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