Measuring the Effects of a Shock to Monetary Policy - Humboldt ...

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Bayesian FAVARs with Agnostic Identification 99 end%for % Note that indexp* P_tt * G’ + Q; % %=======================================================% if t
100 Bayesian FAVARs with Agnostic Identification % Preparing dimension for Transformation regDim = [1:(K+M)]; [l_star] = length(regDim); [l_reg] = length(Q_Prior); T = size(Xsi_Tlag,1); % Transformation of Q in case of singularity Q = Q_Prior; Q_star = Q(1:l_star,1:l_star); % Transformation of G in case of singular Q G = G_Prior; %G_star = zeros(l_star,l_reg); G_star = G(1:l_star,1:l_reg); % Transformation of Xsi in case of singular Q Xsi_F = Xsi_F(1,1:l_reg); Xsi_Tlag = Xsi_Tlag(:,1:l_reg); P_F = P_F(1:l_reg,1:l_reg); P_Tlag = P_Tlag(1:l_reg^2,:); for t=1:T-1 end%for %=======================================================% % Final Updating procedure % %*******************************************************% Xsi_TP = Xsi_Tlag(T-t+1,1:l_star)’; Xsi_TT = Xsi_Tlag(T-t,:)’; P_TL = P_Tlag(:,T-t); P_TT = reshape(P_TL’,(d*(K+M)),(d*(K+M))); %f_ts = pinv(G_star * P_TT * G_star’ + Q_star); f_ts = inv(G_star * P_TT * G_star’ + Q_star); K_ts = P_TT * G_star’ * f_ts; Xsi_TXsi = Xsi_TT + K_ts * (Xsi_TP - G_star * Xsi_TT); P_TXsi = P_TT - K_ts * G_star * P_TT; %*******************************************************% % singles out latent factors indexnM=[ones(K,d);zeros(M,d)]; indexnM=find(indexnM==1); Xsi_Tlag(T-t,:) = Xsi_TXsi’; Xsi_Tlag(T-t,indexnM) = mvnrnd(Xsi_Tlag(T-t,indexnM)’,P_TXsi(indexnM,indexnM),1); Xsi_S = Xsi_Tlag(:,1:(K+M)); P_S = P_TXsi; %%%%% set bk_smoother output structure bk_smoother.Xsi_S = Xsi_S;
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