125 lines
4.5 KiB
Modula-2
125 lines
4.5 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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var Efficiency // $A$
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EfficiencyGrowth // $X$
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Population // $L$
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PopulationGrowth // $N$
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Output // $Y$
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PhysicalCapitalStock ; // $K$
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varexo e_x // $\varepsilon_x$
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e_n ; // $\varepsilon_n$
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parameters alpha // $\alpha$
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epsilon // $\varepsilon$
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delta // $\delta$
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s // $s$
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rho_x // $\rho_x$
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rho_n // $\rho_n$
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EfficiencyGrowth_ss // $X^{\star}$
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PopulationGrowth_ss ; // $N^{\star}$
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alpha = .33;
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epsilon = .70;
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delta = .02;
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s = .20;
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rho_x = .90;
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rho_n = .95;
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EfficiencyGrowth_ss = 1.02;
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PopulationGrowth_ss = 1.02;
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if s>delta*alpha^(-epsilon/(epsilon-1))
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disp('The model admits a unique positive steady state.')
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end
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model;
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Efficiency = EfficiencyGrowth*Efficiency(-1);
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EfficiencyGrowth/EfficiencyGrowth_ss = (EfficiencyGrowth(-1)/EfficiencyGrowth_ss)^(rho_x)*exp(e_x);
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Population = PopulationGrowth*Population(-1);
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PopulationGrowth/PopulationGrowth_ss = (PopulationGrowth(-1)/PopulationGrowth_ss)^(rho_n)*exp(e_n);
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Output = (alpha*PhysicalCapitalStock(-1)^((epsilon-1)/epsilon)+(1-alpha)*(Efficiency*Population)^((epsilon-1)/epsilon))^(epsilon/(epsilon-1));
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PhysicalCapitalStock = (1-delta)*PhysicalCapitalStock(-1) + s*Output;
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end;
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histval;
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Efficiency(0) = 1;
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EfficiencyGrowth(0) = 1.02;
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Population(0) = 1;
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PopulationGrowth(0) = 1.02;
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PhysicalCapitalStock(0) = 1;
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end;
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shocks;
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var e_x = 0.005;
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var e_n = 0.001;
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end;
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TrueData = simul_backward_nonlinear_model([], 100, options_, M_, oo_);
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// Set the periods where some of the endogenous variables will be constrained.
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subsample = 2Y:100Y;
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// Copy 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{'Output','PhysicalCapitalStock'}(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(100, 2), 1Y, {'e_x';'e_n'});
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// Invert the model by calling the model_inversion routine.
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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.Output(subsample).data-endogenousvariables.Output(subsample).data))>1e-12
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error('Constraint on Output path is not satisfied!')
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end
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if max(abs(constrainedpaths.PhysicalCapitalStock(subsample).data-endogenousvariables.PhysicalCapitalStock(subsample).data))>1e-12
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error('Constraint on PhysicalCapitalStock path is not satisfied!')
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end
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// Check the consistency of the deduced innovations with the true innovations.
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/* REMARK
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**
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** In this model the two innovatons, on population growth and efficiency growth, cannot be identified simulatneously because
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** what matters for the dynamic of the physical capital stock and the output is the same non linear function of the two innovations.
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** This explains why we only check that the product of Efficiency and Population are the same in the simulated (true) data and in the
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** data returned by the inversion routine.
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*/
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TrueEfficiency = TrueData.Efficiency;
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TruePopulation = TrueData.Population;
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TrueEfficiencyTimesPopulation = TrueEfficiency*TruePopulation;
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EfficiencyTimesPopulation = endogenousvariables.Efficiency*endogenousvariables.Population;
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if isoctave
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tolerance=2e-5;
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else
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tolerance=1e-5;
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end
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if max(abs(TrueEfficiencyTimesPopulation(2Y:100Y).data-EfficiencyTimesPopulation(2Y:100Y).data))>tolerance
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error('Model inversion is not consistent with true innovations.')
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end
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