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function [JJ, H, gam, gp, dA, dOm, dYss] = getJJ(A, B, estim_params_, M_,oo_,options_,kronflag,indx,indexo,mf,nlags,useautocorr)
% function [JJ, H, gam, gp, dA, dOm, dYss] = getJJ(A, B, estim_params_, M_,oo_,options_,kronflag,indx,indexo,mf,nlags,useautocorr)
% computes derivatives of 1st and 2nd order moments of observables with
% respect to estimated parameters
%
% Inputs:
% A: Transition matrix of lagged states from Kalman filter
% B: Matrix in state transition equation mapping shocks today to
% states today
% M_: structure storing the model information
% oo_: structure storing the results
% options_: structure storing the options
% kronflag: Indicator whether to rely on Kronecker products (1) or
% not (-1 or -2)
% indx: Index of estimated parameters in M_.params
% indexo: Index of estimated standard deviations in M_.exo_names
% mf: Index of observed variables
% nlags: Number of lags to consider for covariances and
% correlations
% useautocorr: Indicator on whether to use correlations (1) instead of
% covariances (0)
%
% Outputs:
% JJ: Jacobian of 1st and 2nd order moments of observables, i.e. dgam/dTHETA
% (see below for definition of gam)
% H: dTAU/dTHETA: Jacobian of TAU, vectorized form of
% linearized reduced form state space model, given ys [steady state],
% A [transition matrix], B [matrix of shocks], Sigma [covariance of shocks]
% TAU = [ys; vec(A); dyn_vech(B*Sigma*B')].
% gam: vector of theoretical moments of observed variables mf [JJ is the Jacobian of gam].
% gam = [ys(mf); dyn_vech(GAM{1}); vec(GAM{j+1})]; for j=1:ar and where
% GAM is the first output of th_autocovariances
% gp: Jacobian of linear rational expectation matrices [i.e.
% Jacobian of dynamic model] with respect to estimated
% structural parameters only (indx)
% dA: [endo_nbr by endo_nbr by (indx+indexo)] Jacobian of transition matrix A
% dOm: Jacobian of Omega = (B*Sigma*B')
% dYss Jacobian of steady state with respect to estimated structural parameters only (indx)
% Copyright (C) 2010-2017 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/>.
if nargin<8 || isempty(indx)
% indx = [1:M_.param_nbr];
end
if nargin<9 || isempty(indexo)
indexo = [];
end
if nargin<11 || isempty(nlags)
nlags=3;
end
if nargin<12 || isempty(useautocorr)
useautocorr=0;
end
% if useautocorr,
warning('off','MATLAB:divideByZero')
% end
if kronflag == -1
fun = 'thet2tau';
params0 = M_.params;
para0 = get_all_parameters(estim_params_, M_);
JJ = fjaco(fun,para0,estim_params_,M_, oo_, indx,indexo,1,mf,nlags,useautocorr);
M_.params = params0;
params0 = M_.params;
H = fjaco(fun,para0,estim_params_,M_, oo_, indx,indexo,0,mf,nlags,useautocorr);
M_.params = params0;
params0 = M_.params;
gp = fjaco(fun,para0,estim_params_,M_, oo_, indx,indexo,-1);
M_.params = params0;
offset = length(para0)-length(indx);
