I am trying to calibrating my parameters for my OLG model to target k/y=2.8 naturkapital/y=0.9 and humankapital/y=2.4.
Can someone help me out?
% 1.1 Define endogenous variables
%--------------------------------------------------------------------------
var s, r, w, k, welfare, welfare1, cons_m, cons_o, naturkapital, cons, y, e, humankapital, budgetconstraint, k_y, naturkapital_y, humankapital_y;
// e=educational expenditure
predetermined_variables k humankapital;
%--------------------------------------------------------------------------
% 1.2 Define exogenous variables
%--------------------------------------------------------------------------
varexo alpha ;
%--------------------------------------------------------------------------
% 1.3 Define parameters
%--------------------------------------------------------------------------
parameters sigma, delta, tau, h0, h1, h2, h3, gamma, A, k_value, cons_value, phi, beta, theta, eta, dep, humankapital_value;
%--------------------------------------------------------------------------
% 1.4 Declare parameter values
%--------------------------------------------------------------------------
sigma = 0.8;
delta = 1.2;
h0 = 4;
h1 = 1;
h2 = 1;
h3 = 0.5;
gamma = 1.837147;
A = 1;
tau = 1.1; //market imperfection (borrowing rate < return on savings)
dep=0.05; //depreciation of physical kapital
phi = 0.1996; // Elasticity of educational inputs on human capital
beta = 0.8; // Intergenerational spillover of human capital
theta = 0.16445; // Elasticity of kapital on human capital
eta=0.11;
//*************************************************************************
% 2. Model
//*************************************************************************
model;
s = (w - tau * (1 + r) * e(-1)) / (1 + (1 + delta)^(1/sigma) * (1 + r(+1))^(1 - 1/sigma));
r= alpha * A*naturkapital*k^(alpha-1)*humankapital-dep;
w = (1-alpha)*A*(h0-h1*k^(gamma)-h2*k(-1)^gamma-h3*k(-2)^gamma)*k^alpha*humankapital;
k(+1) = (1-dep)*k+s;
welfare1 = cons_m^(1-sigma)/(1-sigma)+1/(1+delta)*cons_o(+1)^(1-sigma)/(1-sigma);
welfare = ((w - tau * (1 + r) * e(-1))^(1 - sigma) / (1 - sigma)) * (1 + (1 + delta)^(-1/sigma) * (1 + r(+1))^(1/sigma - 1))^sigma;
cons_m = w-s-(1+r)*tau*e(-1);
cons_o = (1+r)*s(-1);
cons = cons_m + cons_o;
naturkapital = (h0-h1*k^gamma-h2*k(-1)^gamma-h3*k(-2)^gamma);
y = naturkapital*A*k^alpha*humankapital;
humankapital(+1) = e^phi * k^theta * humankapital^beta + eta*naturkapital(+1);
budgetconstraint = w - (1+r)*tau*e(-1) - cons_m - cons_o(+1)/(1+r(+1));
e=((tau*(1+r(+1)))/(naturkapital(+1)*(1-alpha)*A*k(+1)^alpha*k^theta*humankapital^beta*phi))^(1/(phi-1));
k_y= k/y;
naturkapital_y= naturkapital/y;
humankapital_y= humankapital/y;
end;
//*************************************************************************
% 3. Steady State, Initial and End Values Block
//*************************************************************************
%--------------------------------------------------------------------------
% 3.1 initval-block: set initial condition to steady state value
%--------------------------------------------------------------------------
initval;
y = 0.43605;
k = 1.220944;
humankapital = 1.046524;
naturkapital = 0.3924462;
k_y=2.8;
naturkapital_y=0.9;
humankapital_y=2.4;
s = 0.12;
r = 0.11;
w = 0.31;
cons_m = 0.1297;
cons_o = 0.1308;
cons = 0.2605;
e = 0.047;
alpha = 0.3;
end;
steady;
histval;
humankapital(-2) = 0.4;
humankapital(-1) 0.4;
humankapital(0) = 0.4;
k(0) = 0.4;
k(-1) = 0.4;
k(-2) = 0.4;
r(0) = alpha*A*(h0-h1*k_value^(gamma)-h2*k_value^gamma-h3*k_value^gamma)*k_value^(alpha-1)*humankapital-dep;
w(0) = (1-alpha)*A*(h0-h1*k_value^(gamma)-h2*k_value^gamma-h3*k_value^gamma)*k_value^alpha*humankapital;
naturkapital(0) = h0-h1*k_value^gamma-h2*k_value^gamma-h3*k_value^gamma;
end;
%--------------------------------------------------------------------------
% 3.3 steady-command:
%--------------------------------------------------------------------------
steady;
perfect_foresight_setup(periods=15);
perfect_foresight_solver;