adapted dyn_first_order_solver.m for models without lagged variables
and singular coefficient matrix for current variablestime-shift
Michel Juillard
parent
1732db842f
commit
1b3aa73c04
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@ -64,8 +64,11 @@ function [dr,info] = dyn_first_order_solver(jacobia,DynareModel,dr,DynareOptions
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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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persistent reorder_jacobian_columns innovations_idx index_s index_m index_c index_p row_indx index_0m index_0p k1 k2 j3 j4 state_var
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persistent ndynamic nstatic nfwrd npred nboth nd nyf n
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persistent reorder_jacobian_columns innovations_idx index_s index_m index_c
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persistent index_p row_indx index_0m index_0p k1 k2 state_var
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persistent ndynamic nstatic nfwrd npred nboth nd nyf n_current index_d
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persistent index_e index_d1 index_d2 index_e1 index_e2 row_indx_de_1
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persistent row_indx_de_2 cols_b
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if ~nargin
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@ -76,8 +79,11 @@ if ~nargin
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return
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end
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if isempty(reorder_jacobian_columns)
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exo_nbr = DynareModel.exo_nbr;
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if isempty(reorder_jacobian_columns)
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maximum_lag = DynareModel.maximum_endo_lag;
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kstate = dr.kstate;
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nfwrd = dr.nfwrd;
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nboth = dr.nboth;
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@ -85,7 +91,7 @@ if isempty(reorder_jacobian_columns)
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nstatic = dr.nstatic;
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ndynamic = npred+nfwrd+nboth;
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nyf = nfwrd + nboth;
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n = ndynamic+nstatic;
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n = DynareModel.endo_nbr;
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k1 = 1:(npred+nboth);
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k2 = 1:(nfwrd+nboth);
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@ -95,45 +101,61 @@ if isempty(reorder_jacobian_columns)
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lead_lag_incidence = DynareModel.lead_lag_incidence;
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nz = nnz(lead_lag_incidence);
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%lead variables actually present in the model
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j4 = nstatic+npred+1:nstatic+npred+nboth+nfwrd; % Index on the forward and both variables
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j3 = nonzeros(lead_lag_incidence(2,j4)) - nstatic - 2 * npred - nboth; % Index on the non-zeros forward and both variables
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j4 = find(lead_lag_incidence(2,j4));
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no_lead_id = find(lead_lag_incidence(3,:)==0);
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no_lag_id = find(lead_lag_incidence(1,:)==0);
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static_id = intersect(no_lead_id,no_lag_id);
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lag_id = setdiff(no_lead_id,static_id);
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lead_id = setdiff(no_lag_id,static_id);
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both_id = intersect(setdiff(1:n,no_lead_id),setdiff(1:n,no_lag_id));
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lead_idx = lead_lag_incidence(3,lead_id);
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lag_idx = lead_lag_incidence(1,lag_id);
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both_lagged_idx = lead_lag_incidence(1,both_id);
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both_leaded_idx = lead_lag_incidence(3,both_id);
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innovations_idx = (size(jacobia,2)-DynareModel.exo_nbr+1):size(jacobia,2);
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state_var = [lag_idx, both_lagged_idx];
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indexi_0 = 0;
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if DynareModel.maximum_endo_lag > 0 && (npred > 0 || nboth > 0)
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indexi_0 = min(lead_lag_incidence(2,:));
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lead_id = find(lead_lag_incidence(maximum_lag+2,:));
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lead_idx = lead_lag_incidence(maximum_lag+2,lead_id);
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if maximum_lag
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lag_id = find(lead_lag_incidence(1,:));
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lag_idx = lead_lag_incidence(1,lag_id);
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static_id = find((lead_lag_incidence(1,:) == 0) & ...
