is provided as a second argument, then the method computes the cumulated sum with the additional constraint that the variables in the @dseries object @var{B} are zero in period @var{d}. If a single observation @dseries object @var{v} is provided as a third argument, the cumulated sum in @var{B} is such that @code{B(d)} matches @var{v}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts1 = dseries(ones(10,1));
|
||
>> ts2 = ts1.cumsum();
|
||
>> ts2
|
||
|
||
ts2 is a dseries object:
|
||
|
||
| cumsum(Variable_1)
|
||
1Y | 1
|
||
2Y | 2
|
||
3Y | 3
|
||
4Y | 4
|
||
5Y | 5
|
||
6Y | 6
|
||
7Y | 7
|
||
8Y | 8
|
||
9Y | 9
|
||
10Y | 10
|
||
|
||
>> ts3 = cumsum(dates('3Y'));
|
||
>> ts3
|
||
|
||
ts3 is a dseries object:
|
||
|
||
| cumsum(Variable_1)
|
||
1Y | -2
|
||
2Y | -1
|
||
3Y | 0
|
||
4Y | 1
|
||
5Y | 2
|
||
6Y | 3
|
||
7Y | 4
|
||
8Y | 5
|
||
9Y | 6
|
||
10Y | 7
|
||
|
||
>> ts4 = ts1.cumsum(dates('3Y'),dseries(pi));
|
||
>> ts4
|
||
|
||
ts4 is a dseries object:
|
||
|
||
| cumsum(Variable_1)
|
||
1Y | 1.1416
|
||
2Y | 2.1416
|
||
3Y | 3.1416
|
||
4Y | 4.1416
|
||
5Y | 5.1416
|
||
6Y | 6.1416
|
||
7Y | 7.1416
|
||
8Y | 8.1416
|
||
9Y | 9.1416
|
||
10Y | 10.1416
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{C} =} eq (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{eq} (equal, @code{==}) operator. @dseries objects @var{A} and @var{B} must have the same number of observations (say, @math{T}) and variables (@math{N}). The returned argument is a @math{T} by @math{N} matrix of zeros and ones. Element @math{(i,j)} of @var{C} is equal to @code{1} if and only if observation @math{i} for variable @math{j} in @var{A} and @var{B} are the same.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(2*ones(3,1));
|
||
>> ts1 = dseries([2; 0; 2]);
|
||
>> ts0==ts1
|
||
|
||
ans =
|
||
|
||
1
|
||
0
|
||
1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{B} =} exp (@var{A})
|
||
|
||
Overloads the Matlab/Octave @code{exp} function for @dseries objects.
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(rand(10,1));
|
||
>> ts1 = ts0.exp();
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{C} =} extract (@var{A}, @var{B}[, ]...)
|
||
|
||
Extracts some variables from a @dseries object @var{A} and returns a @dseries object @var{C}. The input arguments following @var{A} are strings representing the variables to be selected in the new @dseries object @var{C}. To simplify the creation of sub-objects, the @dseries class overloads the curly braces (@code{D = extract (A, B, C)} is equivalent to @code{D = A@{B,C@}}) and allows implicit loops (defined between a pair of @@ symbol, see examples below) or Matlab/Octave's regular expressions (introduced by square brackets).
|
||
|
||
@exampleshead
|
||
|
||
@noindent The following selections are equivalent:
|
||
@example
|
||
>> ts0 = dseries(ones(100,10));
|
||
>> ts1 = ts0@{'Variable_1','Variable_2','Variable_3'@};
|
||
>> ts2 = ts0@{'Variable_@@1,2,3@@'@}
|
||
>> ts3 = ts0@{'Variable_[1-3]$'@}
|
||
>> isequal(ts1,ts2) && isequal(ts1,ts3)
|
||
|
||
ans =
|
||
|
||
1
|
||
@end example
|
||
|
||
@noindent It is possible to use up to two implicit loops to select variables:
|
||
@example
|
||
names = @{'GDP_1';'GDP_2';'GDP_3'; 'GDP_4'; 'GDP_5'; 'GDP_6'; 'GDP_7'; 'GDP_8'; ...
|
||
'GDP_9'; 'GDP_10'; 'GDP_11'; 'GDP_12'; ...
|
||
'HICP_1';'HICP_2';'HICP_3'; 'HICP_4'; 'HICP_5'; 'HICP_6'; 'HICP_7'; 'HICP_8'; ...
