177 lines
7.1 KiB
Matlab
177 lines
7.1 KiB
Matlab
function y_=simult_(M_,options_,y0,dr,ex_,iorder)
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% Simulates the model using a perturbation approach, given the path for the exogenous variables and the
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% decision rules.
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%
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% INPUTS
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% M_ [struct] model
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% options_ [struct] options
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% y0 [double] n*1 vector, initial value (n is the number of declared endogenous variables plus the number
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% of auxilliary variables for lags and leads); must be in declaration order, i.e. as in M_.endo_names
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% dr [struct] matlab's structure where the reduced form solution of the model is stored.
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% ex_ [double] T*q matrix of innovations.
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% iorder [integer] order of the taylor approximation.
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%
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% OUTPUTS
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% y_ [double] n*(T+1) time series for the endogenous variables.
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright (C) 2001-2020 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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iter = size(ex_,1);
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endo_nbr = M_.endo_nbr;
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exo_nbr = M_.exo_nbr;
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y_ = zeros(size(y0,1),iter+M_.maximum_lag);
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y_(:,1) = y0;
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if options_.loglinear && ~options_.logged_steady_state
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dr.ys=log(dr.ys);
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end
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if ~options_.k_order_solver || (options_.k_order_solver && options_.pruning) %if k_order_pert is not used or if we do not use Dynare++ with k_order_pert
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if iorder==1
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y_(:,1) = y_(:,1)-dr.ys;
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end
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end
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if options_.k_order_solver && ~options_.pruning % Call dynare++ routines.
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ex_ = [zeros(M_.maximum_lag,M_.exo_nbr); ex_];
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y_ = dynare_simul_(options_.order,M_.nstatic,M_.npred,M_.nboth,M_.nfwrd,exo_nbr, ...
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y_(dr.order_var,1),ex_',M_.Sigma_e,options_.DynareRandomStreams.seed, ...
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dr.ys(dr.order_var),dr);
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y_(dr.order_var,:) = y_;
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else
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if options_.block
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if M_.maximum_lag > 0
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k2 = dr.state_var;
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else
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k2 = [];
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end
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order_var = 1:endo_nbr;
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dr.order_var = order_var;
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else
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k2 = dr.kstate(find(dr.kstate(:,2) <= M_.maximum_lag+1),[1 2]);
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k2 = k2(:,1)+(M_.maximum_lag+1-k2(:,2))*endo_nbr;
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order_var = dr.order_var;
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end
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switch iorder
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case 1
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if isempty(dr.ghu)% For (linearized) deterministic models.
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for i = 2:iter+M_.maximum_lag
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yhat = y_(order_var(k2),i-1);
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y_(order_var,i) = dr.ghx*yhat;
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end
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elseif isempty(dr.ghx)% For (linearized) purely forward variables (no state variables).
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y_(dr.order_var,:) = dr.ghu*transpose(ex_);
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else
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epsilon = dr.ghu*transpose(ex_);
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for i = 2:iter+M_.maximum_lag
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yhat = y_(order_var(k2),i-1);
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y_(order_var,i) = dr.ghx*yhat + epsilon(:,i-1);
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end
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end
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y_ = bsxfun(@plus,y_,dr.ys);
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case 2
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constant = dr.ys(order_var)+.5*dr.ghs2;
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if options_.pruning
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y__ = y0;
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for i = 2:iter+M_.maximum_lag
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yhat1 = y__(order_var(k2))-dr.ys(order_var(k2));
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yhat2 = y_(order_var(k2),i-1)-dr.ys(order_var(k2));
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epsilon = ex_(i-1,:)';
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abcOut1 = A_times_B_kronecker_C(.5*dr.ghxx,yhat1);
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abcOut2 = A_times_B_kronecker_C(.5*dr.ghuu,epsilon);
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abcOut3 = A_times_B_kronecker_C(dr.ghxu,yhat1,epsilon);
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y_(order_var,i) = constant + dr.ghx*yhat2 + dr.ghu*epsilon ...
