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Added Posterior distribution of the conditional variance 

decomposition (more tests are needed). 

The results are saved in oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition. 

Contrary to the asymptotic variance decomposition, we do not report
contribution shares but contribution levels of each structural shock.

LIMITATIONS: 
* Won't work in a model with measurement errors.
* Won't work in a model with correlated shocks.
* The routines do not compute the covariance decompositions.


git-svn-id: https://www.dynare.org/svn/dynare/trunk@2719 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
stepan 2009-06-03 14:50:02 +00:00
parent 19b704d54b
commit dedca98dba
7 changed files with 276 additions and 7 deletions
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4
matlab/check_posterior_analysis_data.m
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@ -64,8 +64,8 @@ function [info,description] = check_posterior_analysis_data(type,M_)
generic_post_data_file_name = 'PosteriorVarianceDecomposition';
case 'correlation'
generic_post_data_file_name = 'PosteriorCorrelations';
case 'dynamic_decomposition'
generic_post_data_file_name = 'PosteriorDynamicVarianceDecomposition';
case 'conditional decomposition'
generic_post_data_file_name = 'PosteriorConditionalVarianceDecomposition';
otherwise
disp('This feature is not yest implemented!')
end

7
matlab/compute_moments_varendo.m
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@ -35,6 +35,7 @@ function oo_ = compute_moments_varendo(options_,M_,oo_,var_list_)
NumberOfExogenousVariables = M_.exo_nbr;
list_of_exogenous_variables = M_.exo_names;
NumberOfLags = options_.ar;
Steps = options_.conditional_variance_decomposition_dates;
% COVARIANCE MATRIX.
for i=1:NumberOfEndogenousVariables
for j=i:NumberOfEndogenousVariables
@ -54,4 +55,10 @@ function oo_ = compute_moments_varendo(options_,M_,oo_,var_list_)
for j=1:NumberOfExogenousVariables
oo_ = posterior_analysis('decomposition',var_list_(i,:),M_.exo_names(j,:),[],options_,M_,oo_);
end
end
% CONDITIONAL VARIANCE DECOMPOSITION.
for i=1:NumberOfEndogenousVariables
for j=1:NumberOfExogenousVariables
oo_ = posterior_analysis('conditional decomposition',var_list_(i,:),M_.exo_names(j,:),Steps,options_,M_,oo_);
end
end

54
matlab/conditional_variance_decomposition.m Normal file
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@ -0,0 +1,54 @@
function PackedConditionalVarianceDecomposition = conditional_variance_decomposition(StateSpaceModel, Steps, SubsetOfVariables)
% This function computes the conditional variance decomposition of a given state space model
% for a subset of endogenous variables.
%
% INPUTS
% StateSpaceModel [structure] Specification of the state space model.
% Steps [integer] 1*h vector of dates.
% SubsetOfVariables [integer] 1*q vector of indices.
%
% OUTPUTS
% PackedConditionalVarianceDecomposition [double] n(n+1)/2*p matrix, where p is the number of state innovations and
% n is equal to length(SubsetOfVariables).
%
% SPECIAL REQUIREMENTS
%
% [1] The covariance matrix of the state innovations needs to be diagonal.
% [2] In this version, absence of measurement errors is assumed...
% Copyright (C) 2009 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/>.
ConditionalVariance = zeros(StateSpaceModel.number_of_state_equations,StateSpaceModel.number_of_state_equations);
ConditionalVariance = repmat(ConditionalVariance,[1 1 length(Steps) StateSpaceModel.number_of_state_innovations]);
BB = StateSpaceModel.impulse_matrix*transpose(StateSpaceModel.impulse_matrix);
for h = 1:length(Steps)
for t = 0:Steps(h)
for i=1:StateSpaceModel.number_of_state_innovations
ConditionalVariance(:,:,h,i) = ...
StateSpaceModel.transition_matrix*ConditionalVariance(:,:,h,i)*transpose(StateSpaceModel.transition_matrix) ...
+BB*StateSpaceModel.state_innovations_covariance_matrix(i,i);
end
end
end
ConditionalVariance = ConditionalVariance(SubsetOfVariables,SubsetOfVariables,:,:);
NumberOfVariables = length(SubsetOfVariables);
PackedConditionalVarianceDecomposition = zeros(NumberOfVariables*(NumberOfVariables+1)/2,length(Steps),StateSpaceModel.number_of_state_innovations);
for i=1:StateSpaceModel.number_of_state_innovations
for h = 1:length(Steps)
PackedConditionalVarianceDecomposition(:,h,i) = vech(ConditionalVariance(:,:,h,i));
end
end

