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Document extended_path and oo_.exo_simul in ref manual

time-shift
Sébastien Villemot 2012-06-08 17:36:45 +02:00
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@ -2875,7 +2875,8 @@ The simulated endogenous variables are available in global matrix
@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).
@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
@ -2883,16 +2884,38 @@ 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. Dynare uses a Taylor
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)}.
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::
@ -3052,7 +3075,9 @@ 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}). Default: @code{0}.
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
@ -3250,6 +3275,37 @@ 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)}.
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}).
@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 approximate solution
at every iteration of the algorithm. Default: @code{200}.
@end table
@end deffn
@node Typology and ordering of variables
@subsection Typology and ordering of variables