Commit 4d51f38b authored by Stéphane Adjemian's avatar Stéphane Adjemian
Browse files

Added the possibility to use the cyclic reduction algorithm without the block option.

parent b02c83a9
function disp_dr(dr,order,var_list)
% Display the decision rules
%
......@@ -102,11 +103,7 @@ end
%
for k=1:nx
flag = 0;
if options_.block
str1 = subst_auxvar(dr.state_var(k),-1);
else
str1 = subst_auxvar(k1(klag(k,1)),klag(k,2)-M_.maximum_lag-2);
end;
str1 = subst_auxvar(dr.state_var(k),-1);
str = sprintf('%-20s',str1);
for i=1:nvar
x = dr.ghx(ivar(i),k);
......
function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
function [dr,info] = dyn_first_order_solver(jacobia,DynareModel,dr,DynareOptions,task)
%@info:
%! @deftypefn {Function File} {[@var{dr},@var{info}] =} dyn_first_order_solver (@var{jacobia},@var{M_},@var{dr},@var{options},@var{task})
%! @deftypefn {Function File} {[@var{dr},@var{info}] =} dyn_first_order_solver (@var{jacobia},@var{DynareModel},@var{dr},@var{DynareOptions},@var{task})
%! @anchor{dyn_first_order_solver}
%! @sp 1
%! Computes the first order reduced form of the DSGE model
......@@ -11,7 +11,7 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
%! @table @ @var
%! @item jacobia
%! Matrix containing the Jacobian of the model
%! @item M_
%! @item DynareModel
%! Matlab's structure describing the model (initialized by @code{dynare}).
%! @item dr
%! Matlab's structure describing the reduced form solution of the model.
......@@ -41,7 +41,7 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
%! @item info==5
%! Blanchard & Kahn conditions are not satisfied: indeterminacy due to rank failure.
%! @item info==7
%! One of the generalized eigenvalues is close to 0/0
%! One of the generalized eigenvalues is close to 0/0
%! @end table
%! @end table
%! @end deftypefn
......@@ -63,75 +63,107 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
info = 0;
dr.ghx = [];
dr.ghu = [];
klen = M_.maximum_endo_lag+M_.maximum_endo_lead+1;
kstate = dr.kstate;
kad = dr.kad;
kae = dr.kae;
nstatic = dr.nstatic;
nfwrd = dr.nfwrd;
npred = dr.npred;
nboth = dr.nboth;
persistent reorder_jacobian_columns innovations_idx index_s index_m index_c index_p row_indx index_0m index_0p k1 k2 j3 j4
persistent ndynamic nstatic nfwrd npred nboth nd nyf n
if ~nargin
reorder_jacobian_columns = [];
dr = [];
info = [];
return
end
if isempty(reorder_jacobian_columns)
kstate = dr.kstate;
nfwrd = dr.nfwrd;
nboth = dr.nboth;
npred = dr.npred-nboth;
nstatic = dr.nstatic;
ndynamic = npred+nfwrd+nboth;
nyf = nfwrd + nboth;
n = ndynamic+nstatic;
k1 = 1:(npred+nboth);
k2 = 1:(nfwrd+nboth);
order_var = dr.order_var;
nd = size(kstate,1);
lead_lag_incidence = M_.lead_lag_incidence;
lead_lag_incidence = DynareModel.lead_lag_incidence;
nz = nnz(lead_lag_incidence);
sdyn = M_.endo_nbr - nstatic;
%lead variables actually present in the model
j4 = nstatic+npred+1:nstatic+npred+nboth+nfwrd; % Index on the forward and both variables
j3 = nonzeros(lead_lag_incidence(2,j4)) - nstatic - 2 * npred - nboth; % Index on the non-zeros forward and both variables
j4 = find(lead_lag_incidence(2,j4));
[junk,cols_b,cols_j] = find(lead_lag_incidence(M_.maximum_endo_lag+1,...
