/*
** Lesson 6.6: Maximizing Log-Likelihood Function
** Estimating a CES Production Function
** See Judge, et. al. [1988], Chapter 12
*/
use gpe2;
output file=gpe\output6.6 reset;
load x[30,3]=gpe\judge.txt;

call reset;
_nlopt=1;
_method=5;
_iter=100;
_tol=1.0e-5;
_vcov=1;
_b={1.0,0.5,-1.0,-1.0,1.0};

call estimate(&cesll,x);

end;

/* Objective Function */
proc cesll(data,b); @ log-likelihood function @
    local l,k,q,e,n;
    l=data[.,1];
    k=data[.,2];
    q=data[.,3];
    e=ln(q)-b[1]-b[4]*ln(b[2]*l^b[3]+(1-b[2])*k^b[3]);
    n=rows(e);
    retp(-0.5*n*(ln(2*pi)+ln(b[5]^2))-0.5*sumc((e./b[5])^2));
endp;