diff --git a/matlab/AIM_first_order_solver.m b/matlab/AIM_first_order_solver.m
new file mode 100644
index 0000000000000000000000000000000000000000..962da3deee1950ff313cdcdbeed60b733f8f9d2f
--- /dev/null
+++ b/matlab/AIM_first_order_solver.m
@@ -0,0 +1,33 @@
+function [dr,info]=AIM_first_order_solver(jacobia,M_,dr)
+ try
+ [dr,aimcode]=dynAIMsolver1(jacobia_,M_,dr);
+
+ % reuse some of the bypassed code and tests that may be needed
+
+ if aimcode ~=1
+ info(1) = aimcode;
+ info(2) = 1.0e+8;
+ return
+ end
+ [A,B] =transition_matrix(dr);
+ dr.eigval = eig(A);
+ nba = nd-sdim;
+
+ nyf = sum(kstate(:,2) > M_.maximum_endo_lag+1);
+
+ if nba ~= nyf
+ temp = sort(abs(dr.eigval));
+ if nba > nyf
+ temp = temp(nd-nba+1:nd-nyf)-1-options_.qz_criterium;
+ info(1) = 3;
+ elseif nba < nyf;
+ temp = temp(nd-nyf+1:nd-nba)-1-options_.qz_criterium;
+ info(1) = 4;
+ end
+ info(2) = temp'*temp;
+ return
+ end
+ catch
+ disp(lasterror.message)
+ error('Problem with AIM solver - Try to remove the "aim_solver" option')
+ end
diff --git a/matlab/dyn_first_order_solver.m b/matlab/dyn_first_order_solver.m
new file mode 100644
index 0000000000000000000000000000000000000000..98a186a505bf0f6905fdf93b7835e10e376bd944
--- /dev/null
+++ b/matlab/dyn_first_order_solver.m
@@ -0,0 +1,170 @@
+function [dr,info] = dyn_first_order_solver(jacobia,b,M_,dr,options,task)
+
+ 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;
+ order_var = dr.order_var;
+ nd = size(kstate,1);
+ lead_lag_incidence = M_.lead_lag_incidence;
+ nz = nnz(lead_lag_incidence);
+
+ sdyn = M_.endo_nbr - nstatic;
+
+ [junk,cols_b,cols_j] = find(lead_lag_incidence(M_.maximum_endo_lag+1,...
+ order_var));
+
+ if nstatic > 0
+ [Q,R] = qr(b(:,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
+
+ % 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
+ 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);
+ mexErrCheck('mjdgges', err);
+
+ if info1
+ if info1 == -30
+ info(1) = 7;
+ else
+ info(1) = 2;
+ info(2) = info1;
+ 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);
+ end
+ return
+ end
+
+ if nba ~= nyf
+ temp = sort(abs(dr.eigval));
+ if nba > nyf
+ temp = temp(nd-nba+1:nd-nyf)-1-options.qz_criterium;
+ info(1) = 3;
+ elseif nba < nyf;
+ temp = temp(nd-nyf+1:nd-nba)-1-options.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);
+
+ k1 = find(kstate(n4:nd,2) == M_.maximum_endo_lag+1);
+ k2 = find(kstate(1:n3,2) == M_.maximum_endo_lag+2);
+ dr.ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
+
+ %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;
+ else
+ dr.ghu = [];
+ 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 = [];
+ 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
+
+ dr.Gy = hx;
\ No newline at end of file
diff --git a/matlab/dyn_ramsey_linearized_foc.m b/matlab/dyn_ramsey_linearized_foc.m
new file mode 100644
index 0000000000000000000000000000000000000000..2a1949cba9a0e2de889e772e06b845ba810005d2
--- /dev/null
+++ b/matlab/dyn_ramsey_linearized_foc.m
@@ -0,0 +1,124 @@
+function [jacobia_,dr,info,M_,oo_] = dyn_ramsey_linearized_foc(dr,M_,options_,oo_)
+% function [jacobia_,dr,info,M_,oo_] = dyn_ramsey_linearized_foc(dr,M_,options_,oo_)
+% computes the Jacobian of the linear approximation of the F.O.C of a
+% Ramsey problem
+%
+% INPUTS
+% dr [matlab structure] Decision rules for stochastic simulations.
+% M_ [matlab structure] Definition of the model.
+% options_ [matlab structure] Global options.
+% oo_ [matlab structure] Results
+%
+% OUTPUTS
+% dr [matlab structure] Decision rules for stochastic simulations.
+% info [integer] info=1: the model doesn't define current variables uniquely
+% info=2: problem in mjdgges.dll info(2) contains error code.
+% info=3: BK order condition not satisfied info(2) contains "distance"
+% absence of stable trajectory.
+% info=4: BK order condition not satisfied info(2) contains "distance"
+% indeterminacy.
+% info=5: BK rank condition not satisfied.
+% info=6: The jacobian matrix evaluated at the steady state is complex.
+% M_ [matlab structure]
+% options_ [matlab structure]
+% oo_ [matlab structure]
+%
+% ALGORITHM
+% ...
+%
+% SPECIAL REQUIREMENTS
+% none.
+%
+
+% Copyright (C) 1996-2009 Dynare Team
+%
+% This file is part of Dynare.
+%
+% Dynare is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% Dynare is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% 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;
+
+if isfield(M_,'orig_model')
+ orig_model = M_.orig_model;
+ M_.endo_nbr = orig_model.endo_nbr;
+ M_.orig_endo_nbr = orig_model.orig_endo_nbr;
+ M_.aux_vars = orig_model.aux_vars;
+ M_.endo_names = orig_model.endo_names;
+ M_.lead_lag_incidence = orig_model.lead_lag_incidence;
+ M_.maximum_lead = orig_model.maximum_lead;
+ M_.maximum_endo_lead = orig_model.maximum_endo_lead;
+ M_.maximum_lag = orig_model.maximum_lag;
+ M_.maximum_endo_lag = orig_model.maximum_endo_lag;
+ end
+
+ if options_.steadystate_flag
+ k_inst = [];
+ instruments = options_.instruments;
+ for i = 1:size(instruments,1)
+ k_inst = [k_inst; strmatch(options_.instruments(i,:), ...
+ M_.endo_names,'exact')];
+ end
+ ys = oo_.steady_state;
+ [inst_val,info1] = dynare_solve('dyn_ramsey_static_', ...
+ oo_.steady_state(k_inst),0, ...
+ M_,options_,oo_,it_);
+ M_.params = evalin('base','M_.params;');
+ ys(k_inst) = inst_val;
+ [x,check] = feval([M_.fname '_steadystate'],...
+ ys,[oo_.exo_steady_state; ...
+ oo_.exo_det_steady_state]);
+ if size(x,1) < M_.endo_nbr
+ if length(M_.aux_vars) > 0
+ x = add_auxiliary_variables_to_steadystate(x,M_.aux_vars,...
+ M_.fname,...
+ oo_.exo_steady_state,...
+ oo_.exo_det_steady_state,...
+ M_.params);
+ else
+ error([M_.fname '_steadystate.m doesn''t match the model']);
+ end
+ end
+ oo_.steady_state = x;
+ [junk,junk,multbar] = dyn_ramsey_static_(oo_.steady_state(k_inst),M_,options_,oo_,it_);
+ else
+ [oo_.steady_state,info1] = dynare_solve('dyn_ramsey_static_', ...
+ oo_.steady_state,0,M_,options_,oo_,it_);
+ [junk,junk,multbar] = dyn_ramsey_static_(oo_.steady_state,M_,options_,oo_,it_);
+ end
+
+ check1 = max(abs(feval([M_.fname '_static'],...
+ oo_.steady_state,...
+ [oo_.exo_steady_state; ...
+ oo_.exo_det_steady_state], M_.params))) > options_.dynatol ;
+ if check1
+ info(1) = 20;
+ info(2) = check1'*check1;
+ return
+ end
+
+ [jacobia_,M_] = dyn_ramsey_dynamic_(oo_.steady_state,multbar,M_,options_,oo_,it_);
+ klen = M_.maximum_lag + M_.maximum_lead + 1;
+ dr.ys = [oo_.steady_state;zeros(M_.exo_nbr,1);multbar];
+ oo_.steady_state = dr.ys;
+
+ if options_.noprint == 0
+ disp_steady_state(M_,oo_)
+ for i=M_.orig_endo_nbr:M_.endo_nbr
+ if strmatch('mult_',M_.endo_names(i,:))
+ disp(sprintf('%s \t\t %g',M_.endo_names(i,:), ...
+ dr.ys(i)));
+ end
+ end
+ end
+
diff --git a/matlab/dyn_risky_steadystate_solver.m b/matlab/dyn_risky_steadystate_solver.m
new file mode 100644
index 0000000000000000000000000000000000000000..d32663cb7a6c536be41545599c67016dc7032cda
--- /dev/null
+++ b/matlab/dyn_risky_steadystate_solver.m
@@ -0,0 +1,452 @@
+function [dr,info] = dyn_risky_steadystate_solver(ys0,M, ...