|
||
'HICP_9'; 'HICP_10'; 'HICP_11'; 'HICP_12'@};
|
||
|
||
ts0 = dseries(randn(4,24),dates('1973Q1'),names);
|
||
ts0@{'@@GDP,HICP@@_@@1,3,5@@'@}
|
||
|
||
ans is a dseries object:
|
||
|
||
| GDP_1 | GDP_3 | GDP_5 | HICP_1 | HICP_3 | HICP_5
|
||
1973Q1 | 1.7906 | -1.6606 | -0.57716 | 0.60963 | -0.52335 | 0.26172
|
||
1973Q2 | 2.1624 | 3.0125 | 0.52563 | 0.70912 | -1.7158 | 1.7792
|
||
1973Q3 | -0.81928 | 1.5008 | 1.152 | 0.2798 | 0.88568 | 1.8927
|
||
1973Q4 | -0.03705 | -0.35899 | 0.85838 | -1.4675 | -2.1666 | -0.62032
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{D} =} horzcat (@var{A}, @var{B}[, ]...)
|
||
|
||
Overloads the @code{horzcat} Matlab/Octave's method for @dseries objects. Returns a @dseries object @var{D} containing the variables in @dseries objects passed as inputs: @var{A}, @var{B}, ... If the inputs are not defined on the same time ranges, the method add @code{NaN}s to the variables so that the variables are redefined on the smallest common time range. Note that the names in the @dseries objects passed as inputs must be different and these objects must have common frequency.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(rand(5,2),'1950Q1',@{'nifnif';'noufnouf'@});
|
||
>> ts1 = dseries(rand(7,1),'1950Q3',@{'nafnaf'@});
|
||
>> ts2 = [ts0, ts1];
|
||
>> ts2
|
||
|
||
ts2 is a dseries object:
|
||
|
||
| nifnif | noufnouf | nafnaf
|
||
1950Q1 | 0.17404 | 0.71431 | NaN
|
||
1950Q2 | 0.62741 | 0.90704 | NaN
|
||
1950Q3 | 0.84189 | 0.21854 | 0.83666
|
||
1950Q4 | 0.51008 | 0.87096 | 0.8593
|
||
1951Q1 | 0.16576 | 0.21184 | 0.52338
|
||
1951Q2 | NaN | NaN | 0.47736
|
||
1951Q3 | NaN | NaN | 0.88988
|
||
1951Q4 | NaN | NaN | 0.065076
|
||
1952Q1 | NaN | NaN | 0.50946
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {@var{B} = } hpcycle (@var{A}[, @var{lambda}])
|
||
|
||
Extracts the cycle component from a @dseries @var{A} object using Hodrick Prescott filter and returns a @dseries object, @var{B}. Default value for @var{lambda}, the smoothing parameter, is @math{1600}.
|
||
|
||
@examplehead
|
||
@example
|
||
% Simulate a component model (stochastic trend, deterministic trend, and a
|
||
% stationary autoregressive process).
|
||
e = .2*randn(200,1);
|
||
u = randn(200,1);
|
||
stochastic_trend = cumsum(e);
|
||
deterministic_trend = .1*transpose(1:200);
|
||
x = zeros(200,1);
|
||
for i=2:200
|
||
x(i) = .75*x(i-1) + e(i);
|
||
end
|
||
y = x + stochastic_trend + deterministic_trend;
|
||
|
||
% Instantiates time series objects.
|
||
ts0 = dseries(y,'1950Q1');
|
||
ts1 = dseries(x,'1950Q1'); % stationary component.
|
||
|
||
% Apply the HP filter.
|
||
ts2 = ts0.hpcycle();
|
||
|
||
% Plot the filtered time series.
|
||
plot(ts1(ts2.dates).data,'-k'); % Plot of the stationary component.
|
||
hold on
|
||
plot(ts2.data,'--r'); % Plot of the filtered y.
|
||
hold off
|
||
axis tight
|
||
id = get(gca,'XTick');
|
||
set(gca,'XTickLabel',strings(ts.dates(id)));
|
||
@end example
|
||
|
||
@iftex
|
||
@sp 1
|
||
The previous code should produce something like:
|
||
@center
|
||
@image{dynare.plots/HPCycle,11.32cm,7cm}
|
||
@end iftex
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {@var{B} = } hptrend (@var{A}[, @var{lambda}])
|
||
|
||
Extracts the trend component from a @dseries @var{A} object using Hodrick Prescott filter and returns a @dseries object, @var{B}. Default value for @var{lambda}, the smoothing parameter, is @math{1600}.
|
||
|
||
@examplehead
|
||
Using the same generating data process as in the previous example:
|
||
@example
|
||
ts1 = dseries(stochastic_trend + deterministic_trend,'1950Q1');
|
||
% Apply the HP filter.
|
||
ts2 = ts0.hptrend();
|
||
|
||
% Plot the filtered time series.
