Overlapping Generations Model (OLG)

Dynare contributions and examples
2

Hey,

I noticed that here’s very little OLG related material. So here’s a basic 2 cohort Diamond-Samuelsson.

// Basic OLG with population growth and technological growth
var c c1 c2 k w r s y check1 check2;

parameters beta alpha delta n x;
beta = 0.4010; // 0.97^30
alpha = 1/3; delta = 0.9; n=0.1614; x=0.3478;

kss = ((1+1/beta)*(1+n)/(1-alpha))^(1/(alpha-1));
wss = (1-alpha)*kss^alpha; rss = alpha*kss^(alpha-1)-delta;
sss = (1+n)*kss; c1ss = sss/beta; c2ss = (1+rss)*sss;
yss = kss^alpha; css = c1ss+c2ss/(1+n);

model;
    // In effective labour form
    1/c1 = beta*(1+r(+1))/c2(+1);
    c1 + s = w;
    c2(+1) = (1+r(+1))*s;
    y = k(-1)^alpha; // Y/XL = (K/XL)^alpha
    w = (1-alpha)*k(-1)^alpha;
    r = alpha*k(-1)^(alpha-1) - delta;
    c = c1 + c2/(1+n+x); // C = X*L*c1 + X(-1)*L(-1)*C2;
    // ECNOMY WIDE FEASIBILITY CONSTRAINT
    y = (1+n+x)*k - (1-delta)*k(-1) + c; 
    check1 = y -( (1+n+x)*k - (1-delta)*k(-1) + c);
    check2 = (1+n+x)*k - s;
end;

initval; 
k = kss; c1 = c1ss; c2 = c2ss; r=rss; w=wss; s=sss; c=css; y = yss;
end;

steady;