+ dr,options,oo)
+
+ info = 0;
+ lead_lag_incidence = M.lead_lag_incidence;
+ order_var = dr.order_var;
+ exo_nbr = M.exo_nbr;
+
+ M.var_order_endo_names = M.endo_names(dr.order_var,:);
+
+ [junk,dr.i_fwrd_g,i_fwrd_f] = find(lead_lag_incidence(3,order_var));
+ dr.i_fwrd_f = i_fwrd_f;
+ nd = nnz(lead_lag_incidence) + M.exo_nbr;
+ dr.nd = nd;
+ kk = reshape(1:nd^2,nd,nd);
+ kkk = reshape(1:nd^3,nd^2,nd);
+ dr.i_fwrd2_f = kk(i_fwrd_f,i_fwrd_f);
+ dr.i_fwrd2a_f = kk(i_fwrd_f,:);
+ dr.i_fwrd3_f = kkk(dr.i_fwrd2_f,:);
+ dr.i_uu = kk(end-exo_nbr+1:end,end-exo_nbr+1:end);
+ if options.k_order_solver
+ func = @risky_residuals_k_order;
+ else
+ func = @risky_residuals;
+ end
+
+ if isfield(options,'portfolio') && options.portfolio == 1
+ eq_tags = M.equations_tags;
+ n_tags = size(eq_tags,1);
+ l_var = zeros(n_tags,1);
+ for i=1:n_tags
+ l_var(i) = find(strncmp(eq_tags(i,3),M.endo_names, ...
+ length(cell2mat(eq_tags(i,3)))));
+ end
+ dr.ys = ys0;
+ x0 = ys0(l_var);
+ % dr = first_step_ds(x0,M,dr,options,oo);
+ n = size(ys0);
+ %x0 = ys0;
+ [x, info] = solve1(@risky_residuals_ds,x0,1:n_tags,1:n_tags,0,1,M,dr,options,oo);
+ %[x, info] = solve1(@risky_residuals,x0,1:n,1:n,0,1,M,dr,options,oo);
+ % ys0(l_var) = x;
+ ys0(l_var) = x;
+ dr.ys = ys0;
+ oo.dr = dr;
+ oo.steady_state = ys0;
+ disp_steady_state(M,oo);
+ end
+
+ [ys, info] = csolve(func,ys0,[],1e-10,100,M,dr,options,oo);
+
+ if options.k_order_solver
+ [resid,dr] = risky_residuals_k_order(ys,M,dr,options,oo);
+ else
+ [resid,dr] = risky_residuals(ys,M,dr,options,oo);
+ end
+
+ dr.ys = ys;
+ for i=1:M.endo_nbr
+ disp(sprintf('%16s %12.6f %12.6f',M.endo_names(i,:),ys0(i), ys(i)))
+ end
+
+ dr.ghs2 = zeros(size(dr.ghs2));
+
+ k_var = setdiff(1:M.endo_nbr,l_var);
+ dr.ghx(k_var,:) = dr.ghx;
+ dr.ghu(k_var,:) = dr.ghu;
+ dr.ghxx(k_var,:) = dr.ghxx;
+ dr.ghxu(k_var,:) = dr.ghxu;
+ dr.ghuu(k_var,:) = dr.ghuu;
+ dr.ghs2(k_var,:) = dr.ghs2;
+end
+
+function [resid,dr] = risky_residuals(ys,M,dr,options,oo)
+ persistent old_ys old_resid
+
+ lead_lag_incidence = M.lead_lag_incidence;
+ iyv = lead_lag_incidence';
+ iyv = iyv(:);
+ iyr0 = find(iyv) ;
+
+ if M.exo_nbr == 0
+ oo.exo_steady_state = [] ;
+ end
+
+ z = repmat(ys,1,3);
+ z = z(iyr0) ;
+ [resid1,d1,d2] = feval([M.fname '_dynamic'],z,...
+ [oo.exo_simul ...
+ oo.exo_det_simul], M.params, dr.ys, 2);
+ if ~isreal(d1) || ~isreal(d2)
+ pause
+ end
+
+ if options.use_dll
+ % In USE_DLL mode, the hessian is in the 3-column sparse representation
+ d2 = sparse(d2(:,1), d2(:,2), d2(:,3), ...
+ size(d1, 1), size(d1, 2)*size(d1, 2));
+ end
+
+ if isfield(options,'portfolio') && options.portfolio == 1
+ eq_tags = M.equations_tags;
+ n_tags = size(eq_tags,1);
+ portfolios_eq = cell2mat(eq_tags(strcmp(eq_tags(:,2), ...
+ 'portfolio'),1));
+ eq = setdiff(1:M.endo_nbr,portfolios_eq);
+ l_var = zeros(n_tags,1);
+ for i=1:n_tags
+ l_var(i) = find(strncmp(eq_tags(i,3),M.endo_names, ...
+ length(cell2mat(eq_tags(i,3)))));
+ end
+ k_var = setdiff(1:M.endo_nbr,l_var);
+ lli1 = lead_lag_incidence(:,k_var);
+ lead_incidence = lli1(3,:)';
+ k = find(lli1');
+ lli2 = lli1';
+ lli2(k) = 1:nnz(lli1);
+ lead_lag_incidence = lli2';
+ x = ys(l_var);
+ dr = first_step_ds(x,M,dr,options,oo);
+
+
+ M.lead_lag_incidence = lead_lag_incidence;
+ lli1a = [nonzeros(lli1'); size(d1,2)+(-M.exo_nbr+1:0)'];
+ d1a = d1(eq,lli1a);
+ ih = 1:size(d2,2);
+ ih = reshape(ih,size(d1,2),size(d1,2));
+ ih1 = ih(lli1a,lli1a);
+ d2a = d2(eq,ih1);
+
+ M.endo_nbr = M.endo_nbr-n_tags;
+ dr = set_state_space(dr,M);
+
+ [junk,dr.i_fwrd_g] = find(lead_lag_incidence(3,dr.order_var));
+ i_fwrd_f = nonzeros(lead_incidence(dr.order_var));
+ i_fwrd2_f = ih(i_fwrd_f,i_fwrd_f);
+ dr.i_fwrd_f = i_fwrd_f;
+ dr.i_fwrd2_f = i_fwrd2_f;
+ nd = nnz(lead_lag_incidence) + M.exo_nbr;
+ dr.nd = nd;
+ kk = reshape(1:nd^2,nd,nd);
+ kkk = reshape(1:nd^3,nd^2,nd);
+ dr.i_fwrd2a_f = kk(i_fwrd_f,:);
+ % dr.i_fwrd3_f = kkk(i_fwrd2_f,:);
+ dr.i_uu = kk(end-M.exo_nbr+1:end,end-M.exo_nbr+1:end);
+ else
+ d1a = d1;
+ d2a = d2;
+ end
+
+% $$$ [junk,cols_b,cols_j] = find(lead_lag_incidence(2,dr.order_var));
+% $$$ b = zeros(M.endo_nbr,M.endo_nbr);
+% $$$ b(:,cols_b) = d1a(:,cols_j);
+% $$$
+% $$$ [dr,info] = dyn_first_order_solver(d1a,b,M,dr,options,0);
+% $$$ if info
+% $$$ [m1,m2]=max(abs(ys-old_ys));
+% $$$ disp([m1 m2])
+% $$$ % print_info(info,options.noprint);
+% $$$ resid = old_resid+info(2)/40;
+% $$$ return
+% $$$ end
+% $$$
+% $$$ dr = dyn_second_order_solver(d1a,d2a,dr,M);
+
+ gu1 = dr.ghu(dr.i_fwrd_g,:);
+
+ resid = resid1+0.5*(d1(:,dr.i_fwrd_f)*dr.ghuu(dr.i_fwrd_g,:)+ ...
+ d2(:,dr.i_fwrd2_f)*kron(gu1,gu1))*vec(M.Sigma_e);
+ disp(d1(:,dr.i_fwrd_f)*dr.ghuu(dr.i_fwrd_g,:)*vec(M.Sigma_e));
+ old_ys = ys;
+ disp(max(abs(resid)))
+ old_resid = resid;
+end
+
+function [resid,dr] = risky_residuals_ds(x,M,dr,options,oo)
+ persistent old_ys old_resid old_resid1 old_d1 old_d2
+
+ dr = first_step_ds(x,M,dr,options,oo);
+
+ lead_lag_incidence = M.lead_lag_incidence;
+ iyv = lead_lag_incidence';
+ iyv = iyv(:);
+ iyr0 = find(iyv) ;
+
+ if M.exo_nbr == 0
+ oo.exo_steady_state = [] ;
+ end
+
+ eq_tags = M.equations_tags;
+ n_tags = size(eq_tags,1);
+ portfolios_eq = cell2mat(eq_tags(strcmp(eq_tags(:,2), ...
+ 'portfolio'),1));
+ eq = setdiff(1:M.endo_nbr,portfolios_eq);
+ l_var = zeros(n_tags,1);
+ for i=1:n_tags
+ l_var(i) = find(strncmp(eq_tags(i,3),M.endo_names, ...
+ length(cell2mat(eq_tags(i,3)))));
+ end
+ k_var = setdiff(1:M.endo_nbr,l_var);
+ lli1 = lead_lag_incidence(:,k_var);
+ k = find(lli1');
+ lli2 = lli1';
+ lli2(k) = 1:nnz(lli1);
+ lead_lag_incidence = lli2';
+
+ ys = dr.ys;
+ ys(l_var) = x;
+
+ z = repmat(ys,1,3);
+ z = z(iyr0) ;
+ [resid1,d1,d2] = feval([M.fname '_dynamic'],z,...
