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

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Bayesian FAVARs with Agnostic Identification 101 %%%%%%**********************************************************%%%%% %%%%%% Bayesian FAVAR Code August 26th %%%%% %%%%%%**********************************************************%%%%% %%%%%% DO_CALCULATION_GIBBS_SAMPLING_PARAM_PREC_FAC %%%%% %%%%%% %%%%% %%%%%% see Sequence Diagram Block B.3.4 %%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%% Inference on State Equation function [param_prec_fac] = DO_CALCULATION_GIBBS_SAMPLING_PARAM_PREC_FAC (input, bk_smoother); %function [param_prec_fac] = DO_CALCULATION_GIBBS_SAMPLING_PARAM_PREC_FAC (input, bk_smoother); global calculation; %%%%% set parameters K = input.specification.model.K; M = input.specification.dim.M; T = input.specification.dim.T; d = input.specification.model.d; Xsi_S = bk_smoother.Xsi_S; %****************************% % univariate AR OLS % %****************************% % At this point we are interested in generating the i’th variances: % Only Sigma Required for i=1:K+M end%for [Phi_i,Phi_ci,vi,Qi(i),invFYFYi]=estvar(Xsi_S(:,i),d,[]); % At this point we only need to save Qi(i) which respectively as % diagonal elements forms the Prior Q_0 Q_0 = diag(Qi); % maybe better diag(Qi(:,:)) Q_prior = Q_0; Omega_0 = zeros(d*(K+M));%,size(Qmega_0,2)); Omega_0 = diag(kron(1./Qi,1./[1:d])); % Qmega_0 = Q_prior.*Omega_0; %
102 Bayesian FAVARs with Agnostic Identification end%for F_reg = F_reg(:,:); F_reg = F_reg(d+1:T,:); % For doing inference on the Transition equation one has to first draw Q and the draw vec(Phi) % Note that for generalization it is good to write [kappa1_prior,kappa2_prior; kappa1_post and kappa1_post] % shortcuts VV = V_hat’*V_hat; FF_reg = inv(F_reg’*F_reg); Phi_FF = inv(Omega_prior + FF_reg); % Draw posterior Q Q_bar = Q_prior + VV + Phi_hat’*Phi_FF*Phi_hat; kappa1_prior = K+M+2; kappa1_post = T+kappa1_prior; kappa2_prior = Q_prior; kappa2_post = Q_bar; % Scale Matrix % Inverse Wishart draw % df = degrees of freedom %QW = wishrnd(inv(kappa2_post),kappa1_post); %Q_draw = inv(QW); % =1 % 0.999 end vec_Phi_draw = mvnrnd(vecPhi_posterior,sigma_Phi,1); Phi_draw = reshape(vec_Phi_draw’,d*(K+M),(K+M))’; calculation.stateSpaceStructure.Phi_bar(1:K+M,:) = Phi_draw; Phi_draw = reshape(Phi_draw,K+M,K+M,d); %%%%% set param_prec_obs output structure param_prec_fac.Q_draw = Q_draw; param_prec_fac.Phi_draw = Phi_draw; %%%%%%**********************************************************%%%%% %%%%%% Bayesian FAVAR Code August 26th %%%%%
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