89 lines
3.0 KiB
Matlab
89 lines
3.0 KiB
Matlab
function [lnpriormom] = endogenous_prior(data,Pstar,BayesInfo,H)
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% Computes the endogenous log prior addition to the initial prior
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%
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% INPUTS
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% data [double] n*T vector of data observations
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% Pstar [double] k*k matrix of
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% BayesInfo [structure]
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%
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% OUTPUTS
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% lnpriormom [double] scalar of log endogenous prior value
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% Code to implement notes on endogenous priors by Lawrence Christiano,
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% specified in the appendix of:
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% Introducing Financial Frictions and Unemployment into a Small Open Economy Model
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% by Lawrence J. Christiano, Mathias Trabandt and Karl Walentin (2011), Journal of Economic Dynamics and Control
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% this is the 'mother' of the priors on the model parameters.
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% the priors include a metric across some choosen moments of the (supposedly
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% pre-sample) data.
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% *** Implemented file for variances, but in principle any moment
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% *** could be matched
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% As a default, the prior second moments are computed from the same sample
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% used to find the posterior mode. This could be changed by making the
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% appropriate adjustment to the following code.
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% Copyright (C) 2011 Lawrence J. Christiano, Mathias Trabandt and Karl Walentin
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% Copyright (C) 2013-2017 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 <http://www.gnu.org/licenses/>.
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Y=data';
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[Tsamp,n]=size(Y); % sample length and number of matched moments (here set equal to nr of observables)
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hmat=zeros(n,Tsamp);
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Ydemean=zeros(Tsamp,n);
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C0=zeros(n,n);
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C1=zeros(n,n);
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C2=zeros(n,n);
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for j=1:n
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Ydemean(:,j)=Y(:,j)-mean(Y(:,j));
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end
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Fhat=diag(Ydemean'*Ydemean)/Tsamp;
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% we need ht, where t=1,...,T
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for t=1:Tsamp
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hmat(:,t)=diag(Ydemean(t,:)'*Ydemean(t,:))-Fhat;
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end
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% To calculate Shat we need C0, C1 and C2
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for t=1:Tsamp
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C0=C0+1/Tsamp*hmat(:,t)*hmat(:,t)';
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end
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for t=2:Tsamp
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C1=C1+1/(Tsamp-1)*hmat(:,t)*hmat(:,t-1)';
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end
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for t=3:Tsamp
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C2=C2+1/(Tsamp-2)*hmat(:,t)*hmat(:,t-2)';
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end
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% Finally, we have the sampling uncertainty measure Shat:
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Shat=C0 +(1-1/(2+1))*(C1+C1')...
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+(1-2/(2+1))*(C2+C2');
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% Model variances below:
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mf=BayesInfo.mf1;
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II=eye(size(Pstar,2));
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Z=II(mf,:);
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% This is Ftheta, variance of model variables, given param vector theta:
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Ftheta=diag(Z*Pstar(:,mf)+H);
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% below commented out line is for Del Negro Schorfheide style priors:
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% lnpriormom=-.5*n*TT*log(2*pi)-.5*TT*log(det(sigma))-.5*TT*trace(inv(sigma)*(gamyy-2*phi'*gamxy+phi'*gamxx*phi));
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lnpriormom=.5*n*log(Tsamp/(2*pi))-.5*log(det(Shat))-.5*Tsamp*(Fhat-Ftheta)'/Shat*(Fhat-Ftheta);
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