83
matlab/conditional_variance_decomposition_posterior_analysis.m Normal file
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@ -0,0 +1,83 @@
function oo_ = conditional_variance_decomposition_posterior_analysis(NumberOfSimulations, dname, fname, ...
Steps, exonames, exo, vartan, var, mh_conf_sig, oo_)
% Copyright (C) 2009 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/>.
indx = check_name(vartan,var);
if isempty(indx)
disp(['posterior_analysis:: ' var ' is not a stationary endogenous variable!'])
return
end
endogenous_variable_index = sum(1:indx);
exogenous_variable_index = check_name(exonames,exo);
if isempty(exogenous_variable_index)
disp(['posterior_analysis:: ' exo ' is not a declared exogenous variable!'])
return
end
tmp = dir([ dname '/metropolis/' fname '_PosteriorConditionalVarianceDecomposition*.mat']);
NumberOfFiles = length(tmp);
i1 = 1; tmp = zeros(NumberOfSimulations,length(Steps));
for file = 1:NumberOfFiles
load([dname '/metropolis/' fname '_PosteriorConditionalVarianceDecomposition' int2str(file) '.mat']);
% (endovar,time,exovar,simul)
i2 = i1 + size(Conditional_decomposition_array,4) - 1;
tmp(i1:i2,:) = transpose(dynare_squeeze(Conditional_decomposition_array(endogenous_variable_index,:,exogenous_variable_index,:)));
i1 = i2+1;
end
name = [ var '.' exo ];
if isfield(oo_,'PosteriorTheoreticalMoments')
if isfield(oo_.PosteriorTheoreticalMoments,'dsge')
if isfield(oo_.PosteriorTheoreticalMoments.dsge,'ConditionalVarianceDecomposition')
if isfield(oo_.PosteriorTheoreticalMoments.dsge.VarianceDecomposition.mean,name)
if sum(Steps-oo_.PosteriorTheoreticalMoments.dsge.VarianceDecomposition.mean.(name)(1,:)) == 0
% Nothing (new) to do here...
return
end
end
end
end
end
posterior_mean = NaN(2,length(Steps));
posterior_mean(1,:) = Steps;
posterior_median = NaN(1,length(Steps));
posterior_variance = NaN(1,length(Steps));
posterior_deciles = NaN(9,length(Steps));
posterior_density = NaN(2^9,2,length(Steps));
posterior_hpdinf = NaN(1,length(Steps));
posterior_hpdsup = NaN(1,length(Steps));
for i=1:length(Steps)
if ~isconst(tmp(:,i))
[post_mean, post_median, post_var, hpd_interval, post_deciles, density] = ...
posterior_moments(tmp(:,i),1,mh_conf_sig);
posterior_mean(2,i) = post_mean;
posterior_median(i) = post_median;
posterior_variance(i) = post_var;
posterior_deciles(:,i) = post_deciles;
posterior_hpdinf(i) = hpd_interval(1);
posterior_hpdinf(i) = hpd_interval(2);
posterior_density(:,:,i) = density;
end
end
eval(['oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition.mean.' name ' = posterior_mean;']);
eval(['oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition.median.' name ' = posterior_median;']);
eval(['oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition.variance.' name ' = posterior_variance;']);
eval(['oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition.hpdinf.' name ' = posterior_hpdinf;']);
eval(['oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition.hpdsup.' name ' = posterior_hpdsup;']);
eval(['oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition.deciles.' name ' = posterior_deciles;']);
eval(['oo_.PosteriorTheoreticalMoments.dsge.ConditionalVarianceDecomposition.density.' name ' = posterior_density;']);

