adding simul_backward and simul_backward_linear
Michel Juillard
parent
c2d72d2292
commit
6fd715a3b8
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function DynareOutput = simul_backward_linear_model(initial_conditions, sample_size, DynareOptions, DynareModel, DynareOutput, innovations)
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%@info:
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%! @deftypefn {Function File} {@var{DynareOutput} =} simul_backward_nonlinear_model (@var{sample_size},@var{DynareOptions}, @var{DynareModel}, @var{DynareOutput})
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%! @anchor{@simul_backward_nonlinear_model}
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%! @sp 1
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%! Simulates a stochastic non linear backward looking model with arbitrary precision (a deterministic solver is used).
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%! @sp 2
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%! @strong{Inputs}
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%! @sp 1
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%! @table @ @var
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%! @item sample_size
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%! Scalar integer, size of the sample to be generated.
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%! @item DynareOptions
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%! Matlab/Octave structure (Options used by Dynare).
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%! @item DynareDynareModel
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%! Matlab/Octave structure (Description of the model).
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%! @item DynareOutput
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%! Matlab/Octave structure (Results reported by Dynare).
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%! @end table
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%! @sp 1
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%! @strong{Outputs}
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%! @sp 1
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%! @table @ @var
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%! @item DynareOutput
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%! Matlab/Octave structure (Results reported by Dynare).
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%! @end table
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%! @sp 2
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%! @strong{This function is called by:}
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%! @sp 2
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%! @strong{This function calls:}
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%! @ref{dynTime}
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%!
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%! @end deftypefn
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%@eod:
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% Copyright (C) 2012-2016 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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number_of_shocks = size(DynareOutput.exo_simul,2);
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% Get usefull vector of indices.
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ny0 = nnz(DynareModel.lead_lag_incidence(2,:));
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ny1 = nnz(DynareModel.lead_lag_incidence(1,:));
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iy1 = find(DynareModel.lead_lag_incidence(1,:)>0);
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idx = 1:DynareModel.endo_nbr;
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jdx = idx+ny1;
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hdx = 1:ny1;
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% Get the name of the dynamic model routine.
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model_dynamic = str2func([DynareModel.fname,'_dynamic']);
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% initialization of vector y.
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y = NaN(length(idx)+ny1,1);
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% initialization of the returned simulations.
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DynareOutput.endo_simul = NaN(DynareModel.endo_nbr,sample_size+1);
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if isempty(initial_conditions)
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DynareOutput.endo_simul(:,1) = DynareOutput.steady_state;
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else
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DynareOutput.endo_simul(:,1) = initial_conditions;
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end
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Y = DynareOutput.endo_simul;
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% get coefficients
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[cst,jacob] = model_dynamic(zeros(DynareModel.endo_nbr+ny1,1), ...
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zeros(2,size(DynareOutput.exo_simul, 2)), ...
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DynareModel.params, ...
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DynareOutput.steadystate,2);
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A0inv = inv(jacob(:,jdx));
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A1 = jacob(:,nonzeros(DynareModel.lead_lag_incidence(1,:)));
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B = jacob(:,end-number_of_shocks+1:end);
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% Simulations
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for it = 2:sample_size+1
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Y(:,it) = -A0inv*(cst + A1*Y(iy1,it-1) + B*DynareOutput.exo_simul(it,:)');
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end
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DynareOutput.endo_simul = Y;
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@ -0,0 +1,95 @@
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function DynareOutput = simul_backward_linear_model(initial_conditions, sample_size, DynareOptions, DynareModel, DynareOutput, innovations)
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%@info:
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%! @deftypefn {Function File} {@var{DynareOutput} =} simul_backward_nonlinear_model (@var{sample_size},@var{DynareOptions}, @var{DynareModel}, @var{DynareOutput})
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%! @anchor{@simul_backward_nonlinear_model}
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%! @sp 1
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%! Simulates a stochastic non linear backward looking model with arbitrary precision (a deterministic solver is used).
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%! @sp 2
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%! @strong{Inputs}
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%! @sp 1
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%! @table @ @var
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%! @item sample_size
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%! Scalar integer, size of the sample to be generated.
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%! @item DynareOptions
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%! Matlab/Octave structure (Options used by Dynare).
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%! @item DynareDynareModel
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%! Matlab/Octave structure (Description of the model).
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%! @item DynareOutput
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%! Matlab/Octave structure (Results reported by Dynare).
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%! @end table
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%! @sp 1
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%! @strong{Outputs}
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%! @sp 1
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%! @table @ @var
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%! @item DynareOutput
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%! Matlab/Octave structure (Results reported by Dynare).