|
||
plot(ts1.data,'-k'); % Plot of the nonstationary components.
|
||
hold on
|
||
plot(ts2.data,'--r'); % Plot of the estimated trend.
|
||
hold off
|
||
axis tight
|
||
id = get(gca,'XTick');
|
||
set(gca,'XTickLabel',strings(ts0.dates(id)));
|
||
@end example
|
||
|
||
@iftex
|
||
@sp 1
|
||
The previous code should produce something like:
|
||
@center
|
||
@image{dynare.plots/HPTrend,11.32cm,7cm}
|
||
@end iftex
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {@var{C} = } insert (@var{A}, @var{B}, @var{I})
|
||
|
||
Inserts variables contained in @dseries object @var{B} in @dseries object @var{A} at positions specified by integer scalars in vector @var{I}, returns augmented @dseries object @var{C}. The integer scalars in @var{I} must take values between @code{1} and @code{A.length()+1} and refers to @var{A}'s column numbers. The @dseries objects @var{A} and @var{B} need not to be defined over the same time ranges, but it is assumled that they have common frequency.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(ones(2,4),'1950Q1',{'Sly'; 'Gobbo'; 'Sneaky'; 'Stealthy'});
|
||
>> ts1 = dseries(pi*ones(2,1),'1950Q1',{'Noddy'});
|
||
>> ts2 = ts0.insert(ts1,3)
|
||
|
||
ts2 is a dseries object:
|
||
|
||
| Sly | Gobbo | Noddy | Sneaky | Stealthy
|
||
1950Q1 | 1 | 1 | 3.1416 | 1 | 1
|
||
1950Q2 | 1 | 1 | 3.1416 | 1 | 1
|
||
|
||
>> ts3 = dseries([pi*ones(2,1) sqrt(pi)*ones(2,1)],'1950Q1',{'Noddy';'Tessie Bear'});
|
||
>> ts4 = ts0.insert(ts1,[3, 4])
|
||
|
||
ts4 is a dseries object:
|
||
|
||
| Sly | Gobbo | Noddy | Sneaky | Tessie Bear | Stealthy
|
||
1950Q1 | 1 | 1 | 3.1416 | 1 | 1.7725 | 1
|
||
1950Q2 | 1 | 1 | 3.1416 | 1 | 1.7725 | 1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {@var{B} = } isempty (@var{A})
|
||
|
||
Overloads the Matlab/octave's @code{isempty} function. Returns @code{1} if @dseries object @var{A} is empty, @code{0} otherwise.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {@var{C} = } isequal (@var{A},@var{B})
|
||
|
||
Overloads the Matlab/octave's @code{isequal} function. Returns @code{1} if @dseries objects @var{A} and @code{B} are identical, @code{0} otherwise.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {@var{B} = } lag (@var{A}[, @var{p}])
|
||
|
||
Returns lagged time series. Default value of @var{p}, the number of lags, is @code{1}.
|
||
|
||
@exampleshead
|
||
|
||
@example
|
||
>> ts0 = dseries(transpose(1:4),'1950Q1')
|
||
|
||
ts0 is a dseries object:
|
||
|
||
| Variable_1
|
||
1950Q1 | 1
|
||
1950Q2 | 2
|
||
1950Q3 | 3
|
||
1950Q4 | 4
|
||
|
||
>> ts1 = ts0.lag()
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| lag(Variable_1,1)
|
||
1950Q1 | NaN
|
||
1950Q2 | 1
|
||
1950Q3 | 2
|
||
1950Q4 | 3
|
||
|
||
>> ts2 = ts0.lag(2)
|
||
|
||
ts2 is a dseries object:
|
||
|
||
| lag(Variable_1,2)
|
||
1950Q1 | NaN
|
||
1950Q2 | NaN
|
||
1950Q3 | 1
|
||
1950Q4 | 2
|
||
@end example
|
||
|
||
@noindent @dseries class overloads the parenthesis so that @code{ts.lag(p)} can be written more compactly as @code{ts(-p)}. For instance:
|
||
|
||
@example
|
||
>> ts0.lag(1)
|
||
|
||
ans is a dseries object:
|
||
|
||
| lag(Variable_1,1)
|
||
1950Q1 | NaN
|
||
1950Q2 | 1
|
||
1950Q3 | 2
|
||
1950Q4 | 3
|
||
@end example
|
||
|
||
@noindent or alternatively:
|
||
|
||
@example
|
||
>> ts0(-1)
|
||
|
||
ans is a dseries object:
|
||
|
||
| lag(Variable_1,1)
|
||
1950Q1 | NaN
|
||
1950Q2 | 1
|
||
1950Q3 | 2
|
||
1950Q4 | 3
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn {dseries} {@var{B} = } lead (@var{A}[, @var{p}])
|
||
|
||
Returns leaded time series. Default value of @var{p}, the number of leads, is @code{1}. As for the @code{lag} method, the @dseries class overloads the parenthesis so that @code{ts.lead(p)} is equivalent to @code{ts(p)}.
