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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(block,bytecode,cutoff=0);
// 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;
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/effstar)^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;
Efficiency=effstar;
efficiency=0;
ExpectedTerm=beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)
*(alpha*((Output/Capital)^(1-psi))+1-delta);
LagrangeMultiplier=0;
end;
steady;
shocks;
var EfficiencyInnovation;
periods 4, 5, 6, 7, 8;
values 0.04, 0.05, 0.06, 0.07, 0.08;
end;
perfect_foresight_setup(periods=300);
perfect_foresight_solver;
if ~oo_.deterministic_simulation.status
error('Perfect foresight simulation failed')
end
rplot Consumption;
rplot Capital;
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