Within estimator singleton

[Chris James]

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?

[Clyde Schechter]

Your intuition that the singleton firms are not informative about the within-id relationship between price and displacement is correct. However, the singletons are informative about other things that are results of the regression. Run this:

sysuse auto, clear
split make
encode make1, g(id)
xtset id
xtreg price displacement, fe

by id, sort: gen singleton = _N == 1
xtreg price displacement if !singleton, fe

You will see that the results for the coefficient of displacement are the same either way, as you predict. As is the within R². But notice that the constant term, and sigma_u, sigma_e, and rho are different: the singletons do contribute to those.