dr11

 Copyright (C) 2001 Michel Juillard

0001 % Copyright (C) 2001 Michel Juillard
0002 %
0003 function dr=dr11(iorder,dr,cheik)
0004 
0005 global M_ options_ oo_
0006 global it_ stdexo_ means_ dr1_test_ bayestopt_
0007 
0008 % hack for Bayes
0009 global dr1_test_ bayestopt_
0010 
0011 options_ = set_default_option(options_,'loglinear',0);
0012 
0013 xlen = M_.maximum_lead + M_.maximum_lag + 1;
0014 klen = M_.maximum_lag + M_.maximum_lead + 1;
0015 iyv  = transpose(M_.lead_lag_incidence);
0016 iyv = iyv(:);
0017 iyr0 = find(iyv) ;
0018 it_ = M_.maximum_lag + 1 ;
0019 
0020 
0021 if M_.exo_nbr == 0
0022   oo_.exo_steady_state = [] ;
0023 end
0024 
0025 if ~ M_.lead_lag_incidence(M_.maximum_lag+1,:) > 0
0026   error ('Error in model specification: some variables don"t appear as current') ;
0027 end
0028 
0029 if ~cheik
0030 %  if xlen > 1
0031 %    error (['SS: stochastic exogenous variables must appear only at the' ...
0032 %      ' current period. Use additional endogenous variables']) ;
0033 %  end
0034 end
0035   
0036 if M_.maximum_lead > 1 & iorder > 1
0037   error (['Models with leads on more than one period can only be solved' ...
0038       ' at order 1'])
0039 end
0040 
0041 dr=set_state_space(dr);
0042 kstate = dr.kstate;
0043 kad = dr.kad;
0044 kae = dr.kae;
0045 nstatic = dr.nstatic;
0046 nfwrd = dr.nfwrd;
0047 npred = dr.npred;
0048 nboth = dr.nboth;           
0049 order_var = dr.order_var;
0050 nd = size(kstate,1);
0051 
0052 sdyn = M_.endo_nbr - nstatic;
0053 
0054 
0055 tempex = oo_.exo_simul;
0056 
0057 it_ = M_.maximum_lag + 1;
0058 z = repmat(dr.ys,1,klen);
0059 z = z(iyr0) ;
0060 %M_.jacobia=real(diffext('ff1_',[z; oo_.exo_steady_state])) ;
0061 %M_.jacobia=real(jacob_a('ff1_',[z; oo_.exo_steady_state])) ;
0062 [junk,M_.jacobia] = feval([M_.fname '_dynamic'],z,oo_.exo_simul);
0063 oo_.exo_simul = tempex ;
0064 tempex = [];
0065 
0066 nz = size(z,1);
0067 k1 = M_.lead_lag_incidence(find([1:klen] ~= M_.maximum_lag+1),:);
0068 b = M_.jacobia(:,M_.lead_lag_incidence(M_.maximum_lag+1,order_var));
0069 a = b\M_.jacobia(:,nonzeros(k1')); 
0070 if any(isinf(a(:)))
0071   dr1_test_(1) = 5;
0072   dr1_test_(2) = bayestopt_.penalty;
0073 end
0074 if M_.exo_nbr
0075   fu = b\M_.jacobia(:,nz+1:end);
0076 end
0077 
0078 if M_.maximum_lead == 0 & M_.maximum_lag == 1;  % backward model with one lag
0079   dr.ghx = -a;
0080   dr.ghu = -fu;
0081   return;
0082 elseif M_.maximum_lead == 0 & M_.maximum_lag > 1 % backward model with lags on more than
0083                    % one period
0084   e = zeros(endo_nbr,nd);                
0085   k = find(kstate(:,2) <= M_.maximum_lag+1 & kstate(:,4));
0086   e(:,k) = -a(:,kstate(k,4)) ;
0087   dr.ghx = e;
0088   dr.ghu = -fu;
0089 end
0090 
0091 % buildind D and E
0092 d = zeros(nd,nd) ;
0093 e = d ;
0094 
0095 k = find(kstate(:,2) >= M_.maximum_lag+2 & kstate(:,3));
0096 d(1:sdyn,k) = a(nstatic+1:end,kstate(k,3)) ;
0097 k1 = find(kstate(:,2) == M_.maximum_lag+2);
0098 a1 = eye(sdyn);
0099 e(1:sdyn,k1) =  -a1(:,kstate(k1,1)-nstatic);
0100 k = find(kstate(:,2) <= M_.maximum_lag+1 & kstate(:,4));
0101 e(1:sdyn,k) = -a(nstatic+1:end,kstate(k,4)) ;
0102 k2 = find(kstate(:,2) == M_.maximum_lag+1);
0103 k2 = k2(~ismember(kstate(k2,1),kstate(k1,1)));
0104 d(1:sdyn,k2) = a1(:,kstate(k2,1)-nstatic);
0105 
0106 if ~isempty(kad)
0107   for j = 1:size(kad,1)
0108     d(sdyn+j,kad(j)) = 1 ;
0109     e(sdyn+j,kae(j)) = 1 ;
0110   end
0111 end
0112 options_ = set_default_option(options_,'qz_criterium',1.000001);
0113   
0114 if  ~exist('mjdgges')
0115   % using Chris Sim's routines
0116   use_qzdiv = 1;
0117   [ss,tt,qq,w] = qz(e,d);
0118   [tt,ss,qq,w] = qzdiv(options_.qz_criterium,tt,ss,qq,w);
0119   ss1=diag(ss);
0120   tt1=diag(tt);
0121   warning_state = warning;
0122   warning off;
0123   oo_.eigenvalues = ss1./tt1 ;
0124   warning warning_state;
0125   nba = nnz(abs(eigval) > options_.qz_criterium);
0126 else
0127   use_qzdiv = 0;
0128   [ss,tt,w,sdim,oo_.eigenvalues,info] = mjdgges(e,d,options_.qz_criterium);
0129   if info & info ~= nd+2;
0130     error(['ERROR' info ' in MJDGGES.DLL']);
0131   end
0132   nba = nd-sdim;
0133 end
0134 
0135 nyf = sum(kstate(:,2) > M_.maximum_lag+1);
0136 
0137 if cheik
0138   dr.rank = rank(w(1:nyf,nd-nyf+1:end));
0139   % dr.eigval = oo_.eigenvalues;
0140   return
0141 end
0142 
0143 eigenvalues = sort(oo_.eigenvalues);
0144 
0145 if nba > nyf;
0146 %  disp('Instability !');
0147   dr1_test_(1) = 3; %% More eigenvalues superior to unity than forward variables ==> instability.