order_var));
if nstatic > 0
[Q,R] = qr(jacobia(:,cols_j(1:nstatic)));
aa = Q'*jacobia;
else
aa = jacobia;
end
k1 = find([1:klen] ~= M_.maximum_endo_lag+1);
a = aa(:,nonzeros(lead_lag_incidence(k1,:)'));
b(:,cols_b) = aa(:,cols_j);
b10 = b(1:nstatic,1:nstatic);
b11 = b(1:nstatic,nstatic+1:end);
b2 = b(nstatic+1:end,nstatic+1:end);
if any(isinf(a(:)))
info = 1;
return
end
no_lead_id = find(lead_lag_incidence(3,:)==0);
no_lag_id = find(lead_lag_incidence(1,:)==0);
% buildind D and E
d = zeros(nd,nd) ;
e = d ;
k = find(kstate(:,2) >= M_.maximum_endo_lag+2 & kstate(:,3));
d(1:sdyn,k) = a(nstatic+1:end,kstate(k,3)) ;
k1 = find(kstate(:,2) == M_.maximum_endo_lag+2);
e(1:sdyn,k1) = -b2(:,kstate(k1,1)-nstatic);
k = find(kstate(:,2) <= M_.maximum_endo_lag+1 & kstate(:,4));
e(1:sdyn,k) = -a(nstatic+1:end,kstate(k,4)) ;
k2 = find(kstate(:,2) == M_.maximum_endo_lag+1);
k2 = k2(~ismember(kstate(k2,1),kstate(k1,1)));
d(1:sdyn,k2) = b2(:,kstate(k2,1)-nstatic);
if ~isempty(kad)
for j = 1:size(kad,1)
d(sdyn+j,kad(j)) = 1 ;
e(sdyn+j,kae(j)) = 1 ;
end
static_id = intersect(no_lead_id,no_lag_id);
lag_id = setdiff(no_lead_id,static_id);
lead_id = setdiff(no_lag_id,static_id);
both_id = intersect(setdiff(1:n,no_lead_id),setdiff(1:n,no_lag_id));
lead_idx = lead_lag_incidence(3,lead_id);
lag_idx = lead_lag_incidence(1,lag_id);
both_lagged_idx = lead_lag_incidence(1,both_id);
both_leaded_idx = lead_lag_incidence(3,both_id);
innovations_idx = (size(jacobia,2)-DynareModel.exo_nbr+1):size(jacobia,2);
dr.state_var = [lag_idx, both_lagged_idx];
indexi_0 = 0;
if DynareModel.maximum_endo_lag > 0 && (npred > 0 || nboth > 0)
indexi_0 = min(lead_lag_incidence(2,:));
end
% 1) if mjdgges.dll (or .mexw32 or ....) doesn't exit,
% matlab/qz is added to the path. There exists now qz/mjdgges.m that
% contains the calls to the old Sims code
% 2) In global_initialization.m, if mjdgges.m is visible exist(...)==2,
% this means that the DLL isn't avaiable and use_qzdiv is set to 1
[err,ss,tt,w,sdim,dr.eigval,info1] = mjdgges(e,d,options.qz_criterium);
index_c = lead_lag_incidence(2,:); % Index of all endogenous variables present at time=t
index_s = lead_lag_incidence(2,1:nstatic); % Index of all static endogenous variables present at time=t
index_0m = (nstatic+1:nstatic+npred)+indexi_0-1;
index_0p = (nstatic+npred+1:n)+indexi_0-1;
index_m = 1:(npred+nboth);
index_p = lead_lag_incidence(3,find(lead_lag_incidence(3,:)));
row_indx = nstatic+1:n;
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 ];
end
info = 0;
dr.ghx = [];
dr.ghu = [];
jacobia = jacobia(:,reorder_jacobian_columns);
if nstatic > 0
[Q, junk] = qr(jacobia(:,index_s));
aa = Q'*jacobia;
else
aa = jacobia;
end
A = aa(:,index_m); % Jacobain matrix for lagged endogeneous variables
B = aa(:,index_c); % Jacobian matrix for contemporaneous endogeneous variables
C = aa(:,index_p); % Jacobain matrix for led endogeneous variables
if task ~= 1 && DynareOptions.dr_cycle_reduction == 1
A1 = [aa(row_indx,index_m ) zeros(ndynamic,nfwrd)];
B1 = [aa(row_indx,index_0m) aa(row_indx,index_0p) ];
C1 = [zeros(ndynamic,npred) aa(row_indx,index_p)];
[ghx, info] = cycle_reduction(A1, B1, C1, DynareOptions.dr_cycle_reduction_tol);
ghx = ghx(:,index_m);
hx = ghx(1:npred+nboth,:);
gx = ghx(1+npred:end,:);
end
if (task ~= 1 && ((DynareOptions.dr_cycle_reduction == 1 && info ==1) || DynareOptions.dr_cycle_reduction == 0)) || task == 1
D = [[aa(row_indx,index_0m) zeros(ndynamic,nboth) aa(row_indx,index_p)] ; [zeros(nboth, npred) eye(nboth) zeros(nboth, nboth + nfwrd)]];
E = [-aa(row_indx,[index_m index_0p]) ; [zeros(nboth,nboth+npred) eye(nboth,nboth+nfwrd) ] ];
[err, ss, tt, w, sdim, dr.eigval, info1] = mjdgges(E,D,DynareOptions.qz_criterium);
mexErrCheck('mjdgges', err);
if info1
......@@ -141,21 +173,19 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
else
info(1) = 2;
info(2) = info1;
info(3) = size(e,2);
info(3) = size(E,2);
end
return
end
nba = nd-sdim;