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+ abcOut1 + abcOut2 + abcOut3;
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y__(order_var) = dr.ys(order_var) + dr.ghx*yhat1 + dr.ghu*epsilon;
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end
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else
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for i = 2:iter+M_.maximum_lag
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yhat = y_(order_var(k2),i-1)-dr.ys(order_var(k2));
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epsilon = ex_(i-1,:)';
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abcOut1 = A_times_B_kronecker_C(.5*dr.ghxx,yhat);
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abcOut2 = A_times_B_kronecker_C(.5*dr.ghuu,epsilon);
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abcOut3 = A_times_B_kronecker_C(dr.ghxu,yhat,epsilon);
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y_(dr.order_var,i) = constant + dr.ghx*yhat + dr.ghu*epsilon ...
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+ abcOut1 + abcOut2 + abcOut3;
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end
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end
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case 3
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% only with pruning
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% the third moments of the shocks are assumed null. We don't have
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% an interface for specifying them
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ghx = dr.ghx;
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ghu = dr.ghu;
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ghxx = dr.ghxx;
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ghxu = dr.ghxu;
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ghuu = dr.ghuu;
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ghs2 = dr.ghs2;
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ghxxx = dr.ghxxx;
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ghxxu = dr.ghxxu;
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ghxuu = dr.ghxuu;
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ghuuu = dr.ghuuu;
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ghxss = dr.ghxss;
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ghuss = dr.ghuss;
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nspred = M_.nspred;
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ipred = M_.nstatic+(1:nspred);
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%construction follows Andreasen et al (2013), Technical
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%Appendix, Formulas (65) and (66)
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%split into first, second, and third order terms
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yhat1 = y0(order_var(k2))-dr.ys(order_var(k2));
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yhat2 = zeros(nspred,1);
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yhat3 = zeros(nspred,1);
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for i=2:iter+M_.maximum_lag
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u = ex_(i-1,:)';
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%construct terms of order 2 from second order part, based
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%on linear component yhat1
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gyy = A_times_B_kronecker_C(ghxx,yhat1);
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guu = A_times_B_kronecker_C(ghuu,u);
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gyu = A_times_B_kronecker_C(ghxu,yhat1,u);
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%construct terms of order 3 from second order part, based
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%on order 2 component yhat2
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gyy12 = A_times_B_kronecker_C(ghxx,yhat1,yhat2);
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gy2u = A_times_B_kronecker_C(ghxu,yhat2,u);
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%construct terms of order 3, all based on first order component yhat1
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y2a = kron(yhat1,yhat1);
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gyyy = A_times_B_kronecker_C(ghxxx,y2a,yhat1);
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u2a = kron(u,u);
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guuu = A_times_B_kronecker_C(ghuuu,u2a,u);
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yu = kron(yhat1,u);
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gyyu = A_times_B_kronecker_C(ghxxu,yhat1,yu);
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gyuu = A_times_B_kronecker_C(ghxuu,yu,u);
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%add all terms of order 3, linear component based on third
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%order yhat3
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yhat3 = ghx*yhat3 +gyy12 ... % prefactor is 1/2*2=1, see (65) Appendix Andreasen et al.
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+ gy2u ... % prefactor is 1/2*2=1, see (65) Appendix Andreasen et al.
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+ 1/6*(gyyy + guuu + 3*(gyyu + gyuu + ghxss*yhat1 + ghuss*u)); %note: s is treated as variable, thus xss and uss are third order
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yhat2 = ghx*yhat2 + 1/2*(gyy + guu + 2*gyu + ghs2);
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yhat1 = ghx*yhat1 + ghu*u;
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y_(order_var,i) = dr.ys(order_var)+yhat1 + yhat2 + yhat3; %combine terms again
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yhat1 = yhat1(ipred);
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yhat2 = yhat2(ipred);
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yhat3 = yhat3(ipred);
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end
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otherwise
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error(['pruning not available for order = ' int2str(options_.order)])
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end
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end
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