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On a calibrated model, forecasting is done using the forecast
command. On an estimated model, use the forecast
option of
estimation
command.
It is also possible to compute forecasts on a calibrated or estimated
model for a given constrained path of the future endogenous
variables. This is done, from the reduced form representation of the
DSGE model, by finding the structural shocks that are needed to match
the restricted paths. Use conditional_forecast
,
conditional_forecast_paths
and plot_conditional_forecast
for that purpose.
Finally, it is possible to do forecasting with a Bayesian VAR using
the bvar_forecast
command.
Description
This command computes a simulation of a stochastic model from an arbitrary initial point.
When the model also contains deterministic exogenous shocks, the simulation is computed conditionally to the agents knowing the future values of the deterministic exogenous variables.
forecast
must be called after stoch_simul
.
forecast
plots the trajectory of endogenous variables. When a
list of variable names follows the command, only those variables are
plotted. A 90% confidence interval is plotted around the mean
trajectory. Use option conf_sig
to change the level of the
confidence interval.
Options
periods = INTEGER
Number of periods of the forecast. Default: 5
.
conf_sig = DOUBLE
Level of significance for confidence
interval. Default: 0.90
nograph
See nograph.
nodisplay
See nodisplay.
graph_format = FORMAT
graph_format = ( FORMAT, FORMAT… )
See graph_format.
Initial Values
forecast
computes the forecast taking as initial values the values specified in histval
(see section histval). When no histval
block is present, the initial values are the one stated in initval
. When initval
is followed by command steady
, the initial values are the steady state (see section steady).
Output
The results are stored in oo_.forecast
, which is described below.
Example
varexo_det tau; varexo e; … shocks; var e; stderr 0.01; var tau; periods 1:9; values -0.15; end; stoch_simul(irf=0); forecast; |
Variable set by the forecast
command, or by the
estimation
command if used with the forecast
option and
if no Metropolis-Hastings has been computed (in that case, the
forecast is computed for the posterior mode). Fields are of the form:
|
where FORECAST_MOMENT is one of the following:
HPDinf
Lower bound of a 90% HPD interval(8) of forecast due to parameter uncertainty, but ignoring the effect of measurement error on observed variables
HPDsup
Lower bound of a 90% HPD interval due to parameter uncertainty, but ignoring the effect of measurement error on observed variables
HPDinf_ME
Lower bound of a 90% HPD interval(9) of forecast for observed variables due to parameter uncertainty and measurement error
HPDsup_ME
Lower bound of a 90% HPD interval of forecast for observed variables due to parameter uncertainty and measurement error
Mean
Mean of the posterior distribution of forecasts
Median
Median of the posterior distribution of forecasts
Std
Standard deviation of the posterior distribution of forecasts
Set by the estimation
command, if it is used with the
forecast
option and if either mh_replic > 0
or
load_mh_file
option is used.
Contains the distribution of forecasts taking into account the uncertainty about both parameters and shocks.
Fields are of the form:
|
Set by the estimation
command, if it is used with the
forecast
option and if either mh_replic > 0
or
load_mh_file
option is used.
Contains the distribution of forecasts where the uncertainty about shocks is averaged out. The distribution of forecasts therefore only represents the uncertainty about parameters.
Fields are of the form:
|
This command computes forecasts on an estimated or calibrated model for a given constrained path of some future endogenous variables. This is done using the reduced form first order state-space representation of the DSGE model by finding the structural shocks that are needed to match the restricted paths. Consider the an augmented state space representation that stacks both predetermined and non-predetermined variables into a vector :
Both and are split up into controlled and uncontrolled ones to get:
which can be solved algebraically for .
Using these controlled shocks, the state-space representation can be used
for forecasting. A few things need to be noted. First, it is assumed that
controlled exogenous variables are fully under control of the policy
maker for all forecast periods and not just for the periods where the
endogenous variables are controlled. For all uncontrolled periods, the
controlled exogenous variables are assumed to be 0. This implies that
there is no forecast uncertainty arising from these exogenous variables
in uncontrolled periods. Second, by making use of the first order state
space solution, even if a higher-order approximation was performed, the
conditional forecasts will be based on a first order approximation.
Third, although controlled exogenous variables are taken as instruments
perfectly under the control of the policy-maker, they are nevertheless
random and unforeseen shocks from the perspective of the households. That is,
households are in each period surprised by the realization of a shock
that keeps the controlled endogenous variables at their respective level.
