/*
** Lesson 8.3: Tobit Analysis of Extramarital Affairs
** Greene [1999], Example 20.12 
** See also R. Fair, JPE, 86, 1978, 45-61
*/
use gpe2;
output file=gpe\output8.3 reset;
n=602;
load data[n,15]=gpe\fair.txt;
y=data[2:n,13];
z=data[2:n,5 6 8 11 12]; @ use z2, z3, z5, z7, z8 @

call reset;

@ Uncensored OLS estimation @
call estimate(y,z);

@ Tobit model estimation @
z=z~ones(rows(z),1); @ RHS variables inc. constant @
_nlopt=2;    @ using component likelihood function @
_method=5;
_iter=100;
_b=__b|5.0;
call estimate(&tobitf,y~z);

@ Tobit model interpretation based on E(y) @
b=__b[1:6];
s=__b[7];
ey=cdfn(z*b/s).*(z*b)+s.*pdfn(z*b/s);
em=cdfn(z*b/s).*b';
print "Expected Value                    Marginal Effects";;
print ey~em[.,1:5];

end;

/* Log-likelihood function: tobit model */
proc tobitf(x,b);
    local y,z,k;
    k=rows(b);
    y=x[.,1];
    z=(y-x[.,2:k]*b[1:k-1])/b[k];
    retp((y.==0).*ln(cdfn(z))+(y.>0).*ln(pdfn(z)/b[k]));
endp;