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function Simulations = extended_path_mc(initialconditions, samplesize, replic, exogenousvariables, options_, M_, oo_)
% Simulations = extended_path_mc(initialconditions, samplesize, replic, exogenousvariables, options_, M_, oo_)
% Stochastic simulation of a non linear DSGE model using the Extended Path method (Fair and Taylor 1983). A time
% series of size T is obtained by solving T perfect foresight models.
%
% INPUTS
% o initialconditions [double] m*1 array, where m is the number of endogenous variables in the model.
% o samplesize [integer] scalar, size of the sample to be simulated.
% o exogenousvariables [double] T*n array, values for the structural innovations.
% o options_ [struct] Dynare's options structure
% o M_ [struct] Dynare's model structure
% o oo_ [struct] Dynare's results structure
%
% OUTPUTS
% o ts [dseries] m*samplesize array, the simulations.
% o results [cell]
%
% ALGORITHM
%
% SPECIAL REQUIREMENTS
% Copyright © 2016-2023 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/>.
[initialconditions, innovations, pfm, ep, ~, options_, oo_] = ...
extended_path_initialization(initialconditions, samplesize, exogenousvariables, options_, M_, oo_);
% Check the dimension of the first input argument
if isequal(size(initialconditions, 2), 1)
initialconditions = repmat(initialconditions, 1, replic);
else
if ~isequal(size(initialconditions, 2), replic)
error('Wrong size. Number of columns in first argument should match the value of the third argument!')
end
end
% Check the dimension of the fourth input argument
if isempty(exogenousvariables)
exogenousvariables = repmat(exogenousvariables, [1, 1, replic]);
else
if ~isequal(size(exogenousvariables, 3), replic)
error('Wrong size. !')
end
end
if ~isequal(size(exogenousvariables, 3), replic)
error('Wrong dimensions. Fourth argument must be a 3D array with as many pages as the value of the third argument!')
end
data = NaN(size(initialconditions, 1), samplesize+1, replic);
vexo = NaN(innovations.effective_number_of_shocks, samplesize+1, replic);
info = NaN(replic, 1);
if ep.parallel
% Use the Parallel toolbox.
parfor i=1:replic
innovations_ = innovations;
oo__ = oo_;
[shocks, spfm_exo_simul, innovations_, oo__] = extended_path_shocks(innovations_, ep, exogenousvariables(:,:,i), samplesize, M_, options_, oo__);
endogenous_variables_paths = NaN(M_.endo_nbr,samplesize+1);
endogenous_variables_paths(:,1) = initialconditions(:,1);
exogenous_variables_paths = NaN(innovations_.effective_number_of_shocks,samplesize+1);
exogenous_variables_paths(:,1) = 0;
info_convergence = true;
t = 1;
while t<=samplesize
t = t+1;
spfm_exo_simul(2,:) = shocks(t-1,:);
exogenous_variables_paths(:,t) = shocks(t-1,:);
[endogenous_variables_paths(:,t), info_convergence] = extended_path_core(ep.periods, M_.endo_nbr, M_.exo_nbr, innovations_.positive_var_indx, ...
spfm_exo_simul, ep.init, endogenous_variables_paths(:,t-1), ...
oo__.steady_state, ...
ep.verbosity, ep.stochastic.order, ...
M_, pfm,ep.stochastic.algo, ep.solve_algo, ep.stack_solve_algo, ...
options_.lmmcp, options_, oo__);
if ~info_convergence
msg = sprintf('No convergence of the (stochastic) perfect foresight solver (in period %s, iteration %s)!', int2str(t), int2str(i));
warning(msg)
break
end
end % Loop over t
info(i) = info_convergence;
vexo(:,:,i) = exogenous_variables_paths;
data(:,:,i) = endogenous_variables_paths;
end
else
% Sequential approach.
for i=1:replic
[shocks, spfm_exo_simul, innovations, oo_] = extended_path_shocks(innovations, ep, exogenousvariables(:,:,i), samplesize, M_, options_, oo_);
endogenous_variables_paths = NaN(M_.endo_nbr,samplesize+1);
endogenous_variables_paths(:,1) = initialconditions(:,1);
exogenous_variables_paths = NaN(innovations.effective_number_of_shocks,samplesize+1);
exogenous_variables_paths(:,1) = 0;
t = 1;
while t<=samplesize
t = t+1;
spfm_exo_simul(2,:) = shocks(t-1,:);
exogenous_variables_paths(:,t) = shocks(t-1,:);
[endogenous_variables_paths(:,t), info_convergence] = extended_path_core(ep.periods, M_.endo_nbr, M_.exo_nbr, innovations.positive_var_indx, ...
spfm_exo_simul, ep.init, endogenous_variables_paths(:,t-1), ...
oo_.steady_state, ...
ep.verbosity, ep.stochastic.order, ...
M_, pfm,ep.stochastic.algo, ep.solve_algo, ep.stack_solve_algo, ...
options_.lmmcp, options_, oo_);
if ~info_convergence
msg = sprintf('No convergence of the (stochastic) perfect foresight solver (in period %s, iteration %s)!', int2str(t), int2str(i));
warning(msg)
break
end
end % Loop over t
info(i) = info_convergence;
vexo(:,:,i) = exogenous_variables_paths;
data(:,:,i) = endogenous_variables_paths;
end % Loop over i
end
Simulations.innovations = vexo;
Simulations.data = data;
Simulations.info = info;
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