+ [oo.exo_simul ...
+ oo.exo_det_simul], M.params, dr.ys, 2);
+% $$$ if isempty(old_resid)
+% $$$ old_resid1 = resid1;
+% $$$ old_d1 = d1;
+% $$$ old_d2 = d2;
+% $$$ old_ys = ys;
+% $$$ else
+% $$$ if ~isequal(resid1,old_resid)
+% $$$ disp('ys')
+% $$$ disp((ys-old_ys)');
+% $$$ disp('resids1')
+% $$$ disp((resid1-old_resid1)')
+% $$$ old_resid1 = resid1;
+% $$$ pause
+% $$$ end
+% $$$ if ~isequal(d1,old_d1)
+% $$$ disp('d1')
+% $$$ disp(d1-old_d1);
+% $$$ old_d1 = d1;
+% $$$ pause
+% $$$ end
+% $$$ if ~isequal(d2,old_d2)
+% $$$ disp('d2')
+% $$$ disp(d2-old_d2);
+% $$$ old_d2 = d2;
+% $$$ pause
+% $$$ end
+% $$$ end
+ if ~isreal(d1) || ~isreal(d2)
+ pause
+ end
+
+ if options.use_dll
+ % In USE_DLL mode, the hessian is in the 3-column sparse representation
+ d2 = sparse(d2(:,1), d2(:,2), d2(:,3), ...
+ size(d1, 1), size(d1, 2)*size(d1, 2));
+ end
+
+% $$$ if isfield(options,'portfolio') && options.portfolio == 1
+% $$$ lli1a = [nonzeros(lli1'); size(d1,2)+(-M.exo_nbr+1:0)'];
+% $$$ d1a = d1(eq,lli1a);
+% $$$ ih = 1:size(d2,2);
+% $$$ ih = reshape(ih,size(d1,2),size(d1,2));
+% $$$ ih1 = ih(lli1a,lli1a);
+% $$$ d2a = d2(eq,ih1);
+% $$$
+% $$$ M.endo_nbr = M.endo_nbr-n_tags;
+% $$$ dr = set_state_space(dr,M);
+% $$$
+% $$$ dr.i_fwrd_g = find(lead_lag_incidence(3,dr.order_var)');
+% $$$ else
+% $$$ d1a = d1;
+% $$$ d2a = d2;
+% $$$ end
+% $$$
+% $$$ [junk,cols_b,cols_j] = find(lead_lag_incidence(2,dr.order_var));
+% $$$ b = zeros(M.endo_nbr,M.endo_nbr);
+% $$$ b(:,cols_b) = d1a(:,cols_j);
+% $$$
+% $$$ [dr,info] = dyn_first_order_solver(d1a,b,M,dr,options,0);
+% $$$ if info
+% $$$ [m1,m2]=max(abs(ys-old_ys));
+% $$$ disp([m1 m2])
+% $$$ % print_info(info,options.noprint);
+% $$$ resid = old_resid+info(2)/40;
+% $$$ return
+% $$$ end
+% $$$
+% $$$ dr = dyn_second_order_solver(d1a,d2a,dr,M);
+
+ gu1 = dr.ghu(dr.i_fwrd_g,:);
+
+ % resid = resid1+0.5*(d1(:,dr.i_fwrd_f)*dr.ghuu(dr.i_fwrd_g,:)+ ...
+ % d2(:,dr.i_fwrd2_f)*kron(gu1,gu1))*vec(M.Sigma_e);
+ resid = resid1+0.5*(d2(:,dr.i_fwrd2_f)*kron(gu1,gu1))*vec(M.Sigma_e);
+
+% $$$ if isempty(old_resid)
+% $$$ old_resid = resid;
+% $$$ else
+% $$$ disp('resid')
+% $$$ dr = (resid-old_resid)';
+% $$$ % disp(dr)
+% $$$ % disp(dr(portfolios_eq))
+% $$$ old_resid = resid;
+% $$$ end
+ resid = resid(portfolios_eq)
+end
+
+function [dr] = first_step_ds(x,M,dr,options,oo)
+
+ lead_lag_incidence = M.lead_lag_incidence;
+ iyv = lead_lag_incidence';
+ iyv = iyv(:);
+ iyr0 = find(iyv) ;
+
+ if M.exo_nbr == 0
+ oo.exo_steady_state = [] ;
+ end
+
+ eq_tags = M.equations_tags;
+ n_tags = size(eq_tags,1);
+ portfolios_eq = cell2mat(eq_tags(strcmp(eq_tags(:,2), ...
+ 'portfolio'),1));
+ eq = setdiff(1:M.endo_nbr,portfolios_eq);
+ l_var = zeros(n_tags,1);
+ for i=1:n_tags
+ l_var(i) = find(strncmp(eq_tags(i,3),M.endo_names, ...
+ length(cell2mat(eq_tags(i,3)))));
+ end
+ k_var = setdiff(1:M.endo_nbr,l_var);
+ lli1 = lead_lag_incidence(:,k_var);
+ k = find(lli1');
+ lli2 = lli1';
+ lli2(k) = 1:nnz(lli1);
+ lead_lag_incidence = lli2';
+ M.lead_lag_incidence = lead_lag_incidence;
+
+ ys = dr.ys;
+ ys(l_var) = x;
+
+ z = repmat(ys,1,3);
+ z = z(iyr0) ;
+ [resid1,d1,d2] = feval([M.fname '_dynamic'],z,...
+ [oo.exo_simul ...
+ oo.exo_det_simul], M.params, dr.ys, 2);
+ if ~isreal(d1) || ~isreal(d2)
+ pause
+ end
+
+ if options.use_dll
+ % In USE_DLL mode, the hessian is in the 3-column sparse representation
+ d2 = sparse(d2(:,1), d2(:,2), d2(:,3), ...
+ size(d1, 1), size(d1, 2)*size(d1, 2));
+ end
+
+ if isfield(options,'portfolio') && options.portfolio == 1
+ lli1a = [nonzeros(lli1'); size(d1,2)+(-M.exo_nbr+1:0)'];
+ d1a = d1(eq,lli1a);
+ ih = 1:size(d2,2);
+ ih = reshape(ih,size(d1,2),size(d1,2));
+ ih1 = ih(lli1a,lli1a);
+ d2a = d2(eq,ih1);
+
+ M.endo_nbr = M.endo_nbr-n_tags;
+ dr = set_state_space(dr,M);
+
+ dr.i_fwrd_g = find(lead_lag_incidence(3,dr.order_var)');
+ else
+ d1a = d1;
+ d2a = d2;
+ end
+
+ [junk,cols_b,cols_j] = find(lead_lag_incidence(2,dr.order_var));
+ b = zeros(M.endo_nbr,M.endo_nbr);
+ b(:,cols_b) = d1a(:,cols_j);
+
+ [dr,info] = dyn_first_order_solver(d1a,b,M,dr,options,0);
+ if info
+ [m1,m2]=max(abs(ys-old_ys));
+ disp([m1 m2])
+ % print_info(info,options.noprint);
+ resid = old_resid+info(2)/40;
+ return
+ end
+
+ dr = dyn_second_order_solver(d1a,d2a,dr,M,...
+ options.threads.kronecker.A_times_B_kronecker_C,...
+ options.threads.kronecker.sparse_hessian_times_B_kronecker_C);
+end
+
+function [resid,dr] = risky_residuals_k_order(ys,M,dr,options,oo)
+
+ lead_lag_incidence = M.lead_lag_incidence;
+ npred = dr.npred;
+ exo_nbr = M.exo_nbr;
+ vSigma_e = vec(M.Sigma_e);
+
+ iyv = lead_lag_incidence';
+ iyv = iyv(:);
+ iyr0 = find(iyv) ;
+
+ if M.exo_nbr == 0
+ oo.exo_steady_state = [] ;
+ end
+
+ z = repmat(ys,1,3);
+ z = z(iyr0) ;
+ [resid1,d1,d2,d3] = feval([M.fname '_dynamic'],z,...
+ [oo.exo_simul ...
+ oo.exo_det_simul], M.params, dr.ys, 2);
+
+ hessian = sparse(d2(:,1), d2(:,2), d2(:,3), ...
+ size(d1, 1), size(d1, 2)*size(d1, 2));
+ fy3 = sparse(d2(:,1), d2(:,2), d2(:,3), ...
+ size(d1, 1), size(d1, 2)^3);
+
+ options.order = 3;
+
+ nu2 = exo_nbr*(exo_nbr+1)/2;
+% $$$ d1_0 = d1;
+% $$$ gu1 = dr.ghu(dr.i_fwrd_g,:);
+% $$$ guu = dr.ghuu;
+% $$$ for i=1:2
+% $$$ d1 = d1_0 + 0.5*(hessian(:,dr.i_fwrd2a_f)*kron(eye(dr.nd),guu(dr.i_fwrd_g,:)*vSigma_e)+ ...
