diff --git a/doc/dynare.texi b/doc/dynare.texi index a1282180bb1d67a9abf72cbf9070f46db31afb5d..70cae7148b79f0931d33e316bb4af3c282e70381 100644 --- a/doc/dynare.texi +++ b/doc/dynare.texi @@ -5829,11 +5829,55 @@ Fields are of the form: @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. +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 @math{y_{t}}: + +@math{y_t=Ty_{t-1}+R\varepsilon_t} + +Both +@math{y_t} and @math{\varepsilon_t} are split up into controlled and +uncontrolled ones to get: + +@math{y_t(contr\_vars)=Ty_{t-1}(contr\_vars)+R(contr\_vars,uncontr\_shocks)\varepsilon_t(uncontr\_shocks) ++R(contr\_vars,contr\_shocks)\varepsilon_t(contr\_shocks)} + +which can be solved algebraically for @math{\varepsilon_t(contr\_shocks)}. + +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, due to the use of the above formula to compute the controlled +exogenous variables, only relationships between controlled exogenous +variables embedded in the matrix @math{R} are considered. This implies +that any correlation information embedded in the covariance matrix of the +@math{\varepsilon} as specified in the @code{shocks}-block are via +estimated correlations or covariances is ignored as the controlled +exogenous variables are assumed to be perfectly controlled without any +interdependence. Thus, if you want to specify/preserve a correlation +structure between controlled exogenous variables, you have to embedd that +correlation stucture directly in the model-block by e.g. having the same +shock enter different equations. + + +This +command has to be called after @code{estimation} of @code{stoch_simul}. Use @code{conditional_forecast_paths} block to give the list of constrained endogenous, and their constrained future path.