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var Capital, Output, Labour, Consumption, Efficiency, efficiency, ExpectedTerm;
varexo EfficiencyInnovation;
parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma2;
beta = 0.9900;
theta = 0.3570;
tau = 2.0000;
alpha = 0.4500;
psi = -0.1000;
delta = 0.0200;
rho = 0.8000;
effstar = 1.0000;
sigma2 = 0;
model;
// Eq. n°1:
efficiency = rho*efficiency(-1) + EfficiencyInnovation;
// Eq. n°2:
Efficiency = effstar*exp(efficiency);
// Eq. n°3:
Output = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour^psi))^(1/psi);
// Eq. n°4:
Capital = Output-Consumption + (1-delta)*Capital(-1);
// Eq. n°5:
((1-theta)/theta)*(Consumption/(1-Labour)) - (1-alpha)*(Output/Labour)^(1-psi);
// Eq. n°6:
(((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption = ExpectedTerm(1);
// Eq. n°7:
ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital(-1))^(1-psi))+(1-delta));
end;
steady_state_model;
efficiency = EfficiencyInnovation/(1-rho);
Efficiency = effstar*exp(efficiency);
Output_per_unit_of_Capital=((1/beta-1+delta)/alpha)^(1/(1-psi));
Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-delta;
Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/Efficiency)^psi-alpha)/(1-alpha))^(1/psi);
Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
% Compute steady state share of capital.
ShareOfCapital=alpha/(alpha+(1-alpha)*Labour_per_unit_of_Capital^psi);
% Compute steady state of the endogenous variables.
Labour=1/(1+Consumption_per_unit_of_Labour/((1-alpha)*theta/(1-theta)*Output_per_unit_of_Labour^(1-psi)));
Consumption=Consumption_per_unit_of_Labour*Labour;
Capital=Labour/Labour_per_unit_of_Capital;
Output=Output_per_unit_of_Capital*Capital;
ExpectedTerm=beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)
*(alpha*((Output/Capital)^(1-psi))+1-delta);
end;
steady;
ik = varlist_indices('Capital',M_.endo_names);
CapitalSS = oo_.steady_state(ik);
histval;
Capital(0) = CapitalSS/2;
end;
perfect_foresight_setup(periods=400);
perfect_foresight_solver(stack_solve_algo=0);
if ~oo_.deterministic_simulation.status
error('Perfect foresight simulation failed')
end
oo0 = oo_;
perfect_foresight_setup(periods=400);
perfect_foresight_solver(stack_solve_algo=1);
if ~oo_.deterministic_simulation.status
error('Perfect foresight simulation failed')
end
oo1 = oo_;
maxabsdiff = max(max(abs(oo0.endo_simul-oo1.endo_simul)));
if max(max(abs(oo0.endo_simul-oo1.endo_simul)))>options_.dynatol.x
error('stack_solve_algo={0,1} return different paths for the endogenous variables!')
else
skipline()
fprintf('Maximum (absolute) difference between paths is %s', num2str(maxabsdiff))
skipline()
end
% Also test stack_solve_algo=6, which is a synonymous for stack_solve_algo=1
perfect_foresight_setup(periods=400);
perfect_foresight_solver(stack_solve_algo=6);
if ~oo_.deterministic_simulation.status
error('Perfect foresight simulation failed')
end
oo6 = oo_;
maxabsdiff = max(max(abs(oo0.endo_simul-oo6.endo_simul)));
if max(max(abs(oo0.endo_simul-oo6.endo_simul)))>options_.dynatol.x
error('stack_solve_algo={0,6} return different paths for the endogenous variables!')
else
skipline()
fprintf('Maximum (absolute) difference between paths is %s', num2str(maxabsdiff))
skipline()
end
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