Fourth, keep in mind that if the structural innovations are correlated,
because the calibrated or estimated covariance matrix has non zero off
diagonal elements, the results of the conditional forecasts will depend on
the ordering of the innovations (as declared after varexo
). As in VAR
models, a Cholesky decomposition is used to factorize the covariance matrix
and identify orthogonal impulses. It is preferable to declare the correlations
in the model
block (explicitly imposing the identification restrictions),
unless you are satisfied with the implicit identification restrictions implied
by the Cholesky decomposition.
This command has to be called after estimation
or stoch_simul
.
Use conditional_forecast_paths
block to give the list of
constrained endogenous, and their constrained future path.
Option controlled_varexo
is used to specify the structural shocks
which will be matched to generate the constrained path.
Use plot_conditional_forecast
to graph the results.
Options
parameter_set = calibration
| prior_mode
| prior_mean
| posterior_mode
| posterior_mean
| posterior_median
Specify the parameter set to use for the forecasting. No default
value, mandatory option. Note that in case of estimated models, conditional_forecast
does not support the prefilter
-option.
controlled_varexo = (VARIABLE_NAME…)
Specify the exogenous variables to use as control variables. No default value, mandatory option.
periods = INTEGER
Number of periods of the forecast. Default: 40
. periods
cannot be less than the number of constrained periods.
replic = INTEGER
Number of simulations. Default: 5000
.
conf_sig = DOUBLE
Level of significance for confidence interval. Default: 0.90
Output
The results are not stored in the oo_
structure but in a separate structure forecasts
saved to the harddisk into a file called conditional_forecasts.mat
.
Variable set by the conditional_forecast
command. It stores the conditional forecasts. Fields are periods+1
by 1 vectors storing the steady state (time 0) and the subsequent periods
forecasts periods. Fields are of the form:
|
where FORECAST_MOMENT is one of the following:
Mean
Mean of the conditional forecast distribution.
ci
Confidence interval of the conditional forecast distribution. The size corresponds to conf_sig
.
Variable set by the conditional_forecast
command. It stores the unconditional forecasts. Fields are of the form:
|
Variable set by the conditional_forecast
command. Stores the names of the exogenous instruments.
Variable set by the conditional_forecast
command. Stores the position of the constrained endogenous variables in declaration order.
Variable set by the conditional_forecast
command. Stores the values of the controlled exogenous
variables underlying the conditional forecasts to achieve the constrained endogenous
variables. Fields are number of constrained periods by 1 vectors and are of the form:
|
Variable set by the conditional_forecast
command. Stores the information for generating the conditional forecast plots.
Example
var y a varexo e u; … estimation(…); conditional_forecast_paths; var y; periods 1:3, 4:5; values 2, 5; var a; periods 1:5; values 3; end; conditional_forecast(parameter_set = calibration, controlled_varexo = (e, u), replic = 3000); plot_conditional_forecast(periods = 10) a y; |
Describes the path of constrained endogenous, before calling
conditional_forecast
. The syntax is similar to deterministic
shocks in shocks
, see conditional_forecast
for an
example.
The syntax of the block is the same as for the deterministic shocks in
the shocks
blocks (see section Shocks on exogenous variables). Note that you need to specify the full path for all constrained endogenous
variables between the first and last specified period. If an intermediate period
is not specified, a value of 0 is assumed. That is, if you specify only
values for periods 1 and 3, the values for period 2 will be 0. Currently, it is not
possible to have uncontrolled intermediate periods.
In case of the presence of observation_trends
, the specified controlled path for
these variables needs to include the trend component. When using the loglinear option,
it is necessary to specify the logarithm of the controlled variables.
Description
Plots the conditional (plain lines) and unconditional (dashed lines) forecasts.
To be used after conditional_forecast
.
Options
periods = INTEGER
Number of periods to be plotted. Default: equal to periods
in
conditional_forecast
. The number of periods declared in
plot_conditional_forecast
cannot be greater than the one
declared in conditional_forecast
.
This command computes (out-of-sample) forecasts for an estimated BVAR model, using Minnesota priors.
See ‘bvar-a-la-sims.pdf’, which comes with Dynare distribution, for more information on this command.
If the model contains strong non-linearities or if some perfectly expected shocks are considered, the forecasts and the conditional forecasts
can be computed using an extended path method. The forecast scenario describing the shocks and/or the constrained paths on some endogenous variables should be build.
