Hello everyone,
I am trying to simulate the Ramsey-Cass-Koopmans model (deterministic) starting from initial values that off the steady state to see a path of convergence. However, I am getting the paths for k and c with all their values at their steady states (k,c)=(1.7378,0.9186). How to fix that (chatGPTs suggestions didn’t work so far)?
In addition, what is the correct way to specify the equation for capital: as a forward looking k(+1) = (1/GL_tilda)*((1-delta)k+k^alpha-c); or a backward looking k = (1/GL_tilda)((1-delta)*k(-1)+k(-1)^alpha-c);? Both cases produce the same result.
Thank you.
Argyn
Here is the mod-file:
var GL_tilda, k, c;
parameters gga, ggl, delta, theta, alpha, beta;
gga = 1.03; % gross growth rate of productivity
ggl = 1.02; % gross growth rate of population
delta = 0.1; % depreciation rate
theta = 3; % coefficient of CRRA
alpha = 0.3; % income share of capital
beta = 0.99; % what is the value for beta to match ? 4% growth rate
steady_state_model;
GL_tilda = gga*ggl;
k = ((gga^theta/beta - 1 + delta)/alpha)^(1/(alpha-1));
c = (1-delta)*k+k^alpha-GL_tilda*k;
end;
steady;
check;
model_diagnostics;
model;
% Assume F(K, L_tilda) = K^alpha*(A*L)^(1-alpha) => f(k) = k^alpha
% kstar = (((1+ga)^theta/beta - 1 + delta)/alpha)^(1/(alpha-1));
GL_tilda = gga*ggl;
k(+1) = (1/GL_tilda)*((1-delta)*k+k^alpha-c);
% k = (1/GL_tilda)*((1-delta)*k(-1)+k(-1)^alpha-c);
c(+1) = (1/gga)*beta^(1/theta)*(1-delta+alpha*k^(alpha-1))^(1/theta)*c;
end;
initval;
% NE quadrant
k = 5;
c = 2;
end;
perfect_foresight_setup(periods=50);
perfect_foresight_solver;
rplot k, c;