|
||
|
||
@examplehead
|
||
|
||
@example
|
||
>> ts0 = dseries(transpose(1:4),'1950Q1');
|
||
>> ts1 = ts0.lead()
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| lead(Variable_1,1)
|
||
1950Q1 | 2
|
||
1950Q2 | 3
|
||
1950Q3 | 4
|
||
1950Q4 | NaN
|
||
|
||
>> ts2 = ts0(2)
|
||
|
||
ts2 is a dseries object:
|
||
|
||
| lead(Variable_1,2)
|
||
1950Q1 | 3
|
||
1950Q2 | 4
|
||
1950Q3 | NaN
|
||
1950Q4 | NaN
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@noindent @remarkhead
|
||
|
||
@noindent The overloading of the parenthesis for @dseries objects, allows to easily create new @dseries objects by copying/pasting equations declared in the @code{model} block. For instance, if an Euler equation is defined in the @code{model} block:
|
||
@example
|
||
model;
|
||
...
|
||
1/C - beta/C(1)*(exp(A(1))*K^(alpha-1)+1-delta) ;
|
||
...
|
||
end;
|
||
@end example
|
||
@noindent and if variables @var{C}, @var{A} and @var{K} are defined as @dseries objects, then by writting:
|
||
@example
|
||
Residuals = 1/C - beta/C(1)*(exp(A(1))*K^(alpha-1)+1-delta) ;
|
||
@end example
|
||
@noindent outside of the @code{model} block, we create a new @dseries object, called @var{Residuals}, for the residuals of the Euler equation (the conditional expectation of the equation defined in the @code{model} block is zero, but the residuals are non zero).
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{B} =} log (@var{A})
|
||
|
||
Overloads the Matlab/Octave @code{log} function for @dseries objects.
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(rand(10,1));
|
||
>> ts1 = ts0.log();
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{C} =} merge (@var{A}, @var{B})
|
||
|
||
Merges two @dseries objects @var{A} and @var{B} in @dseries object @var{C}. Objects @var{A} and @var{B} need to have common frequency but can be defined on different time ranges. If a variable, say @code{x}, is defined both in @dseries objects @var{A} and @var{B}, then the merge will select the variable @code{x} as defined in the second input argument, @var{B}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(rand(3,2),'1950Q1',{'A1';'A2'})
|
||
|
||
ts0 is a dseries object:
|
||
|
||
| A1 | A2
|
||
1950Q1 | 0.42448 | 0.92477
|
||
1950Q2 | 0.60726 | 0.64208
|
||
1950Q3 | 0.070764 | 0.1045
|
||
|
||
>> ts1 = dseries(rand(3,1),'1950Q2',{'A1'})
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| A1
|
||
1950Q2 | 0.70023
|
||
1950Q3 | 0.3958
|
||
1950Q4 | 0.084905
|
||
|
||
>> merge(ts0,ts1)
|
||
|
||
ans is a dseries object:
|
||
|
||
| A1 | A2
|
||
1950Q1 | NaN | 0.92477
|
||
1950Q2 | 0.70023 | 0.64208
|
||
1950Q3 | 0.3958 | 0.1045
|
||
1950Q4 | 0.084905 | NaN
|
||
|
||
>> merge(ts1,ts0)
|
||
|
||
ans is a dseries object:
|
||
|
||
| A1 | A2
|
||
1950Q1 | 0.42448 | 0.92477
|
||
1950Q2 | 0.60726 | 0.64208
|
||
1950Q3 | 0.070764 | 0.1045
|
||
1950Q4 | NaN | NaN
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{C} =} minus (@var{A}, @var{B})
|
||
|
||
Overloads the @code{minus} (@code{-}) operator for @dseries objects, element by element substraction. If both @var{A} and @var{B} are @dseries objects, they do not need to be defined over the same time ranges. If @var{A} and @var{B} are @dseries object with @math{T_A} and @math{T_B} observations and @math{N_A} and @math{N_B} variables, then @math{N_A} must be equal to @math{N_B} or @math{1} and @math{N_B} must be equal to @math{N_A} or @math{1}. If @math{T_A=T_B}, @code{isequal(A.init,B.init)} returns 1 and @math{N_A=N_B}, then the @code{minus} operator will compute for each couple @math{(t,n)}, with @math{1<=t<=T_A} and @math{1<=n<=N_A}, @code{C.data(t,n)=A.data(t,n)-B.data(t,n)}. If @math{N_B} is equal to @math{1} and @math{N_A>1}, the smaller @dseries object (@var{B}) is ``broadcast'' across the larger @dseries (@var{A}) so that they have compatible shapes, the @code{minus} operator will substract the variable defined in @var{B} to each variable in @var{A}. If @var{B} is a double scalar, then the method @code{minus} will substract @var{B} to all the observations/variables in @var{A}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(rand(3,2));
