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function innovation_paths = reversed_extended_path(controlled_variable_names, control_innovation_names, dataset)
% Inversion of the extended path simulation approach. This routine computes the innovations needed to
% reproduce the time path of a subset of endogenous variables. The initial condition is teh deterministic
% steady state.
%
% INPUTS
% o controlled_variable_names [string] n*1 matlab's cell.
% o control_innovation_names [string] n*1 matlab's cell.
% o dataset [structure]
% OUTPUTS
% o innovations [double] n*T matrix.
%
% ALGORITHM
%
% SPECIAL REQUIREMENTS
% Copyright (C) 2010-2018 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 <http://www.gnu.org/licenses/>.
global M_ oo_ options_
%% Initialization
% Load data.
eval(dataset.name);
dataset.data = [];
for v = 1:dataset.number_of_observed_variables
eval(['dataset.data = [ dataset.data , ' dataset.variables(v,:) ' ];'])
end
data = dataset.data(dataset.first_observation:dataset.first_observation+dataset.number_of_observations,:);
% Compute the deterministic steady state.
steady_;
% Compute the first order perturbation reduced form.
old_options_order = options_.order; options_.order = 1;
[dr,info,M_,options_,oo_] = resol(0,M_,options_,oo_);
oo_.dr = dr;
options_.order = old_options_order;
% Set various options.
options_.periods = 100;
% Set-up oo_.exo_simul.
oo_=make_ex_(M_,options_,oo_);
% Set-up oo_.endo_simul.
oo_=make_y_(M_,options_,oo_);
% Get indices of the controlled endogenous variables in endo_simul.
n = length(controlled_variable_names);
iy = NaN(n,1);
for k=1:n
iy(k) = strmatch(controlled_variable_names{k}, M_.endo_names, 'exact');
end
% Get indices of the controlled endogenous variables in dataset.
iy_ = NaN(n,1);
for k=1:n
iy_(k) = strmatch(controlled_variable_names{k},dataset.variables,'exact');
end
% Get indices of the control innovations in exo_simul.
ix = NaN(n,1);
for k=1:n
ix(k) = strmatch(control_innovation_names{k},M_.exo_names,'exact');
end
% Get the length of the sample.
T = size(data,1);
% Output initialization.
innovation_paths = zeros(n,T);
% Initialization of the perfect foresight model solver.
perfect_foresight_simulation();
% Set options for fsolve.
options = optimset('MaxIter',10000,'Display','Iter');
%% Call fsolve recursively
for t=1:T
x0 = zeros(n,1);
y_target = transpose(data(t,iy_));
total_variation = y_target-transpose(oo_.endo_simul(t+M_.maximum_lag,iy));
for i=1:100
[t,i]
y = transpose(oo_.endo_simul(t+M_.maximum_lag,iy)) + (i/100)*y_target
[tmp,fval,exitflag] = fsolve('ep_residuals', x0, options, y, ix, iy, oo_.steady_state, oo_.dr, M_.maximum_lag, M_.endo_nbr);
end
if exitflag==1
innovation_paths(:,t) = tmp;
end
% Update endo_simul.
oo_.endo_simul(:,1:end-1) = oo_.endo_simul(:,2:end);
oo_.endo_simul(:,end) = oo_.steady_state;
end
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