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(lead_lag_incidence(3,:) == 0));
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else
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lag_id = [];
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lag_idx = [];
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static_id = find(lead_lag_incidence(2,:)==0);
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end
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index_c = lead_lag_incidence(2,:); % Index of all endogenous variables present at time=t
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index_s = lead_lag_incidence(2,1:nstatic); % Index of all static endogenous variables present at time=t
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index_0m = (nstatic+1:nstatic+npred)+indexi_0-1;
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index_0p = (nstatic+npred+1:n)+indexi_0-1;
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both_id = intersect(lead_id,lag_id);
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if maximum_lag
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no_both_lag_id = setdiff(lag_id,both_id);
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else
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no_both_lag_id = [];
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end
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innovations_idx = nz+(1:exo_nbr);
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state_var = [lag_id, both_id];
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index_c = nonzeros(lead_lag_incidence(maximum_lag+1,:)); % Index of all endogenous variables present at time=t
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n_current = length(index_c);
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index_s = npred+nboth+(1:nstatic); % Index of all static
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% endogenous variables
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% present at time=t
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indexi_0 = npred+nboth;
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npred0 = nnz(lead_lag_incidence(maximum_lag+1,no_both_lag_id));
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index_0m = indexi_0+nstatic+(1:npred0);
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nfwrd0 = nnz(lead_lag_incidence(2,lead_id));
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index_0p = indexi_0+nstatic+npred0+(1:nfwrd0);
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index_m = 1:(npred+nboth);
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index_p = lead_lag_incidence(3,find(lead_lag_incidence(3,:)));
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row_indx = nstatic+1:n;
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index_p = npred+nboth+n_current+(1:(nfwrd+nboth));
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row_indx_de_1 = 1:ndynamic;
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row_indx_de_2 = ndynamic+1:nboth;
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row_indx = nstatic+row_indx_de_1;
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index_d = [index_0m index_p];
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llx = lead_lag_incidence(:,order_var);
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index_d1 = [find(llx(maximum_lag+1,nstatic+(1:npred))), npred+nboth+(1:nyf) ];
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index_d2 = npred+1:nboth;
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reorder_jacobian_columns = [lag_idx, both_lagged_idx, npred+nboth+[static_id lag_id both_id lead_id], both_leaded_idx, lead_idx, innovations_idx ];
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index_e = [index_m index_0p];
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index_e1 = [1:(npred+nboth), npred+nboth+find(llx(maximum_lag+1,nstatic+npred+(1: ...
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nyf)))];
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index_e2 = npred+nboth+nfwrd+1:nboth;
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[junk,cols_b] = find(lead_lag_incidence(maximum_lag+1, order_var));
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reorder_jacobian_columns = [nonzeros(lead_lag_incidence(:,order_var)'); ...
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nz+(1:exo_nbr)'];
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end
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info = 0;
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dr.ghx = [];
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dr.ghu = [];
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@ -149,32 +171,49 @@ else
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end
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A = aa(:,index_m); % Jacobain matrix for lagged endogeneous variables
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B = aa(:,index_c); % Jacobian matrix for contemporaneous endogeneous variables
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B(:,cols_b) = aa(:,index_c); % Jacobian matrix for contemporaneous endogeneous variables
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C = aa(:,index_p); % Jacobain matrix for led endogeneous variables
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info = 0;
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info1 = 1;
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if task ~= 1 && (DynareOptions.dr_cycle_reduction || DynareOptions.dr_logarithmic_reduction)
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if n_current < DynareModel.endo_nbr
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if DynareOptions.dr_cycle_reduction
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error(['The cycle reduction algorithme can''t be used when the ' ...
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'coefficient matrix for current variables is singular'])
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elseif DynareOptions.dr_logarithmic_reduction
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error(['The logarithmic reduction algorithme can''t be used when the ' ...
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'coefficient matrix for current variables is singular'])
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end
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end
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A1 = [aa(row_indx,index_m ) zeros(ndynamic,nfwrd)];
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B1 = [aa(row_indx,index_0m) aa(row_indx,index_0p) ];
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C1 = [zeros(ndynamic,npred) aa(row_indx,index_p)];
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if DynareOptions.dr_cycle_reduction == 1
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[ghx, info] = cycle_reduction(A1, B1, C1, DynareOptions.dr_cycle_reduction_tol);
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[ghx, info1] = cycle_reduction(A1, B1, C1, DynareOptions.dr_cycle_reduction_tol);
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else
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[ghx, info] = logarithmic_reduction(C1, B1, A1, DynareOptions.dr_logarithmic_reduction_tol, DynareOptions.dr_logarithmic_reduction_maxiter);
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[ghx, info1] = logarithmic_reduction(C1, B1, A1, DynareOptions.dr_logarithmic_reduction_tol, DynareOptions.dr_logarithmic_reduction_maxiter);
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end
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ghx = ghx(:,index_m);
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hx = ghx(1:npred+nboth,:);
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gx = ghx(1+npred:end,:);
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end
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if (task ~= 1 && ((DynareOptions.dr_cycle_reduction == 1 && info ==1) || DynareOptions.dr_cycle_reduction == 0)) || task == 1
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D = [[aa(row_indx,index_0m) zeros(ndynamic,nboth) aa(row_indx,index_p)] ; [zeros(nboth, npred) eye(nboth) zeros(nboth, nboth + nfwrd)]];
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if info1 == 1
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D = zeros(ndynamic+nboth);
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E = zeros(ndynamic+nboth);
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D(row_indx_de_1,index_d1) = aa(row_indx,index_d);
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D(row_indx_de_2,index_d2) = eye(nboth);
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E(row_indx_de_1,index_e1) = -aa(row_indx,index_e);
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E(row_indx_de_2,index_e2) = eye(nboth);
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E = [-aa(row_indx,[index_m index_0p]) ; [zeros(nboth,nboth+npred) eye(nboth,nboth+nfwrd) ] ];
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[err, ss, tt, w, sdim, dr.eigval, info1] = mjdgges(E,D,DynareOptions.qz_criterium);
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[err, ss, tt, w, sdim, dr.eigval, info2] = mjdgges(E,D,DynareOptions.qz_criterium);
