1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
|
function [GS,pickn,ok,uis,uiu,vs]=gstate(G1,impact,pick)
%function [GS,pickn,ok,uis,vs]=gstate(G1,impact,pick)
% G1: the coefficient on lagged y from the output of gensys.m.
% impact:the coefficient on exogenous shocks from the output of gensys.m
% pick: an optional guess at a matrix of coefficients that extracts
% the state vector from y
% ok: 0 if pick matrix is just no good.
% 1 if pick matrix is usable forward, but loses initial date information
% 2 if pick matrix is not usable forward, is part of a correct state vector, but is not complete
% 3 if pick matrix is usable forward, is part of a correct state vector, but is not complete
% 4 if pick matrix is not usable forward, summarizes past, but is redundant
% 5 if pick matrix is usable forward, summarizes past, but is redundant
% 6 if pick matrix summarizes past and is not redundant, but is not usable forward
% 7 if pick matrix is perfect, both forward and as history summary
% pickn: a matrix of coefficients that extracts the state vector from y. Equal
% to pick if pick is supplied and ok=1; otherwise, an ok-maximizing pick matrix that
% is somewhat similar to pick.
% GS: the matrix of coefficients on the lagged state variable
% uis,vs: If uis'*vs is square and full rank, ok=7 is possible, otherwise not. If ok<2, an ok>2 can be found by trying
% a pick in the row space of vs'. Any pick with pick*uis full column rank will provide a foward state
% (i.e. ok an odd number).
% uiu: uiu'y(t)=0, and this is interpretable as the decision rule setting controls as functions of the states.
% The solution was in the form y(t)=G1*y(t-1)+impact*z(t). Now it's in the form y(t)=GS*pickn*y(t-1)+impact*z(t).
% In general, pickn is mxn with m<n.
%
% Copyright (C) 1997-2012 Tao Zha
%
% This free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% It is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% If you did not received a copy of the GNU General Public License
% with this software, see <http://www.gnu.org/licenses/>.
%
REALSMALL=1e-9;
[nr,nc]=size(G1);
%if nr<nc
% G1=[G1;zeros(nc-nr,nc)];
%end
[u d v]=svd(G1);
top=find(diag(d)>REALSMALL);
nd=top(end);
us=u(:,top);
uu=u(:,top+1:end);
d=d(top,top);
vs=v(:,top);
if nargin<=2
pick=vs';
vp=v;
vps=vs;
dp=eye(nd);
ups=eye(nr,nd);
ndp=nd;
else
[up dp vp]=svd(pick);
topp=find(diag(dp)>REALSMALL);
ndp=topp(end);
vps=vp(:,topp);
dp=dp(topp,topp);
ups=up(:,topp);
end
% If we were worried about efficiency, we'd skip some of this when pick=vs.
%Does pick summarize history? (pick in v' row space, v in vp' row space).
pinv=all(all((pick'-vs*vs'*pick').^2<REALSMALL));
vinp=all(all((vs-vps*vps'*vs).^2<REALSMALL));
okpast=pinv+vinp;
% Does pick summarize all current info? (impact in us column space, pick*uu full rank)
[ui,di,vi]=svd([impact us]);
topi=find(diag(di)>REALSMALL);
ndi=length(topi);
uis=ui(:,topi);
uiu=ui(:,ndi+1:size(ui,2));
if ndi<size(G1,1)
if(size(pick,1)<size(uis,2))
oknow=0;
else
[ut,dt,vt]=svd(pick*uis);
toppu=find(diag(dt)>REALSMALL);
if length(toppu)<size(us,2)
oknow=0;
else
oknow=1;
end
end
else
oknow=0;
end
if vinp
GS=G1/pick;
pickn=pick;
elseif pinv
r=vs-vps*vps'*vs;
[ur,dr,vr]=svd(r);
topr=find(dr>REALSMALL);
p2=ur(:,topr);
pickn=[pick;p2'];
GS=G1/pickn;
elseif oknow
GS=G1/[pick;uiu'];
GS=GS(:,1:size(pick,1));
pickn=pick;
else
pickn=vs';
GS=us*d;
end
ok=oknow+2*pinv+4*vinp;
|
