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In a deterministic context, when one wants to study the transition of
one equilibrium position to another, it is equivalent to analyze the
consequences of a permanent shock and this in done in Dynare through
the proper use of initval
and endval
.
Another typical experiment is to study the effects of a temporary
shock after which the system goes back to the original equilibrium (if
the model is stable…). A temporary shock is a temporary change of
value of one or several exogenous variables in the model. Temporary
shocks are specified with the command shocks
.
In a stochastic framework, the exogenous variables take random values
in each period. In Dynare, these random values follow a normal
distribution with zero mean, but it belongs to the user to specify the
variability of these shocks. The non-zero elements of the matrix of
variance-covariance of the shocks can be entered with the shocks
command. Or, the entire matrix can be directly entered with
Sigma_e
(this use is however deprecated).
If the variance of an exogenous variable is set to zero, this variable will appear in the report on policy and transition functions, but isn’t used in the computation of moments and of Impulse Response Functions. Setting a variance to zero is an easy way of removing an exogenous shock.
Note that, by default, if there are several shocks
or mshocks
blocks in the same ‘.mod’ file, then they are cumulative: all the shocks
declared in all the blocks are considered; however, if a shocks
or
mshocks
block is declared with the overwrite
option, then it
replaces all the previous shocks
and mshocks
blocks.
See above for the meaning of the overwrite
option.
In deterministic context
For deterministic simulations, the shocks
block specifies
temporary changes in the value of exogenous variables. For
permanent shocks, use an endval
block.
The block should contain one or more occurrences of the following group of three lines:
var VARIABLE_NAME; periods INTEGER[:INTEGER] [[,] INTEGER[:INTEGER]]…; values DOUBLE | (EXPRESSION) [[,] DOUBLE | (EXPRESSION) ]…; |
It is possible to specify shocks which last several periods and which can
vary over time. The periods
keyword accepts a list of
several dates or date ranges, which must be matched by as many shock values
in the values
keyword. Note that a range in the
periods
keyword can be matched by only one value in the
values
keyword. If values
represents a scalar, the same
value applies to the whole range. If values
represents a vector,
it must have as many elements as there are periods in the range.
Note that shock values are not restricted to numerical constants: arbitrary expressions are also allowed, but you have to enclose them inside parentheses.
Here is an example:
shocks; var e; periods 1; values 0.5; var u; periods 4:5; values 0; var v; periods 4:5 6 7:9; values 1 1.1 0.9; var w; periods 1 2; values (1+p) (exp(z)); end; |
A second example with a vector of values:
xx = [1.2; 1.3; 1]; shocks; var e; periods 1:3; values (xx); end; |
In stochastic context
For stochastic simulations, the shocks
block specifies the non
zero elements of the covariance matrix of the shocks of exogenous
variables.
You can use the following types of entries in the block:
var VARIABLE_NAME; stderr EXPRESSION;
Specifies the standard error of a variable.
var VARIABLE_NAME = EXPRESSION;
Specifies the variance of a variable.
var VARIABLE_NAME, VARIABLE_NAME = EXPRESSION;
Specifies the covariance of two variables.
corr VARIABLE_NAME, VARIABLE_NAME = EXPRESSION;
Specifies the correlation of two variables.
In an estimation context, it is also possible to specify variances and
covariances on endogenous variables: in that case, these values are interpreted
as the calibration of the measurement errors on these variables. This requires
the varobs
command to be specified before the shocks
block.
Here is an example:
shocks; var e = 0.000081; var u; stderr 0.009; corr e, u = 0.8; var v, w = 2; end; |
Mixing deterministic and stochastic shocks
It is possible to mix deterministic and stochastic shocks to build
models where agents know from the start of the simulation about future
exogenous changes. In that case stoch_simul
will compute the
rational expectation solution adding future information to the state
space (nothing is shown in the output of stoch_simul
) and
forecast
will compute a simulation conditional on initial
conditions and future information.
Here is an example:
varexo_det tau; varexo e; … shocks; var e; stderr 0.01; var tau; periods 1:9; values -0.15; end; stoch_simul(irf=0); forecast; |
The purpose of this block is similar to that of the shocks
block for deterministic shocks, except that the numeric values given
will be interpreted in a multiplicative way. For example, if a value
of 1.05
is given as shock value for some exogenous at some
date, it means 5% above its steady state value (as given by the last
initval
or endval
block).
The syntax is the same than shocks
in a deterministic context.
This command is only meaningful in two situations:
See above for the meaning of the overwrite
option.
Warning
The use of this special variable is deprecated and is strongly
discouraged. You should use a shocks
block instead.
Description
This special variable specifies directly the covariance matrix of the
stochastic shocks, as an upper (or lower) triangular matrix. Dynare
builds the corresponding symmetric matrix. Each row of the triangular
matrix, except the last one, must be terminated by a semi-colon
;
. For a given element, an arbitrary EXPRESSION is
allowed (instead of a simple constant), but in that case you need to
enclose the expression in parentheses. The order of the
covariances in the matrix is the same as the one used in the
varexo
declaration.
Example
varexo u, e; … Sigma_e = [ 0.81 (phi*0.9*0.009); 0.000081]; |
This sets the variance of u
to 0.81, the variance of e
to 0.000081, and the correlation between e
and u
to
phi
.
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