The first step is the forecast scenario initialization using the function init_plan
:
Creates a new forecast scenario for a forecast period (indicated as a dates class, see dates class members). This function return a handle on the new forecast scenario.
The forecast scenario can contain some simple shocks on the exogenous variables. This shocks are described using the function basic_plan
:
Adds to the forecast scenario a shock on the exogenous variable indicated between quotes in the second argument. The shock type has to be specified in the third argument between quotes: ’surprise’ in case of an unexpected shock or ’perfect_foresight’ for a perfectly anticipated shock. The fourth argument indicates the period of the shock using a dates class (see dates class members). The last argument is the shock path indicated as a Matlab vector of double. This function return the handle of the updated forecast scenario.
The forecast scenario can also contain a constrained path on an endogenous variable. The values of the related exogenous variable compatible with the constrained path are in this case computed. In other words, a conditional forecast is performed. This kind of shock is described with the function flip_plan
:
Adds to the forecast scenario a constrained path on the endogenous variable specified between quotes in the second argument. The associated exogenous variable provided in the third argument between quotes, is considered as an endogenous variable and its values compatible with the constrained path on the endogenous variable will be computed. The nature of the expectation on the constrained path has to be specified in the fourth argument between quotes: ’surprise’ in case of an unexpected path or ’perfect_foresight’ for a perfectly anticipated path. The fifth argument indicates the period where the path of the endogenous variable is constrained using a dates class (see dates class members). The last argument contains the constrained path as a Matlab vector of double. This function return the handle of the updated forecast scenario.
Once the forecast scenario if fully described, the forecast is computed with the command det_cond_forecast
:
Computes the forecast or the conditional forecast using an extended path method for the given forecast scenario (first argument). The past values of the endogenous and exogenous variables provided with a dseries class (see dseries class members) can be indicated in the second argument. By default, the past values of the variables are equal to their steady-state values. The initial date of the forecast can be provided in the third argument. By default, the forecast will start at the first date indicated in the init_plan
command. This function returns a dset containing the historical and forecast values for the endogenous and exogenous variables.
Example
/* conditional forecast using extended path method with perfect foresight on r path*/ var y r varexo e u; … smoothed = dseries('smoothed_variables.csv'); fplan = init_plan(2013Q4:2029Q4); fplan = flip_plan(fplan, 'y', 'u', 'surprise', 2013Q4:2014Q4, [1 1.1 1.2 1.1 ]); fplan = flip_plan(fplan, 'r', 'e', 'perfect_foresight', 2013Q4:2014Q4, [2 1.9 1.9 1.9 ]); dset_forecast = det_cond_forecast(fplan, smoothed); plot(dset_forecast.{'y','u'}); plot(dset_forecast.{'r','e'}); |
Description
The purpose of this command is to construct initial conditions (for a subsequent simulation) that are the smoothed values of a previous estimation.
More precisely, after an estimation run with the smoother
option,
smoother2histval
will extract the smoothed values (from
oo_.SmoothedVariables
, and possibly from oo_.SmoothedShocks
if
there are lagged exogenous), and will use these values to construct initial
conditions (as if they had been manually entered through histval
).
Options
period = INTEGER
Period number to use as the starting point for the subsequent simulation.
It should be between 1
and the number of observations that were used to produce the
smoothed values. Default: the last observation.
infile = FILENAME
Load the smoothed values from a ‘_results.mat’ file created by a previous Dynare run. Default: use the smoothed values currently in the global workspace.
invars = ( VARIABLE_NAME [VARIABLE_NAME …] )
A list of variables to read from the smoothed values. It can contain state endogenous variables, and also exogenous variables having a lag. Default: all the state endogenous variables, and all the exogenous variables with a lag.
outfile = FILENAME
Write the initial conditions to a file. Default: write the initial conditions in the current workspace, so that a simulation can be performed.
outvars = ( VARIABLE_NAME [VARIABLE_NAME …] )
A list of variables which will be given the initial conditions. This list must
have the same length than the list given to invars
, and there will be a
one-to-one mapping between the two list. Default: same value as option
invars
.
Use cases
There are three possible ways of using this command:
smoother2histval
(without the infile
and outfile
options), then run a stochastic simulation.
smoother2histval
with the outfile
option; in the second file, run histval_file
to load the initial conditions, and run a (deterministic or stochastic) simulation
smoother2histval
with the infile
option equal to the ‘_results.mat’ file created by the first file, and then run a (deterministic or stochastic) simulation
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