When I taught at the Essex Summer School they produced every year a souvenir T-shirt. One year it, must have been in the early 90s, the T- shirt had a cartoon of a dinosaur wrestling with some Greek symbols and the legend Heteroscedastic Park. I always wondered who came up with it: I bet most of the students and even some of the faculty didn't get all of the joke.
Which is all in aid of saying that I've put some STATA code up on my web-site (scroll to the bottom) to estimate a heteroscedastic normal pdf regression which allows predictors both for the mean and the dispersion.
If you looked hard enough there has always been code floating about to do this sort of thing. Scott Eliason has some Gauss code in his little ML book, and the old SYSTAT manuals had an example of how to do it (anyone remember SYSTAT?). More recently Bruce Western and Deirdre Bloome discuss this sort of model and provide code in their Sociological Methodology piece. I thought their code, which as far as I can see works fine, was a bit involved, so I've written something simpler and more direct.