Fixed effect for cross sectional regression model

[Anne Todd]

Hi all, I have a question that is equally conceptual asmechanical in terms of its execution in Stata.

I was just in a discussion where someone mentioned what they described as adding a "fixed effect" variable to a regression model. I have a variable in our data which represents essentially the neighborhood area (postal code) of residence for individuals. We are only running a cross-sectional regression, however, and I am only familiar with longitudinal fixed effects models.

So in a model specified like this:

```
reg y x1 x2 x3 i.neighborhood
```

Could one refer to the neighborhood covariate in this model as a neighborhood "fixed effect"? Or is there some other way to specify this in a model that would match such terminology?

[Clyde Schechter]

Yes, you can refer to that as a neighborhood-level fixed-effect model. Alternatively, you could do the same thing with:

xtset neighborhood
xtreg y x1 x2 x3, fe

The results would be the same, except for the constant term, which is calculated somewhat differently in the two models. And the -xtreg, fe- regression won't show you any output for the different neighborhood levels--but that's OK because the ones you get from -regress- are not what they appear to be anyway.

[Jeff Wooldridge]

Agree with Clyde. It's very common to do FE estimation at a higher level than the unit of observation. I do think the label "fixed effects" is applied to broadly -- very likely trying to piggy back off of the positive views of FE estimation. For example, I've hear the phrases "religious fixed effects," occupational fixed effects," and so on. In the end, the labels don't matter too much, but it still strikes me as a bit odd.

[Anne Todd]

Thank you both. The broad use of terminology does also strike me as a bit odd and confusing, because some may be familiar with one usage but not the other (as with myself). But I am glad I understood the mechanics regardless.