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// Example that triggers homotopy in perfect foresight simulation.
// Simulation starts out of steady state and returns to it.
var Consumption, Capital, LoggedProductivity;
varexo LoggedProductivityInnovation;
parameters beta, alpha, delta, rho;
beta = .985;
alpha = 1/3;
delta = alpha/10;
rho = .9;
model;
[name='Euler equation'] // This is an equation tag!
1/Consumption = beta/Consumption(1)*(alpha*exp(LoggedProductivity(1))*Capital^(alpha-1)+1-delta);
[name='Physical capital stock law of motion']
Capital = exp(LoggedProductivity)*Capital(-1)^alpha+(1-delta)*Capital(-1)-Consumption;
[name='Logged productivity law of motion']
LoggedProductivity = rho*LoggedProductivity(-1)+LoggedProductivityInnovation;
end;
steady_state_model;
LoggedProductivity = LoggedProductivityInnovation/(1-rho);
Capital = (exp(LoggedProductivity)*alpha/(1/beta-1+delta))^(1/(1-alpha));
Consumption = exp(LoggedProductivity)*Capital^alpha-delta*Capital;
end;
set_time(1Q1);
initval;
LoggedProductivityInnovation = 0;
LoggedProductivity = 10;
Capital = 1;
Consumption=2.02049;
end;
steady;
histval;
Capital(0)=17.9836;
LoggedProductivity(0)=10;
end;
perfect_foresight_setup(periods=200);
perfect_foresight_solver;
if ~oo_.deterministic_simulation.status
error('Perfect foresight simulation failed')
end
plot(Simulated_time_series.Capital(1Q1:25Q4));
if max(abs(oo_.endo_simul(:,1)-M_.endo_histval))>1e-6
error('Homotopy changed initial conditions')
end
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