|
||
>> ts1 = ts0@{'Variable_2'@};
|
||
>> ts0-ts1
|
||
|
||
ans is a dseries object:
|
||
|
||
| minus(Variable_1,Variable_2) | minus(Variable_2,Variable_2)
|
||
1Y | -0.48853 | 0
|
||
2Y | -0.50535 | 0
|
||
3Y | -0.32063 | 0
|
||
|
||
>> ts1
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| Variable_2
|
||
1Y | 0.703
|
||
2Y | 0.75415
|
||
3Y | 0.54729
|
||
|
||
>> ts1-ts1.data(1)
|
||
|
||
ans is a dseries object:
|
||
|
||
| minus(Variable_2,0.703)
|
||
1Y | 0
|
||
2Y | 0.051148
|
||
3Y | -0.15572
|
||
|
||
>> ts1.data(1)-ts1
|
||
|
||
ans is a dseries object:
|
||
|
||
| minus(0.703,Variable_2)
|
||
1Y | 0
|
||
2Y | -0.051148
|
||
3Y | 0.15572
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{C} =} mrdivide (@var{A}, @var{B})
|
||
|
||
Overloads the @code{mrdivide} (@code{/}) operator for @dseries objects, element by element division (like the @code{./} Matlab/Octave operator). If both @var{A} and @var{B} are @dseries objects, they do not need to be defined over the same time ranges. If @var{A} and @var{B} are @dseries object with @math{T_A} and @math{T_B} observations and @math{N_A} and @math{N_B} variables, then @math{N_A} must be equal to @math{N_B} or @math{1} and @math{N_B} must be equal to @math{N_A} or @math{1}. If @math{T_A=T_B}, @code{isequal(A.init,B.init)} returns 1 and @math{N_A=N_B}, then the @code{mrdivide} operator will compute for each couple @math{(t,n)}, with @math{1<=t<=T_A} and @math{1<=n<=N_A}, @code{C.data(t,n)=A.data(t,n)/B.data(t,n)}. If @math{N_B} is equal to @math{1} and @math{N_A>1}, the smaller @dseries object (@var{B}) is ``broadcast'' across the larger @dseries (@var{A}) so that they have compatible shapes, @code{mrdivides} operator will divide each variable defined in @var{A} by the variable in @var{B}, observation per observation. If @var{B} is a double scalar, then the method @code{mrdivide} will divide all the observations/variables in @var{A} by @var{B}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(rand(3,2))
|
||
|
||
ts0 is a dseries object:
|
||
|
||
| Variable_1 | Variable_2
|
||
1Y | 0.72918 | 0.90307
|
||
2Y | 0.93756 | 0.21819
|
||
3Y | 0.51725 | 0.87322
|
||
|
||
>> ts1 = ts0@{'Variable_2'@};
|
||
>> ts0/ts1
|
||
|
||
ans is a dseries object:
|
||
|
||
| divide(Variable_1,Variable_2) | divide(Variable_2,Variable_2)
|
||
1Y | 0.80745 | 1
|
||
2Y | 4.2969 | 1
|
||
3Y | 0.59235 | 1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{C} =} mtimes (@var{A}, @var{B})
|
||
|
||
Overloads the @code{mtimes} (@code{*}) operator for @dseries objects, Hadammard product (the @code{.*} Matlab/Octave operator). If both @var{A} and @var{B} are @dseries objects, they do not need to be defined over the same time ranges. If @var{A} and @var{B} are @dseries object with @math{T_A} and @math{T_B} observations and @math{N_A} and @math{N_B} variables, then @math{N_A} must be equal to @math{N_B} or @math{1} and @math{N_B} must be equal to @math{N_A} or @math{1}. If @math{T_A=T_B}, @code{isequal(A.init,B.init)} returns 1 and @math{N_A=N_B}, then the @code{mtimes} operator will compute for each couple @math{(t,n)}, with @math{1<=t<=T_A} and @math{1<=n<=N_A}, @code{C.data(t,n)=A.data(t,n)*B.data(t,n)}. If @math{N_B} is equal to @math{1} and @math{N_A>1}, the smaller @dseries object (@var{B}) is ``broadcast'' across the larger @dseries (@var{A}) so that they have compatible shapes, @code{mtimes} operator will multiply each variable defined in @var{A} by the variable in @var{B}, observation per observation. If @var{B} is a double scalar, then the method @code{mtimes} will multiply all the observations/variables in @var{A} by @var{B}.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{C} =} ne (@var{A}, @var{B})
