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identification_analysis.m
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Johannes Pfeifer authoredJohannes Pfeifer authored
identification_analysis.m 17.07 KiB
function [ide_hess, ide_moments, ide_model, ide_lre, derivatives_info, info, options_ident] = identification_analysis(params,indx,indexo,options_ident,dataset_,dataset_info, prior_exist,name_tex,init,tittxt,bounds)
% function [ide_hess, ide_moments, ide_model, ide_lre, derivatives_info, info] = identification_analysis(params,indx,indexo,options_ident,data_info, prior_exist,name_tex,init,analyis_type)
% given the parameter vector params, wraps all identification analyses
%
% INPUTS
% o params [array] parameter values for identification checks
% o indx [array] index of estimated parameters
% o indexo [array] index of estimated shocks
% o options_ident [structure] identification options
% o dataset_ [structure] the dataset after required transformation
% o dataset_info [structure] Various informations about the dataset (descriptive statistics and missing observations) info for Kalman Filter
% o prior_exist [integer]
% =1 when prior exists and indentification is checked only for estimated params and shocks
% =0 when prior is not defined and indentification is checked for all params and shocks
% o name_tex [char] list of tex names
% o init [integer] flag for initialization of persistent vars
% o tittxt [string] string indicating the title text for
% graphs and figures
%
% OUTPUTS
% o ide_hess [structure] identification results using Asymptotic Hessian
% o ide_moments [structure] identification results using theoretical moments
% o ide_model [structure] identification results using reduced form solution
% o ide_lre [structure] identification results using LRE model
% o derivatives_info [structure] info about analytic derivs
% o info output from dynare resolve
%
% SPECIAL REQUIREMENTS
% None
% Copyright (C) 2008-2018 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_ options_ bayestopt_ estim_params_
persistent indH indJJ indLRE
nparam=length(params);
np=length(indx);
offset=nparam-np;
if ~isempty(estim_params_)
M_ = set_all_parameters(params,estim_params_,M_);
end
nlags = options_ident.ar;
useautocorr = options_ident.useautocorr;
advanced = options_ident.advanced;
replic = options_ident.replic;
periods = options_ident.periods;
max_dim_cova_group = options_ident.max_dim_cova_group;
normalize_jacobians = options_ident.normalize_jacobians;
kron_flag = options_ident.analytic_derivation_mode;
[I,J]=find(M_.lead_lag_incidence');
ide_hess = struct();
ide_moments = struct();ide_model = struct();
ide_lre = struct();
derivatives_info = struct();
[A,B,ys,info,M_,options_,oo_] = dynare_resolve(M_,options_,oo_);
if info(1)==0
oo0=oo_;
tau=[oo_.dr.ys(oo_.dr.order_var); vec(A); dyn_vech(B*M_.Sigma_e*B')];
yy0=oo_.dr.ys(I);
[residual, g1 ] = feval([M_.fname,'_dynamic'],yy0, ...
repmat(oo_.exo_steady_state',[M_.maximum_exo_lag+M_.maximum_exo_lead+1]), M_.params, ...
oo_.dr.ys, 1);
vg1 = [oo_.dr.ys(oo_.dr.order_var); vec(g1)];
[JJ, H, gam, gp, dA, dOm, dYss] = getJJ(A, B, estim_params_, M_,oo0,options_,kron_flag,indx,indexo,bayestopt_.mf2,nlags,useautocorr);
derivatives_info.DT=dA;
derivatives_info.DOm=dOm;
derivatives_info.DYss=dYss;
if init
indJJ = (find(max(abs(JJ'),[],1)>1.e-8));
if isempty(indJJ) && any(any(isnan(JJ)))
error('There are NaN in the JJ matrix. Please check whether your model has units roots and you forgot to set diffuse_filter=1.' )
elseif any(any(isnan(gam)))
error('There are NaN''s in the theoretical moments: make sure that for non-stationary models stationary transformations of non-stationary observables are used for checking identification. [TIP: use first differences].')
