150 lines
4.6 KiB
Modula-2
150 lines
4.6 KiB
Modula-2
// --+ options: stochastic +--
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/* © 2022 Dynare Team
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*
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* This file 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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* It is distributed in the hope that it will be useful, but
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* 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 the file. If not, see <http://www.gnu.org/licenses/>.
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*/
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@#define USE_HISTVAL = 0
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var y1 y2 y3 ;
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varexo e1 e2 e3 u1 u2 u3 ;
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parameters a11 a12 a13 a21 a22 a23 a31 a32 a33 b11 b12 b13 b22 b23 b33 ;
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/*
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** Simulate the elements of the first order autoregressive matrix (we impose stability of the model, note that
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** inversion fails if the model is explosive, ie the autoregressive matrix has at least one root greater than
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** one in modulus) probably because of the propagation of roundoff errors.
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*/
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D = diag([.9 .7 .8]);
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P = randn(3,3);
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A = P*D*inv(P);
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a11 = A(1,1);
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a12 = A(1,2);
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a13 = A(1,3);
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a21 = A(2,1);
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a22 = A(2,2);
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a23 = A(2,3);
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a31 = A(3,1);
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a32 = A(3,2);
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a33 = A(3,3);
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b11 = .10;
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b12 = -.30;
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b13 = .05;
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b22 = .20;
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b23 = -.05;
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b33 = .10;
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model(linear);
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diff(y1) = a11*diff(y1(-1)) + a12*diff(y2(-1)) + a13*diff(y3(-1)) + b11*e1 + b12*e2 + b13*e3 + u1 ;
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diff(y2) = a21*diff(y1(-1)) + a22*diff(y2(-1)) + a23*diff(y3(-1)) + b22*e2 + b23*e3 + u2 ;
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diff(y3) = a31*diff(y1(-1)) + a32*diff(y2(-1)) + a33*diff(y3(-1)) + b33*e3 + u3 ;
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end;
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shocks;
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var e1 = 1.0;
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var e2 = 1.0;
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var e3 = 1.0;
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var u1 = .1;
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var u2 = .3;
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var u3 = .2;
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end;
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steady;
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check;
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@#if USE_HISTVAL
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histval;
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y1(0) = .1;
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y2(0) = .2;
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y3(0) = .3;
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y1(-1) = -.1;
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y2(-1) = -.2;
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y3(-1) = -.3;
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end;
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TrueData = simul_backward_model([], 200);
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@#else
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initdata = zeros(2, 3+3+3);
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initdata(1,1:3) = [-.1 -.2 -.3];
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initdata(2,1:3) = [.1 .2 .3];
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initialconditions = dseries(initdata, '1Y', vertcat(M_.endo_names(1:M_.orig_endo_nbr), M_.exo_names));
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TrueData = simul_backward_model(initialconditions, 200);
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@#endif
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// Set the periods where some of the endogenous variables will be constrained.
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subsample = 3Y:100Y;
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// Load the generated data
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SimulatedData = copy(TrueData);
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// Set the constrained paths for the endogenous variables (Output and PhysicalCapitalStock).
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constrainedpaths = SimulatedData{'y1','y2','y3'}(subsample);
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// Set the instruments (innovations used to control the paths for the endogenous variables).
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exogenousvariables = dseries([NaN(98, 3) TrueData{'u1','u2','u3'}.data(3:100,:)], '3Y', M_.exo_names);
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/* REMARK
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**
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** Here we will control y1, y2, and y3 with e1, e2 and e3, u1, u2 and u3 are treated as observed
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** exogenous variables.
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*/
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// Invert the model by calling the model_inversion routine.
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options_.dynatol.f = 1e-9;
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[endogenousvariables, exogenousvariables] = model_inversion(constrainedpaths, exogenousvariables, SimulatedData, M_, options_, oo_);
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// Check that all the constraints are satisfied.
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if max(abs(constrainedpaths(subsample).y1.data-endogenousvariables(subsample).y1.data))>1e-12
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error('Constraint on y1 path is not satisfied!')
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end
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if max(abs(constrainedpaths(subsample).y2.data-endogenousvariables(subsample).y2.data))>1e-12
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error('Constraint on y2 path is not satisfied!')
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end
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if max(abs(constrainedpaths(subsample).y3.data-endogenousvariables(subsample).y3.data))>1e-12
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error('Constraint on y3 path is not satisfied!')
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end
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if max(abs(exogenousvariables(subsample).u1.data-SimulatedData(subsample).u1.data))>1e-12
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error('Constraint on u1 path is not satisfied!')
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end
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if max(abs(exogenousvariables(subsample).u2.data-SimulatedData(subsample).u2.data))>1e-12
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error('Constraint on u2 path is not satisfied!')
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end
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if max(abs(exogenousvariables(subsample).u3.data-SimulatedData(subsample).u3.data))>1e-12
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error('Constraint on u3 path is not satisfied!')
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end
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// Check consistency of the results.
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if max(abs(exogenousvariables(subsample).e1.data-SimulatedData(subsample).e1.data))>1e-8
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error('Model inversion is not consistent with true innovations (e1)')
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end
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if max(abs(exogenousvariables(subsample).e2.data-SimulatedData(subsample).e2.data))>1e-8
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error('Model inversion is not consistent with true innovations (e3)')
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end
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if max(abs(exogenousvariables(subsample).e3.data-SimulatedData(subsample).e3.data))>1e-8
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error('Model inversion is not consistent with true innovations (e3)')
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end
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