/*
** NLLS Estimation
*/

new ;

@ LOADING DATA @

    load dat[923,17] = wage2.txt ; 

@ OPEN OUTPUT FILE @

    output file = nlls.out reset ;

@ DEFINE VARIABLES @

    wage    = dat[.,1]  ; 
    hours   = dat[.,2]  ; 
    iq      = dat[.,3]  ;
    kww     = dat[.,4]  ; 
    educ    = dat[.,5]  ; 
    exper   = dat[.,6]  ; 
    tenure  = dat[.,7]  ; 
    age     = dat[.,8]  ; 
    married = dat[.,9]  ; 
    black   = dat[.,10] ; 
    south   = dat[.,11] ; 
    urban   = dat[.,12] ; 
    sibs    = dat[.,13] ; 
    brthord = dat[.,14] ; 
    meduc   = dat[.,15] ; 
    feduc   = dat[.,16] ; 
    lwage   = dat[.,17] ; 
    

@ DEFINE # of OBSERVATIONS @

	 tt = rows(dat) ;

@  DEFINE MODEL ERROR TERM @

    yy = wage;
    vny = {"wage"};

proc  res(b) ;
local e      ;

	e = yy - exp(b[1] + b[2]*educ + b[3]*exper)  ; 

retp(  e  ) ;
endp  ;

@   DEFINE INITIAL VALUE @

    bb = {0,0,0} ;
    
library optmum;
#include optmum.ext;
optset ;

proc  f(b) ;
local ltt   ;

	ltt = res(b)'res(b) ; 

retp(  ltt  ) ;
ENDP  ;

b0 = bb ;
__title = "NLLS";
_opgtol = 1e-4;
_opstmth = "bfgs, half";
__output = 0 ;

{b,func,grad,retcode} = optmum(&f,b0) ;

	
@ Covariance matrix @

	hh = - gradp(&res,b);
    s2 = func/tt;
    cov = s2*invpd(hh'hh);
    se  = sqrt(diag(cov));
    r2  = 1- func/(yy'yy-tt*meanc(yy)^2);

format /rd 10,4 ;
"" ;
"NLLS Estimation Result" ;
"------------------------" ;
" dependent variable: " $vny ;
"" ;
" R-square:    " r2 ;
"" ;
"    coeff.    std. err.   t-st " ;
b~se~(b./se);
"" ;


output off ;