197 lines
8.2 KiB
Matlab
197 lines
8.2 KiB
Matlab
function ms_mardd(options_)
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% Applies to both linear and exclusion restrictions.
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% (1) Marginal likelihood function p(Y) for constant structural VAR models, using Chib (1995)'s ``Marginal Likelihood from the Gibbs Output'' in JASA.
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% (2) Conditional likelihood function f(Y|A0, A+) on the ML estimate for constant exclusion-identified models.
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% See Forecast (II) pp.67-80.
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%
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% Tao Zha, September 1999. Quick revisions, May 2003. Final revision, September 2004.
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% Copyright © 2011-2017 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 <https://www.gnu.org/licenses/>.
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msstart2 % start the program in which everyhting is initialized through msstart2.m
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if ~options_.ms.indxestima
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warning(' ')
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disp('You must set IxEstima=1 in msstart to run this program')
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disp('Press ctrl-c to abort now')
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pause
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end
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A0xhat = zeros(size(A0hat));
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Apxhat = zeros(size(Aphat));
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if (0)
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%Robustness check to see if the same result is obtained with the purterbation of the parameters.
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for k=1:nvar
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bk = Uiconst{k}'*A0hat(:,k);
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gk = Viconst{k}'*Aphat(:,k);
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A0xhat(:,k) = Uiconst{k}*(bk + 5.2*randn(size(bk))); % Perturbing the posterior estimate.
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Apxhat(:,k) = Viconst{k}*(gk + 5.2*randn(size(gk))); % Perturbing the posterior estimate.
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end
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else
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%At the posterior estimate.
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A0xhat = A0hat; % ML estimate of A0
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Apxhat = Aphat; % ML estimate of A+
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end
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%--- Rename variables.
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YatYa = yty;
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XatYa = xty;
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ytx = xty';
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YatXa = ytx;
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XatXa = xtx;
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%--------- The log value of p(A0,A+) at some point such as the peak ----------
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vlog_a0p = 0;
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Yexpt=0; % exponential term for Y in p(Y|A0,A+) at some point such as the peak
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Apexpt=0.0; % 0.0 because we have chosen posterior estimate of A+ as A+*. Exponential term for A+ conditional on A0 and Y
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%======= Computing the log prior pdf of a0a+ and the exponential term for Y in p(Y|A0,A+).
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for k=1:nvar
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a0k = A0xhat(:,k); % meaningful parameters in the kth equation.
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apk = Apxhat(:,k); % meaningful parameters in the kth equation.
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%--- Prior settings.
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S0bar = H0invtld{k}; %See Claim 2 on p.69b.
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Spbar = Hpinvtld{k};
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bk = Uiconst{k}'*a0k; % free parameters in the kth equation.
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gk = Viconst{k}'*apk; % free parameters in the kth equation.
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gbark = Ptld{k}*bk; % bar: prior
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%--- The exponential term for Y in p(Y|A0,A+)
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Yexpt = Yexpt - 0.5*(a0k'*YatYa*a0k - 2*apk'*XatYa*a0k + apk'*XatXa*apk);
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%--- The log prior pdf.
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vlog_a0p = vlog_a0p - 0.5*(size(Uiconst{k},2)+size(Viconst{k},2))*log(2*pi) + 0.5*log(abs(det(S0bar))) + ...
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0.5*log(abs(det(Spbar))) - 0.5*(bk'*S0bar*bk+(gk-gbark)'*Spbar*(gk-gbark));
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%--- For p(A+|Y,a0) only.
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tmpd = gk - Pmat{k}*bk;
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Apexpt = Apexpt - 0.5*tmpd'*(Hpinv{k}*tmpd);
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end
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vlog_a0p
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%--------- The log value of p(Y|A0,A+) at some point such as the peak. ----------
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%--------- Note that logMarLHres is the same as vlog_Y_a, just to double check. ----------
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vlog_Y_a = -0.5*nvar*fss*log(2*pi) + fss*log(abs(det(A0xhat))) + Yexpt
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% a: given a0 and a+
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logMarLHres = 0; % Initialize log of the marginal likelihood (restricted or constant parameters).
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for ki=1:fss %ndobs+1:fss % Forward recursion to get the marginal likelihood. See F on p.19 and pp. 48-49.
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%---- Restricted log marginal likelihood function (constant parameters).
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[A0l,A0u] = lu(A0xhat);
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ada = sum(log(abs(diag(A0u)))); % log|A0|
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termexp = y(ki,:)*A0xhat - phi(ki,:)*Apxhat; % 1-by-nvar
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logMarLHres = logMarLHres - (0.5*nvar)*log(2*pi) + ada - 0.5*termexp*termexp'; % log value
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end
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logMarLHres
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%--------- The log value of p(A+|Y,A0) at some point such as the peak ----------
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totparsp = 0.0;
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tmpd = 0.0;
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for k=1:nvar
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totparsp = totparsp + size(Viconst{k},2);
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tmpd = tmpd + 0.5*log(abs(det(Hpinv{k})));
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end
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vlog_ap_Ya0 = -0.5*totparsp*log(2*pi) + tmpd + Apexpt;
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%===================================
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% Compute p(a0,k|Y,ao) at some point such as the peak (in this situation, we simply
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% generate results from the original Gibbs sampler). See FORECAST (2) pp.70-71
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%===================================
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%--- Global set up for Gibbs.
