st: How much can we trust Stata's non-linear solver(s)?

[joachim Wagner <wagner@uni-lueneburg.de>]

Dear Listmembers,

at the weekend I read a paper by McCullough and Vinod on "Verifying the 
solution from a nonlinear solver: A case study" in the June 2003 issue of 
the American Economic Review. For those of you who are not in economics, 
this is an absolute top-journal in our discipline, and the authors are 
considered to be top-experts in the field. I was shocked (really, believe 
me!) to learn how much can go wrong and goes wrong when one tries to find 
the ML solution of such day-to-day problems as the parameters of a probit 
model using a PC and several programs. The authors give examples, and they 
argue that "the researcher's job is not done when the program reports 
convergence - it is only beginning" (p. 876), and ask us to examine the 
gradient, inspect the solution path, evaluate the Hessian, including an 
eigensystem analysis, and profile the likelihood. Uff. Do I really have to 
learn how to do all this? Do I have to use three or more different packages 
to compare the solutions? Shall I demand this when I sit down to write my 
next referee report later this week? Must I be aware that the next report I 
receive will demand me to do all this?

Unfortunately, the authors do not name horses and riders (as we say in 
Germany - in German, of course), so I have no idea whether Stata is among 
the programs one can trust or not. Obviously, I want to know, and I am sure 
many of the list-members share my view. Given that the acknowledgement 
footnote of the paper mentions W. Gould, I hope he can tell us more.

From a slightly different perspective, would it be a good idea to 
implement the steps suggested by the authors for a "post-convergence" check 
in Stata ?

Given that I am no expert in numerical computing and all the related 
difficulties, I would like to learn your opinions, experiences etc.

Best,

Joachim

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