0148   dr1_test_(2) = (abs(eigenvalues(nd-nba+1:nd-nyf))-1-1e-5)'*...
0149       (abs(eigenvalues(nd-nba+1:nd-nyf))-1-1e-5);% Distance to Blanchard-Khan conditions (penalty)
0150   return
0151 elseif nba < nyf;
0152 %  disp('Indeterminacy !');
0153   dr1_test_(1) = 2; %% ==> Indeterminacy.
0154   dr1_test_(2) = (abs(eigenvalues(nd-nyf+1:nd-nba))-1-1e-5)'*...
0155       (abs(eigenvalues(nd-nyf+1:nd-nba))-1-1e-5);% Distance to Blanchard-Khan conditions (penality)
0156   %% warning('DR1: Blanchard-Kahn conditions are not satisfied. Run CHEIK to learn more!');
0157   return
0158 end
0159 
0160 np = nd - nyf;
0161 n2 = np + 1;
0162 n3 = nyf;
0163 n4 = n3 + 1;
0164 % derivatives with respect to dynamic state variables
0165 % forward variables
0166 
0167 if condest(w(1:n3,n2:nd)) > 1e9
0168 %  disp('Indeterminacy !!');
0169   dr1_test_(1) = 2; 
0170   dr1_test_(2) = 1;
0171   return
0172 end
0173 
0174 warning_state = warning;
0175 lastwarn('');
0176 warning off;
0177 gx = -w(1:n3,n2:nd)'\w(n4:nd,n2:nd)';
0178 
0179 if length(lastwarn) > 0;
0180 %  disp('Indeterminacy !!');
0181   dr1_test_(1) = 2; 
0182   dr1_test_(2) = 1;
0183   warning(warning_state);
0184   return
0185 end
0186 
0187 % predetermined variables
0188 hx = w(1:n3,1:np)'*gx+w(n4:nd,1:np)';
0189 hx = (tt(1:np,1:np)*hx)\(ss(1:np,1:np)*hx);
0190 
0191 lastwarn('');
0192 if length(lastwarn) > 0;
0193 %  disp('Singularity problem in dr11.m');
0194   dr1_test_(1) = 2; 
0195   dr1_test_(2) = 1;
0196   warning(warning_state);
0197   return
0198 end
0199 
0200 k1 = find(kstate(n4:nd,2) == M_.maximum_lag+1);
0201 k2 = find(kstate(1:n3,2) == M_.maximum_lag+2);
0202 dr.ghx = [hx(k1,:); gx(k2(nboth+1:end),:)];
0203   
0204 %lead variables actually present in the model
0205 j3 = nonzeros(kstate(:,3));
0206 j4  = find(kstate(:,3));
0207 % derivatives with respect to exogenous variables
0208 if M_.exo_nbr
0209   a1 = eye(M_.endo_nbr);
0210   aa1 = [];
0211   if nstatic > 0
0212     aa1 = a1(:,1:nstatic);
0213   end
0214   dr.ghu = -[aa1 a(:,j3)*gx(j4,1:npred)+a1(:,nstatic+1:nstatic+ ...
0215                           npred) a1(:,nstatic+npred+1:end)]\fu;
0216 
0217 
0218     lastwarn('');
0219     if length(lastwarn) > 0;
0220 %    disp('Singularity problem in dr11.m');
0221         dr1_test_(1) = 2; 
0222         dr1_test_(2) = 1;
0223         return
0224     end
0225 end
0226 warning(warning_state);
0227 
0228 % static variables
0229 if nstatic > 0
0230   temp = -a(1:nstatic,j3)*gx(j4,:)*hx;
0231   j5 = find(kstate(n4:nd,4));
0232   temp(:,j5) = temp(:,j5)-a(1:nstatic,nonzeros(kstate(:,4)));
0233   dr.ghx = [temp; dr.ghx];
0234   temp = [];
0235 end
0236 
0237 if options_.loglinear == 1
0238     k = find(dr.kstate(:,2) <= M_.maximum_lag+1);
0239     klag = dr.kstate(k,[1 2]);
0240     k1 = dr.order_var;
0241 
0242     dr.ghx = repmat(1./dr.ys(k1),1,size(dr.ghx,2)).*dr.ghx.* ...
0243          repmat(dr.ys(k1(klag(:,1)))',size(dr.ghx,1),1);
0244     dr.ghu = repmat(1./dr.ys(k1),1,size(dr.ghu,2)).*dr.ghu;
0245 end
0246 
0247 % necessary when using Sims' routines
0248 if use_qzdiv
0249   gx = real(gx);
0250   hx = real(hx);
0251   dr.ghx = real(dr.ghx);
0252   dr.ghu = real(dr.ghu);
0253 end
0254 
0255