nyf = sum(kstate(:,2) > M_.maximum_endo_lag+1);
if task == 1
dr.rank = rank(w(1:nyf,nd-nyf+1:end));
% Under Octave, eig(A,B) doesn't exist, and
% lambda = qz(A,B) won't return infinite eigenvalues
if ~exist('OCTAVE_VERSION')
dr.eigval = eig(e,d);
dr.eigval = eig(E,D);
end
return
end
......@@ -163,74 +193,86 @@ function [dr,info] = dyn_first_order_solver(jacobia,M_,dr,options,task)
if nba ~= nyf
temp = sort(abs(dr.eigval));
if nba > nyf
temp = temp(nd-nba+1:nd-nyf)-1-options.qz_criterium;
temp = temp(nd-nba+1:nd-nyf)-1-DynareOptions.qz_criterium;
info(1) = 3;
elseif nba < nyf;
temp = temp(nd-nyf+1:nd-nba)-1-options.qz_criterium;
temp = temp(nd-nyf+1:nd-nba)-1-DynareOptions.qz_criterium;
info(1) = 4;
end
info(2) = temp'*temp;
return
end
np = nd - nyf;
n2 = np + 1;
n3 = nyf;
n4 = n3 + 1;
% derivatives with respect to dynamic state variables
% forward variables
w1 =w(1:n3,n2:nd);
if ~isscalar(w1) && (condest(w1) > 1e9);
% condest() fails on a scalar under Octave
info(1) = 5;
info(2) = condest(w1);
return;
else
gx = -w1'\w(n4:nd,n2:nd)';
end
% predetermined variables
hx = w(1:n3,1:np)'*gx+w(n4:nd,1:np)';
hx = (tt(1:np,1:np)*hx)\(ss(1:np,1:np)*hx);
%First order approximation
if task ~= 1
indx_stable_root = 1: (nd - nyf); %=> index of stable roots
indx_explosive_root = npred + nboth + 1:nd; %=> index of explosive roots
% derivatives with respect to dynamic state variables
% forward variables
Z = w';
Z11t = Z(indx_stable_root, indx_stable_root)';
Z21 = Z(indx_explosive_root, indx_stable_root);
Z22 = Z(indx_explosive_root, indx_explosive_root);
if ~isfloat(Z21) && (condest(Z21) > 1e9)
info(1) = 5;
info(2) = condest(Z21);
return;
else
gx = - Z22 \ Z21;
end
% predetermined variables
hx = Z11t * inv(tt(indx_stable_root, indx_stable_root)) * ss(indx_stable_root, indx_stable_root) * inv(Z11t);
ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
end;
end
k1 = find(kstate(n4:nd,2) == M_.maximum_endo_lag+1);
k2 = find(kstate(1:n3,2) == M_.maximum_endo_lag+2);
dr.gx = gx;
dr.ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
if task~= 1
%lead variables actually present in the model
j3 = nonzeros(kstate(:,3));
j4 = find(kstate(:,3));
% derivatives with respect to exogenous variables
if M_.exo_nbr
fu = aa(:,nz+(1:M_.exo_nbr));
a1 = b;
aa1 = [];
if nstatic > 0
aa1 = a1(:,1:nstatic);
end
dr.ghu = -[aa1 a(:,j3)*gx(j4,1:npred)+a1(:,nstatic+1:nstatic+ ...
npred) a1(:,nstatic+npred+1:end)]\fu;
if nstatic > 0
B_static = B(:,1:nstatic); % submatrix containing the derivatives w.r. to static variables
else
dr.ghu = [];
end
B_static = [];
end;
%static variables, backward variable, mixed variables and forward variables
B_pred = B(:,nstatic+1:nstatic+npred+nboth);
B_fyd = B(:,nstatic+npred+nboth+1:end);
% static variables
if nstatic > 0
temp = -a(1:nstatic,j3)*gx(j4,:)*hx;
j5 = find(kstate(n4:nd,4));
temp(:,j5) = temp(:,j5)-a(1:nstatic,nonzeros(kstate(:,4)));
temp = b10\(temp-b11*dr.ghx);
dr.ghx = [temp; dr.ghx];
temp = - C(1:nstatic,j3)*gx(j4,:)*hx;
b = aa(:,index_c);
b10 = b(1:nstatic, 1:nstatic);
b11 = b(1:nstatic, nstatic+1:n);
temp(:,index_m) = temp(:,index_m)-A(1:nstatic,:);
temp = b10\(temp-b11*ghx);
ghx = [temp; ghx];
temp = [];
end
if options.use_qzdiv
%% Necessary when using Sims' routines for QZ
gx = real(gx);
hx = real(hx);
dr.ghx = real(dr.ghx);
dr.ghu = real(dr.ghu);
end
A_ = real([B_static C(:,j3)*gx+B_pred B_fyd]); % The state_variable of the block are located at [B_pred B_both]
if DynareModel.exo_nbr
if nstatic > 0
fu = Q' * jacobia(:,innovations_idx);
else
fu = jacobia(:,innovations_idx);
end;
ghu = - A_ \ fu;
else
ghu = [];
end;
end
dr.ghx = ghx;
dr.ghu = ghu;
if DynareOptions.aim_solver ~= 1 && DynareOptions.use_qzdiv
% Necessary when using Sims' routines for QZ
dr.ghx = real(ghx);
dr.ghu = real(ghu);
hx = real(hx);
end
dr.Gy = hx;
\ No newline at end of file
dr.Gy = hx;
\ No newline at end of file
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