Complete re-writing to make the function modular (the input being either J or H or Hess etc.).
Marco Ratto
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a512436295
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c51066d76d
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@ -1,35 +1,22 @@
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function [McoH, McoJ, McoGP, PcoH, PcoJ, PcoGP, condH, condJ, condGP, eH, eJ, eGP, ind01, ind02, indnoH, indnoJ, ixnoH, ixnoJ] = identification_checks(H, JJ, gp)
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% function [McoH, McoJ, McoGP, PcoH, PcoJ, PcoGP, condH, condJ, condGP, eH,
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% eJ, eGP, ind01, ind02, indnoH, indnoJ, ixnoH, ixnoJ] = identification_checks(H, JJ, gp)
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function [condJ, ind0, indnoJ, ixnoJ, McoJ, PcoJ, jweak, jweak_pair] = identification_checks(JJ, hess_flag)
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% function [condJ, ind0, indnoJ, ixnoJ, McoJ, PcoJ, jweak, jweak_pair] = identification_checks(JJ, hess_flag)
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% checks for identification
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%
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% INPUTS
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% o H [matrix] [(entries in st.sp. model solutio) x nparams]
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% derivatives of model solution w.r.t. parameters and shocks
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% o JJ [matrix] [moments x nparams]
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% derivatives of moments w.r.t. parameters and shocks
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% o gp [matrix] [jacobian_entries x nparams]
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% derivatives of jacobian (i.e. LRE model) w.r.t. parameters and shocks
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% o JJ [matrix] [output x nparams] IF hess_flag==0
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% derivatives of output w.r.t. parameters and shocks
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% o JJ [matrix] [nparams x nparams] IF hess_flag==1
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% information matrix
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%
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% OUTPUTS
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% o McoH [array] multicollinearity coefficients in the model solution
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% o McoJ [array] multicollinearity coefficients in the moments
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% o McoGP [array] multicollinearity coefficients in the LRE model
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% o PcoH [matrix] pairwise correlations in the model solution
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% o PcoJ [matrix] pairwise correlations in the moments
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% o PcoGP [matrix] pairwise correlations in the LRE model
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% o condH condition number of H
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% o condJ condition number of JJ
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% o condGP condition number of gp
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% o eH eigevectors of H
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% o eJ eigevectors of JJ
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% o eGP eigevectors of gp
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% o ind01 [array] binary indicator for non-zero columns of H
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% o ind02 [array] binary indicator for non-zero columns of JJ
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% o indnoH [matrix] index of non-identified params in H
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% o indnoJ [matrix] index of non-identified params in JJ
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% o ixnoH number of rows in ind01
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% o ixnoJ number of rows in ind02
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% o cond condition number of JJ
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% o ind0 [array] binary indicator for non-zero columns of H
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% o indnoJ [matrix] index of non-identified params
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% o ixnoJ number of rows in indnoJ
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% o Mco [array] multicollinearity coefficients
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% o Pco [matrix] pairwise correlations
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% o jweak [binary array] gives 1 if the parameter has Mco=1(with tolerance 1.e-10)
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% o jweak_pair [binary matrix] gives 1 if a couple parameters has Pco=1(with tolerance 1.e-10)
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%
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% SPECIAL REQUIREMENTS
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% None
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@ -54,145 +41,90 @@ function [McoH, McoJ, McoGP, PcoH, PcoJ, PcoGP, condH, condJ, condGP, eH, eJ, eG
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% My suggestion is to have the following steps for identification check in
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% dynare:
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% 1. check rank of H, JJ, gp at theta
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npar = size(H,2);
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npar0 = size(gp,2); % shocks do not enter jacobian
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indnoH = zeros(1,npar);
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% 1. check rank of JJ at theta
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npar = size(JJ,2);
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indnoJ = zeros(1,npar);
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indnoLRE = zeros(1,npar0);
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% H matrix
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ind1 = find(vnorm(H)>=eps); % take non-zero columns
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H1 = H(:,ind1);
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[eu,e2,e1] = svd( H1, 0 );
