73 lines
3.0 KiB
Matlab
73 lines
3.0 KiB
Matlab
function [h, lrcp] = hVectors(params, H, auxmodel, kind, id)
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% INPUTS
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% - params [double] (m+1)*1 vector, PAC parameters (lag polynomial coefficients and discount factor).
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% - H [double] (np*np) matrix, companion matrix of the VAR(p) model.
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% - auxmodel [char] kind of auxiliary model, possible values are: 'var' and 'trend_component'.
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% - kind [char] kind of expectation in PAC equation (See FRB/US doc), possible values are 'll', 'dl' and 'dd'.
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% - id [integer] scalar, index pointing to the target in the auxiliary model.
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%
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% OUTPUTS
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% - h [double] 1*n vector of weights (used to compute the linear combination of the variables in the companion VAR representation of the auxiliary model).
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% - lrcp [double] scalar, parameter for the growth neutrality correction.
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%
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% REMARKS
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% The parameters are ordered as follows in the params vector:
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%
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% params(1) ⟶ Error correction parameter.
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% params(2:end-1) ⟶ Autoregressive parameters.
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% params(end) ⟶ Discount factor.
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% Copyright © 2018-2024 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 <https://www.gnu.org/licenses/>.
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if nargout>1 && nargin<4
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error('Wrong number of Inputs/Outputs!')
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end
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[G, alpha, beta] = buildGmatrixWithAlphaAndBeta(params);
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A = [alpha; 1];
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A_1 = polyval(A, 1.0);
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A_b = polyval(A, beta);
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m = length(alpha);
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n = length(H);
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tmp = eye(n*m)-kron(G, transpose(H)); % inv(W2)
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switch kind
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case 'll' % (A.84), page 28 in Brayton, Davis and Tulip (2000) ⟹ The target is stationary (level-level).
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h = A_1*A_b*((kron(iota(m, m), H))'*(tmp\kron(iota(m, m), iota(n, id))));
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case 'dd' % (A.79), page 26 in Brayton, Davis and Tulip (2000) ⟹ The target appears in first difference as a dependent variable in the auxiliary model.
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h = A_1*A_b*(kron(iota(m, m)'*inv(eye(m)-G), H')*(tmp\kron(iota(m, m), iota(n, id))));
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case 'dl' % (A.74), page 24 in Brayton, Davis and Tulip (2000) ⟹ The target appears in level as a dependent variable in the auxiliary model.
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h = A_1*A_b*(kron(iota(m, m)'*inv(eye(m)-G), (H'-eye(length(H))))*(tmp\kron(iota(m, m), iota(n, id))));
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otherwise
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error('Unknown kind value in PAC model.')
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end
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if nargout>1
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if isequal(kind, 'll')
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lrcp = NaN;
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else
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d = A_1*A_b*(iota(m, m)'*inv((eye(m)-G)*(eye(m)-G))*iota(m, m));
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lrcp = (1-sum(params(2:end-1))-d);
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end
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end
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