+% $$$ fy3(:,dr.i_fwrd3_f)*kron(eye(dr.nd),kron(gu1,gu1)*vSigma_e));
+% $$$ [junk,cols_b,cols_j] = find(lead_lag_incidence(2,dr.order_var));
+% $$$ b = zeros(M.endo_nbr,M.endo_nbr);
+% $$$ b(:,cols_b) = d1(:,cols_j);
+
+% $$$ [dr,info] = dyn_first_order_solver(d1,b,M,dr,options,0);
+ [g_0, g_1, g_2, g_3] = k_order_perturbation(dr,0,M,options, oo , ['.' ...
+ mexext],d1,d2,d3);
+ gu1 = g_1(dr.i_fwrd_g,end-exo_nbr+1:end);
+ guu = unfold(g_2(:,end-nu2+1:end),exo_nbr);
+ d1old = d1;
+ % disp(max(max(abs(d1-d1old))));
+ % end
+
+ [junk,cols_b,cols_j] = find(lead_lag_incidence(2,dr.order_var));
+
+ resid = resid1+0.5*(d1(:,dr.i_fwrd_f)*guu(dr.i_fwrd_g,:)+hessian(:,dr.i_fwrd2_f)*kron(gu1,gu1))*vec(M.Sigma_e);
+
+ if nargout > 1
+ [dr,info] = k_order_pert(dr,M,options,oo);
+ end
+end
+
+function y=unfold(x,n)
+ y = zeros(size(x,1),n*n);
+ k = 1;
+ for i=1:n
+ for j=i:n
+ y(:,(i-1)*n+j) = x(:,k);
+ if i ~= j
+ y(:,(j-1)*n+i) = x(:,k);
+ end
+ end
+ end
+end
diff --git a/matlab/dyn_second_order_solver.m b/matlab/dyn_second_order_solver.m
new file mode 100644
index 0000000000000000000000000000000000000000..17129dcd3191f284876e00c110736c35f8e426f3
--- /dev/null
+++ b/matlab/dyn_second_order_solver.m
@@ -0,0 +1,199 @@
+function dr = dyn_second_order_solver(jacobia,hessian1,dr,M_,threads_ABC,threads_BC)
+
+
+ dr.ghxx = [];
+ dr.ghuu = [];
+ dr.ghxu = [];
+ dr.ghs2 = [];
+ Gy = dr.Gy;
+
+ kstate = dr.kstate;
+ kad = dr.kad;
+ kae = dr.kae;
+ nstatic = dr.nstatic;
+ nfwrd = dr.nfwrd;
+ npred = dr.npred;
+ nboth = dr.nboth;
+ nyf = nfwrd+nboth;
+ order_var = dr.order_var;
+ nd = size(kstate,1);
+ lead_lag_incidence = M_.lead_lag_incidence;
+
+ np = nd - nyf;
+ n2 = np + 1;
+ n3 = nyf;
+ n4 = n3 + 1;
+
+ k1 = nonzeros(lead_lag_incidence(:,order_var)');
+ kk = [k1; length(k1)+(1:M_.exo_nbr+M_.exo_det_nbr)'];
+ nk = size(kk,1);
+ kk1 = reshape([1:nk^2],nk,nk);
+ kk1 = kk1(kk,kk);
+ hessian = hessian1(:,kk1(:));
+ clear hessian1
+
+ zx = zeros(np,np);
+ zu=zeros(np,M_.exo_nbr);
+ zx(1:np,:)=eye(np);
+ k0 = [1:M_.endo_nbr];
+ gx1 = dr.ghx;
+ hu = dr.ghu(nstatic+[1:npred],:);
+ k0 = find(lead_lag_incidence(M_.maximum_endo_lag+1,order_var)');
+ zx = [zx; gx1(k0,:)];
+ zu = [zu; dr.ghu(k0,:)];
+ k1 = find(lead_lag_incidence(M_.maximum_endo_lag+2,order_var)');
+ zu = [zu; gx1(k1,:)*hu];
+ zx = [zx; gx1(k1,:)*Gy];
+ zx=[zx; zeros(M_.exo_nbr,np);zeros(M_.exo_det_nbr,np)];
+ zu=[zu; eye(M_.exo_nbr);zeros(M_.exo_det_nbr,M_.exo_nbr)];
+ [nrzx,nczx] = size(zx);
+
+ [rhs, err] = sparse_hessian_times_B_kronecker_C(hessian,zx,threads_BC);
+ mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
+ rhs = -rhs;
+
+ %lhs
+ n = M_.endo_nbr+sum(kstate(:,2) > M_.maximum_endo_lag+1 & kstate(:,2) < M_.maximum_endo_lag+M_.maximum_endo_lead+1);
+ A = zeros(M_.endo_nbr,M_.endo_nbr);
+ B = zeros(M_.endo_nbr,M_.endo_nbr);
+ A(:,k0) = jacobia(:,nonzeros(lead_lag_incidence(M_.maximum_endo_lag+1,order_var)));
+ % variables with the highest lead
+ k1 = find(kstate(:,2) == M_.maximum_endo_lag+2);
+ % Jacobian with respect to the variables with the highest lead
+ fyp = jacobia(:,kstate(k1,3)+nnz(M_.lead_lag_incidence(M_.maximum_endo_lag+1,:)));
+ B(:,nstatic+npred-dr.nboth+1:end) = fyp;
+ offset = M_.endo_nbr;
+ gx1 = dr.ghx;
+ [junk,k1,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+M_.maximum_endo_lead+1,order_var));
+ A(1:M_.endo_nbr,nstatic+1:nstatic+npred)=...
+ A(1:M_.endo_nbr,nstatic+[1:npred])+fyp*gx1(k1,1:npred);
+ C = Gy;
+ D = [rhs; zeros(n-M_.endo_nbr,size(rhs,2))];
+
+
+ [err, dr.ghxx] = gensylv(2,A,B,C,D);
+ mexErrCheck('gensylv', err);
+
+ %ghxu
+ %rhs
+ hu = dr.ghu(nstatic+1:nstatic+npred,:);
+ [rhs, err] = sparse_hessian_times_B_kronecker_C(hessian,zx,zu,threads_BC);
+ mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
+
+ hu1 = [hu;zeros(np-npred,M_.exo_nbr)];
+ [nrhx,nchx] = size(Gy);
+ [nrhu1,nchu1] = size(hu1);
+
+ [abcOut,err] = A_times_B_kronecker_C(dr.ghxx,Gy,hu1,threads_ABC);
+ mexErrCheck('A_times_B_kronecker_C', err);
+ B1 = B*abcOut;
+ rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
+
+
+ %lhs
+ dr.ghxu = A\rhs;
+
+ %ghuu
+ %rhs
+ [rhs, err] = sparse_hessian_times_B_kronecker_C(hessian,zu,threads_BC);
+ mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
+
+ [B1, err] = A_times_B_kronecker_C(B*dr.ghxx,hu1,threads_ABC);
+ mexErrCheck('A_times_B_kronecker_C', err);
+ rhs = -[rhs; zeros(n-M_.endo_nbr,size(rhs,2))]-B1;
+
+ %lhs
+ dr.ghuu = A\rhs;
+
+ dr.ghxx = dr.ghxx(1:M_.endo_nbr,:);
+ dr.ghxu = dr.ghxu(1:M_.endo_nbr,:);
+ rdr.ghuu = dr.ghuu(1:M_.endo_nbr,:);
+
+
+ % dr.ghs2
+ % derivatives of F with respect to forward variables
+ % reordering predetermined variables in diminishing lag order
+ O1 = zeros(M_.endo_nbr,nstatic);
+ O2 = zeros(M_.endo_nbr,M_.endo_nbr-nstatic-npred);
+ LHS = zeros(M_.endo_nbr,M_.endo_nbr);
+ LHS(:,k0) = jacobia(:,nonzeros(lead_lag_incidence(M_.maximum_endo_lag+1,order_var)));
+ RHS = zeros(M_.endo_nbr,M_.exo_nbr^2);
+ kk = find(kstate(:,2) == M_.maximum_endo_lag+2);
+ gu = dr.ghu;
+ guu = dr.ghuu;
+ Gu = [dr.ghu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr)];
+ Guu = [dr.ghuu(nstatic+[1:npred],:); zeros(np-npred,M_.exo_nbr*M_.exo_nbr)];
+ E = eye(M_.endo_nbr);
+ kh = reshape([1:nk^2],nk,nk);
+ kp = sum(kstate(:,2) <= M_.maximum_endo_lag+1);
+ E1 = [eye(npred); zeros(kp-npred,npred)];
+ H = E1;
+ hxx = dr.ghxx(nstatic+[1:npred],:);
+ [junk,k2a,k2] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+2,order_var));
+ k3 = nnz(M_.lead_lag_incidence(1:M_.maximum_endo_lag+1,:))+(1:dr.nsfwrd)';
+ [B1, err] = sparse_hessian_times_B_kronecker_C(hessian(:,kh(k3,k3)),gu(k2a,:),threads_BC);
+ mexErrCheck('sparse_hessian_times_B_kronecker_C', err);
+ RHS = RHS + jacobia(:,k2)*guu(k2a,:)+B1;
+
+ % LHS
+ LHS = LHS + jacobia(:,k2)*(E(k2a,:)+[O1(k2a,:) dr.ghx(k2a,:)*H O2(k2a,:)]);
+
+ RHS = RHS*M_.Sigma_e(:);
+ dr.fuu = RHS;
+ %RHS = -RHS-dr.fbias;
+ RHS = -RHS;
+ dr.ghs2 = LHS\RHS;
+
+ % deterministic exogenous variables
+ if M_.exo_det_nbr > 0
+ hud = dr.ghud{1}(nstatic+1:nstatic+npred,:);
+ zud=[zeros(np,M_.exo_det_nbr);dr.ghud{1};gx(:,1:npred)*hud;zeros(M_.exo_nbr,M_.exo_det_nbr);eye(M_.exo_det_nbr)];
+ R1 = hessian*kron(zx,zud);
+ dr.ghxud = cell(M_.exo_det_length,1);
+ kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
+ kp = nstatic+[1:npred];
+ dr.ghxud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{1}(kp,:)));
+ Eud = eye(M_.exo_det_nbr);
+ for i = 2:M_.exo_det_length
+ hudi = dr.ghud{i}(kp,:);
+ zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
+ R2 = hessian*kron(zx,zudi);
+ dr.ghxud{i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(Gy,Eud)+dr.ghxx(kf,:)*kron(dr.ghx(kp,:),dr.ghud{i}(kp,:)))-M1*R2;
+ end
+ R1 = hessian*kron(zu,zud);
+ dr.ghudud = cell(M_.exo_det_length,1);
+ kf = [M_.endo_nbr-nyf+1:M_.endo_nbr];
+
+ dr.ghuud{1} = -M1*(R1+f1*dr.ghxx(kf,:)*kron(dr.ghu(kp,:),dr.ghud{1}(kp,:)));
+ Eud = eye(M_.exo_det_nbr);
+ for i = 2:M_.exo_det_length
+ hudi = dr.ghud{i}(kp,:);
+ zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
+ R2 = hessian*kron(zu,zudi);
+ dr.ghuud{i} = -M2*dr.ghxud{i-1}(kf,:)*kron(hu,Eud)-M1*R2;
+ end
+ R1 = hessian*kron(zud,zud);
+ dr.ghudud = cell(M_.exo_det_length,M_.exo_det_length);
+ dr.ghudud{1,1} = -M1*R1-M2*dr.ghxx(kf,:)*kron(hud,hud);
+ for i = 2:M_.exo_det_length
+ hudi = dr.ghud{i}(nstatic+1:nstatic+npred,:);
+ zudi=[zeros(np,M_.exo_det_nbr);dr.ghud{i};gx(:,1:npred)*hudi+dr.ghud{i-1}(kf,:);zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
+ R2 = hessian*kron(zudi,zudi);
+ dr.ghudud{i,i} = -M2*(dr.ghudud{i-1,i-1}(kf,:)+...