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eH = zeros(npar,npar);
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% eH(ind1,:) = e1;
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eH(ind1,length(find(vnorm(H)<eps))+1:end) = e1; % non-zero eigenvectors
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eH(find(vnorm(H)<eps),1:length(find(vnorm(H)<eps)))=eye(length(find(vnorm(H)<eps)));
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condH = cond(H1);
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rankH = rank(H);
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rankHH = rank(H'*H);
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ind2 = find(vnorm(JJ)>=eps); % take non-zero columns
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JJ1 = JJ(:,ind2);
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ind1 = find(vnorm(JJ)>=eps); % take non-zero columns
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JJ1 = JJ(:,ind1);
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[eu,ee2,ee1] = svd( JJ1, 0 );
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eJ = zeros(npar,npar);
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eJ(ind2,length(find(vnorm(JJ)<eps))+1:end) = ee1; % non-zero eigenvectors
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eJ(find(vnorm(JJ)<eps),1:length(find(vnorm(JJ)<eps)))=eye(length(find(vnorm(JJ)<eps)));
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condJ = cond(JJ1);
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rankJJ = rank(JJ'*JJ);
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condJ= cond(JJ1);
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rankJ = rank(JJ);
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rankJJ = rankJ;
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if hess_flag==0,
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rankJJ = rank(JJ'*JJ);
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end
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ind3 = find(vnorm(gp)>=eps); % take non-zero columns
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gp1 = gp(:,ind3);
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covgp = gp1'*gp1;
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sdgp = sqrt(diag(covgp));
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sdgp = sdgp*sdgp';
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[eu,ex2,ex1] = svd(gp1, 0 );
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eGP = zeros(npar0,npar0);
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eGP(ind3,length(find(vnorm(gp)<eps))+1:end) = ex1; % non-zero eigenvectors
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eGP(find(vnorm(gp)<eps),1:length(find(vnorm(gp)<eps)))=eye(length(find(vnorm(gp)<eps)));
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% condJ = cond(JJ1'*JJ1);
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condGP = cond(gp1);
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ind0 = zeros(1,npar);
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ind0(ind1) = 1;
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ind01 = zeros(npar,1);
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ind02 = zeros(npar,1);
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ind01(ind1) = 1;
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ind02(ind2) = 1;
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% find near linear dependence problems:
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McoH = NaN(npar,1);
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McoJ = NaN(npar,1);
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McoGP = NaN(npar0,1);
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for ii = 1:size(H1,2);
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McoH(ind1(ii),:) = [cosn([H1(:,ii),H1(:,find([1:1:size(H1,2)]~=ii))])];
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end
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for ii = 1:size(JJ1,2);
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McoJ(ind2(ii),:) = [cosn([JJ1(:,ii),JJ1(:,find([1:1:size(JJ1,2)]~=ii))])];
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end
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for ii = 1:size(gp1,2);
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McoGP(ind3(ii),:) = [cosn([gp1(:,ii),gp1(:,find([1:1:size(gp1,2)]~=ii))])];
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end
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ixno = 0;
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if rankH<npar || rankHH<npar || min(1-McoH)<1.e-10
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% - find out which parameters are involved,
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% using the vnorm and the svd of H computed before;
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% disp('Some parameters are NOT identified in the model: H rank deficient')
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% disp(' ')
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if length(ind1)<npar,
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% parameters with zero column in H
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ixno = ixno + 1;
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indnoH(ixno,:) = (~ismember([1:npar],ind1));
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if hess_flag==0,
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% find near linear dependence problems:
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McoJ = NaN(npar,1);
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for ii = 1:size(JJ1,2);
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McoJ(ind1(ii),:) = cosn([JJ1(:,ii),JJ1(:,find([1:1:size(JJ1,2)]~=ii))]);
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end
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e0 = [rankHH+1:length(ind1)];
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for j=1:length(e0),
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% linearely dependent parameters in H
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ixno = ixno + 1;
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indnoH(ixno,ind1) = (abs(e1(:,e0(j))) > 1.e-3 )';
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end
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else % rank(H)==length(theta), go to 2
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% 2. check rank of J
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% disp('All parameters are identified at theta in the model (rank of H)')
