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extended_path.m
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Stéphane Adjemian authoredStéphane Adjemian authored
extended_path.m 12.61 KiB
function time_series = extended_path(initial_conditions,sample_size)
% 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 initial_conditions [double] m*nlags array, where m is the number of endogenous variables in the model and
% nlags is the maximum number of lags.
% o sample_size [integer] scalar, size of the sample to be simulated.
%
% OUTPUTS
% o time_series [double] m*sample_size array, the simulations.
%
% ALGORITHM
%
% SPECIAL REQUIREMENTS
% Copyright (C) 2009, 2010, 2011 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_ options_ oo_
debug = 0;
verbosity = options_.ep.verbosity+debug;
% Test if bytecode and block options are used (these options are mandatory)
if ~( options_.bytecode && options_.block )
error('extended_path:: Options bytecode and block are mandatory!')
end
% Set default initial conditions.
if isempty(initial_conditions)
initial_conditions = oo_.steady_state;
end
% Set maximum number of iterations for the deterministic solver.
options_.maxit_ = options_.ep.maxit;
% Set the number of periods for the perfect foresight model
options_.periods = options_.ep.periods;
% Set the algorithm for the perfect foresight solver
options_.stack_solve_algo = options_.ep.stack_solve_algo;
% Compute the first order reduced form if needed.
%
% REMARK. It is assumed that the user did run the same mod file with stoch_simul(order=1) and save
% all the globals in a mat file called linear_reduced_form.mat;
if options_.ep.init
lrf = load('linear_reduced_form','oo_');
oo_.dr = lrf.oo_.dr; clear('lrf');
if options_.ep.init==2
lambda = .8;
end
end
% Do not use a minimal number of perdiods for the perfect foresight solver (with bytecode and blocks)
options_.minimal_solving_period = options_.ep.periods;
% Get indices of variables with non zero steady state
idx = find(abs(oo_.steady_state)>0);
% Initialize the exogenous variables.
make_ex_;
% Initialize the endogenous variables.
make_y_;
% Initialize the output array.
time_series = zeros(M_.endo_nbr,sample_size);
% Set the covariance matrix of the structural innovations.
variances = diag(M_.Sigma_e);
positive_var_indx = find(variances>0);
covariance_matrix = M_.Sigma_e(positive_var_indx,positive_var_indx);
number_of_structural_innovations = length(covariance_matrix);
covariance_matrix_upper_cholesky = chol(covariance_matrix);
% Set seed.
if options_.ep.set_dynare_seed_to_default
set_dynare_seed('default');
end
% Simulate shocks.
switch options_.ep.innovation_distribution
case 'gaussian'
oo_.ep.shocks = randn(sample_size,number_of_structural_innovations)*covariance_matrix_upper_cholesky;
otherwise
error(['extended_path:: ' options_.ep.innovation_distribution ' distribution for the structural innovations is not (yet) implemented!'])
end
% Set future shocks (Stochastic Extended Path approach)
if options_.ep.stochastic
[r,w] = gauss_hermite_weights_and_nodes(options_.ep.number_of_nodes);
switch options_.ep.stochastic
case 1
if M_.exo_nbr>1
rr = cell(1);
ww = cell(1);
for i=1:size(M_.Sigma_e,1)
rr = {r};
ww = {w};
end
rrr = cartesian_product_of_sets(rr{:});
www = cartesian_product_of_sets(ww{:});
else
rrr = r;
www = w;
end
www = prod(www,2);
nnn = length(www);
otherwise
error(['Order ' int2str(options_.ep.stochastic) ' Stochastic Extended Path method is not implemented!'])
end
else
rrr = zeros(1,number_of_structural_innovations);
www = 1;
nnn = 1;
end
% Initializes some variables.
t = 0;
% Set waitbar (graphic or text mode)
graphic_waitbar_flag = ~( options_.console_mode || exist('OCTAVE_VERSION') );
if graphic_waitbar_flag hh = waitbar(0,['Please wait. Extended Path simulations...']);
set(hh,'Name','EP simulations');
else
for i=1:2, disp(' '), end
if ~exist('OCTAVE_VERSION')
back = [];
end
end
% Main loop.
while (t<sample_size)
if ~mod(t,10)
if graphic_waitbar_flag
waitbar(t/sample_size);
else
if exist('OCTAVE_VERSION')
printf('Please wait. Extended Path simulations... %3.f%%\r done', 100*t/sample_size);
else
str = sprintf('Please wait. Extended Path simulations... %3.f%% done.', 100*t/sample_size);
fprintf([back '%s'],str);
back=repmat('\b',1,length(str));
end
end
end
% Set period index.
t = t+1;
shocks = oo_.ep.shocks(t,:);
% Put it in oo_.exo_simul (second line).
