Non-convergence in Non-linear estimation

1. Can you estimate a linear regression with the same variable set? Maybe one of your variables has no variation, or otherwise defective? If -reg- fails, a non-linear estimator is unlikely to succeed.
2. Insignificant variables are flat spots in the liklihood function. What happens if you remove most of the independent variables and keep only a few very significant ones? Does it converge then? If so, add the other variables back slowly and identify the problematic ones for disposal. This is especially important for high-dimensionality problems.
3. Are your data items of wildly different magnitudes? Year and year cubed are less of a strain on the optimizer if rescaled to (year-1980) and (year-1980)^3 (assuming 1980 is the mean year). As a bonus the coeficients are easier to understand. Scale the data so that all variables fall into similar ranges.

   There are several -maximize_options- that can be useful. See the Stata documentation, but here are my sugestions:

4. -trace- displays the parameter values at each iteration. Are there pairs of variables that are shooting off to plus or minus infinity? That indicates a perfect predictor. If the liklihood continues to improve, with stablizing parameter values, that is progress.
5. -tolerance- allows you to loosen the convergence criterion. If the optimizer seems to be stuck at a particular place, perhaps that is the optimum?
6. -from- allows you to specify starting values. This is especially appropriate for the situation where "It used to converge, but doesn't now".
7. -technique- allows you to specify which of several hill-climbing techniques should be used, or which combination. Where one fails, another may succeed. Furthermore, what is appropriate at the initial values may not be optimal near convergence.
8. -difficult- is said to be useful when the optimizer complains "not concave".

You might also consider moving to a mean likelihood estimate, rather than maximum likelihood. That will sidestep any convergence problems, and may be much cheaper to calculate, especially if your function requires simulation or quadrature.