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4.15 Forecasting

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. If the model contains strong non-linearities, the conditional forecasts can be computed using an extended path method with the simulation_type option in conditional_forecast command set to 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 conditional_forecast_paths block, using the command 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 bvar_forecast command.

Command: forecast [VARIABLE_NAME…];
Command: forecast (OPTIONS…) [VARIABLE_NAME…];

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 conditionaly 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: 40

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;
MATLAB/Octave variable: oo_.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:

 
oo_.forecast.FORECAST_MOMENT.VARIABLE_NAME

where FORECAST_MOMENT is one of the following:

HPDinf

Lower bound of a 90% HPD interval(6) of forecast due to parameter uncertainty

HPDsup

Lower bound of a 90% HPD interval due to parameter uncertainty

HPDTotalinf

Lower bound of a 90% HPD interval of forecast due to parameter uncertainty and future shocks (only with the estimation command)

HPDTotalsup

Lower bound of a 90% HPD interval due to parameter uncertainty and future shocks (only with the estimation command)

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

MATLAB/Octave variable: oo_.PointForecast

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:

 
oo_.PointForecast.MOMENT_NAME.VARIABLE_NAME
MATLAB/Octave variable: oo_.MeanForecast

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:

 
oo_.MeanForecast.MOMENT_NAME.VARIABLE_NAME
Command: conditional_forecast (OPTIONS…) [VARIABLE_NAME…];

Description

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 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 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.

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: 0.80

simulation_type = stochastic | deterministic

Indicates the nature of simulations used to compute the conditional forecast. The default value 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, simulation_type has to be set equal to deterministic.

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.

MATLAB/Octave variable: forecasts.cond

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:

 
forecasts.cond.FORECAST_MOMENT.VARIABLE_NAME

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.

MATLAB/Octave variable: forecasts.uncond

Variable set by the conditional_forecast command. It stores the unconditional forecasts. Fields are of the form:

 
forecasts.uncond.FORECAST_MOMENT.VARIABLE_NAME
MATLAB/Octave variable: forecasts.instruments

Variable set by the conditional_forecast command. Stores the names of the exogenous instruments.

MATLAB/Octave variable: forecasts.controlled_variables

Variable set by the conditional_forecast command. Stores the position of the constrained endogenous variables in declaration order.

MATLAB/Octave variable: forecasts.graphs

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;

Example

 
/* conditional forecast using extended path method
with perfect foresight on r path*/
var y r
varexo e u;

…

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;
Block: conditional_forecast_paths ;

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 than the deterministic shocks in the shocks blocks (see section 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 expectation = surprise | perfect_foresight. By default, expectation is equal to surprise.

Command: plot_conditional_forecast [VARIABLE_NAME…];
Command: plot_conditional_forecast (periods = INTEGER) [VARIABLE_NAME…];

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.

Command: bvar_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.

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