Fixed Effects & Ordered Probit (RE) for same panel?

[Andreas Baltin]

Edit: Thread title says ordered probit, what I actually meant is ordered Logit!. Please excuse this.

Hey Folks!

I hope I am not getting too annoying with my questions. I have encountered the following problem. I am using a panel data set (unbalanced) over 2 periods.

I have 2 types of dependent variables: The first type is continuous, whereas the second type is ordinal (and I can not assume second type is continuous as well), and I am using a bunch of different regressors on them.

I use a Fixed Effects estimator to estimate effects on the first type of dependent variables. This gives me sensible results and a hausman test indeed confirms that I should use FE rather than RE.

However, for the second type of regressions, I want to use an ordered logit model (xtologit). As far as I know, this uses Random Effects,and it is not straightforward including FE with ologit.

So the question is: Can I use an FE estimator and a RE ordered logit model in the same paper/for the same dataset? It sounds so counterintuitive to me that I rule out RE for the first type of variables, and then proceed to use it for the second type, or is RE just something different regarding to ordered logits and this does make sense?

Any thoughts?

Many thanks!

[Clyde Schechter]

First, what is acceptable for publication is going to depend on the traditions of your particular field, the preferences and prejudices of particular editors and reviewers, and other matters that I don't consider myself qualified to comment on. Editors and reviewers often have strongly held beliefs about such matters, whether they actually know what they are talking about or not.

But here's a statistical perspective on this issue. First, there is no option for a fixed effects ordinal logistic regression of panel data in Stata. And to my knowledge it is not available anywhere else either. Last I heard, nobody has ever found a computation that will estimate such a model. I do not know what the technical problems are that make this so difficult (or perhaps, in principle, impossible). So if an ordinal logistic model is truly appropriate for your situation, you really don't have a choice about FE vs RE.

The other thing is that when you use a Hausman test, all it is doing is looking at the coefficients you get from a FE estimator and the coefficients you get from an RE estimator and comparing them. In fact, all the Hausman test is, is a test of the joint hypothesis that both models are giving the same results. This is useful because the FE estimator is known to be consistent, whereas the RE estimator may or may not be. But if the RE estimator is producing essentially the same results, then we don't have to worry about it. When you think about it that way, it is clear that if you now move to a different model and different variables, there is absolutely no reason why the Hausman results (if you could get them) would be consistently FE or consistently RE across all of the different situations. So, yes, it may be perfectly appropriate to do a FE model for one outcome and an RE model for another. The Hausman test is really only a verdict on the particular specific model you run it on. It has no implications for any other model.

Now I'll go a bit beyond what you've asked about. One should not mindlessly do a Hausman test and follow its dictates. There are other differences between FE and RE models besides consistency of estimation and efficiency. In particular, FE models are estimating within-panel effects only. RE models estimate a weighted average of within- and between-panel effects, because they are predicated on the hypothesis that the within and between panel effects of a predictor are the same. But in the real world, within- and between-panel effects do not have to be the same. They can differ greatly, even be of opposite signs. If your research goals require you to estimate within-panel effects, then you should use an FE model, even if Hausman says RE is OK. Similarly, if your research goal requires the estimation of a between-panel effect of a variable that is constant within panels, that effect is not estimable in an FE model, so you must go to an RE model (or a hybrid model, which is really just an augmented RE model) to get that, and again, nothing a Hausman test has to say about that could overrule that.

At the most general level, I think that statistical practitioners need to understand what their models actually are estimating, and choose the models that answer the questions you set out to answer. If there are several models that are equally good from that perspective, then it may be helpful to select among them based on some preliminary analysis of the data, including possibly some statistical test. But answering the right question should always be the priority, no matter what any statistical test says. A flawed answer to the right question will usually be better than a pristine answer to the wrong question.

[Andreas Baltin]

Hi Clyde,

Many thanks for taking the time for this excellent answer to my question. You have really helped me a lot. I am only a masters student, so not really looking to publish anything (as of yet).
Your explanations have made everything a lot clearer to me and I now know how to proceed! Many thanks for this.

Best
Andreas