+ 2*dr.ghxud{i-1}(kf,:)*kron(hudi,Eud) ...
+ +dr.ghxx(kf,:)*kron(hudi,hudi))-M1*R2;
+ R2 = hessian*kron(zud,zudi);
+ dr.ghudud{1,i} = -M2*(dr.ghxud{i-1}(kf,:)*kron(hud,Eud)+...
+ dr.ghxx(kf,:)*kron(hud,hudi))...
+ -M1*R2;
+ for j=2:i-1
+ hudj = dr.ghud{j}(kp,:);
+ zudj=[zeros(np,M_.exo_det_nbr);dr.ghud{j};gx(:,1:npred)*hudj;zeros(M_.exo_nbr+M_.exo_det_nbr,M_.exo_det_nbr)];
+ R2 = hessian*kron(zudj,zudi);
+ dr.ghudud{j,i} = -M2*(dr.ghudud{j-1,i-1}(kf,:)+dr.ghxud{j-1}(kf,:)* ...
+ kron(hudi,Eud)+dr.ghxud{i-1}(kf,:)* ...
+ kron(hudj,Eud)+dr.ghxx(kf,:)*kron(hudj,hudi))-M1*R2;
+ end
+
+ end
+ end
diff --git a/matlab/stochastic_solvers.m b/matlab/stochastic_solvers.m
new file mode 100644
index 0000000000000000000000000000000000000000..08f15e388a0a6528c5c4dcd189c12742d2a63c7a
--- /dev/null
+++ b/matlab/stochastic_solvers.m
@@ -0,0 +1,206 @@
+function [dr,info,M_,options_,oo_] = stochastic_solvers(dr,task,M_,options_,oo_)
+% function [dr,info,M_,options_,oo_] = stochastic_solvers(dr,task,M_,options_,oo_)
+% computes the reduced form solution of a rational expectation model (first or second order
+% approximation of the stochastic model around the deterministic steady state).
+%
+% INPUTS
+% dr [matlab structure] Decision rules for stochastic simulations.
+% task [integer] if task = 0 then dr1 computes decision rules.
+% if task = 1 then dr1 computes eigenvalues.
+% M_ [matlab structure] Definition of the model.
+% options_ [matlab structure] Global options.
+% oo_ [matlab structure] Results
+%
+% OUTPUTS
+% dr [matlab structure] Decision rules for stochastic simulations.
+% info [integer] info=1: the model doesn't define current variables uniquely
+% info=2: problem in mjdgges.dll info(2) contains error code.
+% info=3: BK order condition not satisfied info(2) contains "distance"
+% absence of stable trajectory.
+% info=4: BK order condition not satisfied info(2) contains "distance"
+% indeterminacy.
+% info=5: BK rank condition not satisfied.
+% info=6: The jacobian matrix evaluated at the steady state is complex.
+% M_ [matlab structure]
+% options_ [matlab structure]
+% oo_ [matlab structure]
+%
+% ALGORITHM
+% ...
+%
+% SPECIAL REQUIREMENTS
+% none.
+%
+
+% Copyright (C) 1996-2009 Dynare Team
+%
+% This file is part of Dynare.
+%
+% Dynare is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+%
+% Dynare is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% 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;
+
+if (options_.aim_solver == 1) && (options_.order > 1)
+ error('Option "aim_solver" is incompatible with order >= 2')
+end
+
+if options_.k_order_solver;
+ if options_.risky_steadystate
+ [dr,info] = dyn_risky_steadystate_solver(oo_.steady_state,M_,dr, ...
+ options_,oo_);
+ else
+ dr = set_state_space(dr,M_);
+ [dr,info] = k_order_pert(dr,M_,options_,oo_);
+ end
+ return;
+end
+
+if options_.ramsey_policy
+ % expanding system for Optimal Linear Regulator
+ [jacobia_,dr,info,M_,oo_] = dyn_ramsey_linearized_foc(dr,M_,options_,oo_);
+else
+ klen = M_.maximum_lag + M_.maximum_lead + 1;
+ iyv = M_.lead_lag_incidence';
+ iyv = iyv(:);
+ iyr0 = find(iyv) ;
+ it_ = M_.maximum_lag + 1 ;
+
+ if M_.exo_nbr == 0
+ oo_.exo_steady_state = [] ;
+ end
+
+ it_ = M_.maximum_lag + 1;
+ z = repmat(dr.ys,1,klen);
+ z = z(iyr0) ;
+ if options_.order == 1
+ [junk,jacobia_] = feval([M_.fname '_dynamic'],z,[oo_.exo_simul ...
+ oo_.exo_det_simul], M_.params, dr.ys, it_);
+ elseif options_.order == 2
+ [junk,jacobia_,hessian1] = feval([M_.fname '_dynamic'],z,...
+ [oo_.exo_simul ...
+ oo_.exo_det_simul], M_.params, dr.ys, it_);
+ if options_.use_dll
+ % In USE_DLL mode, the hessian is in the 3-column sparse representation
+ hessian1 = sparse(hessian1(:,1), hessian1(:,2), hessian1(:,3), ...
+ size(jacobia_, 1), size(jacobia_, 2)*size(jacobia_, 2));
+ end
+ end
+end
+
+if options_.debug
+ save([M_.fname '_debug.mat'],'jacobia_')
+end
+
+if ~isreal(jacobia_)
+ if max(max(abs(imag(jacobia_)))) < 1e-15
+ jacobia_ = real(jacobia_);
+ else
+ info(1) = 6;
+ info(2) = sum(sum(imag(jacobia_).^2));
+ return
+ end
+end
+
+kstate = dr.kstate;
+kad = dr.kad;
+kae = dr.kae;
+nstatic = dr.nstatic;
+nfwrd = dr.nfwrd;
+npred = dr.npred;
+nboth = dr.nboth;
+order_var = dr.order_var;
+nd = size(kstate,1);
+nz = nnz(M_.lead_lag_incidence);
+
+sdyn = M_.endo_nbr - nstatic;
+
+[junk,cols_b,cols_j] = find(M_.lead_lag_incidence(M_.maximum_endo_lag+1, ...
