152 lines
4.2 KiB
Modula-2
152 lines
4.2 KiB
Modula-2
@#define extended_path_version = 1
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var Capital, Output, Labour, Consumption, Investment, Output1, Labour1, Consumption1, Output2, Labour2, Consumption2, Efficiency, efficiency, ExpectedTerm;
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varexo EfficiencyInnovation;
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parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma2;
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/*
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** Calibration
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*/
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beta = 0.990;
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theta = 0.357;
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tau = 2.000;
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alpha = 0.450;
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psi = -0.500;
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delta = 0.020;
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rho = 0.995;
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effstar = 1.000;
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sigma2 = 0.001;
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@#if extended_path_version
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rho = 0.800;
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@#endif
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external_function(name=mean_preserving_spread,nargs=2);
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model;
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efficiency = rho*efficiency(-1) + EfficiencyInnovation;
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Efficiency = effstar*exp(efficiency-mean_preserving_spread(rho,sigma2));
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(((Consumption1^theta)*((1-Labour1)^(1-theta)))^(1-tau))/Consumption1 - ExpectedTerm(1);
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ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital(-1))^(1-psi))+1-delta);
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((1-theta)/theta)*(Consumption1/(1-Labour1)) - (1-alpha)*(Output1/Labour1)^(1-psi);
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Output1 = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour1^psi))^(1/psi);
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Consumption2 = Output2;
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((1-theta)/theta)*(Consumption2/(1-Labour2)) - (1-alpha)*(Output2/Labour2)^(1-psi);
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Output2 = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour2^psi))^(1/psi);
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Consumption = (Output1 > Consumption1)*Consumption1 + (1-(Output1 > Consumption1))*Consumption2;
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Labour = (Output1 > Consumption1)*Labour1 + (1-(Output1 > Consumption1))*Labour2;
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Output = (Output1 > Consumption1)*Output1 + (1-(Output1 > Consumption1))*Output2;
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Capital = Output-Consumption + (1-delta)*Capital(-1);
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Investment = Capital - (1-delta)*Capital(-1);
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end;
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steady_state_model;
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efficiency = 0;
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Efficiency = effstar*exp(efficiency-mean_preserving_spread(rho,sigma2));
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// Compute steady state ratios.
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Output_per_unit_of_Capital=((1/beta-1+delta)/alpha)^(1/(1-psi));
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Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-delta;
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Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/Efficiency)^psi-alpha)/(1-alpha))^(1/psi);
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Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
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Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
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// Compute steady state share of capital.
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ShareOfCapital=alpha/(alpha+(1-alpha)*Labour_per_unit_of_Capital^psi);
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/// Compute steady state of the endogenous variables.
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Labour=1/(1+Consumption_per_unit_of_Labour/((1-alpha)*theta/(1-theta)*Output_per_unit_of_Labour^(1-psi)));
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Consumption = Consumption_per_unit_of_Labour*Labour;
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Capital = Labour/Labour_per_unit_of_Capital;
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Output = Output_per_unit_of_Capital*Capital;
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Investment = delta*Capital;
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ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital)^(1-psi))+1-delta);
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Output1 = Output;
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Output2 = Output;
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Labour1 = Labour;
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Labour2 = Labour;
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Consumption1 = Consumption;
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Consumption2 = Consumption;
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end;
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@#if extended_path_version
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shocks;
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var EfficiencyInnovation = sigma2;
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end;
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steady(nocheck);
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options_.maxit_ = 100;
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options_.ep.verbosity = 0;
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options_.ep.stochastic.order = 0;
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options_.ep.stochastic.nodes = 5;
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options_.console_mode = 0;
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ts = extended_path([],100);
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options_.ep.stochastic.order = 1;
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sts = extended_path([],100);
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options_.ep.stochastic.order = 2;
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sts2 = extended_path([],100);
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// options_.ep.stochastic.order = 3;
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// sts3 = extended_path([],100);
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save rbcii ts sts sts2 sts3;
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figure(1)
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plot(ts(2,:)-ts(4,:));
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figure(2)
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plot(sts(2,:)-sts(4,:));
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figure(3)
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plot(sts(2,:)-ts(2,:))
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figure(4)
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// plot([(ts(2,:)-ts(4,:))' (sts(2,:)-sts(4,:))' (sts2(2,:)-sts2(4,:))' (sts3(2,:)-sts3(4,:))'])
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plot([(ts(2,:)-ts(4,:))' (sts(2,:)-sts(4,:))'])
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@#else
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shocks;
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var EfficiencyInnovation;
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periods 1;
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values -.4;
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end;
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steady;
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options_.maxit_ = 100;
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simul(periods=4000);
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n = 100;
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figure('Name','(rbcii) Investment.');
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plot(Output(1:n)-Consumption(1:n),'-b','linewidth',2)
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figure('Name','(rbcii) Lagrange multiplier associated to the positivity constraint on investment.');
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plot(LagrangeMultiplier(1:n),'-b','linewidth',2)
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@#endif |