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%! @end table
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%! @sp 2
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%! @strong{This function is called by:}
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%! @sp 2
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%! @strong{This function calls:}
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%! @ref{dynTime}
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%!
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%! @end deftypefn
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%@eod:
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% Copyright (C) 2012-2016 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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if DynareModel.maximum_lead
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error(['simul_backward_nonlinear_model:: The specified model is not backward looking!'])
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end
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if nargin<6
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% Set the covariance matrix of the structural innovations.
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variances = diag(DynareModel.Sigma_e);
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number_of_shocks = length(DynareModel.Sigma_e);
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positive_var_indx = find(variances>0);
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effective_number_of_shocks = length(positive_var_indx);
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covariance_matrix = DynareModel.Sigma_e(positive_var_indx,positive_var_indx);
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covariance_matrix_upper_cholesky = chol(covariance_matrix);
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% Set seed to its default state.
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if DynareOptions.bnlms.set_dynare_seed_to_default
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set_dynare_seed('default');
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end
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% Simulate structural innovations.
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switch DynareOptions.bnlms.innovation_distribution
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case 'gaussian'
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DynareOutput.bnlms.shocks = randn(sample_size,effective_number_of_shocks)*covariance_matrix_upper_cholesky;
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otherwise
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error(['simul_backward_nonlinear_model:: ' DynareOption.bnlms.innovation_distribution ' distribution for the structural innovations is not (yet) implemented!'])
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end
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% Put the simulated innovations in DynareOutput.exo_simul.
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DynareOutput.exo_simul = zeros(sample_size+1,number_of_shocks);
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DynareOutput.exo_simul(2:end,positive_var_indx) = DynareOutput.bnlms.shocks;
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else
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number_of_shocks = size(innovations,2);
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DynareOutput.exo_simul = innovations;
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end
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if DynareOptions.linear
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DynareOutput = simul_backward_linear_model(initial_conditions, sample_size, DynareOptions, ...
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DynareModel, DynareOutput, innovations);
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else
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DynareOutput = simul_backward_nonlinear_model(initial_conditions, sample_size, DynareOptions, ...
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DynareModel, DynareOutput, innovations);
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end
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@ -240,6 +240,7 @@ MODFILES = \
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ep/linearmodel1.mod \
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stochastic-backward-models/solow_cd.mod \
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stochastic-backward-models/solow_ces.mod \
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stochastic-backward-models/backward_linear.mod \
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deterministic_simulations/purely_forward/ar1.mod \
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deterministic_simulations/purely_forward/nk.mod \
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deterministic_simulations/purely_backward/ar1.mod \
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@ -0,0 +1,41 @@
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var y gdp gdp_pot g pi P rs;
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varexo e_y e_g e_p;
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parameters alpha_1 alpha_2 beta_1 beta_2 theta gamma_1 gamma_2 pi_tar g_ss rr_bar;
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alpha_1 = 0.9;
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alpha_2 = -0.1;
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beta_1 = 0.8;
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beta_2 = 0.1;
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theta = 0.9;
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gamma_1 = 1.5;
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gamma_2 = 0.5;
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pi_tar = 2;
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g_ss = 0.005;
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rr_bar = 1;
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model(linear);
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gdp = gdp_pot + y;
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y = alpha_1*y(-1) + alpha_2*(rs - pi - rr_bar) + e_y;
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gdp_pot = gdp_pot(-1) + g;
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g = (1 - theta)*g_ss + theta*g(-1) + e_g;
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pi = (1 - beta_1)*pi_tar + beta_1*pi(-1) + beta_2*y + e_p;
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P = pi/400 + P(-1);
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rs = rr_bar + pi_tar + gamma_1*(pi(-1) - pi_tar) + gamma_2*y(-1);
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end;
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histval;
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gdp_pot(0) = 1;
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P(0) = 1;
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g(0) = g_ss;
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pi(0) = pi_tar;
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end;
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oo_.steadystate = NaN(7,1);
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oo_ = simul_backward_model(M_.endo_histval, 10, options_, M_, oo_, zeros(11,3));
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err1 = norm(abs(oo_.endo_simul([1 4 5 7],2:end) - repmat([0 0.005 2 3]',1,10)));
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err2 = norm(abs(oo_.endo_simul([2 3 6],2:end) - repmat(linspace(1.005,1.05,10),3,1)));
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if err1 > 1e-14 || err2 > 1e-14;
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error('Error in backward_linear.mod');
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end;
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