Re: [Gretl-users] mle with & without derivatives

I have been comparing the output of gretl and Stata for the half-normal stochastic frontier model (Example 17.1) in the User's Guide. They are extremely close, which is reassuring. Without detailed timings my impression is that the execution times are not substantially different - my sample is ~ 550 observations and the model has 13 parameters.

This exercise prompts me to raise a question. The default mle setup relies upon numerical rather than analytical derivatives. In the days when I was programming maximum likelihood models, this would have imposed a huge performance penalty. But writing out all of the derivatives is rather tedious in mle if one wants to test a lot of different specification - unless one does it properly via a function that can parse the number of independent variables, etc. So, the question is - has anyone assessed the performance penalty from using numerical rather than analytical derivatives? For example, I note that the ZIP model shown as Example 17.3 does not have any deriv statements, so clearly it was not thought worthwhile including them.

One point is that in my experience the use of numerical derivatives can problems when the starting values are poor. I found this with the standard deviation parameters (su & sv) in SFA model when I got the scale wrong - mle blew up very quickly reporting that something was not a number. This should not happen with analytical derivatives.