end
while length(indJJ)<nparam && nlags<10
disp('The number of moments with non-zero derivative is smaller than the number of parameters')
disp(['Try increasing ar = ', int2str(nlags+1)])
nlags=nlags+1;
[JJ, H, gam, gp, dA, dOm, dYss] = getJJ(A, B, estim_params_, M_,oo0,options_,kron_flag,indx,indexo,bayestopt_.mf2,nlags,useautocorr);
derivatives_info.DT=dA;
derivatives_info.DOm=dOm;
derivatives_info.DYss=dYss;
options_.ar=nlags;
options_ident.ar=nlags;
indJJ = (find(max(abs(JJ'),[],1)>1.e-8));
end
if length(indJJ)<nparam
disp('The number of moments with non-zero derivative is smaller than the number of parameters')
disp('up to 10 lags: check your model')
disp('Either further increase ar or reduce the list of estimated parameters')
error('identification_analysis: there are not enough moments and too many parameters'),
end
indH = (find(max(abs(H'),[],1)>1.e-8));
indLRE = (find(max(abs(gp'),[],1)>1.e-8));
end
TAU(:,1)=tau(indH);
LRE(:,1)=vg1(indLRE);
GAM(:,1)=gam(indJJ);
siJ = (JJ(indJJ,:));
siH = (H(indH,:));
siLRE = (gp(indLRE,:));
ide_strength_J=NaN(1,nparam);
ide_strength_J_prior=NaN(1,nparam);
if init
normaliz = NaN(1,nparam);
if prior_exist
if ~isempty(estim_params_.var_exo)
normaliz1 = estim_params_.var_exo(:,7)'; % normalize with prior standard deviation
else
normaliz1=[];
end
if ~isempty(estim_params_.corrx)
normaliz1 = [normaliz1 estim_params_.corrx(:,8)']; % normalize with prior standard deviation
end
if ~isempty(estim_params_.param_vals)
normaliz1 = [normaliz1 estim_params_.param_vals(:,7)']; % normalize with prior standard deviation
end
% normaliz = max([normaliz; normaliz1]);
normaliz1(isinf(normaliz1)) = 1;
else
normaliz1 = NaN(1,nparam);
end
try
options_.irf = 0;
options_.noprint = 1;
options_.order = 1;
options_.SpectralDensity.trigger = 0;
options_.periods = periods+100;
if options_.kalman_algo > 2
options_.kalman_algo = 1;
end
analytic_derivation = options_.analytic_derivation;
options_.analytic_derivation = -2;
info = stoch_simul(options_.varobs);
dataset_ = dseries(oo_.endo_simul(options_.varobs_id,100+1:end)',dates('1Q1'), options_.varobs);
derivatives_info.no_DLIK=1;
bounds = prior_bounds(bayestopt_, options_.prior_trunc); %reset bounds as lb and ub must only be operational during mode-finding
[fval,info,cost_flag,DLIK,AHess,ys,trend_coeff,M_,options_,bayestopt_,oo_] = dsge_likelihood(params',dataset_,dataset_info,options_,M_,estim_params_,bayestopt_,bounds,oo_,derivatives_info);
% fval = DsgeLikelihood(xparam1,data_info,options_,M_,estim_params_,bayestopt_,oo_);
options_.analytic_derivation = analytic_derivation;
AHess=-AHess;
if min(eig(AHess))<-1.e-10
error('identification_analysis: Analytic Hessian is not positive semi-definite!')
end
% chol(AHess);
ide_hess.AHess= AHess;
deltaM = sqrt(diag(AHess));
iflag=any((deltaM.*deltaM)==0);
tildaM = AHess./((deltaM)*(deltaM'));
if iflag || rank(AHess)>rank(tildaM)
[ide_hess.cond, ide_hess.ind0, ide_hess.indno, ide_hess.ino, ide_hess.Mco, ide_hess.Pco] = identification_checks(AHess, 1);
else
[ide_hess.cond, ide_hess.ind0, ide_hess.indno, ide_hess.ino, ide_hess.Mco, ide_hess.Pco] = identification_checks(tildaM, 1);
end
indok = find(max(ide_hess.indno,[],1)==0);
cparam(indok,indok) = inv(AHess(indok,indok));
normaliz(indok) = sqrt(diag(cparam(indok,indok)))';
cmm = NaN(size(siJ,1),size(siJ,1));
ind1=find(ide_hess.ind0);
cmm = siJ(:,ind1)*((AHess(ind1,ind1))\siJ(:,ind1)');
temp1=((AHess(ind1,ind1))\siH(:,ind1)');
diag_chh=sum(siH(:,ind1)'.*temp1)';
% chh = siH(:,ind1)*((AHess(ind1,ind1))\siH(:,ind1)');
ind1=ind1(ind1>offset);
clre = siLRE(:,ind1-offset)*((AHess(ind1,ind1))\siLRE(:,ind1-offset)');
rhoM=sqrt(1./diag(inv(tildaM(indok,indok))));
% deltaM = deltaM.*abs(params');
flag_score=1;
catch
% replic = max([replic, nparam*(nparam+1)/2*10]);
replic = max([replic, length(indJJ)*3]);
cmm = simulated_moment_uncertainty(indJJ, periods, replic,options_,M_,oo_);
% [V,D,W]=eig(cmm);
sd=sqrt(diag(cmm));
cc=cmm./(sd*sd');
if isoctave || matlab_ver_less_than('8.3')
[V,D]=eig(cc);
%fix for older Matlab versions that do not support computing left eigenvalues, see http://mathworks.com/help/releases/R2012b/matlab/ref/eig.html
[W,junk] = eig(cc.');
W = conj(W);
else
[V,D,W]=eig(cc);
end
id=find(diag(D)>1.e-8);
siTMP=siJ./repmat(sd,[1 nparam]);
MIM=(siTMP'*V(:,id))*(D(id,id)\(W(:,id)'*siTMP));
clear siTMP;
% MIM=siJ(:,indok)'*(cmm\siJ(:,indok)); % look for independent moments!
