101 lines
3.8 KiB
Matlab
101 lines
3.8 KiB
Matlab
function [Bh,e,xtx,xty,phi,y,ncoe,xr] = sye(z,lags)
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% Now [Bh,e,xtx,xty,phi,y,ncoe,xr] = sye(z,lags)
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% Old: [Bh,e,xtx,xty,phi,y,ncoe,Sigu,xtxinv] = sye(z,lags)
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%
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% Estimate a system of equations in the form of y(T*nvar) = XB + u,
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% X--phi: T*k, B: k*nvar; where T=sp-lags, k=ncoe,
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%
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% z: (T+lags)-by-(nvar+1) raw data matrix (nvar of variables + constant).
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% lags: number of lags
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%--------------------
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% Bh: k-by-nvar estimated reduced-form parameter; column: nvar;
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% row: k=ncoe=[nvar for 1st lag, ..., nvar for last lag, const]
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% e: estimated residual e = y -xBh, T-by-nvar
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% xtx: X'X: k-by-k
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% xty: X'Y: k-by-nvar
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% phi: X; T-by-k; column: [nvar for 1st lag, ..., nvar for last lag, const]
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% y: Y: T-by-nvar
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% ncoe: number of coeffcients per equation: nvar*lags + 1
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% xr: the economy size (k-by-k) in qr(phi) so that xr=chol(X'*X)
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% Sigu: e'*e: nvar-by-nvar. Note, not divided (undivided) by "nobs"
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% xtxinv: inv(X'X): k-by-k
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%
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% See also syed.m (allowing for more predetermined terms) which has not
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% been yet updated as "sye.m".
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%
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% Note, "lags" is something I changed recently, so it may not be compatible
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% with old programs, 10/15/98 by TAZ.
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%
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% Revised, 5/2/99. Replaced outputs Sigu and xtxinv with xr so that previous
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% programs may be incompatible.
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% Copyright (C) 1998-2011 Tao Zha
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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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% ** setup of orders and lengths **
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[sp,nvar] = size(z); % sp: sample period T include lags
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nvar = nvar-1; % -1: takes out the counting of constant
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ess = sp-lags; % effective sample size
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sb = lags+1; % sample beginning
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sl = sp; % sample last period
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ncoe = nvar*lags + 1; % with constant
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% ** construct X for Y = X*B + U where phi = X **
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x = z(:,1:nvar);
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C = z(:,nvar+1);
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phi = zeros(ess,ncoe);
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phi(:,ncoe) = C(1:ess);
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for k=1:lags, phi(:,nvar*(k-1)+1:nvar*k) = x(sb-k:sl-k,:); end
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% row: T-lags; column: [nvar for 1st lag, ..., nvar for last lag, const]
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% Thus, # of columns is nvar*lags+1 = ncoef.
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% ** estimate: B, XTX, residuals **
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y = x(sb:sl,:);
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%
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%**** The following, though stable, is too slow *****
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% [u d v]=svd(phi,0); %trial
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% %xtx = phi'*phi; % X'X, k*k (ncoe*ncoe)
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% vd=v.*(ones(size(v,2),1)*diag(d)'); %trial
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% dinv = 1./diag(d); % inv(diag(d))
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% vdinv=v.*(ones(size(v,2),1)*dinv'); %trial
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% xtx=vd*vd';
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% xtxinv = vdinv*vdinv';
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% %xty = phi'*y; % X'Y
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% uy = u'*y; %trial
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% xty = vd*uy; %trial
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% %Bh = xtx\xty; %inv(X'X)*(X'Y), k*m (ncoe*nvar).
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% Bh = xtxinv*xty;
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% %e = y - phi*Bh; % from Y = XB + U, e: (T-lags)*nvar
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% e = y - u*uy;
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%**** The following, though stable, is too slow *****
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%===== (Fast but perhaps less accurate) alternative to the above =========
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[xq,xr]=qr(phi,0);
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xtx=xr'*xr;
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xty=phi'*y;
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Bh = xr\(xr'\xty);
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e=y-phi*Bh;
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%===== (Fast but perhaps less accurate) alternative to the above =========
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%* not numerically stable way of computing e'*e
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%Sigu = y'*y-xty'*Bh;
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%Sigu = y'*(eye(ess)-phi*xtxinv*phi')*y; % probablly better way, commented out
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% by TZ, 2/28/98. See following
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%Sigu = y'*(eye(ess)-u*u')*y; % I think this is the best, TZ, 2/28/98
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% Note, u*u'=x*inv(x'x)*x.
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