40 lines
2.4 KiB
Matlab
40 lines
2.4 KiB
Matlab
function [Ptld,H0invtld,Hpinvtld] = fn_rlrprior(Ui,Vi,Pi,H0multi,Hpmulti,nvar)
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% [Ptld,H0invtld,Hpinvtld] = fn_rlrprior(Ui,Vi,Pi,H0multi,Hpmulti,nvar)
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%
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% Exporting random Bayesian prior with linear restrictions
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% See Waggoner and Zha's Gibbs sampling paper
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%
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% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
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% equation contemporaneous restriction matrix where qi is the number of free parameters.
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% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
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% of total original parameters and bi is a vector of free parameters. When no
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% restrictions are imposed, we have Ui = I. There must be at least one free
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% parameter left for the ith equation. Imported from dnrprior.m.
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% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
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% equation lagged restriction matrix where k (ncoef) is a total number of RHS variables and
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% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
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% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
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% vector of free parameters. There must be at least one free parameter left for
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% the ith equation. Imported from dnrprior.m.
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% Pi: ncoef-by-nvar matrix for the ith equation under random walk. Same for all equations
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% H0multi: nvar-by-nvar-by-nvar; H0 for different equations under asymmetric prior
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% Hpmulti: ncoef-by-ncoef-by-nvar; H+ for different equations under asymmetric prior
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% nvar: number of endogenous variables
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% --------------------
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% Ptld: cell(nvar,1). The prior mean of g_i is Ptld{i}*b_i;
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% H0invtld: cell(nvar,1). Transformed inv covaraince for b_i, the free parameters in A0(:,i);
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% Hpinvtld: cell(nvar,1). Transformed inv covaraince for g_i, the free parameters in A+(:,i);
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%
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% Tao Zha, February 2000
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Ptld = cell(nvar,1); % tld: tilda
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H0invtld = cell(nvar,1); % H0 for different equations under linear restrictions
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Hpinvtld = cell(nvar,1); % H+ for different equations under linear restrictions
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for n=1:nvar % one for each equation
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Hpinvtld{n} = Vi{n}'*(Hpmulti(:,:,n)\Vi{n});
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Ptld{n} = (Hpinvtld{n}\Vi{n}')*(Hpmulti(:,:,n)\Pi)*Ui{n};
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H0invtld{n} = Ui{n}'*(H0multi(:,:,n)\Ui{n}) + Ui{n}'*Pi'*(Hpmulti(:,:,n)\Pi)*Ui{n} ...
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- Ptld{n}'*Hpinvtld{n}*Ptld{n};
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end
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