@ NLS ESTIMATION BY MINIMIZING RSS@

new; cls;
rndseed(1234);

// DGP begins 
n=100;
x=rndu(n,1);
eps=rndn(n,1);
beta={2 2 2};
y=beta[1]+beta[2]*x^beta[3]+eps;
// DGP ENDS

// ESTIMATION

//Starting values
beta0={3, 3, 3};

{bnls,f,g,retcode} = QNewton(&ssr,beta0);

// VarCov Matrix
vbeta=vcov(bnls);

//Standard Errors;
sterr=sqrt(diag(vbeta));

//RESULTS

format /rds 10,3;

"Press a Key to see a Summary Table";
wait;
cls;

"Results by Minimizing SSR:";
"-------------------------";
"Coefficients   Std Err";;
bnls~sterr;
"-------------------------";



//PROCEDURES

// RSS for the Nonlinear model
proc ssr(beta0);
	local e;
	e=y-beta0[1]-beta0[2]*x^beta0[3];
retp(e'e);
endp;


//Var Cov Matrix of the NLS estimator
proc vcov(bnls);

	local sig2hat,xd,xd1,xd2,xd3,e,k;
	k=rows(bnls);

	e=y-bnls[1]-bnls[2]*x^bnls[3];
	sig2hat=e'e/(n-k);

	//First derivatives
	xd1 = ones(n,1);
	xd2 = x^bnls[3];
	xd3 = (bnls[2]*x^bnls[3]).*ln(x);

	xd=xd1~xd2~xd3;

retp(sig2hat*inv(xd'xd));
endp;