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% disp(' ')
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else
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deltaJ = sqrt(diag(JJ));
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tildaJ = JJ./((deltaJ)*(deltaJ'));
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McoJ(:,1)=(1-1./diag(inv(tildaJ)));
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rhoM=sqrt(1-McoJ);
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% PcoJ=inv(tildaJ);
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PcoJ=inv(JJ);
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sd=sqrt(diag(PcoJ));
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PcoJ = PcoJ./((sd)*(sd'));
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end
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ixnoH=ixno;
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ixno = 0;
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ixnoJ = 0;
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if rankJ<npar || rankJJ<npar || min(1-McoJ)<1.e-10
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% - find out which parameters are involved
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% disp('Some parameters are NOT identified by the moments included in J')
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% disp(' ')
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if length(ind2)<npar,
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if length(ind1)<npar,
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% parameters with zero column in JJ
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ixno = ixno + 1;
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indnoJ(ixno,:) = (~ismember([1:npar],ind2));
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ixnoJ = ixnoJ + 1;
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indnoJ(ixnoJ,:) = (~ismember([1:npar],ind1));
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end
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ee0 = [rankJJ+1:length(ind2)];
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ee0 = [rankJJ+1:length(ind1)];
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for j=1:length(ee0),
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% linearely dependent parameters in JJ
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ixno = ixno + 1;
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indnoJ(ixno,ind2) = (abs(ee1(:,ee0(j))) > 1.e-3)';
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ixnoJ = ixnoJ + 1;
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indnoJ(ixnoJ,ind1) = (abs(ee1(:,ee0(j))) > 1.e-3)';
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end
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else %rank(J)==length(theta) =>
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% disp('All parameters are identified at theta by the moments included in J')
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end
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ixnoJ=ixno;
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% here there is no exact linear dependence, but there are several
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% near-dependencies, mostly due to strong pairwise colliniearities, which can
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% be checked using
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PcoH = NaN(npar,npar);
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jweak=zeros(1,npar);
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jweak_pair=zeros(npar,npar);
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if hess_flag==0,
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PcoJ = NaN(npar,npar);
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PcoGP = NaN(npar0,npar0);
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for ii = 1:size(H1,2);
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PcoH(ind1(ii),ind1(ii)) = 1;
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for jj = ii+1:size(H1,2);
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PcoH(ind1(ii),ind1(jj)) = [cosn([H1(:,ii),H1(:,jj)])];
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PcoH(ind1(jj),ind1(ii)) = PcoH(ind1(ii),ind1(jj));
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end
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end
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for ii = 1:size(JJ1,2);
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PcoJ(ind2(ii),ind2(ii)) = 1;
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PcoJ(ind1(ii),ind1(ii)) = 1;
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for jj = ii+1:size(JJ1,2);
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PcoJ(ind2(ii),ind2(jj)) = [cosn([JJ1(:,ii),JJ1(:,jj)])];
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PcoJ(ind2(jj),ind2(ii)) = PcoJ(ind2(ii),ind2(jj));
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PcoJ(ind1(ii),ind1(jj)) = cosn([JJ1(:,ii),JJ1(:,jj)]);
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PcoJ(ind1(jj),ind1(ii)) = PcoJ(ind1(ii),ind1(jj));
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end
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end
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for ii = 1:size(gp1,2);
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PcoGP(ind3(ii),ind3(ii)) = 1;
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for jj = ii+1:size(gp1,2);
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PcoGP(ind3(ii),ind3(jj)) = [cosn([gp1(:,ii),gp1(:,jj)])];
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PcoGP(ind3(jj),ind3(ii)) = PcoGP(ind3(ii),ind3(jj));
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for j=1:npar,
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if McoJ(j)>(1-1.e-10),
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jweak(j)=1;
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[ipair, jpair] = find(PcoJ(j,j+1:end)>(1-1.e-10));
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for jx=1:length(jpair),
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jweak_pair(j, jpair(jx)+j)=1;
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jweak_pair(jpair(jx)+j, j)=1;
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end
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end
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end
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end
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jweak_pair=dyn_vech(jweak_pair)';
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