+ order_var));
+b = zeros(M_.endo_nbr,M_.endo_nbr);
+b(:,cols_b) = jacobia_(:,cols_j);
+
+if M_.maximum_endo_lead == 0
+ % backward models: simplified code exist only at order == 1
+ % If required, use AIM solver if not check only
+ if options_.order == 1
+ [k1,junk,k2] = find(kstate(:,4));
+ temp = -b\jacobia_(:,[k2 nz+1:end]);
+ dr.ghx = temp(:,1:npred);
+ if M_.exo_nbr
+ dr.ghu = temp(:,npred+1:end);
+ end
+ dr.eigval = eig(transition_matrix(dr));
+ dr.rank = 0;
+ if any(abs(dr.eigval) > options_.qz_criterium)
+ temp = sort(abs(dr.eigval));
+ nba = nnz(abs(dr.eigval) > options_.qz_criterium);
+ temp = temp(nd-nba+1:nd)-1-options_.qz_criterium;
+ info(1) = 3;
+ info(2) = temp'*temp;
+ end
+ else
+ error(['2nd and 3rd order approximation not implemented for purely ' ...
+ 'backward models'])
+ end
+elseif M_.maximum_endo_lag == 0
+ % purely forward model
+ dr.ghx = [];
+ dr.ghu = -b\jacobia_(:,nz+1:end);
+elseif options_.risky_steadystate
+ [dr,info] = dyn_risky_steadystate_solver(oo_.steady_state,M_,dr, ...
+ options_,oo_);
+else
+ % If required, use AIM solver if not check only
+ if (options_.aim_solver == 1) && (task == 0)
+ [dr,info] = AIM_first_order_solver(jacobia_,M_,dr,sdim);
+
+ else % use original Dynare solver
+ [dr,info] = dyn_first_order_solver(jacobia_,b,M_,dr,options_,task);
+ if info
+ return;
+ end
+ end
+
+ if options_.loglinear == 1
+ k = find(dr.kstate(:,2) <= M_.maximum_endo_lag+1);
+ klag = dr.kstate(k,[1 2]);
+ k1 = dr.order_var;
+
+ dr.ghx = repmat(1./dr.ys(k1),1,size(dr.ghx,2)).*dr.ghx.* ...
+ repmat(dr.ys(k1(klag(:,1)))',size(dr.ghx,1),1);
+ dr.ghu = repmat(1./dr.ys(k1),1,size(dr.ghu,2)).*dr.ghu;
+ end
+
+ %exogenous deterministic variables
+ if M_.exo_det_nbr > 0
+ f1 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+2:end,order_var))));
+ f0 = sparse(jacobia_(:,nonzeros(M_.lead_lag_incidence(M_.maximum_endo_lag+1,order_var))));
+ fudet = sparse(jacobia_(:,nz+M_.exo_nbr+1:end));
+ M1 = inv(f0+[zeros(M_.endo_nbr,nstatic) f1*gx zeros(M_.endo_nbr,nyf-nboth)]);
+ M2 = M1*f1;
+ dr.ghud = cell(M_.exo_det_length,1);
+ dr.ghud{1} = -M1*fudet;
+ for i = 2:M_.exo_det_length
+ dr.ghud{i} = -M2*dr.ghud{i-1}(end-nyf+1:end,:);
+ end
+ end
+
+ if options_.order > 1
+ % Second order
+ dr = dyn_second_order_solver(jacobia_,hessian1,dr,M_,...
+ options_.threads.kronecker.A_times_B_kronecker_C,...
+ options_.threads.kronecker.sparse_hessian_times_B_kronecker_C);
+ end
+end
+oo.dr = dr;
\ No newline at end of file
diff --git a/tests/risky_ss/agent2stock2.mod b/tests/risky_ss/agent2stock2.mod
new file mode 100644
index 0000000000000000000000000000000000000000..cac3b6be9385a0fe2c9ace21e041738fc892ab5a
--- /dev/null
+++ b/tests/risky_ss/agent2stock2.mod
@@ -0,0 +1,49 @@
+var c1 c2 x1 x2 p1 p2 d1 d2 y1 y2;
+varexo eps_1 eps_2 eta_1 eta_2;
+
+parameters beta, gamma, kappa, rho_y, rho_d;
+
+beta = 0.96;
+gamma = 4;
+kappa = -0.5;
+rho_y = 0.9;
+rho_d = 0.9;
+
+model;
+p1*c1^(-gamma-1) = beta*c1(+1)^(-gamma-1)*(d1(+1)+p1(+1));
+p2*c1^(-gamma-1) = beta*c1(+1)^(-gamma-1)*(d2(+1)+p2(+1));
+p1*c2^(-gamma-1) = beta*c2(+1)^(-gamma-1)*(d1(+1)+p1(+1));
+p2*c2^(-gamma-1) = beta*c2(+1)^(-gamma-1)*(d2(+1)+p2(+1));
+c1 = y1 - (x1(-1)*(p1+d1)-x1*p1) + (x2(-1)*(p2+d2)-x2*p2);
+c2 = y2 + (x1(-1)*(p1+d1)-x1*p1) - (x2(-1)*(p2+d2)-x2*p2);
+y1 = (1-rho_y)*0.5 + rho_y*y1(-1) + eps_1;
+y2 = (1-rho_y)*0.5 + rho_y*y2(-1) + eps_2;
+d1 = (1-rho_d)*0.5 + rho_d*d1(-1) + eta_1;
+d2 = (1-rho_d)*0.5 + rho_d*d2(-1) + eta_2;
+end;
+
+shocks;
+var eps_1; stderr 0.01;
+var eps_2; stderr 0.01;
+var eta_1; stderr 0.01;
+var eta_2; stderr 0.01;
+corr eps_1,eta_1 = -0.5;
+corr eps_2,eta_2 = -0.5;
+end;
+
+initval;
+c1 = 0.5;
+c2 = 0.5;
+y1 = 0.5;
+y2 = 0.5;
+d1 = 0.5;
+d2 = 0.5;
+p1 = 12.51;
+p2 = 12.51;
+x1 = 0.26;
+x2 = 0.25;
+end;
+
+options_.risky_steadystate = 1;
+
+stoch_simul(irf=0);
diff --git a/tests/risky_ss/agent2stock2_dss.mod b/tests/risky_ss/agent2stock2_dss.mod
new file mode 100644
index 0000000000000000000000000000000000000000..87bad3c1c86ca5b70635e8d12a480a0c44e68d60
--- /dev/null
+++ b/tests/risky_ss/agent2stock2_dss.mod
@@ -0,0 +1,47 @@
+var c1 c2 p1 p2 d1 d2 y1 y2;
+varexo eps_1 eps_2 eta_1 eta_2;
+
+parameters beta, gamma, kappa, rho_y, rho_d, x1, x2;
+
+beta = 0.96;
+gamma = 4;
+kappa = -0.5;
+rho_y = 0.9;
+rho_d = 0.9;
+x1 = 0;
+x2 = 0;
+
+model;
+p1*c1^(-gamma-1) = beta*c1(+1)^(-gamma-1)*(d1(+1)+p1(+1));
+//p2*c1^(-gamma-1) = beta*c1(+1)^(-gamma-1)*(d2(+1)+p2(+1));
+//p1*c2^(-gamma-1) = beta*c2(+1)^(-gamma-1)*(d1(+1)+p1(+1));
+p2*c2^(-gamma-1) = beta*c2(+1)^(-gamma-1)*(d2(+1)+p2(+1));
+c1 = y1 - (x1(-1)*(p1+d1)-x1*p1) + (x2(-1)*(p2+d2)-x2*p2);
+c2 = y2 + (x1(-1)*(p1+d1)-x1*p1) - (x2(-1)*(p2+d2)-x2*p2);
+y1 = (1-rho_y)*0.5 + rho_y*y1(-1)+eps_1;
+y2 = (1-rho_y)*0.5 + rho_y*y2(-1) + eps_2;
+d1 = (1-rho_d)*0.5 + rho_d*d1(-1) + eta_1;
+d2 = (1-rho_d)*0.5 + rho_d*d2(-1) + eta_2;
+end;
+
+shocks;
+var eps_1; stderr 0.01;
+var eps_2; stderr 0.01;
+var eta_1; stderr 0.01;
+var eta_2; stderr 0.01;
+corr eps_1,eta_1 = -0.5;
+corr eps_2,eta_2 = -0.5;
+end;
+
+initval;
+c1 = 0.5;
+c2 = 0.5;
+y1 = 0.5;
+y2 = 0.5;
+d1 = 0.5;
+d2 = 0.5;
+p1 = 1;
+p2 = 1;
+end;
+
+stoch_simul(irf=0);
diff --git a/tests/risky_ss/example1.mod b/tests/risky_ss/example1.mod
new file mode 100644
index 0000000000000000000000000000000000000000..ca7cefd09c650399b19304aad809297ab833719d
--- /dev/null
+++ b/tests/risky_ss/example1.mod
@@ -0,0 +1,47 @@
+// Example 1 from Collard's guide to Dynare
+var y, c, k, a, h, b;
+varexo e, u;
+
+parameters beta, rho, alpha, delta, theta, psi, tau;
+
+alpha = 0.36;
+rho = 0.95;
+tau = 0.025;
+beta = 0.99;
+delta = 0.025;
+psi = 0;
+theta = 2.95;
+
+phi = 0.1;
+
+model;
+c*theta*h^(1+psi)=(1-alpha)*y;
+k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
+ *(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
+y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
+k = exp(b)*(y-c)+(1-delta)*k(-1);
+a = rho*a(-1)+tau*b(-1) + e;
+b = tau*a(-1)+rho*b(-1) + u;
+end;
+
+initval;
+y = 1.08068253095672;
+c = 0.80359242014163;
+h = 0.29175631001732;
+k = 11.08360443260358;
+a = 0;
+b = 0;
+e = 0;
+u = 0;
+end;
+
+options_.solve_tolf = 1e-11;
+steady;
+
+shocks;
+var e; stderr 0.009;
+var u; stderr 0.009;
+var e, u = phi*0.009*0.009;
+end;
+
+stoch_simul;
diff --git a/tests/risky_ss/example1_korder.mod b/tests/risky_ss/example1_korder.mod
new file mode 100644
index 0000000000000000000000000000000000000000..2296fea5610fb7b88a380c141b102db77f455f93
--- /dev/null
+++ b/tests/risky_ss/example1_korder.mod
