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

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Bayesian FAVARs with Agnostic Identification 103 %%%%%%**********************************************************%%%%% %%%%%% DO_CALCULATION_GIBBS_SAMPLING_PARAM_PREC_OBS %%%%% %%%%%% %%%%% %%%%%% see Sequence Diagram Block B.3.3 %%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%% Inference on Observation Equation function [param_prec_obs] = DO_CALCULATION_GIBBS_SAMPLING_PARAM_PREC_OBS (input, bk_smoother); %function [param_prec_obs] = DO_CALCULATION_GIBBS_SAMPLING_PARAM_PREC_OBS (input, bk_smoother); global calculation; %%%%% set parameters XX = calculation.stateSpaceStructure.XX; K = input.specification.model.K; M = input.specification.dim.M; N = input.specification.dim.N; T = input.specification.dim.T; Xsi_S = bk_smoother.Xsi_S(:,1:K+M); % prior distributions for VAR part, need Lam and R s0 = 3; alpha = 0.001; M0 = eye(K+M); % Variance Parameter in prior on i-th coeff Param1 = inv( M0 + inv(Xsi_S’*Xsi_S) ) ; for i=1:N if i K %**********************% % b) draw Lam_ii % %**********************% % Given : Factors,Data, and Previously generated R_ii
104 Bayesian FAVARs with Agnostic Identification end%for end%if % Variables needed M_i_bar = inv ( inv(M0) + Xsi_S’*Xsi_S ); %M0 + Xsi_S(:,1:K+M)’*Xsi_S(:,1:K+M); Lam_i_bar = M_i_bar *(Xsi_S’*Xsi_S)*Lam_i_hat; %inv(M_i_bar) *(Xsi_S(:,1:K+M)’*Xsi_S(:,1:K+M)) * Lam_i_hat; Lam_i_hat = Lam_i_bar’ + randn (1, K+M) * chol (R_draw*M_i_bar); calculation.stateSpaceStructure.Lam(i,1:K+M) = Lam_i_hat; %%%% Alternative Approach %Lam_Sigma = calculation.stateSpaceStructure.RR(i,i) * inv(M_i_bar); % Draw Lam from Normal Distribution %Lam_draw = mvnrnd(Lam_i_bar’, Lam_Sigma,1); %calculation.stateSpaceStructure.Lam(i,1:K+M) = Lam_draw; % Ldraw(nit,NN,:)=Lam_bar(1:N,1:K); % Fdraw(nit,:,:)=Xsi_S(:,1:K); %%%%% set param_prec_obs output structure %param_prec_obs.Lam_draw = Lam_draw; %param_prec_obs.R_draw = R_draw; param_prec_obs = 1; %%%%%%**********************************************************%%%%% %%%%%% Bayesian FAVAR Code August 26th %%%%% %%%%%%**********************************************************%%%%% %%%%%% DO _CALCULATION_IRA %%%%% %%%%%% Impule-Response-Analysis %%%%% %%%%%% see Sequence Diagram Block B.4 %%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%% This function starts the DO_CALCULATION_IRA_UHLIG or the %%%%%% DO_CALCULATION_IRA_BBE function depending on the value of %%%%%% input.version.ira_mode which contains information about %%%%%% the selected Impule Response Mode to run. function [ira] = DO_CALCULATION_IRA (input) %function [ira] = DO_CALCULATION_IRA (input) % declare calculation As global structure global calculation; switch input.version.ira_mode end case 1 case 2 [ira.finalresponses] = DO_CALCULATION_IRA_UHLIG (input); % See Sequence Diagram Block B.4.1 [ira.finalresponses] = DO_CALCULATION_IRA_BBE (input); % See Sequence Diagram Block B.4.2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % clear calculation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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