94 lines
3.0 KiB
Modula-2
94 lines
3.0 KiB
Modula-2
/*
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* This model shows how to use the differentiate_forward_vars option to simulate
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* perfect foresight models when the steady state is unknown
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* or when the model is very persistent. In this file, we consider an RBC model
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* with a CES technology and very persistent productivity shock. We set the
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* autoregressive parameter of this exogenous productivity to 0.999, so that
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* in period 400 the level of productivity, after an initial one percent shock,
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* is still 0.67\% above its steady state level.
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*
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* Written by Stéphane Adjemian. For more information, see
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* http://gitlab.ithaca.fr/Dynare/differentiate-forward-variables
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*/
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var Capital, Output, Labour, Consumption, Efficiency, efficiency, ExpectedTerm;
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varexo EfficiencyInnovation;
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parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma;
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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 = 30.000;
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alpha = 0.450;
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psi = -1.000; // So that the elasticity of substitution between inputs is 1/(1-psi)=1/10
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delta = 0.020;
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rho = 0.999;
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effstar = 1.000;
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sigma = 0.010;
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model(differentiate_forward_vars);
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// Eq. n°1:
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efficiency = rho*efficiency(-1) + sigma*EfficiencyInnovation;
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// Eq. n°2:
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Efficiency = effstar*exp(efficiency);
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// Eq. n°3:
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Output = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour^psi))^(1/psi);
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// Eq. n°4:
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Consumption + Capital - Output - (1-delta)*Capital(-1);
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// Eq. n°5:
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((1-theta)/theta)*(Consumption/(1-Labour)) - (1-alpha)*(Output/Labour)^(1-psi);
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// Eq. n°6:
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(((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption - ExpectedTerm(1);
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// Eq. n°7:
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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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end;
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steady_state_model;
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efficiency = 0;
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Efficiency = effstar;
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// Compute some 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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ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital)^(1-psi))+1-delta);
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end;
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shocks;
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var EfficiencyInnovation;
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periods 1;
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values 1;
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end;
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steady;
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check;
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perfect_foresight_setup(periods=500);
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perfect_foresight_solver;
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