sur: first draft
Houtan Bastani
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74fe63c945
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7a61bff6c4
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function sur(ds, varargin)
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%function sur(ds)
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% Run a Seemingly Unrelated Regression on the provided equations
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%
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% INPUTS
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% ds [dseries] data
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%
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% OUTPUTS
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% none
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%
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% SPECIAL REQUIREMENTS
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% none
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% Copyright (C) 2017 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 <http://www.gnu.org/licenses/>.
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global M_ oo_
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%% Check input
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assert(nargin == 1 || nargin == 3, 'Incorrect number of arguments passed to sur');
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jsonfile = [M_.fname '_original.json'];
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if exist(jsonfile, 'file') ~= 2
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error('Could not find %s! Please use the json option (See the Dynare invocation section in the reference manual).', jsonfile);
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end
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%% Get Equations
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jsonmodel = loadjson(jsonfile);
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jsonmodel = jsonmodel.model;
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[lhs, rhs, lineno] = getEquationsByTags(jsonmodel, varargin{:});
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m = length(lhs);
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if m <= 1
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error('SUR estimation requires the selection of at least two equations')
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end
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%% Construct regression matrices
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Y = dseries();
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Xi = cell(m, 1);
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pnamesall = [];
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vwlagsall = [];
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for i = 1:m
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Y = [Y ds{lhs{i}}];
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rhs_ = strsplit(rhs{i}, {'+','-','*','/','^','log(','exp(','(',')'});
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rhs_(cellfun(@(x) all(isstrprop(x, 'digit')), rhs_)) = [];
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vnames = setdiff(rhs_, cellstr(M_.param_names));
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regexprnoleads = cell2mat(strcat('(', vnames, {'\(\d+\))|'}));
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if ~isempty(regexp(rhs{i}, regexprnoleads(1:end-1), 'match'))
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error(['olseqs: you cannot have leads in equation on line ' ...
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lineno{i} ': ' lhs{i} ' = ' rhs{i}]);
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end
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regexpr = cell2mat(strcat('(', vnames, {'\(-\d+\))|'}));
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vwlags = regexp(rhs{i}, regexpr(1:end-1), 'match');
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% Find parameters
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pnames = cell(1, length(vwlags));
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for j = 1:length(vwlags)
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regexmatch = regexp(rhs{i}, ['(\w*\*?)?' strrep(strrep(vwlags{j}, '(', '\('), ')', '\)') '(\*?\w*)?'], 'match');
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regexmatch = strsplit(regexmatch{:}, '*');
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assert(length(regexmatch) == 2);
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if strcmp(vwlags{j}, regexmatch{1})
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pnames{j} = regexmatch{2};
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else
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pnames{j} = regexmatch{1};
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end
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end
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pnamesall = [pnamesall pnames];
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vwlagsall = [vwlagsall vwlags];
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Xi{i} = cellfun(@eval, strcat('ds.', vwlags), 'UniformOutput', false);
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end
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fp = Y.firstobservedperiod;
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lp = Y.lastobservedperiod;
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for i = 1:m
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X = dseries();
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for j = 1:length(Xi{i})
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X = [X dseries(Xi{i}{j}.data, Xi{i}{j}.dates, ['V' num2str(i) num2str(j)])];
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end
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Xi{i} = X;
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fp = max(fp, X.firstobservedperiod);
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lp = min(lp, X.lastobservedperiod);
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end
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Y = Y(fp:lp).data(:);
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X = [];
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for i = 1:m
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Xi{i} = Xi{i}(fp:lp).data;
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ind = size(X);
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X(ind(1)+1:ind(1)+size(Xi{i}, 1), ind(2)+1:ind(2)+size(Xi{i},2)) = Xi{i};
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end
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%% Estimation
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nobs = length(fp:lp);
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nvars = size(X, 2);
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[q, r] = qr(X, 0);
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xpxi = (r'*r)\eye(nvars);
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resid = Y - X * (r\(q'*Y));
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resid = reshape(resid, nobs, m);
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oo_.sur.s2 = resid'*resid/nobs;
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tmp = kron(inv(oo_.sur.s2), eye(nobs));
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oo_.sur.beta = (X'*tmp*X)\X'*tmp*Y;
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for j = 1:length(pnamesall)
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M_.params(strmatch(pnamesall{j}, M_.param_names, 'exact')) = oo_.sur.beta(j);
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end
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% Yhat
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oo_.sur.Yhat = X * oo_.sur.beta;
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% Residuals
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oo_.sur.resid = Y - oo_.sur.Yhat;
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%% Calculate statistics
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oo_.sur.dof = nobs;
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% Estimate for sigma^2
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SS_res = oo_.sur.resid'*oo_.sur.resid;
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oo_.sur.s2 = SS_res/oo_.sur.dof;
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% R^2
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ym = Y - mean(Y);
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SS_tot = ym'*ym;
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oo_.sur.R2 = 1 - SS_res/SS_tot;
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% Adjusted R^2
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oo_.sur.adjR2 = oo_.sur.R2 - (1 - oo_.sur.R2)*nvars/(oo_.sur.dof-1);
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% Durbin-Watson
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ediff = oo_.sur.resid(2:nobs) - oo_.sur.resid(1:nobs-1);
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oo_.sur.dw = (ediff'*ediff)/SS_res;
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% Standard Error
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oo_.sur.stderr = sqrt(oo_.sur.s2*diag(xpxi));
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% T-Stat
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oo_.sur.tstat = oo_.sur.beta./oo_.sur.stderr;
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%% Print Output
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fprintf('SUR Estimation');
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if nargin == 1
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fprintf(' of all equations')
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else
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fprintf(' [%s = {', varargin{1});
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for i = 1:length(varargin{2})
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if i ~= 1
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fprintf(', ');
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end
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fprintf('%s', varargin{2}{i});
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end
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fprintf('}]');
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end
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fprintf('\n Dependent Variable: %s\n', lhs{i});
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fprintf(' No. Independent Variables: %d\n', nvars);
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fprintf(' Observations: %d\n', nobs);
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maxstrlen = 0;
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for j=1:length(vwlagsall)
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slen = length(vwlagsall{j});
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if slen > maxstrlen
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maxstrlen = slen;
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end
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end
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titlespacing = repmat(' ', 1, 4 + maxstrlen + 4) ;
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fprintf('%sCoefficients t-statistic Std. Error\n', titlespacing);
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fprintf('%s____________ ____________ ____________\n\n', titlespacing);
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format = [' %-' num2str(maxstrlen) 's'];
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for j = 1:length(vwlagsall)
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fprintf(format, vwlagsall{j});
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fprintf('%12.5f %12.5f %12.5f\n', ...
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oo_.sur.beta(j), ...
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oo_.sur.tstat(j), ...
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oo_.sur.stderr(j));
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end
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fprintf('\n R^2: %f\n', oo_.sur.R2);
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fprintf(' R^2 Adjusted: %f\n', oo_.sur.adjR2);
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fprintf(' s^2: %f\n', oo_.sur.s2);
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fprintf(' Durbin-Watson: %f\n', oo_.sur.dw);
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fprintf('%s\n\n', repmat('-', 1, 4 + maxstrlen + 4 + 44));
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end
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@ -30,4 +30,6 @@ ds0 = dseries(zeros(30, 3), 1, {'ffr', 'unrate', 'cpi'});
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olseqs(ds1, 'eqnum', {'ffr', 'cpi'});
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sur(ds1);
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plot_contributions('eqnum', 'ffr', ds1, ds0);
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