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Commit d19f2aeb authored by Houtan Bastani's avatar Houtan Bastani
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function [vd,str,imf] = errors(Bh,swish,nn)
% Computing variance decompositions and impulse functions with
% [vd,str,imf] = errors(Bh,swish,nn)
% where imf and vd is of the same format as in RATS, that is to say:
% Column: nvar responses to 1st shock,
% nvar responses to 2nd shock, and so on.
% Row: steps of impulse responses.
% vd: variance decompositions
% str: standard errors of each variable, steps-by-nvar
% imf: impulse response functions
% Bh is the estimated reduced form coefficient in the form
% Y(T*nvar) = XB + U, X: T*k, B: k*nvar. The matrix
% form or dimension is the same as "Bh" from the function "sye";
% swish is the inv(A0) in the structural model A(L)y(t) = e(t).
% nn is the numbers of inputs [nvar,lags,# of impulse responses].
nvar = nn(1);
lags = nn(2);
imstep = nn(3); % number of steps for impulse responses
Ah = Bh';
% Row: nvar equations
% Column: 1st lag (with nvar variables) to lags (with nvar variables) + const = k.
imf = zeros(imstep,nvar*nvar);
vd = imf;
% Column: nvar responses to 1st shock, nvar responses to 2nd shock, and so on.
% Row: steps of impulse responses.
str = zeros(imstep,nvar); % initializing standard errors of each equation
M = zeros(nvar*(lags+1),nvar);
% Stack M0;M1;M2;...;Mlags
M(1:nvar,:) = swish;
Mtem = M(1:nvar,:); % temporary M -- impulse responses.
%
Mvd = Mtem.^2; % saved for the cumulative sum later
Mvds = (sum(Mvd'))';
str(1,:) = sqrt(Mvds'); % standard errors of each equation
Mvds = Mvds(:,ones(size(Mvds,1),1));
Mvdtem = (100.0*Mvd) ./ Mvds; % tempoary Mvd -- variance decompositions
% first or initial responses to
% one standard deviation shock (or forecast errors).
% Row: responses; Column: shocks
%
% * put in the form of "imf"
imf(1,:) = Mtem(:)';
vd(1,:) = Mvdtem(:)';
t = 1;
ims1 = min([imstep-1 lags]);
while t <= ims1
Mtem = zeros(nvar,nvar);
for k = 1:t
Mtem = Ah(:,nvar*(k-1)+1:nvar*k)*M(nvar*(t-k)+1:nvar*(t-k+1),:) + Mtem;
% Row: nvar equations, each for the nvar variables at tth lag
end
% ** impulse response functions
M(nvar*t+1:nvar*(t+1),:) = Mtem;
imf(t+1,:) = Mtem(:)';
% stack imf with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
% ** variance decompositions
Mvd = Mvd + Mtem.^2; % saved for the cumulative sum later
Mvds = (sum(Mvd'))';
str(t+1,:) = sqrt(Mvds'); % standard errors of each equation
Mvds = Mvds(:,ones(size(Mvds,1),1));
Mvdtem = (100.0*Mvd) ./ Mvds; % tempoary Mvd -- variance decompositions
vd(t+1,:) = Mvdtem(:)';
% stack vd with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
t= t+1;
end
for t = lags+1:imstep-1
M(1:nvar*lags,:) = M(nvar+1:nvar*(lags+1),:);
Mtem = zeros(nvar,nvar);
for k = 1:lags
Mtem = Ah(:,nvar*(k-1)+1:nvar*k)*M(nvar*(lags-k)+1:nvar*(lags-k+1),:) + Mtem;
% Row: nvar equations, each for the nvar variables at tth lag
end
% ** impulse response functions
M(nvar*lags+1:nvar*(lags+1),:) = Mtem;
imf(t+1,:) = Mtem(:)';
% stack imf with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
% ** variance decompositions
Mvd = Mvd + Mtem.^2; % saved for the cumulative sum later
Mvds = (sum(Mvd'))';
str(t+1,:) = sqrt(Mvds'); % standard errors of each equation
Mvds = Mvds(:,ones(size(Mvds,1),1));
Mvdtem = (100.0*Mvd) ./ Mvds; % tempoary Mvd -- variance decompositions
vd(t+1,:) = Mvdtem(:)';
% stack vd with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
end

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function imf = impulse(Bh,swish,nn)
% Computing impulse functions with
% imf = impulse(Bh,swish,nn)
% where imf is in a format that is the SAME as in RATS.
% Column: nvar responses to 1st shock,
% nvar responses to 2nd shock, and so on.
% Row: steps of impulse responses.
% Bh is the estimated reduced form coefficient in the form
% Y(T*nvar) = XB + U, X: T*k, B: k*nvar. The matrix
% form or dimension is the same as "Bh" from the function "sye";
% swish is the inv(A0) in the structural model A(L)y(t) = e(t).
% nn is the numbers of inputs [nvar,lags,# of impulse responses].
nvar = nn(1);
lags = nn(2);
imstep = nn(3); % number of steps for impulse responses
Ah = Bh';
% Row: nvar equations
% Column: 1st lag (with nvar variables) to lags (with nvar variables) + const = k.
imf = zeros(imstep,nvar*nvar);
% Column: nvar responses to 1st shock, nvar responses to 2nd shock, and so on.
% Row: steps of impulse responses.
M = zeros(nvar*(lags+1),nvar);
% Stack M0;M1;M2;...;Mlags
M(1:nvar,:) = swish;
Mtem = M(1:nvar,:); % temporary M.
% first (initial) responses to 1 standard deviation shock. Row: responses; Column: shocks
% * put in the form of "imf"
imf(1,:) = Mtem(:)';
t = 1;
ims1 = min([imstep-1 lags]);
while t <= ims1
Mtem = zeros(nvar,nvar);
for k = 1:t
Mtem = Ah(:,nvar*(k-1)+1:nvar*k)*M(nvar*(t-k)+1:nvar*(t-k+1),:) + Mtem;
% Row: nvar equations, each for the nvar variables at tth lag
end
M(nvar*t+1:nvar*(t+1),:) = Mtem;
imf(t+1,:) = Mtem(:)';
% stack imf with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
t= t+1;
end
for t = lags+1:imstep-1
M(1:nvar*lags,:) = M(nvar+1:nvar*(lags+1),:);
Mtem = zeros(nvar,nvar);
for k = 1:lags
Mtem = Ah(:,nvar*(k-1)+1:nvar*k)*M(nvar*(lags-k)+1:nvar*(lags-k+1),:) + Mtem;
% Row: nvar equations, each for the nvar variables at tth lag
end
M(nvar*lags+1:nvar*(lags+1),:) = Mtem;
imf(t+1,:) = Mtem(:)';
% stack imf with each step, Row: 6 var to 1st shock, 6 var to 2nd shock, etc.
end

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