## Friday, July 5, 2013

### Allocation Models With Bounded Dependent Variables

My post yesterday, on Allocation Models, drew a comment to the effect that in such models the dependent variables take values that must to be non-negative fractions. Well, as I responded, that's true sometimes (e.g., in the case of market shares); but not in other cases- such as the Engel curve example that I mentioned in the post.

The anonymous comment was rather terse, but I'm presuming that the point that was intended is that if the y variables have to be positive fractions, we wouldn't want to use OLS. Ideally, that's so. Of course, we could use OLS and then check that all of the within-sample predicted values are between zero and one. Better still, we could use a more suitable estimator - one that takes the restriction on the data values into account.

The obvious solution is to assume that the errors, and hence the y values, follow a Beta distribution, and then estimate the equations by MLE. As I noted in my response to the comment, the "adding up" restictions that are needed on the parameters will be satisfied automatically, just as they are under OLS estimation.

Here's a demonstration of this.

### Paper With Jacob Schwartz

It was nice to get the final "acceptance" yesterday for a paper co-authored with former grad. student, Jacob Schwartz.

The paper, titled "Bias-Reduced Maximum Likelihood Estimation of the Zero-Inflated Poisson Distribution", and with Jacob as lead author, will appear in Communications in Statistics - Theory & Methods. You can download a copy of the paper from here.

Jacob has been in the Ph.D. program at UBC for a while now. It seems quieter around the computing lab. without him!