dynare/matlab/identification_checks.m

function [McoH, McoJ, McoGP, PcoH, PcoJ, PcoGP, condH, condJ, condGP, eH, eJ, eGP, ind01, ind02, indnoH, indnoJ, ixnoH, ixnoJ] = identification_checks(H,JJ, gp, bayestopt_)

% Copyright (C) 2008-2011 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/>.

% My suggestion is to have the following steps for identification check in
% dynare:

% 1. check rank of H at theta
npar = size(H,2);
npar0 = size(gp,2);
indnoH = zeros(1,npar);
indnoJ = zeros(1,npar);
indnoLRE = zeros(1,npar0);
ind1 = find(vnorm(H)>=eps);
H1 = H(:,ind1);
covH = H1'*H1;
sdH = sqrt(diag(covH));
sdH = sdH*sdH';
% [e1,e2] = eig( (H1'*H1)./sdH );
[eu,e2,e1] = svd( H1, 0 );
eH = zeros(npar,npar);
% eH(ind1,:) = e1;
eH(ind1,length(find(vnorm(H)==0))+1:end) = e1;
eH(find(vnorm(H)==0),1:length(find(vnorm(H)==0)))=eye(length(find(vnorm(H)==0)));
condH = cond(H1);
condHH = cond(H1'*H1);
rankH = rank(H);
rankHH = rank(H'*H);

ind2 = find(vnorm(JJ)>=eps);
JJ1 = JJ(:,ind2);
covJJ = JJ1'*JJ1;
sdJJ = sqrt(diag(covJJ));
sdJJ = sdJJ*sdJJ';
% [ee1,ee2] = eig( (JJ1'*JJ1)./sdJJ );
[eu,ee2,ee1] = svd( JJ1, 0 );
% eJ = NaN(npar,length(ind2));
eJ = zeros(npar,npar);
eJ(ind2,length(find(vnorm(JJ)==0))+1:end) = ee1;
eJ(find(vnorm(JJ)==0),1:length(find(vnorm(JJ)==0)))=eye(length(find(vnorm(JJ)==0)));
condJJ = cond(JJ1'*JJ1);
condJ = cond(JJ1);
rankJJ = rank(JJ'*JJ);
rankJ = rank(JJ);

ind3 = find(vnorm(gp)>=eps);
gp1 = gp(:,ind3);
covgp = gp1'*gp1;
sdgp = sqrt(diag(covgp));
sdgp = sdgp*sdgp';
[ex1,ex2] = eig( (gp1'*gp1)./sdgp );
% eJ = NaN(npar,length(ind2));
eGP = zeros(npar0,npar0);
eGP(ind3,length(find(vnorm(gp)==0))+1:end) = ex1;
eGP(find(vnorm(gp)==0),1:length(find(vnorm(gp)==0)))=eye(length(find(vnorm(gp)==0)));
% condJ = cond(JJ1'*JJ1);
condGP = cond(gp1);


ind01 = zeros(npar,1);
ind02 = zeros(npar,1);
ind01(ind1) = 1;
ind02(ind2) = 1;

% rank(H1)==size(H1,2)
% rank(JJ1)==size(JJ1,2)

% to find near linear dependence problems  I use

McoH = NaN(npar,1);
McoJ = NaN(npar,1);
McoGP = NaN(npar0,1);
for ii = 1:size(H1,2);
    McoH(ind1(ii),:) = [cosn([H1(:,ii),H1(:,find([1:1:size(H1,2)]~=ii))])];
end
for ii = 1:size(JJ1,2);
    McoJ(ind2(ii),:) = [cosn([JJ1(:,ii),JJ1(:,find([1:1:size(JJ1,2)]~=ii))])];
end
for ii = 1:size(gp1,2);
    McoGP(ind3(ii),:) = [cosn([gp1(:,ii),gp1(:,find([1:1:size(gp1,2)]~=ii))])];
end

