[Gretl-users] Alternative way of formulating mle

[Gordon Hughes]

Another query about mle.  As before, I have been experimenting with 
stochastic frontier models and I have found that mle behaves entirely 
differently with two formulations that seem to be equivalent.

Version 1:
mle logl=ln(cnorm(e*lambda/ss))-(ln(ss)+0.5*(e/ss)^2)
   scalar ss = sqrt(su^2 + sv^2)
   scalar lambda=su/sv
   series e=y-lincomb(xlist,b)
   params b su sv
end mle --hessian --verbose

Version 2
mle logl=llnow
   scalar ss = sqrt(su^2 + sv^2)
   scalar lambda=su/sv
   series e=y-lincomb(xlist,b)
   series llnow=ln(cnorm(e*lambda/ss))-(ln(ss)+0.5*(e/ss)^2)
   params b su sv
end mle --hessian --verbose

Both report identical log-likelihoods & gradients at iteration 1, but 
version 2 blows up  at iteration 2 while version 1 continues 
properly.  Technically, the reason for the blow-up in version 2 is 
that it uses a step length of 1, whereas version 1 uses a step length 
of 1e-7.  I cannot understand the reason for the different behaviour 
but in this case it is critical.

Gordon Hughes