92 lines
2.3 KiB
Modula-2
92 lines
2.3 KiB
Modula-2
close all
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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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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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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 = 1.0;
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PopulationGrowth_ss = 1.0;
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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 = PhysicalCapitalStock(-1)^alpha*(Efficiency*Population)^(1-alpha);
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PhysicalCapitalStock = (1-delta)*PhysicalCapitalStock(-1) + s*Output;
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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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histval;
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Efficiency(0) = 1;
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EfficiencyGrowth(0) = .5;
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Population(0) = 1;
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PopulationGrowth(0) = .5;
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PhysicalCapitalStock(0) = 1;
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end;
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/*
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** First approach: Use the covariance matrix to define the impulses.
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*/
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// Define the shocks for which we want to compute the IRFs
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listofshocks = {'e_x', 'e_n'};
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// Define the variables for which we want to compute the IRFs
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listofvariables = {'Efficiency', 'Population', 'Output'};
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// Compute the IRFs
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irfs1 = backward_model_irf([], dseries(), listofshocks, listofvariables, 50);
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/*
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** Second approach: Explicitely comunnicate the paths for the exogneous variables.
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*/
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x0 = zeros(50,2);
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x0_1 = x0;
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x0_2 = x0;
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x0_1(1,1) = sqrt(M_.Sigma_e(1,1));
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x0_2(1,2) = sqrt(M_.Sigma_e(2,2));
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simshocks = {dseries(x0_1, 2, M_.exo_names), dseries(x0_2, 2, M_.exo_names) };
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// Compute the IRFs
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irfs2 = backward_model_irf([], dseries(), simshocks, listofvariables, 50);
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/*
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** Check that the two approaches do provide the same results.
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*/
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verbatim;
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if max(abs(irfs1.e_x.Efficiency.data-irfs2.experiment_1.Efficiency.data))>1e-12
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error('There is something wrong in the IRFs.')
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end
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if max(abs(irfs1.e_x.Output.data-irfs2.experiment_1.Output.data))>1e-12
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error('There is something wrong in the IRFs.')
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end
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end; |