112
matlab/dsge_posterior_theoretical_conditional_variance_decomposition.m Normal file
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@ -0,0 +1,112 @@
function [nvar,vartan,NumberOfConditionalDecompFiles] = ...
dsge_posterior_theoretical_conditional_variance_decomposition(SampleSize,Steps,M_,options_,oo_)
% This function estimates the posterior distribution of the conditional variance
% decomposition of the endogenous variables (or a subset of the endogenous variables).
%
% INPUTS
% SampleSize [integer] scalar, number of draws in the posterior distribution.
% Steps [integer] 1*h vector of dates.
%
% OUTPUTS
% nvar [integer] scalar, number of endogenous variables.
% vartan [string] array, list of endogenous variables.
% NumberOfConditionalDecompFiles [integer] scalar.
% Copyright (C) 2009 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/>.
type = 'posterior';% To be defined as a input argument later...
% Set varlist (vartan)
[ivar,vartan] = set_stationary_variables_list;
nvar = length(ivar);
% Set the size of the auto-correlation function to zero.
nar = options_.ar;
options_.ar = 0;
% Get informations about the _posterior_draws files.
DrawsFiles = dir([M_.dname '/metropolis/' M_.fname '_' type '_draws*' ]);
NumberOfDrawsFiles = length(DrawsFiles);
NumberOfDrawsFiles = rows(DrawsFiles);
NumberOfSavedElementsPerSimulation = nvar*(nvar+1)/2*M_.exo_nbr*length(Steps);
MaXNumberOfConditionalDecompLines = ceil(options_.MaxNumberOfBytes/NumberOfSavedElementsPerSimulation/8);
if SampleSize<=MaXNumberOfConditionalDecompLines
Conditional_decomposition_array = zeros(nvar*(nvar+1)/2,length(Steps),M_.exo_nbr,SampleSize);
NumberOfConditionalDecompFiles = 1;
else
Conditional_decomposition_array = zeros(nvar*(nvar+1)/2,length(Steps),M_.exo_nbr,MaXNumberOfConditionalDecompLines);
NumberOfLinesInTheLastConditionalDecompFile = mod(SampleSize,MaXNumberOfConditionalDecompLines);
NumberOfConditionalDecompFiles = ceil(SampleSize/MaXNumberOfCOnditionalDecompLines);
end
NumberOfConditionalDecompLines = rows(Conditional_decomposition_array);
ConditionalDecompFileNumber = 1;
StateSpaceModel.number_of_state_equations = M_.endo_nbr;
StateSpaceModel.number_of_state_innovations = M_.exo_nbr;
endo_nbr = M_.endo_nbr;
nstatic = oo_.dr.nstatic;
npred = oo_.dr.npred;
iv = (1:endo_nbr)';
ic = [ nstatic+(1:npred) endo_nbr+(1:size(oo_.dr.ghx,2)-npred) ]';
aux = oo_.dr.transition_auxiliary_variables;
k = find(aux(:,2) > npred);
aux(:,2) = aux(:,2) + nstatic;
aux(k,2) = aux(k,2) + oo_.dr.nfwrd;
linea = 0;
for file = 1:NumberOfDrawsFiles
load([M_.dname '/metropolis/' DrawsFiles(file).name ]);
isdrsaved = columns(pdraws)-1;
NumberOfDraws = rows(pdraws);
for linee = 1:NumberOfDraws
linea = linea+1;
if isdrsaved
set_parameters(pdraws{linee,1});% Needed to update the covariance matrix of the state innovations.
dr = pdraws{linee,2};
else
set_parameters(pdraws{linee,1});
[dr,info] = resol(oo_.steady_state,0);
end
[StateSpaceModel.transition_matrix,StateSpaceModel.impulse_matrix] = kalman_transition_matrix(dr,iv,ic,aux,M_.exo_nbr);
StateSpaceModel.state_innovations_covariance_matrix = M_.Sigma_e;
clear('dr');
Conditional_decomposition_array(:,:,:,linea) = conditional_variance_decomposition(StateSpaceModel, Steps, ivar);
if linea == NumberOfConditionalDecompLines
save([M_.dname '/metropolis/' M_.fname '_PosteriorConditionalVarianceDecomposition' int2str(ConditionalDecompFileNumber) '.mat' ], ...
'Conditional_decomposition_array');
ConditionalDecompFileNumber = ConditionalDecompFileNumber + 1;
linea = 0;
test = ConditionalDecompFileNumber-NumberOfConditionalDecompFiles;
if ~test% Prepare the last round...
Conditional_decomposition_array = zeros(nvar*(nvar+1)/2,length(Steps),M_.exo_nbr,NumberOfLinesInTheLastConditionalDecompFile);
NumberOfConditionalDecompLines = NumberOfLinesInTheLastConditionalDecompFile;
ConditionalDecompFileNumber = ConditionalDecompFileNumber - 1;
elseif test<0;
Conditional_decomposition_array = zeros(nvar*(nvar+1)/2,length(Steps),M_.exo_nbr,MaXNumberOfConditionalDecompLines);
else
clear('Conditional_decomposition_array');
end
end
end
end
options_.ar = nar;

