dynare/matlab/calib.m

function M_.Sigma_e = calib(var_indices,targets,var_weights,nar,cova,M_.Sigma_e)

% Copyright (C) 2005 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/>.

  global oo_ M_  vx
  
  ncstr = 0;
  ni = size(var_indices,1);
  for i=1:nar+3
    ncstr = ncstr + size(var_indices{i},1);
  end
  if cova
    if ncstr < M_.exo_nbr*(M_.exo_nbr+1)/2
      error(['number of preset variances is smaller than number of shock' ...
	     ' variances and covariances to be estimated !'])
    end
  else
    if ncstr < M_.exo_nbr
      error(['number of preset variances is smaller than number of shock' ...
	     ' variances to be estimated !'])
    end
  end
  
  % computes approximate solution at order 1
  dr = resol(oo_.steady_state,0,0,1);
  
  ghx = dr.ghx;
  ghu = dr.ghu;
  npred = dr.npred;
  nstatic = dr.nstatic;
  kstate = dr.kstate;
  order = dr.order_var;
  iv(order) = [1:M_.endo_nbr];
  iv = iv';
  nx = size(ghx,2);

  ikx = [nstatic+1:nstatic+npred];
  
  A = zeros(nx,nx);
  A(1:npred,:)=ghx(ikx,:);
  offset_r = npred;
  offset_c = 0;
  i0 = find(kstate(:,2) == M_.maximum_lag+1);
  n0 = size(i0,1);
  for i=M_.maximum_lag:-1:2
    i1 = find(kstate(:,2) == i);
    n1 = size(i1,1);
    j = zeros(n1,1);
    for j1 = 1:n1
      j(j1) = find(kstate(i0,1)==kstate(i1(j1),1));
    end
    A(offset_r+1:offset_r+n1,offset_c+j)=eye(n1);
    offset_r = offset_r + n1;
    offset_c = offset_c + n0;
    i0 = i1;
    n0 = n1;
  end
  ghu1 = [ghu(ikx,:);zeros(nx-npred,M_.exo_nbr)];
%  IA = speye(nx*nx)-kron(A,A);
%  kron_ghu = kron(ghu1,ghu1);
  
  % vx1 such that vec(sigma_x) = vx1 * vec(M_.Sigma_e) (predetermined vars) 
vx1 = [];
  % vx1 = IA\kron_ghu;
  IA = [];
  kron_ghu = [];
  
  % computes required variables and indices among required variables
  iiy = [];
  for i=1:nar+3
    if i ~= 3 & ~isempty(var_indices{i})
      iiy = union(iiy, iv(var_indices{i}(:,1)));
    end
  end
  if ~isempty(var_indices{2})
    iiy = union(iiy, iv(var_indices{2}(:,2)));
  end
  ny = size(iiy,1);

  for i=1:nar+3
    if i ~= 3 & ~isempty(var_indices{i})
      var_indices{i}(:,1) = indnv(iv(var_indices{i}(:,1)),iiy);
    end
    if i ~= 2 & i ~= 3 & ~isempty(var_indices{i})
      var_indices{i} = sub2ind([ny ny],var_indices{i},var_indices{i});
    end
  end
  if ~isempty(var_indices{2})
    var_indices{2}(:,2) = indnv(iv(var_indices{2}(:,2)),iiy);
    var_indices{2} = sub2ind([ny ny],var_indices{2}(:,1),var_indices{2}(:,2));
  end
  if ~isempty(var_indices{3})
    var_indices{3} = sub2ind([M_.exo_nbr M_.exo_nbr],var_indices{3}(:,1),var_indices{3}(:,2));
  end
  if isempty(M_.Sigma_e)
    M_.Sigma_e = 0.01*eye(M_.exo_nbr);
    b = 0.1*ghu1*ghu1';
  else
    b = ghu1*M_.Sigma_e*ghu1';
    M_.Sigma_e = chol(M_.Sigma_e+1e-14*eye(M_.exo_nbr));
  end
  options=optimset('LargeScale','on','MaxFunEvals',20000*ny,'TolX',1e-4, ...
		   'TolFun',1e-4,'Display','Iter','MaxIter',10000);
%  [M_.Sigma_e,f]=fminunc(@calib_obj,M_.Sigma_e,options,A,ghu1,ghx(iiy,:),ghu(iiy,:),targets,var_weights,var_indices,nar);
  [M_.Sigma_e,f]=fmincon(@calib_obj,diag(M_.Sigma_e).^2,-eye(M_.exo_nbr),zeros(M_.exo_nbr,1),[],[],[],[],[],options,A,ghu1,ghx(iiy,:),ghu(iiy,:),targets,var_weights,var_indices,nar);
  M_.Sigma_e = diag(M_.Sigma_e);
  
