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


From   joachim Wagner <wagner@uni-lueneburg.de>
To   statalist@hsphsun2.harvard.edu
Subject   st: How much can we trust Stata's non-linear solver(s)?
Date   Mon, 25 Aug 2003 09:46:01 +0200

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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