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function [forcs, e] = get_shock_paths(cL, H, mcValue, shocks, forcs, T, R, mv, mu)
% [forcs, e] = get_shock_paths(cL, H, mcValue, shocks, forcs, T, R, mv, mu)
% Computes the shock values for constrained forecasts necessary to keep
% endogenous variables at their constrained paths
%
% INPUTS:
% - cL [integer] scalar, number of controlled periods
% - H [integer] scalar, number of forecast periods
% - mcValue [double] n_controlled_vars*cL array, paths for constrained variables
% - shocks [double] n_controlled_vars*cL array, shock values draws (with zeros for controlled_varexo)
% - forcs [double] n_endovars*(H+1) matrix of endogenous variables storing the inital condition
% - T [double] n_endovars*n_endovars array, transition matrix of the state equation.
% - R [double] n_endovars*n_exo array, matrix relating the endogenous variables to the innovations in the state equation.
% - mv [logical] n_controlled_exo*n_endovars array, indicator selecting constrained endogenous variables
% - mu [logical] n_controlled_vars*nexo array, indicator selecting controlled exogenous variables
%
% OUTPUTS:
% - forcs [double] n_endovars*(H+1) array, forecasted endogenous variables
% - e [double] nexo*H array, exogenous variables
%
% ALGORITHM:
%
% Relies on state-space form:
%
% yₜ = T yₜ₋₁ + R εₜ
%
% Both yₜ, the vector of endogenous variables, and εₜ are split up into controlled
% and uncontrolled ones, and we assume, without loss of generality, that the
% constrained endogenous variables and the controlled shocks come first :
%
% ⎧ y₁ₜ ⎫ ⎧ T₁₁ T₁₂ ⎫ ⎧ y₁ₜ₋₁ ⎫ ⎧ R₁₁ R₁₂ ⎫ ⎧ ε₁ₜ ⎫
% ⎩ y₂ₜ ⎭ = ⎩ T₂₁ T₂₂ ⎭ ⎩ y₂ₜ₋₁ ⎭ + ⎩ R₂₁ R₂₂ ⎭ ⎩ ε₂ₜ ⎭
%
% where matrices T and R are partitioned consistently with the
% vectors of endogenous variables and innovations. Provided that matrix
% R₁₁ is square and full rank (a necessary condition is that the
% number of free endogenous variables matches the number of free innovations),
% given y₁ₜ, ε₂ₜ and yₜ₋₁ the first block of equations can be solved for ε₁ₜ:
%
% ε₁ₜ = R₁₁ \ ( y₁ₜ - T₁₁y₁ₜ₋₁ - T₁₂y₂ₜ₋₁ - R₁₂ε₂ₜ )
%
% and y₂ₜ can be updated by evaluating the second block of equations:
%
% y₂ₜ = T₂₁y₁ₜ₋₁ + T₂₂y₂ₜ₋₁ + R₂₁ε₁ₜ + R₂₂ε₂ₜ
%
% By iterating over these two blocks of equations, we can build a forecast for
% all the endogenous variables in the system conditional on paths for a subset of the
% endogenous variables. This exercise is replicated by drawing different
% sequences of free innovations. The result is a predictive distribution for
% the uncontrolled endogenous variables, y₂ₜ, that Dynare will use to report
% confidence bands around the point conditional forecast.
% is used for forecasting
% Copyright © 2006-2022 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
if cL
e = zeros(size(mcValue,1),cL);
for t = 1:cL % Loop over the two blocks of equations
k = find(isfinite(mcValue(:,t))); % missing conditional values are indicated by NaN
e(k,t) = inv(mv(k,:)*R*mu(:,k))*(mcValue(k,t)-mv(k,:)*T*forcs(:,t)-mv(k,:)*R*shocks(:,t));
forcs(:,t+1) = T*forcs(:,t)+R*(mu(:,k)*e(k,t)+shocks(:,t));
end
end
for t = cL+1:H
forcs(:,t+1) = T*forcs(:,t)+R*shocks(:,t);
end
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