Code:
sysuse auto
split make
encode make1, g(id)
xtset id
xtreg price displacement, fe
Assume that each id is a car company and we are interested in how displacement relates to price controlling for invariant firm characteristics. We would use the above regression to get our answer (xtreg price displacement, fe).

Why are singleton firm observations not dropped out of the estimate?

In this example, there is only one observation for BMW, Fiat, Mazda, Peugeot, Renault, Subaru, and Volvo. I would expect that a within-firm estimator would not use singeltons. Can we use this regression to say that the relationship between displacement and price is positive within firm?