I can see I'm not getting much love on this one! :) It's ok though.
I'll add a few comments and then surrender.
1. For command line users this is not relevant since those of us who work that way know that ols is an estimator and that ARIMA is a model that can be estimated in various ways. These are experienced users who know the fine distinctions and see the issue as much ado about nothing. However, GUI users tend to be less 'sophisticated' (ok, I admit that I often use it) and less likely to know that ols is an estimator and not a model. I have some evidence since I asked that question (Is least squares a model or an estimator?) to an introductory graduate class and only half got it right.
2. Econometrics software like Gretl doesn't model, Gretl users model. Gretl only estimates the parameters of a model known to the user and which hopefully encompasses the DGP from the collected sample.
Estimators are chosen because of their sampling properties; the sampling properties depend on the (statistical) model. A model is not chosen because of the properties of its estimator. In my mind, a model should be (carefully) chosen before the software is opened (e.g., Hendry's GUM?).
Even in the model pull-down menus, the tree (or dialog box) ends in every instance at an estimator, e.g. simultaneous equations>sur or tsls or whatever. Now, I know there may be some of us who do the following: grab some data, run some regressions, decide upon a model that explains the results. Write it up as if this were done in reverse order. Can anyone be surprised that people are skeptical of what our studies find?
3. "Model" can be a very good organizing structure: Panel, Time-series, Linear, Nonlinear, Simultaneous Equations, etc, but the user is expected to choose the method by which the parameters of that model are estimated. As we all know, an estimator can be used to estimate parameters in many different models, just as a model can have several estimators. If Model is kept as the top level organizing principle, then I think each of the options in the first level of the pull-down should be models. All roads down the tree end at an estimator.
OK. Now I surrender!
FYI, Stata uses "Statistics" as the top level in their very unwieldy and confusing GUI. Their manuals are organized according to models, with estimators and statistics within each context specifically documented. Although Stata's use of 'Statistics' is correct, it is by no means better than what gretl has now. Gretl separates out things into "sample" that Stata does not. Gretl is much cleaner.
I'm just cranky because after 8 weeks of talking models and estimators not being the same thing, half my class decided OLS is a model, not an estimator. Argh!.
Cheers,
Lee
And of course, I can be completely wrong..... :)