189 lines
6.8 KiB
Matlab
189 lines
6.8 KiB
Matlab
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_reac_function_4v(lags,nvar,nexo,indxC0Pres)
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% vlist = [ff+ch fh dpgdp ffr)
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%
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% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
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% See Waggoner and Zha's Gibbs sampling paper.
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%
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% HERE FIRTS 3 EQUATIONS ARE AR2 AND THE LAST EQUATION IS AN UNRESTRICTED
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% REACTION FUNCTION 2 lags
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%
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% q_m: quarter or month
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% lags: the maximum length of lag
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% nvar: number of endogeous variables
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% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
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% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
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% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
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% These restrictions have to be manually and carefully keyed in.
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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.
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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 is a total of exogenous 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.
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% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
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% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
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% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
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% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
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% In the jth cell representing equation, we have 4 columns:
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% 1st: the jth column (equation) of A+ or A0: f_j or a_j
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% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
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% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
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% 4th: the number s such that f_j(i) = s * a_j(h) holds.
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%
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% Tao Zha, May 2000
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% BN
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nvar=4;
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lags=4;
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nexo=1;
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Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
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Vi = cell(nvar,1); % initializing for lagged and exogenous variables
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n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
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np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
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if (nargin==2)
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nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
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elseif (nargin==3)
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indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
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end
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k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
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Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
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Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
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% Row corresponds to equation. 0 means no restriction.
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% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
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%nfvar = 6; % number of foreign (Granger causing) variables
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%nhvar = nvar-nfvar; % number of home (affected) variables.
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%-------------------------------------------------------------
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% Beginning the manual input of the restrictions one quation at a time
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%-------------------------------------------------------------
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%
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%======== The first equation ===========
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Qi(1:3,:,1) = [
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0 1 0 0
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0 0 1 0
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0 0 0 1
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];
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%======== The second equation ===========
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Qi(1:2,:,2) = [
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0 0 1 0
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0 0 0 1
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];
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%======== The third equation =========== NOTE THAT WE FORBID A
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%CONTEMPORANEOUS IMPACT OF OUTPUTON PRICES TO AVOID A CONSTRAINT THAT
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%INVOLVE A0 and Aplus
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Qi(1:3,:,3) = [
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1 0 0 0
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0 1 0 0
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0 0 0 1
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];
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%======== The fourth equation ===========
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% Restrictions on the A+ in order to focus strictly on the reaction fucntion
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% indicates free parameterers X i
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% Ap = [
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% X X X X
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% X X X X
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% -a1 -b1 X X
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% a1 b1 0 X (1st lag)
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% X X X X
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% X X X X
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% -a2 -b2 X X
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% b2 b2 0 X (2nd lag)
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% X 0 X X
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% X X X X
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% -a3 -b3 X X
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% a3 a3 0 X (3rd lag)
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% X X X X
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% X X X X
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% -a4 -b4 X X
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% a4 b4 0 X (4th lag)
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% X X X X (constant terms)
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% ];
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k=nvar*lags+nexo;
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Ri = zeros(k,k,nvar);
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% constraints on IS curve /conso+corporate investment
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for nv=1:2
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for ll=1:lags
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Ri(ll,3+lags*(ll-1),nv)=1;
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Ri(ll,4+lags*(ll-1),nv)=1;
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end
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end
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% constraints on IS curve /conso+corporate investment only on the long run
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% impact
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% for nv=1:2
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% for ll=1:lags
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% Ri(1,3+lags*(ll-1),nv)=1;
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% Ri(1,4+lags*(ll-1),nv)=1;
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% end
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% end
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% constraints on Ph curve / inflation does not react to interest rates
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for ll=1:lags
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Ri(ll,4+lags*(ll-1),3)=1;
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end
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for n=1:nvar % initializing loop for each equation
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Ui{n} = null(Qi(:,:,n));
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Vi{n} = null(Ri(:,:,n));
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n0(n) = size(Ui{n},2);
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np(n) = size(Vi{n},2);
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end
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%(2)-------------------------------------------------------------
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% Cross-A0-and-A+ rerestrictions one quation at a time
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% i.e., the first, second, ..., kjth, ..., equation
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%(2)-------------------------------------------------------------
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%
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if indxC0Pres
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neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
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ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
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% 1st: the jth column (equation) of A+ or A0: f_j or a_j
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% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
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% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
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% 4th: the number s such that f_j(i) = s * a_j(h) holds.
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%** 1st equation
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ixmC0Pres{1} = [1 2 2 1
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1 7 1 1];
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%** 2nd equation
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ixmC0Pres{2} = [2 2 2 2];
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%** 3rd equation
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ixmC0Pres{3} = [3 7 1 1
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3 2 2 1];
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% % 4 columns.
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% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
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% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
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% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
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% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
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% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
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else
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ixmC0Pres = NaN;
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end
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