Heckpoisson for nonnegative continuous dependent variables

[Maxime Bercholz]

Dear Statalisters,

Stata's command heckpoisson only runs for nonnegative discrete dependent variables, but poisson and other poisson estimation commands do run for other types of dependent variables, such as nonnegative continuous ones (alternative to taking logs). Does anyone know the reason for this restriction or an alternative implementation of poisson regression with sample selection in Stata that would work with nonnegative continuous dependent variables?

Maxime

[Jeff Wooldridge]

If it follows the two step approach that’s described in my MIT Press book, it should apply to non-counts. You might be able to remove the data check in the ado file. Or, you can implement it “by hand” in two steps and bootstrap the standard errors. I’m going by memory but I think it’s probit for the selection equation and then Poisson adding the log of the inverse Mills ratio from the probit.

[Maxime Bercholz]

Amazing, thanks Jeff! Unfortunately, heckpoisson implements Terza's ML estimator rather than the two-step estimator you describe in your book (Terza, J. V. 1998. Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects. Journal of Econometrics 84: 129–154), unless I'm missing something. I don't think removing the data check will work in this case but I will give it a try. (Actually, that probably answers my question as to why the restriction.)

In the two-step approach, does adding the log of the inverse Mills ratio from the probit correct for sample selection, or is it just a test of it? In your book, you warn against adding the estimated IMR in the second-stage probit in binary response models as a sample selection correction (p. 814), so I'm wondering if this is specific to the binary response model or if it also applies to the exponential mean model.

[Jeff Wooldridge]

Good call, Maxime. I'm traveling and don't have my book, but now I remember that Terza's method is the one I discuss, and the conditional mean function is more complicated. Above I described what is essentially the variable addition test that comes from the Lagrange multiplier testing principle.

It appears that Stata implements the joint MLE, which is too bad because that is assuming the Poisson distribution is correct conditional on the unobservable. It wouldn't be hard to program the conditional mean function derived in Terza, and that should be in my book, too. Then you can use that in Poisson regression. The test I proposed is like the linearized version of it about the null of no selection. Maybe it works as an approximation, as I discuss in my 2014 Journal of Econometrics paper. But there the argument is a bit different because we're interested in an average partial effect of an endogenous binary variable, not sample selection.

[Maxime Bercholz]

Thanks Jeff, that's good to know. I'll see what I can do!