% % % sd=sqrt(diag(cmm));
% % % cc=cmm./(sd*sd');
% % % ix=[];
% % % for jc=1:length(cmm),
% % % jcheck=find(abs(cc(:,jc))>(1-1.e-6));
% % % ix=[ix; jcheck(jcheck>jc)];
% % % end
% % % iy=find(~ismember([1:length(cmm)],ix));
% % % indJJ=indJJ(iy);
% % % GAM=GAM(iy);
% % % cmm=cmm(iy,iy);
% % % siJ = (JJ(indJJ,:));
% % % MIM=siJ'*(cmm\siJ);
ide_hess.AHess= MIM;
deltaM = sqrt(diag(MIM));
iflag=any((deltaM.*deltaM)==0);
tildaM = MIM./((deltaM)*(deltaM'));
if iflag || rank(MIM)>rank(tildaM)
[ide_hess.cond, ide_hess.ind0, ide_hess.indno, ide_hess.ino, ide_hess.Mco, ide_hess.Pco] = identification_checks(MIM, 1);
else
[ide_hess.cond, ide_hess.ind0, ide_hess.indno, ide_hess.ino, ide_hess.Mco, ide_hess.Pco] = identification_checks(tildaM, 1);
end
indok = find(max(ide_hess.indno,[],1)==0);
% rhoM=sqrt(1-1./diag(inv(tildaM)));
% rhoM=(1-1./diag(inv(tildaM)));
ind1=find(ide_hess.ind0);
temp1=((MIM(ind1,ind1))\siH(:,ind1)');
diag_chh=sum(siH(:,ind1)'.*temp1)';
% chh = siH(:,ind1)*((MIM(ind1,ind1))\siH(:,ind1)');
ind1=ind1(ind1>offset);
clre = siLRE(:,ind1-offset)*((MIM(ind1,ind1))\siLRE(:,ind1-offset)');
if ~isempty(indok)
rhoM(indok)=sqrt(1./diag(inv(tildaM(indok,indok))));
normaliz(indok) = (sqrt(diag(inv(tildaM(indok,indok))))./deltaM(indok))'; %sqrt(diag(inv(MIM(indok,indok))))';
end
% deltaM = deltaM.*abs(params')
flag_score=0;
end
ide_strength_J(indok) = (1./(normaliz(indok)'./abs(params(indok)')));
ide_strength_J_prior(indok) = (1./(normaliz(indok)'./normaliz1(indok)'));
ide_strength_J(params==0)=1./normaliz(params==0)';
deltaM_prior = deltaM.*abs(normaliz1');
deltaM = deltaM.*abs(params');
deltaM(params==0)=deltaM_prior(params==0);
quant = siJ./repmat(sqrt(diag(cmm)),1,nparam);
if size(quant,1)==1
siJnorm = abs(quant).*normaliz1;
else
siJnorm = vnorm(quant).*normaliz1;
end
% siJnorm = vnorm(siJ(inok,:)).*normaliz;
quant=[];
% inok = find((abs(TAU)<1.e-8));
% isok = find((abs(TAU)>=1.e-8));
% quant(isok,:) = siH(isok,:)./repmat(TAU(isok,1),1,nparam);
% quant(inok,:) = siH(inok,:)./repmat(mean(abs(TAU)),length(inok),nparam);
% quant = siH./repmat(sqrt(diag(chh)),1,nparam);
iy = find(diag_chh);
indH=indH(iy);
siH=siH(iy,:);
if ~isempty(iy)
quant = siH./repmat(sqrt(diag_chh(iy)),1,nparam);
if size(quant,1)==1
siHnorm = abs(quant).*normaliz1;
else
siHnorm = vnorm(quant).*normaliz1;
end
else
siHnorm = []; end
% siHnorm = vnorm(siH./repmat(TAU,1,nparam)).*normaliz;
quant=[];
% inok = find((abs(LRE)<1.e-8));
% isok = find((abs(LRE)>=1.e-8));
% quant(isok,:) = siLRE(isok,:)./repmat(LRE(isok,1),1,np);
% quant(inok,:) = siLRE(inok,:)./repmat(mean(abs(LRE)),length(inok),np);
diag_clre = diag(clre);
iy = find(diag_clre);
indLRE=indLRE(iy);
