[ben earnhart]

As my diagram indicates, xtreg, fe is OLS (and vice versa) under special conditions. In general, it's not OLS. Only if you remove all between-unit variance by subtracting off the group means do they become equivalent. It's kinda like asking if correlation is the same thing as ANOVA is the same thing as regression is the same thing as a T-test. Well, under certain conditions, yes, they are the same. But only if the right conditions (one dummy variable and one continuous variable) are they the same. They overlap, but only under special conditions.

clear
set seed 1971
set obs 150
gen y=rnormal()
gen x=1 if y>0 & uniform()>.75
replace x=0 if x==.

pwcorr y x, sig
ttest y, by(x)
reg y x    
anova y x

[Jeff Wooldridge]

ben: I'm not sure what you mean. If I start with an equation such as y_it = x_itb + c_i + u_it then there are many ways I can estimate b. One is to just use pooled OLS, where c_i +u_it is effectively the error term. This is usually called the pooled OLS estimator. Or, I can deviate y_it and x_it from the time averages, and then use pooled OLS on the deviations. That is what we call fixed effects. Or, I can leave y and x in there original forms and add a dummy variable indicating each i. That also gives the FE estimator of b. In other words, we can think of three different pooled OLS regressions. Two of them give the FE estimator. The first one almost never does. I guess maybe that is what you mean. But FE is itself a pooled OLS estimator, it just uses a different dependent variable and explanatory variables. You can't just talk about "OLS" here. You have to be very specific about what you are regressing on what.

Heck, even the random effects estimator can be characterized as a pooled OLS estimator, but where the dependent and independent variables have had fractions of the time averages removed. So, every common estimator applied to linear panel data models is pooled OLS of something on something.

[daniel klein]

Jeff already addressed one of the most important points causing confusion here: OLS is an estimator. And the linear model that xtreg ,fe estimates is indeed estimated using OLS - under any conditions - which is clearly documented. Anyone interested can even look up the code, as this is implemented as an ado file.*

It is interesting to me, that there is such a long discussion, when the first answer to the original question in my view should have been: there is not the formal name for this model. Ask economists, they will tell you it is a fixed effects model. Go on and read in the multilevel-literature, starting with xtmixed (or mixed, as it is called now), and you will see that the term "fixed effects" means something very different there.

So what you call the model, and how detailed you describe what you are doing, depends much on who you are talking to.

Best
Daniel


* I admit that this will only get you to the point where regress is used to estimate the model, but I do not think anyone doubts that regress uses OLS to estimate the parameters of the model.