132 lines
4.2 KiB
Matlab
132 lines
4.2 KiB
Matlab
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 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 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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% Copyright (C) 2008-2011 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 JJ at theta
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npar = size(JJ,2);
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indnoJ = zeros(1,npar);
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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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condJ= cond(JJ1);
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rankJ = rank(JJ./norm(JJ),1.e-10);
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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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ind0 = zeros(1,npar);
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ind0(ind1) = 1;
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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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else
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deltaJ = sqrt(diag(JJ(ind1,ind1)));
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tildaJ = JJ(ind1,ind1)./((deltaJ)*(deltaJ'));
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McoJ(ind1,1)=(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=NaN(npar,npar);
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PcoJ(ind1,ind1)=inv(JJ(ind1,ind1));
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sd=sqrt(diag(PcoJ));
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PcoJ = abs(PcoJ./((sd)*(sd')));
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end
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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(ind1)<npar,
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% parameters with zero column in JJ
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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(ind1)];
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for j=1:length(ee0),
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% linearely dependent parameters in JJ
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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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% 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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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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for ii = 1:size(JJ1,2);
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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(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 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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