% format long  % some are nearly 1
% McoJ

ixno = 0;
if rankH<npar | rankHH<npar | min(1-McoH)<1.e-10
    %         - find out which parameters are involved,
    % using something like the vnorm and the eigenvalue decomposition of H;
    %   disp('Some parameters are NOT identified in the model: H rank deficient')
    %   disp(' ')
    if length(ind1)<npar,
        ixno = ixno + 1;
        %         indnoH(ixno) = {find(~ismember([1:npar],ind1))};
        indnoH(ixno,:) = (~ismember([1:npar],ind1));
        %     disp('Not identified params')
        %     disp(bayestopt_.name(indnoH{1}))
        %     disp(' ')
    end
    e0 = [rankHH+1:length(ind1)];
    for j=1:length(e0),
        ixno = ixno + 1;
        %         indnoH(ixno) = {ind1(find(abs(e1(:,e0(j)))) > 1.e-6 )};
        indnoH(ixno,:) = (abs(e1(:,e0(j))) > 1.e-6 )';
        %     disp('Perfectly collinear parameters')
        %     disp(bayestopt_.name(indnoH{ixno}))
        %     disp(' ')
        %         ind01(indnoH{ixno})=0;
    end
else % rank(H)==length(theta), go to 2
     % 2. check rank of J
     %   disp('All parameters are identified at theta in the model (rank of H)')
     %   disp(' ')
end
ixnoH=ixno;

ixno = 0;
if rankJ<npar | rankJJ<npar | min(1-McoJ)<1.e-10
    %         - find out which parameters are involved
    %   disp('Some parameters are NOT identified by the moments included in J')
    %   disp(' ')
    if length(ind2)<npar,
        ixno = ixno + 1;
        %         indnoJ(ixno) = {find(~ismember([1:npar],ind2))};
        indnoJ(ixno,:) = (~ismember([1:npar],ind2));
    end
    ee0 = [rankJJ+1:length(ind2)];
    if isempty(ee0),
        cccc=0';
    end
    for j=1:length(ee0),
        ixno = ixno + 1;
        %         indnoJ(ixno) = {ind2( find(abs(ee1(:,ee0(j))) > 1.e-6) )};
        indnoJ(ixno,:) = (abs(ee1(:,ee0(j))) > 1.e-6)';
        %     disp('Perfectly collinear parameters in moments J')
        %     disp(bayestopt_.name(indnoJ{ixno}))
        %     disp(' ')
        %         ind02(indnoJ{ixno})=0;
    end
else  %rank(J)==length(theta) =>
      %         disp('All parameters are identified at theta by the moments included in J')
end
ixnoJ=ixno;

% here there is no exact linear dependence, but there are several
%     near-dependencies, mostly due to strong pairwise colliniearities, which can
%     be checked using

PcoH = NaN(npar,npar);
PcoJ = NaN(npar,npar);
PcoGP = NaN(npar0,npar0);
for ii = 1:size(H1,2);
    PcoH(ind1(ii),ind1(ii)) = 1;
    for jj = ii+1:size(H1,2);
        PcoH(ind1(ii),ind1(jj)) = [cosn([H1(:,ii),H1(:,jj)])];
        PcoH(ind1(jj),ind1(ii)) = PcoH(ind1(ii),ind1(jj));
    end
end

for ii = 1:size(JJ1,2);
    PcoJ(ind2(ii),ind2(ii)) = 1;
    for jj = ii+1:size(JJ1,2);
        PcoJ(ind2(ii),ind2(jj)) = [cosn([JJ1(:,ii),JJ1(:,jj)])];
        PcoJ(ind2(jj),ind2(ii)) = PcoJ(ind2(ii),ind2(jj));
    end
end

for ii = 1:size(gp1,2);
    PcoGP(ind3(ii),ind3(ii)) = 1;
    for jj = ii+1:size(gp1,2);
        PcoGP(ind3(ii),ind3(jj)) = [cosn([gp1(:,ii),gp1(:,jj)])];
        PcoGP(ind3(jj),ind3(ii)) = PcoGP(ind3(ii),ind3(jj));
    end
end


% ind01 = zeros(npar,1);
% ind02 = zeros(npar,1);
% ind01(ind1) = 1;
% ind02(ind2) = 1;