146 lines
4.1 KiB
Matlab
146 lines
4.1 KiB
Matlab
function [McoH, McoJ, PcoH, PcoJ, condH, condJ, eH, eJ, ind01, ind02, indnoH, indnoJ] = identification_checks(H,JJ, bayestopt_)
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% Copyright (C) 2008 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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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 at theta
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npar = size(H,2);
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indnoH = {};
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indnoJ = {};
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ind1 = find(vnorm(H)~=0);
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H1 = H(:,ind1);
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covH = H1'*H1;
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sdH = sqrt(diag(covH));
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sdH = sdH*sdH';
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[e1,e2] = eig( (H1'*H1)./sdH );
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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)==0))+1:end) = e1;
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eH(find(vnorm(H)==0),1:length(find(vnorm(H)==0)))=eye(length(find(vnorm(H)==0)));
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condH = cond(H1);
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% condH = cond(H1'*H1);
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ind2 = find(vnorm(JJ)~=0);
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JJ1 = JJ(:,ind2);
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covJJ = JJ1'*JJ1;
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sdJJ = sqrt(diag(covJJ));
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sdJJ = sdJJ*sdJJ';
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[ee1,ee2] = eig( (JJ1'*JJ1)./sdJJ );
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% eJ = NaN(npar,length(ind2));
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eJ = zeros(npar,npar);
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eJ(ind2,length(find(vnorm(JJ)==0))+1:end) = ee1;
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eJ(find(vnorm(JJ)==0),1:length(find(vnorm(JJ)==0)))=eye(length(find(vnorm(JJ)==0)));
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% condJ = cond(JJ1'*JJ1);
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condJ = cond(JJ1);
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if rank(H)<npar
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ixno = 0;
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% - find out which parameters are involved,
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% using something like the vnorm and the eigenvalue decomposition of H;
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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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ixno = ixno + 1;
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indnoH(ixno) = {find(~ismember([1:npar],ind1))};
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% disp('Not identified params')
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% disp(bayestopt_.name(indnoH{1}))
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% disp(' ')
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end
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e0 = find(abs(diag(e2))<eps);
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for j=1:length(e0),
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ixno = ixno + 1;
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indnoH(ixno) = {ind1(find(e1(:,e0(j))))};
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% disp('Perfectly collinear parameters')
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% disp(bayestopt_.name(indnoH{ixno}))
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% disp(' ')
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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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end
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if rank(JJ)<npar
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ixno = 0;
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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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ixno = ixno + 1;
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indnoJ(ixno) = {find(~ismember([1:npar],ind2))};
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end
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ee0 = find(abs(diag(ee2))<eps);
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for j=1:length(ee0),
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ixno = ixno + 1;
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indnoJ(ixno) = {ind2(find(ee1(:,ee0(j))))};
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% disp('Perfectly collinear parameters in moments J')
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% disp(bayestopt_.name(indnoJ{ixno}))
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% disp(' ')
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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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% rank(H1)==size(H1,2)
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% rank(JJ1)==size(JJ1,2)
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% to find near linear dependence problems I use
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McoH = NaN(npar,1);
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McoJ = NaN(npar,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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% format long % some are nearly 1
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% McoJ
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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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PcoJ = NaN(npar,npar);
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for ii = 1:size(H1,2);
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for jj = 1:size(H1,2);
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PcoH(ind1(ii),ind1(jj)) = [cosn([H1(:,ii),H1(:,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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for jj = 1:size(JJ1,2);
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PcoJ(ind2(ii),ind2(jj)) = [cosn([JJ1(:,ii),JJ1(:,jj)])];
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end
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end
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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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