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mexErrCheck('mjdgges', err);
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if info1
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if info1 == -30
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if info2
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if info2 == -30
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% one eigenvalue is close to 0/0
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info(1) = 7;
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else
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@ -211,66 +250,65 @@ if (task ~= 1 && ((DynareOptions.dr_cycle_reduction == 1 && info ==1) || DynareO
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end
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%First order approximation
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if task ~= 1
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indx_stable_root = 1: (nd - nyf); %=> index of stable roots
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indx_explosive_root = npred + nboth + 1:nd; %=> index of explosive roots
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% derivatives with respect to dynamic state variables
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% forward variables
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Z = w';
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Z11t = Z(indx_stable_root, indx_stable_root)';
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Z21 = Z(indx_explosive_root, indx_stable_root);
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Z22 = Z(indx_explosive_root, indx_explosive_root);
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if ~isfloat(Z21) && (condest(Z21) > 1e9)
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info(1) = 5;
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info(2) = condest(Z21);
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return;
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else
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gx = - Z22 \ Z21;
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end
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% predetermined variables
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hx = Z11t * inv(tt(indx_stable_root, indx_stable_root)) * ss(indx_stable_root, indx_stable_root) * inv(Z11t);
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ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
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end;
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end
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if task~= 1
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if nstatic > 0
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B_static = B(:,1:nstatic); % submatrix containing the derivatives w.r. to static variables
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indx_stable_root = 1: (nd - nyf); %=> index of stable roots
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indx_explosive_root = npred + nboth + 1:nd; %=> index of explosive roots
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% derivatives with respect to dynamic state variables
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% forward variables
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Z = w';
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Z11t = Z(indx_stable_root, indx_stable_root)';
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Z21 = Z(indx_explosive_root, indx_stable_root);
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Z22 = Z(indx_explosive_root, indx_explosive_root);
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if ~isfloat(Z21) && (condest(Z21) > 1e9)
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info(1) = 5;
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info(2) = condest(Z21);
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return;
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else
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B_static = [];
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end;
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%static variables, backward variable, mixed variables and forward variables
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B_pred = B(:,nstatic+1:nstatic+npred+nboth);
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B_fyd = B(:,nstatic+npred+nboth+1:end);
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% static variables
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if nstatic > 0
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temp = - C(1:nstatic,j3)*gx(j4,:)*hx;
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b = aa(:,index_c);
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b10 = b(1:nstatic, 1:nstatic);
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b11 = b(1:nstatic, nstatic+1:n);
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temp(:,index_m) = temp(:,index_m)-A(1:nstatic,:);
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temp = b10\(temp-b11*ghx);
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ghx = [temp; ghx];
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temp = [];
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gx = - Z22 \ Z21;
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end
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% predetermined variables
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hx = Z11t * inv(tt(indx_stable_root, indx_stable_root)) * ss(indx_stable_root, indx_stable_root) * inv(Z11t);
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ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
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A_ = real([B_static C(:,j3)*gx+B_pred B_fyd]); % The state_variable of the block are located at [B_pred B_both]
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if DynareModel.exo_nbr
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if nstatic > 0
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fu = Q' * jacobia(:,innovations_idx);
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else
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fu = jacobia(:,innovations_idx);
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end;
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ghu = - A_ \ fu;
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else
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ghu = [];
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end;
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end
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dr.gx = gx;
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if nstatic > 0
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B_static = B(:,1:nstatic); % submatrix containing the derivatives w.r. to static variables
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else
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B_static = [];
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end;
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%static variables, backward variable, mixed variables and forward variables
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B_pred = B(:,nstatic+1:nstatic+npred+nboth);
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B_fyd = B(:,nstatic+npred+nboth+1:end);
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% static variables
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if nstatic > 0
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temp = - C(1:nstatic,:)*gx*hx;
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b(:,cols_b) = aa(:,index_c);
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b10 = b(1:nstatic, 1:nstatic);
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b11 = b(1:nstatic, nstatic+1:end);
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temp(:,index_m) = temp(:,index_m)-A(1:nstatic,:);
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temp = b10\(temp-b11*ghx);
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ghx = [temp; ghx];
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temp = [];
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end
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A_ = real([B_static C*gx+B_pred B_fyd]); % The state_variable of the block are located at [B_pred B_both]
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if exo_nbr
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if nstatic > 0
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fu = Q' * jacobia(:,innovations_idx);
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else
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fu = jacobia(:,innovations_idx);
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end;
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ghu = - A_ \ fu;
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else
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ghu = [];
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end;
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dr.ghx = ghx;
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dr.ghu = ghu;
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