Dear Professor Johannes Pfeifer,
I am trying to compute the transition path for the simplest rbc model with log utility and full depreciation. I am unable to find a reasonable transition path (although the “solution is found”, it does not find it, as you can see in the figure).
I have tried with multiple solvers. There appear to be no problem if delta (the depreciation rate) is set to a sufficiently low value. Do you have any insight on what could be the issue? I was trying to implement several simple algorithms for the case that we have a closed form solution, and I was surprised that I cannot get the path with Dynare.
Thanks a lot in advance for you time. The code is below.
%--Solving a simple RBC model var c k; predetermined_variables k; parameters alpha bet delta sigma k_b; alpha = 0.27; %parameter production function f=k^alpha bet = 0.994; %discount factor delta = 1; %depreciation rate sigma = 1; %risk aversion k_b = (alpha*bet/(1-bet*(1-delta)))^(1/(1-alpha)); %k in steady state model; %--- Eq 1 resource constraint k(+1)-(1-delta)*k+c = k^alpha; %--- Eq 2 Euler equation c^(-sigma) = bet*c(+1)^(-sigma)*(alpha*k^(alpha-1)+1-delta); end; initval; k = 0.1*k_b; end; endval; k = k_b; c = k_b^alpha-delta*k_b; end; resid; perfect_foresight_setup(periods=200); perfect_foresight_solver; %perfect_foresight_solver(stack_solve_algo=7, solve_algo=9); rplot k;