@@ -0,0 +1,45 @@
+// Example 1 from Collard's guide to Dynare
+var y, c, k, a, h, b;
+varexo e, u;
+
+parameters beta, rho, alpha, delta, theta, psi, tau;
+
+alpha = 0.36;
+rho = 0.95;
+tau = 0.025;
+beta = 0.99;
+delta = 0.025;
+psi = 0;
+theta = 2.95;
+
+phi = 0.1;
+
+model(use_dll);
+c*theta*h^(1+psi)=(1-alpha)*y;
+k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
+ *(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
+y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
+k = exp(b)*(y-c)+(1-delta)*k(-1);
+a = rho*a(-1)+tau*b(-1) + e;
+b = tau*a(-1)+rho*b(-1) + u;
+end;
+
+initval;
+y = 1.08068253095672;
+c = 0.80359242014163;
+h = 0.29175631001732;
+k = 11.08360443260358;
+a = 0;
+b = 0;
+e = 0;
+u = 0;
+end;
+
+shocks;
+var e; stderr 0.009;
+var u; stderr 0.009;
+var e, u = phi*0.009*0.009;
+end;
+
+//options_.risky_steadystate = 1;
+stoch_simul(k_order_solver,order=3,irf=0);
diff --git a/tests/risky_ss/example1_risky_2.mod b/tests/risky_ss/example1_risky_2.mod
new file mode 100644
index 0000000000000000000000000000000000000000..01056949abae81ae152449f1fc5de1f44521a91e
--- /dev/null
+++ b/tests/risky_ss/example1_risky_2.mod
@@ -0,0 +1,45 @@
+// Example 1 from Collard's guide to Dynare
+var y, c, k, a, h, b;
+varexo e, u;
+
+parameters beta, rho, alpha, delta, theta, psi, tau;
+
+alpha = 0.36;
+rho = 0.95;
+tau = 0.025;
+beta = 0.99;
+delta = 0.025;
+psi = 0;
+theta = 2.95;
+
+phi = 0.1;
+
+model;
+c*theta*h^(1+psi)=(1-alpha)*y;
+k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
+ *(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
+y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
+k = exp(b)*(y-c)+(1-delta)*k(-1);
+a = rho*a(-1)+tau*b(-1) + e;
+b = tau*a(-1)+rho*b(-1) + u;
+end;
+
+initval;
+y = 1.08068253095672;
+c = 0.80359242014163;
+h = 0.29175631001732;
+k = 11.08360443260358;
+a = 0;
+b = 0;
+e = 0;
+u = 0;
+end;
+
+shocks;
+var e; stderr 0.009;
+var u; stderr 0.009;
+var e, u = phi*0.009*0.009;
+end;
+
+options_.risky_steadystate = 1;
+stoch_simul(irf=0);
diff --git a/tests/risky_ss/example1_risky_3.mod b/tests/risky_ss/example1_risky_3.mod
new file mode 100644
index 0000000000000000000000000000000000000000..4db175ea8b45f156e354285b50c42a7490fa44ad
--- /dev/null
+++ b/tests/risky_ss/example1_risky_3.mod
@@ -0,0 +1,47 @@
+// Example 1 from Collard's guide to Dynare
+var y, c, k, a, h, b;
+varexo e, u;
+
+parameters beta, rho, alpha, delta, theta, psi, tau;
+
+alpha = 0.36;
+rho = 0.95;
+tau = 0.025;
+beta = 0.99;
+delta = 0.025;
+psi = 0;
+theta = 2.95;
+
+phi = 0.1;
+
+model(use_dll);
+c*theta*h^(1+psi)=(1-alpha)*y;
+k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
+ *(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
+y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
+k = exp(b)*(y-c)+(1-delta)*k(-1);
+a = rho*a(-1)+tau*b(-1) + e;
+b = tau*a(-1)+rho*b(-1) + u;
+end;
+
+initval;
+y = 1.08068253095672;
+c = 0.80359242014163;
+h = 0.29175631001732;
+k = 11.08360443260358;
+a = 0;
+b = 0;
+e = 0;
+u = 0;
+end;
+
+shocks;
+var e; stderr 0.009;
+var u; stderr 0.009;
+var e, u = phi*0.009*0.009;
+end;
+
+stoch_simul(order=2,irf=0);
+
+options_.risky_steadystate = 1;
+stoch_simul(order=3,irf=0);
diff --git a/tests/risky_ss/jermann98.mod b/tests/risky_ss/jermann98.mod
new file mode 100644
index 0000000000000000000000000000000000000000..eaf0d5397e620ed6f4dd1ef2e3ae4cfea7b8c087
--- /dev/null
+++ b/tests/risky_ss/jermann98.mod
@@ -0,0 +1,95 @@
+// This is the Ramsey model with adjustment costs. Jermann(1998),JME 41, pages 257-275
+// Olaf Weeken
+// Bank of England, 13 June, 2005
+// modified January 20, 2006 by Michel Juillard
+
+//---------------------------------------------------------------------
+// 1. Variable declaration
+//---------------------------------------------------------------------
+
+var c, d, erp1, i, k, m1, r1, rf1, w, y, z, mu;
+varexo ez;
+
+//---------------------------------------------------------------------
+// 2. Parameter declaration and calibration
+//---------------------------------------------------------------------
+
+parameters alf, chihab, xi, delt, tau, g, rho, zbar, a1, a2, betstar, bet;
+
+alf = 0.36; // capital share in production function
+//chihab = 0.819; // habit formation parameter
+chihab = 0.98; // habit formation parameter
+xi = 1/4.3; // capital adjustment cost parameter
+delt = 0.025; // quarterly deprecition rate
+g = 1.005; //quarterly growth rate (note zero growth =>g=1)
+tau = 5; // curvature parameter with respect to c
+rho = 0.95; // AR(1) parameter for technology shock
+
+a1 = (g-1+delt)^(1/xi);
+a2 = (g-1+delt)-(((g-1+delt)^(1/xi))/(1-(1/xi)))*((g-1+delt)^(1-(1/xi)));
+betstar = g/1.011138;
+bet = betstar/(g^(1-tau));
+
+//---------------------------------------------------------------------
+// 3. Model declaration
+//---------------------------------------------------------------------
+
+model(use_dll);
+g*k = (1-delt)*k(-1) + ((a1/(1-1/xi))*(g*i/k(-1))^(1-1/xi)+a2)*k(-1);
+d = y - w - i;
+w = (1-alf)*y;
+y = z*g^(-alf)*k(-1)^alf;
+c = w + d;
+mu = (c-chihab*c(-1)/g)^(-tau)-chihab*bet*(c(+1)*g-chihab*c)^(-tau);
+mu = (betstar/g)*mu(+1)*(a1*(g*i/k(-1))^(-1/xi))*(alf*z(+1)*g^(1-alf)*
+ (k^(alf-1))+((1-delt+(a1/(1-1/xi))*(g*i(+1)/k)^(1-1/xi)+a2))/
+ (a1*(g*i(+1)/k)^(-1/xi))-g*i(+1)/k);
+log(z) = rho*log(z(-1)) + ez;
+
+m1 = (betstar/g)*mu(+1)/mu;
+rf1 = 1/m1;
+r1 = (a1*(g*i/k(-1))^(-1/xi))*(alf*z(+1)*g^(1-alf)*(k^(alf-1))+
+ (1-delt+(a1/(1-1/xi))*(g*i(+1)/k)^(1-1/xi)+a2)/
+ (a1*(g*i(+1)/k)^(-1/xi))-g*i(+1)/k);
+erp1 = r1 - rf1;
+
+end;
+
+//---------------------------------------------------------------------
+// 4. Initial values and steady state
+//---------------------------------------------------------------------
+
+initval;
+m1 = betstar/g;
+rf1 = (1/m1);
+r1 = (1/m1);
+erp1 = r1-rf1;
+
+z = 1;
+k = (((g/betstar)-(1-delt))/(alf*g^(1-alf)))^(1/(alf-1));
+y = (g^(-alf))*k^alf;
+w = (1-alf)*y;
+i = (1-(1/g)*(1-delt))*k;
+d = y - w - i;
+c = w + d;
+
+mu = ((c-(chihab*c/g))^(-tau))-chihab*bet*((c*g-chihab*c)^(-tau));
+
+ez = 0;
+end;
+
+resid(1);
+
+steady;
+
+//---------------------------------------------------------------------
+// 5. Shock declaration
+//
+//---------------------------------------------------------------------
+
+shocks;
+var ez; stderr 0.001;
+end;
+
+options_.risky_steadystate = 1;
+stoch_simul (order=3,irf=0,periods=20000) erp1, rf1, m1, r1, y, z, c, d, mu, k;
diff --git a/tests/risky_ss/jermann98_2.mod b/tests/risky_ss/jermann98_2.mod
new file mode 100644