|
||
|
||
Overloads the Matlab/Octave @code{ne} (equal, @code{~=}) operator. @dseries objects @var{A} and @var{B} must have the same number of observations (say, @math{T}) and variables (@math{N}). The returned argument is a @math{T} by @math{N} matrix of zeros and ones. Element @math{(i,j)} of @var{C} is equal to @code{1} if and only if observation @math{i} for variable @math{j} in @var{A} and @var{B} are not equal.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(2*ones(3,1));
|
||
>> ts1 = dseries([2; 0; 2]);
|
||
>> ts0~=ts1
|
||
|
||
ans =
|
||
|
||
0
|
||
1
|
||
0
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{C} =} plus (@var{A}, @var{B})
|
||
|
||
Overloads the @code{plus} (@code{+}) operator for @dseries objects, element by element addition. If both @var{A} and @var{B} are @dseries objects, they do not need to be defined over the same time ranges. If @var{A} and @var{B} are @dseries object with @math{T_A} and @math{T_B} observations and @math{N_A} and @math{N_B} variables, then @math{N_A} must be equal to @math{N_B} or @math{1} and @math{N_B} must be equal to @math{N_A} or @math{1}. If @math{T_A=T_B}, @code{isequal(A.init,B.init)} returns 1 and @math{N_A=N_B}, then the @code{minus} operator will compute for each couple @math{(t,n)}, with @math{1<=t<=T_A} and @math{1<=n<=N_A}, @code{C.data(t,n)=A.data(t,n)+B.data(t,n)}. If @math{N_B} is equal to @math{1} and @math{N_A>1}, the smaller @dseries object (@var{B}) is ``broadcast'' across the larger @dseries (@var{A}) so that they have compatible shapes, the @code{plus} operator will add the variable defined in @var{B} to each variable in @var{A}. If @var{B} is a double scalar, then the method @code{add} will add @var{B} to all the observations/variables in @var{A}.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{B} =} pop (@var{A}[, @var{a}])
|
||
|
||
Removes variable @var{a} from @dseries object @var{A}. By default, if the second argument is not provided, the last variable is removed.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(ones(3,3));
|
||
>> ts1 = ts0.pop('Variable_2');
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| Variable_1 | Variable_3
|
||
1Y | 1 | 1
|
||
2Y | 1 | 1
|
||
3Y | 1 | 1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{B} =} qdiff (@var{A})
|
||
@deftypefnx{dseries} {@var{B} =} qgrowth (@var{A})
|
||
|
||
Computes quaterly differences or growth rates.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(transpose(1:4),'1950Q1');
|
||
>> ts1 = ts0.qdiff()
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| qdiff(Variable_1)
|
||
1950Q1 | NaN
|
||
1950Q2 | 1
|
||
1950Q3 | 1
|
||
1950Q4 | 1
|
||
|
||
>> ts0 = dseries(transpose(1:6),'1950M1');
|
||
>> ts1 = ts0.qdiff()
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| qdiff(Variable_1)
|
||
1950M1 | NaN
|
||
1950M2 | NaN
|
||
1950M3 | NaN
|
||
1950M4 | 3
|
||
1950M5 | 3
|
||
1950M6 | 3
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{B} =} rename (@var{A},@var{oldname},@var{newname})
|
||
|
||
Rename variable @var{oldname} to @var{newname} in @dseries object @var{A}, returns a @dseries object.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(ones(2,2));
|
||
>> ts1 = ts0.rename('Variable_1','Stinkly')
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| Stinkly | Variable_2
|
||
1Y | 1 | 1
|
||
2Y | 1 | 1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} save (@var{A}[, @var{basename}[, @var{format}]])
|
||
|
||
Overloads the Matlab/Octave @code{save} function, saves @dseries object @var{A} to disk. Possible formats are @code{csv} (this is the default), @code{m} (Matlab/Octave script), and @code{mat} (Matlab binary data file). The name of the file without extension is specified by @var{basename}, by default @var{basename} is the name of the first input (namely, the @dseries object @var{A}).