  objective = calib_obj2(diag(M_.Sigma_e),A,ghu1,ghx(iiy,:),ghu(iiy,:),targets,var_weights,var_indices,nar);
  disp('CALIBRATION')
  disp('')
  if ~isempty(var_indices{1})
    disp(sprintf('%16s %14s %14s %14s %14s','Std. Dev','Target','Obtained','Diff'));
    str = '   ';
    for i=1:size(var_indices{1},1)
      [i1,i2] = ind2sub([ny ny],var_indices{1}(i));
      str = sprintf('%16s: %14.2f %14.2f %14.2f',M_.endo_names(order(iiy(i1)),:),targets{1}(i),objective{1}(i),objective{1}(i)-targets{1}(i));
      disp(str);
    end
  end
  if ~isempty(var_indices{2})
    disp(sprintf('%32s %14s %14s','Correlations','Target','Obtained','Diff'));
    str = '   ';
    for i=1:size(var_indices{2},1)
      [i1,i2]=ind2sub([ny ny],var_indices{2}(i));
      str = sprintf('%16s,%16s: %14.2f %14.2f %14.2f',M_.endo_names(order(iiy(i1)),:), ...
		    M_.endo_names(order(iiy(i2)),:),targets{2}(i),objective{2}(i),objective{2}(i)-targets{2}(i));
      disp(str);
    end
  end
  if ~isempty(var_indices{3})
    disp(sprintf('%32s %16s %16s','Constrained shocks (co)variances','Target','Obtained'));
    str = '   ';
    for i=1:size(var_indices{3},1)
      [i1,i2]=ind2sub([M_.exo_nbr M_.exo_nbr],var_indices{3}(i));
      if i1 == i2
	str = sprintf('%32s: %16.4f %16.4f',M_.exo_name(order(i1),:), ...
		      targets{3}(i),objective{3}(i));
      else
	str = sprintf('%16s,%16s: %16.4f %16.4f',M_.exo_name(order(i1),:), ...
		      M_.exo_name(order(i2), :),targets{3}(i),objective{3}(i));
      end
      disp(str);
    end
  end
  flag = 1;
  for j=4:nar+3
    if ~isempty(var_indices{j})
      if flag
	disp(sprintf('%16s %16s %16s','Autocorrelations','Target','Obtained'));
	str = '   ';
	flag = 0;
      end
      for i=1:size(var_indices{j},1)
	[i1,i2] = ind2sub([ny ny],var_indices{j}(i));
	str = sprintf('%16s(%d): %16.4f %16.4f',M_.endo_names(order(iiy(i1)),:), ...
		      j-3,targets{j}(i),objective{j}(i));
	  disp(str);
      end
    end
  end    
  
  disp('');
  disp('Calibrated variances')
  str = '   ';
  for i=1:M_.exo_nbr
    str = [str sprintf('%16s',M_.exo_name(i,:))];
  end
  disp(str);
  disp('');
  str = '      ';
  for i=1:M_.exo_nbr
    str = [str sprintf('%16f',M_.Sigma_e(i,i))];
  end
  disp(str);
  

  
  % 10/9/02 MJ