Is there no way to include "industry fixed effects" in an FE regression?

[Franz Hopp]

Dear Stata community,

I am running a model of the following form:

xtset CompanyID Year, yearly
xtreg firm_profitability firm_investment_strategy firm_size, fe vce(robust)

I would now like to add industry fixed effects to my model, to control for industry difference (a dummy for each 2-digit SIC industry: using i.SIC).

However, there seem to be some problems with that. All the estimates for the industry SIC dummies are omitted in Stata:

note: 7.SIC omitted because of collinearity
...
7 | 0 (omitted)

I am wondering why this is the case:

Might it have to do with using fixed effects regression? The dummies for the SIC industries are time-invariant, they don't change over time.

Any idea what one might do, so that I can control for different industry effects by including industry-fixed effects?

Including industry-fixed effects seems to be a very common thing in strategic management research. I would be quite surprised if there was no way to use it when using FE regression.

(Isn't FE normally said to be the much "safer" choice? As compared to an RE regression -- as RE makes additional statistical assumptions that need to be satisfied to run a proper model. So wouldn't it be weird if there was no way to include using industry-fixed effects in the standard estimation method of FE estimation?)

Thanks a lot!

Franz

[Clyde Schechter]

Might it have to do with using fixed effects regression? The dummies for the SIC industries are time-invariant, they don't change over time.

Yes, that is exactly what is the source of the problem. Because they are time-invariant attributes of the firm, they are colinear with the firm effects.

Any idea what one might do, so that I can control for different industry effects by including industry-fixed effects?

Do nothing at all. The entire point (well, not the entire point, but a major part of the reason) for using fixed effects is that by doing this you automatically also adjust for all time-invariant attributes of the fixed effects, whether observed or not. So by using firm-level fixed effects, industry-level effects are automatically adjusted for without anything extra required. You are not able to estimate the industry-level effects this way, but they are adjusted for nonetheless. (From the pedantry corner: although people often speak of "controlling for" variables, in fact, with observational data it is not possible in any way to actually control for anything--the correct term is "adjust for" them.)

Including industry-fixed effects seems to be a very common thing in strategic management research. I would be quite surprised if there was no way to use it when using FE regression.

Well, you might be surprised, but, in fact, there is no way to do it when using firm-level-FE regression. If you look for analyses that explicitly use industry-level effects in a fixed-effects regression you will find that they do not use firm-level fixed effects. They ignore the firm level and use only industry-level fixed effects. (Or, rarely, they study firms that change industry over time, thereby eliminating the colinearity issue.) But the laws of linear algebra are inviolable and it is simply not possible to simultaneously include explicit industry and firm level fixed effects in the same FE regression.

Isn't FE normally said to be the much "safer" choice? As compared to an RE regression -- as RE makes additional statistical assumptions that need to be satisfied to run a proper model.

Yes, this is commonly said, but without more careful elaboration it's simply wrong. It is true that RE estimation, strictly speaking, requires additional assumptions that may fail. But it is also the case that an FE regression estimates only within-unit effects. It is not all that uncommon for the within- and between- unit effects of some predictor to be different. In that case, the FE regression provides consistent estimates of the within effects but it is incapable of providing any information at all about the between-unit effects--which might be as important or more important. In that case, an RE estimator, with some extra terms included to separately estimate the within- and between- effects is preferred. There isn't much point in getting consistent estimates of the wrong effect! Similarly, the situation I mentioned above where an analysis is carried out using industry-level fixed effects and ignoring firm-level effects is, strictly speaking, a mis-specified model by virtue of ignoring the firm-level effects. What is really needed there is a (random effects) multi-level model. So yes, in certain disciplines, especially economics and finance, there is a culturally dominant strong preference for fixed effects regression over random effects, almost to the point of a phobia about random effects. But that preference is not actually warranted in every situation.

[Jesse Wursten]

Well, you might be surprised, but, in fact, there is no way to do it when using firm-level-FE regression. If you look for analyses that explicitly use industry-level effects in a fixed-effects regression you will find that they do not use firm-level fixed effects. They ignore the firm level and use only industry-level fixed effects. (Or, rarely, they study firms that change industry over time, thereby eliminating the colinearity issue.) But the laws of linear algebra are inviolable and it is simply not possible to simultaneously include explicit industry and firm level fixed effects in the same FE regression.

While I don't know the strategic management research, one thing that people often do is include industry-time fixed effects, which might be an alternative source of confusion.

[Maarten Buis]

I suspect that a company does not change its industry. In that case you cannot add industry fixed effects in Stata (or any other program) if you already have company fixed effects. Fixed effects only looks at changes within a company, so anything that does not change within a company is just constant, and no effect can be estimated. Alternatively you can say that the industry is perfectly collinear with the company fixed effects, which is what the error message told you. However, if you only want to include the industry fixed effects as a control variable, then there is nothing to worry about, the company fixed effects already controlled for the industry even without you explicitly adding it as an control variable. That is the strength of fixed effects: it controls for all time constant variables, observed and unobserved, without you having to add them to your model (which would be rather hard for the unobserved variables). This gives yet another, equivalent, reason why the industry effects are dropped, you cannot control for the same variable twice. Things get harder when you are substantively interested in the industry fixed effects.