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(ones(2,2));
|
||
>> ts0.save();
|
||
@end example
|
||
@noindent The last command will create a file @code{ts0.csv} with the following content:
|
||
@example
|
||
,Variable_1,Variable_2
|
||
1Y, 1, 1
|
||
2Y, 1, 1
|
||
@end example
|
||
To create a Matlab/octave script, the following command:
|
||
@example
|
||
>> ts0.save([],'m');
|
||
@end example
|
||
will produce a file @code{ts0.m} with the following content:
|
||
@example
|
||
% File created on 14-Nov-2013 12:08:52.
|
||
|
||
FREQ__ = 1;
|
||
INIT__ = ' 1Y';
|
||
|
||
NAMES__ = {'Variable_1'; 'Variable_2'};
|
||
TEX__ = {'Variable_{1}'; 'Variable_{2}'};
|
||
|
||
Variable_1 = [
|
||
1
|
||
1];
|
||
|
||
Variable_2 = [
|
||
1
|
||
1];
|
||
@end example
|
||
@noindent The generated (@code{csv}, @code{m}, or @code{mat}) files can be loaded when instantiating a @dseries object as explained above.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{B} =} set_names (@var{A}, @var{s1}, @var{s2}, ...)
|
||
|
||
Renames variables in @dseries object @var{A}, returns a @dseries object @var{B} with new names @var{s1}, @var{s2}, @var{s3}, ... The number of input arguments after the first one (@dseries object @var{A}) must be equal to @code{A.vobs} (the number of variables in @var{A}). @var{s1} will be the name of the first variable in @var{B}, @var{s2} the name of the second variable in @var{B}, and so on.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(ones(1,3));
|
||
>> ts1 = ts0.set_names('Barbibul',[],'Barbouille')
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| Barbibul | Variable_2 | Barbouille
|
||
1Y | 1 | 1 | 1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {[@var{T}, @var{N} ] = } size (@var{A}[, @var{dim}])
|
||
|
||
Overloads the Matlab/Octave's @code{size} function. Returns the number of observations in @dseries object @var{A} (@emph{ie} @code{A.nobs}) and the number of variables (@emph{ie} @code{A.vobs}). If a second input argument is passed, the @code{size} function returns the number of observations if @code{dim=1} or the number of variables if @code{dim=2} (for all other values of @var{dim} an error is issued).
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(ones(1,3));
|
||
>> ts0.size()
|
||
|
||
ans =
|
||
|
||
1 3
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{B} =} tex_rename (@var{A},@var{name},@var{newtexname})
|
||
|
||
Redefines the tex name of variable @var{name} to @var{newtexname} in @dseries object @var{A}, returns a @dseries object.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{B} =} uminus (@var{A})
|
||
|
||
Overloads @code{uminus} (@code{-}, unary minus) for @dseries object.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(1)
|
||
|
||
ts0 is a dseries object:
|
||
|
||
| Variable_1
|
||
1Y | 1
|
||
|
||
>> ts1 = -ts0
|
||
|
||
ts1 is a dseries object:
|
||
|
||
| -Variable_1
|
||
1Y | -1
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
@deftypefn{dseries} {@var{D} =} vertcat (@var{A}, @var{B}[, ]...)
|
||
|
||
Overloads the @code{vertcat} Matlab/Octave's method for @dseries objects. This method is used to append more observations to a @dseries object. Returns a @dseries object @var{D} containing the variables in @dseries objects passed as inputs. All the input arguments must be @dseries objects with the same variables defined on @emph{different time ranges}.
|
||
|
||
@examplehead
|
||
@example
|
||
>> ts0 = dseries(rand(2,2),'1950Q1',@{'nifnif';'noufnouf'@});
|
||
>> ts1 = dseries(rand(2,2),'1950Q3',@{'nifnif';'noufnouf'@});
|
||
>> ts2 = [ts0; ts1]
|
||
|
||
ts2 is a dseries object:
|
||
|
||
| nifnif | noufnouf
|
||
1950Q1 | 0.82558 | 0.31852
|
||
1950Q2 | 0.78996 | 0.53406
|
||
1950Q3 | 0.089951 | 0.13629
|
||
1950Q4 | 0.11171 | 0.67865
|
||
@end example
|
||
|
||
@end deftypefn
|
||
|
||
@deftypefn{dseries} {@var{B} =} ydiff (@var{A})
|
||
@deftypefnx{dseries} {@var{B} =} ygrowth (@var{A})
|
||
|
||
Computes yearly differences or growth rates.
|
||
|
||
@end deftypefn
|
||
|
||
@sp 1
|
||
|
||
|
||
|
||
|
||
|
||
@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:
|
||
the result of @code{findtexmf --file-type=exe pdflatex}, Mac OS X and
|
||
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, graphSize, showGrid, showLegend, showLegendBox, legendLocation, legendOrientation, legendFontSize, seriesToUse, shade, shadeColor, shadeOpacity, title, xlabel, ylabel, xrange, xTickLabels, yrange, showZeroline
|
||
Adds a @code{Graph} to a @code{Section}.