oo_.exo_simul(2,positive_var_indx) = shocks;
for s = 1:nnn
oo_.exo_simul(3,positive_var_indx) = rrr(s,:)*covariance_matrix_upper_cholesky;
if options_.ep.init && s==1% Compute first order solution. t==1 &&
initial_path = simult_(initial_conditions,oo_.dr,oo_.exo_simul(2:end,:),1);
if options_.ep.init==1
oo_.endo_simul(:,1:end-1) = initial_path(:,1:end-1);% Last column is the steady state.
elseif options_.ep.init==2
oo_.endo_simul(:,1:end-1) = initial_path(:,1:end-1)*lambda+oo_.endo_simul(:,1:end-1)*(1-lambda);
end
end
% Solve a perfect foresight model (using bytecoded version).
increase_periods = 0;
endo_simul = oo_.endo_simul;
while 1
if ~increase_periods
t0 = tic;
[flag,tmp] = bytecode('dynamic');
ctime = toc(t0);
info.convergence = ~flag;
info.time = ctime;
end
if verbosity
if info.convergence
if t<10
disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
elseif t<100
disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
elseif t<1000
disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
else
disp(['Time: ' int2str(t) '. Convergence of the perfect foresight model solver!'])
end
else
if t<10
disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
elseif t<100
disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
elseif t<1000
disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
else disp(['Time: ' int2str(t) '. No convergence of the perfect foresight model solver!'])
end
end
end
% Test if periods is big enough.
if ~increase_periods && max(max(abs(tmp(idx,end-options_.ep.lp:end)./tmp(idx,end-options_.ep.lp-1:end-1)-1)))<options_.dynatol.x
break
else
options_.periods = options_.periods + options_.ep.step;
options_.minimal_solving_period = options_.periods;
increase_periods = increase_periods + 1;
if verbosity
if t<10
disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
elseif t<100
disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
elseif t<1000
disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
else
disp(['Time: ' int2str(t) '. I increase the number of periods to ' int2str(options_.periods) '.'])
end
end
if info.convergence
oo_.endo_simul = [ tmp , repmat(oo_.steady_state,1,options_.ep.step) ];
oo_.exo_simul = [ oo_.exo_simul ; zeros(options_.ep.step,size(shocks,2)) ];
tmp_old = tmp;
else
oo_.endo_simul = [ oo_.endo_simul , repmat(oo_.steady_state,1,options_.ep.step) ];
oo_.exo_simul = [ oo_.exo_simul ; zeros(options_.ep.step,size(shocks,2)) ];
end
t0 = tic;
[flag,tmp] = bytecode('dynamic');
ctime = toc(t0);
info.time = info.time+ctime;
if info.convergence
maxdiff = max(max(abs(tmp(:,2:options_.ep.fp)-tmp_old(:,2:options_.ep.fp))));
if maxdiff<options_.dynatol.x
options_.periods = options_.ep.periods;
options_.minimal_solving_period = options_.periods;
oo_.exo_simul = oo_.exo_simul(1:(options_.periods+2),:);
break
end
else
info.convergence = ~flag;
if info.convergence
continue
else
if increase_periods==10;
if verbosity
if t<10
disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
elseif t<100
disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
elseif t<1000
disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
else
disp(['Time: ' int2str(t) '. Even with ' int2str(options_.periods) ', I am not able to solve the perfect foresight model. Use homotopy instead...'])
end
end
break
end
end
end
end
end
if ~info.convergence% If the previous step was unsuccesfull, use an homotopic approach
[INFO,tmp] = homotopic_steps(.5,.01,t);
% Cumulate time.
info.time = ctime+INFO.time;
if (~isstruct(INFO) && isnan(INFO)) || ~INFO.convergence disp('Homotopy:: No convergence of the perfect foresight model solver!')
error('I am not able to simulate this model!');
else
info.convergence = 1;
oo_.endo_simul = tmp;
if verbosity && info.convergence
disp('Homotopy:: Convergence of the perfect foresight model solver!')
end
end
else
oo_.endo_simul = tmp;
end
% Save results of the perfect foresight model solver.
time_series(:,t) = time_series(:,t)+ www(s)*oo_.endo_simul(:,2);
%save('simulated_paths.mat','time_series');
% Set initial condition for the nex round.
%initial_conditions = oo_.endo_simul(:,2);
end
%oo_.endo_simul = oo_.endo_simul(:,1:options_.periods+M_.maximum_endo_lag+M_.maximum_endo_lead);
oo_.endo_simul(:,1:end-1) = oo_.endo_simul(:,2:end);
oo_.endo_simul(:,1) = time_series(:,t);
oo_.endo_simul(:,end) = oo_.steady_state;
end
if graphic_waitbar_flag
close(hh);
else
if ~exist('OCTAVE_VERSION')
fprintf(back);
end
end
oo_.endo_simul = oo_.steady_state;