gp = gp(:,offset+1:end);
dYss = H(1:M_.endo_nbr,offset+1:end);
dA = reshape(H(M_.orig_endo_nbr+[1:numel(A)],:),[size(A),size(H,2)]);
dOm = dA*0;
for j=1:size(H,2)
dOm(:,:,j) = dyn_unvech(H(M_.endo_nbr+numel(A)+1:end,j));
end
assignin('base','M_', M_);
assignin('base','oo_', oo_);
else
[H, dA, dOm, dYss, gp] = getH(A, B, estim_params_,M_,oo_,options_,kronflag,indx,indexo);
gp = reshape(gp,size(gp,1)*size(gp,2),size(gp,3));
gp = [dYss; gp];
% if isempty(H),
% JJ = [];
% GAM = [];
% return
% end
m = length(A);
GAM = lyapunov_symm(A,B*M_.Sigma_e*B',options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,1,options_.debug);
k = find(abs(GAM) < 1e-12);
GAM(k) = 0;
% if useautocorr,
sdy = sqrt(diag(GAM));
sy = sdy*sdy';
% end
% BB = dOm*0;
% for j=1:length(indx),
% BB(:,:,j)= dA(:,:,j)*GAM*A'+A*GAM*dA(:,:,j)'+dOm(:,:,j);
% end
% XX = lyapunov_symm_mr(A,BB,options_.qz_criterium,options_.lyapunov_complex_threshold,0);
for j=1:length(indexo)
dum = lyapunov_symm(A,dOm(:,:,j),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,2,options_.debug);
% dum = XX(:,:,j);
k = find(abs(dum) < 1e-12);
dum(k) = 0;
if useautocorr
dsy = 1/2./sdy.*diag(dum);
dsy = dsy*sdy'+sdy*dsy';
dum1=dum;
dum1 = (dum1.*sy-dsy.*GAM)./(sy.*sy);
dum1 = dum1-diag(diag(dum1))+diag(diag(dum));
dumm = dyn_vech(dum1(mf,mf));
else
dumm = dyn_vech(dum(mf,mf));
end
for i=1:nlags
dum1 = A^i*dum;
if useautocorr
dum1 = (dum1.*sy-dsy.*(A^i*GAM))./(sy.*sy);
end
dumm = [dumm; vec(dum1(mf,mf))];
end
JJ(:,j) = dumm;
end
nexo = length(indexo);
for j=1:length(indx)
dum = lyapunov_symm(A,dA(:,:,j+nexo)*GAM*A'+A*GAM*dA(:,:,j+nexo)'+dOm(:,:,j+nexo),options_.lyapunov_fixed_point_tol,options_.qz_criterium,options_.lyapunov_complex_threshold,2,options_.debug);
% dum = XX(:,:,j);
k = find(abs(dum) < 1e-12);
dum(k) = 0;
if useautocorr
dsy = 1/2./sdy.*diag(dum);
dsy = dsy*sdy'+sdy*dsy';
dum1=dum;
dum1 = (dum1.*sy-dsy.*GAM)./(sy.*sy);
dum1 = dum1-diag(diag(dum1))+diag(diag(dum));
dumm = dyn_vech(dum1(mf,mf));
else
dumm = dyn_vech(dum(mf,mf));
end
for i=1:nlags
dum1 = A^i*dum;
for ii=1:i
dum1 = dum1 + A^(ii-1)*dA(:,:,j+nexo)*A^(i-ii)*GAM;
end
if useautocorr
dum1 = (dum1.*sy-dsy.*(A^i*GAM))./(sy.*sy);
end
dumm = [dumm; vec(dum1(mf,mf))];
end
JJ(:,j+nexo) = dumm;
end
JJ = [ [zeros(length(mf),nexo) dYss(mf,:)]; JJ];
end
if nargout >2
% sy=sy(mf,mf);
options_.ar=nlags;
nodecomposition = 1;
[GAM,stationary_vars] = th_autocovariances(oo_.dr,oo_.dr.order_var(mf),M_,options_,nodecomposition);
sy=sqrt(diag(GAM{1}));
sy=sy*sy';
if useautocorr
sy=sy-diag(diag(sy))+eye(length(mf));
GAM{1}=GAM{1}./sy;
else
for j=1:nlags
GAM{j+1}=GAM{j+1}.*sy;
end
end
gam = dyn_vech(GAM{1});
for j=1:nlags
gam = [gam; vec(GAM{j+1})];
end
end
gam = [oo_.dr.ys(oo_.dr.order_var(mf)); gam];
% if useautocorr,
warning('on','MATLAB:divideByZero')
% end
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