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[Tinv,UT] = fn_gibbsrvar_setup(H0inv, Uiconst, Hpinv, Pmat, Viconst, nvar, fss);
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%
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vlog_a0_Yao = zeros(nvar,1);
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% the log value of p(a0k|Y,ao) where ao: other a's at some point such as the peak of ONLY some a0's
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vlog=zeros(ndraws2,1);
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for k=1:nvar
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bk = Uiconst{k}'*A0xhat(:,k);
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indx_ks=[k:nvar]; % the columns that exclude 1-(k-1)th columns
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A0gbs0 = A0hat; % starting at some point such as the peak
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nk = n0(k);
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if k<nvar
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%--------- The 1st set of draws to be tossed away. ------------------
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for draws = 1:ndraws1
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if ~mod(draws,nbuffer)
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skipline()
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dprintf('The %dth column or equation in A0 with %d 1st tossed-away draws in Gibbs', k, draws)
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end
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A0gbs1 = fn_gibbsrvar(A0gbs0,UT,nvar,fss,n0,indx_ks);
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A0gbs0=A0gbs1; % repeat the Gibbs sampling
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end
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%--------- The 2nd set of draws to be used. ------------------
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for draws = 1:ndraws2
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if ~mod(draws,nbuffer)
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skipline()
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dprintf('The %dth column or equation in A0 with %d usable draws in Gibbs', k, draws)
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end
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[A0gbs1, Wcell] = fn_gibbsrvar(A0gbs0,UT,nvar,fss,n0,indx_ks);
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%------ See p.71, Forecast (II).
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%------ Computing p(a0_k|Y,a_others) at some point such as the peak along the dimensions of indx_ks.
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Vk = Tinv{k}\Wcell{k}; %V_k on p.71 of Forecast (II).
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gbeta = Vk\bk; % inv(V_k)*b_k on p.71 of Forecast (II) where alpha_k = b_k in our notation.
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[Vtq,Vtr]=qr(Vk',0); %To get inv(V_k)'*inv(V_k) in (*) on p.71 of Forecast (II).
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%
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vlog(draws) = 0.5*(fss+nk)*log(fss)-log(abs(det(Vk)))-0.5*(nk-1)*log(2*pi)-...
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0.5*(fss+1)*log(2)-gammaln(0.5*(fss+1))+fss*log(abs(gbeta(1)))-...
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0.5*fss*bk'*(Vtr\(Vtr'\bk));
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A0gbs0=A0gbs1; % repeat the Gibbs sampling
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end
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vlogm=max(vlog);
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qlog=vlog-vlogm;
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vlogxhat=vlogm-log(ndraws2)+log(sum(exp(qlog)));
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vlog_a0_Yao(k) = vlogxhat;
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% The log value of p(a0_k|Y,a_others) where a_others: other a's at some point such as the peak of ONLY some a0's
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else
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skipline()
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disp('The last(6th) column or equation in A0 with no Gibbs draws')
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[A0gbs1, Wcell] = fn_gibbsrvar(A0gbs0,UT,nvar,fss,n0,indx_ks)
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%------ See p.71, Forecast (II).
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%------ Computing p(a0_k|Y,a_others) at some point such as the peak along the dimensions of indx_ks.
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Vk = Tinv{k}\Wcell{k}; %V_k on p.71 of Forecast (II).
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gbeta = Vk\bk; % inv(V_k)*b_k on p.71 of Forecast (II) where alpha_k = b_k in our notation.
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[Vtq,Vtr]=qr(Vk',0); %To get inv(V_k)'*inv(V_k) in (*) on p.71 of Forecast (II).
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%
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vloglast = 0.5*(fss+nk)*log(fss)-log(abs(det(Vk)))-0.5*(nk-1)*log(2*pi)-...
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0.5*(fss+1)*log(2)-gammaln(0.5*(fss+1))+fss*log(abs(gbeta(1)))-...
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0.5*fss*bk'*(Vtr\(Vtr'\bk));
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vlog_a0_Yao(k) = vloglast;
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end
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end
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ndraws2
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disp('Prior pdf -- log(p(a0hat, a+hat)):');
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vlog_a0p
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disp('LH pdf -- log(p(Y|a0hat, a+hat)):');
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vlog_Y_a
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disp('Posterior Kernal -- logp(ahat) + logp(Y|ahat):');
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vlog_Y_a + vlog_a0p
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disp('Posterior pdf -- log(p(a0_i_hat|a0_other_hat, Y)):');
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vlog_a0_Yao
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disp('Posterior pdf -- log(p(aphat|a0hat, Y)):');
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vlog_ap_Ya0
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%--------- The value of marginal density p(Y) ----------
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skipline()
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disp('************ Marginal Likelihood of Y or Marginal Data Density: ************');
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vlogY = vlog_a0p+vlog_Y_a-sum(vlog_a0_Yao)-vlog_ap_Ya0
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