/* Example that triggers homotopy in perfect foresight simulation with
   expectation errors, and tests linearization. */

var Consumption, Capital, LoggedProductivity;

varexo LoggedProductivityInnovation;

parameters beta, alpha, delta, rho;

beta = .985;
alpha = 1/3;
delta = alpha/10;
rho = .9;

model;
  1/Consumption = beta/Consumption(1)*(alpha*exp(LoggedProductivity(1))*Capital^(alpha-1)+1-delta);
  Capital = exp(LoggedProductivity)*Capital(-1)^alpha+(1-delta)*Capital(-1)-Consumption;
  LoggedProductivity = rho*LoggedProductivity(-1)+LoggedProductivityInnovation;
end;

initval;
  LoggedProductivityInnovation = 0;
end;

steady;

endval;
  LoggedProductivityInnovation = 0.6;
end;

endval(learnt_in = 5);
  LoggedProductivityInnovation = 1;
end;

perfect_foresight_with_expectation_errors_setup(periods=200);
perfect_foresight_with_expectation_errors_solver(homotopy_max_completion_share = 0.8, homotopy_linearization_fallback, steady_solve_algo = 13);

if ~oo_.deterministic_simulation.status
   error('Perfect foresight simulation failed')
end