index 0000000000000000000000000000000000000000..2b066c9d74b11b03d1d420a5c46e51d0e10bd8cb
--- /dev/null
+++ b/tests/risky_ss/jermann98_2.mod
@@ -0,0 +1,99 @@
+// This is the Ramsey model with adjustment costs. Jermann(1998),JME 41, pages 257-275
+// Olaf Weeken
+// Bank of England, 13 June, 2005
+// modified January 20, 2006 by Michel Juillard
+
+//---------------------------------------------------------------------
+// 1. Variable declaration
+//---------------------------------------------------------------------
+
+var c, d, erp1, i, k, m1, r1, rf1, w, y, z, mu;
+varexo ez;
+
+//---------------------------------------------------------------------
+// 2. Parameter declaration and calibration
+//---------------------------------------------------------------------
+
+parameters alf, chihab, xi, delt, tau, g, rho, zbar, a1, a2, betstar, bet;
+
+alf = 0.36; // capital share in production function
+//chihab = 0.819; // habit formation parameter
+chihab = 0.98; // habit formation parameter
+xi = 1/4.3; // capital adjustment cost parameter
+delt = 0.025; // quarterly deprecition rate
+g = 1.005; //quarterly growth rate (note zero growth =>g=1)
+tau = 5; // curvature parameter with respect to c
+rho = 0.95; // AR(1) parameter for technology shock
+
+a1 = (g-1+delt)^(1/xi);
+a2 = (g-1+delt)-(((g-1+delt)^(1/xi))/(1-(1/xi)))*((g-1+delt)^(1-(1/xi)));
+betstar = g/1.011138;
+bet = betstar/(g^(1-tau));
+
+//---------------------------------------------------------------------
+// 3. Model declaration
+//---------------------------------------------------------------------
+
+model;
+g*k = (1-delt)*k(-1) + ((a1/(1-1/xi))*(g*i/k(-1))^(1-1/xi)+a2)*k(-1);
+d = y - w - i;
+w = (1-alf)*y;
+y = z*g^(-alf)*k(-1)^alf;
+c = w + d;
+mu = ((c-chihab*c(-1)/g)^(-tau)-chihab*bet*(c(+1)*g-chihab*c)^(-tau))/1e4;
+mu = (betstar/g)*mu(+1)*(a1*(g*i/k(-1))^(-1/xi))*(alf*z(+1)*g^(1-alf)*
+ (k^(alf-1))+((1-delt+(a1/(1-1/xi))*(g*i(+1)/k)^(1-1/xi)+a2))/
+ (a1*(g*i(+1)/k)^(-1/xi))-g*i(+1)/k);
+log(z) = rho*log(z(-1)) + ez;
+
+m1 = (betstar/g)*mu(+1)/mu;
+rf1 = 1/m1;
+r1 = (a1*(g*i/k(-1))^(-1/xi))*(alf*z(+1)*g^(1-alf)*(k^(alf-1))+
+ (1-delt+(a1/(1-1/xi))*(g*i(+1)/k)^(1-1/xi)+a2)/
+ (a1*(g*i(+1)/k)^(-1/xi))-g*i(+1)/k);
+erp1 = r1 - rf1;
+
+end;
+
+//---------------------------------------------------------------------
+// 4. Initial values and steady state
+//---------------------------------------------------------------------
+
+initval;
+m1 = betstar/g;
+rf1 = (1/m1);
+r1 = (1/m1);
+erp1 = r1-rf1;
+
+z = 1;
+k = (((g/betstar)-(1-delt))/(alf*g^(1-alf)))^(1/(alf-1));
+y = (g^(-alf))*k^alf;
+w = (1-alf)*y;
+i = (1-(1/g)*(1-delt))*k;
+d = y - w - i;
+c = w + d;
+
+mu = (((c-(chihab*c/g))^(-tau))-chihab*bet*((c*g-chihab*c)^(-tau)))/1e4;
+
+ez = 0;
+end;
+
+resid(1);
+
+steady;
+
+//---------------------------------------------------------------------
+// 5. Shock declaration
+//
+//---------------------------------------------------------------------
+
+for i=1:100:101;
+s = i/10000;
+shocks;
+var ez; stderr s;
+end;
+
+options_.risky_steadystate = 1;
+stoch_simul (order=2,irf=0,noprint) erp1, rf1, m1, r1, y, z, c, d, mu, k;
+oo_.steady_state = oo_.dr.ys;
+end
\ No newline at end of file
diff --git a/tests/risky_ss/jermann98_3.mod b/tests/risky_ss/jermann98_3.mod
new file mode 100644
index 0000000000000000000000000000000000000000..74972955e7a699d6f4aebd7d2f81389b6580da5a
--- /dev/null
+++ b/tests/risky_ss/jermann98_3.mod
@@ -0,0 +1,99 @@
+// This is the Ramsey model with adjustment costs. Jermann(1998),JME 41, pages 257-275
+// Olaf Weeken
+// Bank of England, 13 June, 2005
+// modified January 20, 2006 by Michel Juillard
+
+//---------------------------------------------------------------------
+// 1. Variable declaration
+//---------------------------------------------------------------------
+
+var c, d, erp1, i, k, m1, r1, rf1, w, y, z, mu;
+varexo ez;
+
+//---------------------------------------------------------------------
+// 2. Parameter declaration and calibration
+//---------------------------------------------------------------------
+
+parameters alf, chihab, xi, delt, tau, g, rho, zbar, a1, a2, betstar, bet;
+
+alf = 0.36; // capital share in production function
+//chihab = 0.819; // habit formation parameter
+chihab = 0.98; // habit formation parameter
+xi = 1/4.3; // capital adjustment cost parameter
+delt = 0.025; // quarterly deprecition rate
+g = 1.005; //quarterly growth rate (note zero growth =>g=1)
+tau = 5; // curvature parameter with respect to c
+rho = 0.95; // AR(1) parameter for technology shock
+
+a1 = (g-1+delt)^(1/xi);
+a2 = (g-1+delt)-(((g-1+delt)^(1/xi))/(1-(1/xi)))*((g-1+delt)^(1-(1/xi)));
+betstar = g/1.011138;
+bet = betstar/(g^(1-tau));
+
+//---------------------------------------------------------------------
+// 3. Model declaration
+//---------------------------------------------------------------------
+
+model(use_dll);
+g*k = (1-delt)*k(-1) + ((a1/(1-1/xi))*(g*i/k(-1))^(1-1/xi)+a2)*k(-1);
+d = y - w - i;
+w = (1-alf)*y;
+y = z*g^(-alf)*k(-1)^alf;
+c = w + d;
+mu = ((c-chihab*c(-1)/g)^(-tau)-chihab*bet*(c(+1)*g-chihab*c)^(-tau))/1e4;
+mu = (betstar/g)*mu(+1)*(a1*(g*i/k(-1))^(-1/xi))*(alf*z(+1)*g^(1-alf)*
+ (k^(alf-1))+((1-delt+(a1/(1-1/xi))*(g*i(+1)/k)^(1-1/xi)+a2))/
+ (a1*(g*i(+1)/k)^(-1/xi))-g*i(+1)/k);
+log(z) = rho*log(z(-1)) + ez;
+
+m1 = (betstar/g)*mu(+1)/mu;
+rf1 = 1/m1;
+r1 = (a1*(g*i/k(-1))^(-1/xi))*(alf*z(+1)*g^(1-alf)*(k^(alf-1))+
+ (1-delt+(a1/(1-1/xi))*(g*i(+1)/k)^(1-1/xi)+a2)/
+ (a1*(g*i(+1)/k)^(-1/xi))-g*i(+1)/k);
+erp1 = r1 - rf1;
+
+end;
+
+//---------------------------------------------------------------------
+// 4. Initial values and steady state
+//---------------------------------------------------------------------
+
+initval;
+m1 = betstar/g;
+rf1 = (1/m1);
+r1 = (1/m1);
+erp1 = r1-rf1;
+
+z = 1;
+k = (((g/betstar)-(1-delt))/(alf*g^(1-alf)))^(1/(alf-1));
+y = (g^(-alf))*k^alf;
+w = (1-alf)*y;
+i = (1-(1/g)*(1-delt))*k;
+d = y - w - i;
+c = w + d;
+
+mu = (((c-(chihab*c/g))^(-tau))-chihab*bet*((c*g-chihab*c)^(-tau)))/1e4;
+
+ez = 0;
+end;
+
+resid(1);
+
+steady;
+
+//---------------------------------------------------------------------
+// 5. Shock declaration
+//
+//---------------------------------------------------------------------
+
+for i=1:1:100;
+s = i/10000;
+shocks;
+var ez; stderr s;
+end;
+
+options_.risky_steadystate = 1;
+stoch_simul (order=3,irf=0,noprint) erp1, rf1, m1, r1, y, z, c, d, mu, k;
+oo_.steady_state = oo_.dr.ys;
+end;
\ No newline at end of file