# st: Why is the adj. R-squared lower with time FE than with time & firm FE?

 From itchiftc@rumms.uni-mannheim.de To statalist@hsphsun2.harvard.edu Subject st: Why is the adj. R-squared lower with time FE than with time & firm FE? Date Tue, 29 Sep 2009 14:27:53 +0200

Dear Statlist,

i know that this is rather an econometrical question, but may be still someone could help me... I'm estimating panel regressions (in Stata 10) and have two equations which are exactly the same, except for the included fixed effects:
Equation #1 includes both company and time fixed effects:
-xtreg y x1 x2 x3 timedummy2-timedummy9, fe cluster(firmid)
whereas
Equation #2 has only time fixed effects:
-reg y x1 x2 x3 timedummy2-timedummy9, cluster(firmid).

Looking at the adjusted R-Squared I was surprised to see that it is lower in Eq.1 than in Eq.2. As explained in econometric books (e.g. Stock and Watson 2007) icorporating fixed effects is simmilar to including dummies for each individual (in my case 80 firms). Thus, intuitively, as there are more variables in the Eq.1, I thought that the adjusted R-squared should be higher than in Eq.2.

I found a thread with very comprehensive explanation on panel data R-squared:
http://www.stata.com/statalist/archive/2006-03/msg00180.html

stating in the end that
"In the -xtreg, fe- calculation, we are washing out the explanatory
effects of the intercepts."

Is this the explanation for the lower adj. R-squared in Eq.1? I'm not quite sure and would appreciate any comment!

Thanks,
Ida

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