147 lines
4.6 KiB
Matlab
147 lines
4.6 KiB
Matlab
function time_series = extended_path(initial_conditions,sample_size,init)
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% Stochastic simulation of a non linear DSGE model using the Extended Path method (Fair and Taylor 1983). A time
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% series of size T is obtained by solving T perfect foresight models.
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%
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% INPUTS
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% o initial_conditions [double] m*nlags array, where m is the number of endogenous variables in the model and
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% nlags is the maximum number of lags.
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% o sample_size [integer] scalar, size of the sample to be simulated.
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% o init [integer] scalar, method of initialization of the perfect foresight equilibrium paths
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% init=0 previous solution is used,
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% init=1 a path generated with the first order reduced form is used.
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% init=2 mix of cases 0 and 1.
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%
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% OUTPUTS
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% o time_series [double] m*sample_size array, the simulations.
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%
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% ALGORITHM
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%
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% SPECIAL REQUIREMENTS
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% Copyright (C) 2009-2010 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 <http://www.gnu.org/licenses/>.
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global M_ oo_ options_
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% Set default initial conditions.
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if isempty(initial_conditions)
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initial_conditions = repmat(oo_.steady_state,1,M_.maximum_lag);
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end
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% Set default value for the last input argument
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if nargin<3
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init = 0;
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end
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% Set the number of periods for the deterministic solver.
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%options_.periods = 40;
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% Initialize the exogenous variables.
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make_ex_;
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% Initialize the endogenous variables.
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make_y_;
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% Compute the first order reduced form if needed.
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if init
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oldopt = options_;
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options_.order = 1;
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[dr,info,M_,options_,oo_] = resol(0,M_,options_,oo_);
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oo_.dr = dr;
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options_ = oldopt;
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if init==2
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lambda = .8;
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end
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end
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% Initialize the output array.
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time_series = NaN(M_.endo_nbr,sample_size+1);
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% Set the covariance matrix of the structural innovations.
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variances = diag(M_.Sigma_e);
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positive_var_indx = find(variances>0);
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covariance_matrix = M_.Sigma_e(positive_var_indx,positive_var_indx);
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number_of_structural_innovations = length(covariance_matrix);
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covariance_matrix_upper_cholesky = chol(covariance_matrix);
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tdx = M_.maximum_lag+1;
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norme = 0;
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% Set verbose option
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verbose = 0;
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t = 0;
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new_draw = 1;
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perfect_foresight_simulation();
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while (t<=sample_size)
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t = t+1;
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if new_draw
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gaussian_draw = randn(1,number_of_structural_innovations);
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else
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gaussian_draw = .5*gaussian_draw ;
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new_draw = 1;
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end
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shocks = exp(gaussian_draw*covariance_matrix_upper_cholesky-.5*variances(positive_var_indx)');
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oo_.exo_simul(tdx,positive_var_indx) = shocks;
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if init
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% Compute first order solution.
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exogenous_variables = zeros(size(oo_.exo_simul));
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exogenous_variables(tdx,positive_var_indx) = log(shocks);
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initial_path = simult_(oo_.steady_state,dr,exogenous_variables,1);
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if init==1
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oo_.endo_simul = initial_path(:,1:end-1);
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else
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oo_.endo_simul = initial_path(:,1:end-1)*lambda + oo_.endo_simul*(1-lambda);
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end
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end
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if init
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info = perfect_foresight_simulation(dr,oo_.steady_state);
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else
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info = perfect_foresight_simulation;
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end
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time = info.time;
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if verbose
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[t,options_.periods]
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info
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info.iterations
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end
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if ~info.convergence
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INFO = homotopic_steps(tdx,positive_var_indx,shocks,norme,.5,init,0);
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if verbose
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norme
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INFO
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end
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if ~isstruct(INFO) && isnan(INFO)
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t = t-1;
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new_draw = 0;
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else
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info = INFO;
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end
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else
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norme = sqrt(sum((shocks-1).^2,2));
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end
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%if ~info.convergence
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% error('I am not able to simulate this model!')
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%end
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if new_draw
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info.time = info.time+time;
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time_series(:,t+1) = oo_.endo_simul(:,tdx);
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oo_.endo_simul(:,1:end-1) = oo_.endo_simul(:,2:end);
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oo_.endo_simul(:,end) = oo_.steady_state;
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end
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end |