74 lines
2.8 KiB
Modula-2
74 lines
2.8 KiB
Modula-2
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 = 1.00; // Do not change this calibration
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PopulationGrowth_ss = 1.00; // Do not change this calibration
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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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d = dseries([.5 1 1 1.04 15], 2000Q1, {'Efficiency'; 'EfficiencyGrowth'; 'Population'; 'PopulationGrowth'; 'PhysicalCapitalStock'});
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histval;
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Efficiency(0) = .5;
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EfficiencyGrowth(0) = 1;
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Population(0) = 1;
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PopulationGrowth(0) = 1.04;
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PhysicalCapitalStock(0) = 15;
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end;
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LongRunEfficiency = d.Efficiency*d.EfficiencyGrowth^(rho_x/(1-rho_x));
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LongRunPopulation = d.Population*d.PopulationGrowth^(rho_n/(1-rho_n));
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LongRunEfficiencyGrowth = EfficiencyGrowth_ss;
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LongRunPopulationGrowth = PopulationGrowth_ss;
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LongRunIntensiveCapitalStock = (s/(LongRunEfficiencyGrowth*LongRunPopulationGrowth-1+delta))^(1/(1-alpha)); //LongRunEfficiencyGrowth*LongRunPopulationGrowth*
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precision = 1e-6;
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T = 5*floor(log(precision)/log(max(rho_x, rho_n)));
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e = dseries(zeros(T, 2), 2000Q2, {'e_x'; 'e_n'});
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options_.solve_algo = 9;
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simulations = simul_backward_model([], T, e);
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if abs(simulations.Efficiency.data(end)-LongRunEfficiency.data)>1e-10
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error('Wrong long run level (Efficiency, diff=%s)!', num2str(abs(simulations.Efficiency.data(end)-LongRunEfficiency.data)))
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end
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if abs(simulations.Population.data(end)-LongRunPopulation.data)>1e-10
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error('Wrong long run level (Population, diff=%s)!', num2str(abs(simulations.Population.data(end)-LongRunPopulation.data)))
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end
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IntensiveCapitalStock = simulations.PhysicalCapitalStock/(simulations.Efficiency*simulations.Population);
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if abs(IntensiveCapitalStock.data(end)-LongRunIntensiveCapitalStock)>1e-3
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error('Wrong long run level (Intensive capital stock)!')
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end
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