11
matlab/global_initialization.m
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@ -183,10 +183,17 @@ function global_initialization()
options_.student_degrees_of_freedom = 3;
options_.trace_plot_ma = 200;
options_.mh_autocorrelation_function_size = 30;
options_.plot_priors = 0;
options_.plot_priors = 1;
options_.cova_compute = 1;
options_.parallel = 0;
options_.number_of_grid_points_for_kde = 2^9;
quarter = 1;
years = [1 2 3 4 5 10 20 30 40 50];
options_.conditional_variance_decomposition_dates = zeros(1,length(years));
for i=1:length(years)
options_.conditional_variance_decomposition_dates(i) = ...
(years(i)-1)*4+quarter;
end
% Misc
options_.conf_sig = 0.6;
oo_.exo_simul = [];

12
matlab/posterior_analysis.m
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@ -1,5 +1,4 @@
function oo_ = posterior_analysis(type,arg1,arg2,arg3,options_,M_,oo_)
% Copyright (C) 2008 Dynare Team
%
% This file is part of Dynare.
@ -46,7 +45,7 @@ function oo_ = posterior_analysis(type,arg1,arg2,arg3,options_,M_,oo_)
function oo_ = job(type,SampleSize,arg1,arg2,arg3,options_,M_,oo_,nvar,vartan)
narg1 = 8;
narg2 = 10;
if ~(nargin==narg1 | nargin==narg2)
if ~(nargin==narg1 || nargin==narg2)
error('posterior_analysis:: Call to function job is buggy!')
end
switch type
@ -70,7 +69,14 @@ function oo_ = job(type,SampleSize,arg1,arg2,arg3,options_,M_,oo_,nvar,vartan)
dsge_posterior_theoretical_correlation(SampleSize,arg3,M_,options_,oo_);
end
oo_ = correlation_posterior_analysis(SampleSize,M_.dname,M_.fname,...
vartan,nvar,arg1,arg2,arg3,options_.mh_conf_sig,oo_,M_,options_);
vartan,nvar,arg1,arg2,arg3,options_.mh_conf_sig,oo_,M_,options_);
case 'conditional decomposition'
if nargin==narg1
[nvar,vartan,NumberOfFiles] = ...
dsge_posterior_theoretical_conditional_variance_decomposition(SampleSize,arg3,M_,options_,oo_);
end
oo_ = conditional_variance_decomposition_posterior_analysis(SampleSize,M_.dname,M_.fname,...
arg3,M_.exo_names,arg2,vartan,arg1,options_.mh_conf_sig,oo_);
otherwise
disp('Not yet implemented')
end