121 lines
3.5 KiB
Modula-2
121 lines
3.5 KiB
Modula-2
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, sigma2;
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beta = 0.9900;
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theta = 0.3570;
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tau = 2.0000;
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alpha = 0.4500;
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psi = -0.1000;
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delta = 0.0200;
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rho = 0.8000;
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effstar = 1.0000;
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sigma2 = 0;
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model;
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// Eq. n°1:
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efficiency = rho*efficiency(-1) + 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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Capital = Output-Consumption + (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 = EfficiencyInnovation/(1-rho);
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Efficiency = effstar*exp(efficiency);
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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)
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*(alpha*((Output/Capital)^(1-psi))+1-delta);
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end;
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steady;
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ik = varlist_indices('Capital',M_.endo_names);
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CapitalSS = oo_.steady_state(ik);
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histval;
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Capital(0) = CapitalSS/2;
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end;
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perfect_foresight_setup(periods=400);
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perfect_foresight_solver(stack_solve_algo=0);
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if ~oo_.deterministic_simulation.status
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error('Perfect foresight simulation failed')
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end
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oo0 = oo_;
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perfect_foresight_setup(periods=400);
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perfect_foresight_solver(stack_solve_algo=1);
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if ~oo_.deterministic_simulation.status
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error('Perfect foresight simulation failed')
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end
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oo1 = oo_;
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maxabsdiff = max(max(abs(oo0.endo_simul-oo1.endo_simul)));
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if max(max(abs(oo0.endo_simul-oo1.endo_simul)))>options_.dynatol.x
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error('stack_solve_algo={0,1} return different paths for the endogenous variables!')
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else
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skipline()
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fprintf('Maximum (absolute) differrence between paths is %s', num2str(maxabsdiff))
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skipline()
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end
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% Also test stack_solve_algo=6, which is a synonymous for stack_solve_algo=1
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perfect_foresight_setup(periods=400);
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perfect_foresight_solver(stack_solve_algo=6);
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if ~oo_.deterministic_simulation.status
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error('Perfect foresight simulation failed')
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end
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oo6 = oo_;
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maxabsdiff = max(max(abs(oo0.endo_simul-oo6.endo_simul)));
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if max(max(abs(oo0.endo_simul-oo6.endo_simul)))>options_.dynatol.x
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error('stack_solve_algo={0,6} return different paths for the endogenous variables!')
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else
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skipline()
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fprintf('Maximum (absolute) differrence between paths is %s', num2str(maxabsdiff))
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skipline()
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end
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