|
||
@optionshead
|
||
@table @code
|
||
@anchor{data}
|
||
@item data, @code{dseries}
|
||
The @code{dseries} 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 graphSize, @code{NUMERICAL_VECTOR}
|
||
The width and height to be passed to the third and fourth elements of
|
||
the array passed to the @code{`Position'} option of Matlab's
|
||
@code{figure} command, passed as a vector of size @math{2}. Default:
|
||
Matlab sets width and height
|
||
|
||
@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{dseries} provided to
|
||
the @ref{data} option. If empty, use all series provided to
|
||
@ref{data} option. Default: @code{empty}
|
||
|
||
@item shade, @code{dates}
|
||
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{dates}
|
||
The boundary on the x-axis to display in the graph. Default: all
|
||
|
||
@item xTickLabels, @code{CELL_ARRAY_STRINGS}
|
||
The labels to use for the xticks in the graph. Default: the dates of
|
||
the @code{dseries}
|
||
|
||
@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 annualAverages, data, showHlines, precision, range, seriesToUse, title, titleSize, vlineAfter, vlineAfterEndOfPeriod, showVlines
|
||
Adds a @code{Table} to a @code{Section}.
|
||
@optionshead
|
||
@table @code
|
||
|
||
@item annualAverages, @code{bool}
|
||
Compute the average over every year in the table and display it in a
|
||
column to the right of the data (one column for every year). Only
|
||
works for quarterly data. Default: @code{false}
|
||
|
||
@item data, @code{dseries}
|
||
@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{dates}
|
||
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{dates}
|
||
Show a vertical line after the specified date. Default: @code{empty}
|
||
|
||
@item vlineAfterEndOfPeriod, @code{BOOLEAN}
|
||
Show a vertical line after the end of every period (@i{i.e.} after
|
||
every year, after the fourth quarter, etc.). Default: @code{false}
|
||
|
||
@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, tableRowColor, tableShowMarkers, tableAlignRight, tableNegColor, tablePosColor, tableSubSectionHeader, zerotol
|
||
Adds a @code{Series} to a @code{Graph} or a @code{Table}.
|
||
@optionshead
|
||
@table @code
|
||
|
||
@item data, @code{dseries}
|
||
@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 tableRowColor, @code{STRING}
|
||
The color that you want the row to be. Predefined values include
|
||
@code{LightCyan} and @code{Gray}. Default: @code{white}.
|
||
|
||
@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'}
|
||
|
||
@item tableSubSectionHeader, @code{STRING}
|
||
A header for a subsection of the table. No data will be associated
|
||
with it. It is equivalent to adding an empty series with a
|
||
name. Default: @code{''}
|
||
|
||
@item zerotol, @code{DOUBLE}
|
||
The zero tolerance. Anything smaller than @code{zerotol} and larger
|
||
than @code{-zerotol} will be set to zero before being
|
||
graphed. Default: @math{1e-6}
|
||
|
||
@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 dseries
|
||
dsq = dseries(`quarterly.csv');
|
||
dsa = dseries(`annual.csv');
|
||
dsca = dseries(`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', dates(`2007q1'):dates(`2013q4'), ...
|
||
`shade', dates(`2012q2'):dates(`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', dates(`2007q1'):dates(`2013q4'), ...
|
||
`shade', dates(`2012q2'):dates(`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', dates(`2012Y'):dates(`2014Y'));
|
||
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
|
||
Milton Abramowitz, Irene A. Stegun (1964): ``Handbook of Mathematical Functions'', Courier Dover Publications
|
||
|
||
@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
|
||
Cardoso, Margarida F., R. L. Salcedo and S. Feyo de Azevedo (1996): ``The simplex simulated annealing approach to continuous non-linear optimization'', @i{Computers chem. Engng}, 20(9), 1065-1080
|
||
|
||
|
||
@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
|
||
Geweke, John (1992): ``Evaluating the accuracy of sampling-based approaches
|
||
to the calculation of posterior moments'', in J.O. Berger, J.M. Bernardo,
|
||
A.P. Dawid, and A.F.M. Smith (eds.) Proceedings of the Fourth Valencia
|
||
International Meeting on Bayesian Statistics, pp. 169--194, Oxford University Press
|
||
|
||
@item
|
||
Geweke, John (1999): ``Using simulation methods for Bayesian econometric models:
|
||
Inference, development and communication,'' @i{Econometric Reviews}, 18(1), 1--73
|
||
|
||
@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
|