siLRE=siLRE(iy,:);
if ~isempty(iy)
quant = siLRE./repmat(sqrt(diag_clre(iy)),1,np);
if size(quant,1)==1
siLREnorm = abs(quant).*normaliz1(offset+1:end);
else
siLREnorm = vnorm(quant).*normaliz1(offset+1:end);
end
else
siLREnorm=[];
end
% siLREnorm = vnorm(siLRE./repmat(LRE,1,nparam-offset)).*normaliz(offset+1:end);
ide_hess.ide_strength_J=ide_strength_J;
ide_hess.ide_strength_J_prior=ide_strength_J_prior;
ide_hess.deltaM=deltaM;
ide_hess.deltaM_prior=deltaM_prior;
ide_moments.siJnorm=siJnorm;
ide_model.siHnorm=siHnorm;
ide_lre.siLREnorm=siLREnorm;
ide_hess.flag_score=flag_score;
end
if normalize_jacobians
normH = max(abs(siH)')';
normH = normH(:,ones(nparam,1));
normJ = max(abs(siJ)')';
normJ = normJ(:,ones(nparam,1));
normLRE = max(abs(siLRE)')';
normLRE = normLRE(:,ones(size(gp,2),1));
else
normH = 1;
normJ = 1;
normLRE = 1;
end
ide_moments.indJJ=indJJ;
ide_model.indH=indH;
ide_lre.indLRE=indLRE;
ide_moments.siJ=siJ;
ide_model.siH=siH;
ide_lre.siLRE=siLRE;
ide_moments.GAM=GAM;
ide_model.TAU=TAU;
ide_lre.LRE=LRE;
% [ide_checks.idemodel_Mco, ide_checks.idemoments_Mco, ide_checks.idelre_Mco, ...
% ide_checks.idemodel_Pco, ide_checks.idemoments_Pco, ide_checks.idelre_Pco, ...
% ide_checks.idemodel_cond, ide_checks.idemoments_cond, ide_checks.idelre_cond, ...
% ide_checks.idemodel_ee, ide_checks.idemoments_ee, ide_checks.idelre_ee, ...
% ide_checks.idemodel_ind, ide_checks.idemoments_ind, ...
% ide_checks.idemodel_indno, ide_checks.idemoments_indno, ...
% ide_checks.idemodel_ino, ide_checks.idemoments_ino] = ...
% identification_checks(H(indH,:)./normH(:,ones(nparam,1)),JJ(indJJ,:)./normJ(:,ones(nparam,1)), gp(indLRE,:)./normLRE(:,ones(size(gp,2),1)));
[ide_moments.cond, ide_moments.ind0, ide_moments.indno, ide_moments.ino, ide_moments.Mco, ide_moments.Pco, ide_moments.jweak, ide_moments.jweak_pair] = ...
identification_checks(JJ(indJJ,:)./normJ, 0);
[ide_model.cond, ide_model.ind0, ide_model.indno, ide_model.ino, ide_model.Mco, ide_model.Pco, ide_model.jweak, ide_model.jweak_pair] = ...
identification_checks(H(indH,:)./normH, 0);
[ide_lre.cond, ide_lre.ind0, ide_lre.indno, ide_lre.ino, ide_lre.Mco, ide_lre.Pco, ide_lre.jweak, ide_lre.jweak_pair] = ...
identification_checks(gp(indLRE,:)./normLRE, 0);
normJ=1;
[U, S, V]=svd(JJ(indJJ,:)./normJ,0);
S=diag(S);
S=[S;zeros(size(JJ,2)-length(indJJ),1)]; if nparam>8
ide_moments.S = S([1:4, end-3:end]);
ide_moments.V = V(:,[1:4, end-3:end]);
else
ide_moments.S = S;
ide_moments.V = V;
end
indok = find(max(ide_moments.indno,[],1)==0);
if advanced
[ide_moments.pars, ide_moments.cosnJ] = ident_bruteforce(JJ(indJJ,:)./normJ,max_dim_cova_group,options_.TeX,name_tex,tittxt);
end
end