# Re: st: AW: 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 Re: st: AW: Why is the adj. R-squared lower with time FE than with time & firm FE? Date Tue, 29 Sep 2009 16:00:48 +0200

```Hello Martin,

```
I also thought of the "penalizing effect" of including more variables (firm dummies) on the R-squared. However, in Eq.1, the adj. R-squared and the within R-squared (which corresponds to the unadjusted R-squared, that Stata reports with xtreg) are not much different from each other. For example the adjusted R-squared equals 0.627 and the within R-squared equals 0.615 in Eq.1 (the between R-squared however is higher: 0.723). In Eq. 2, the adj. R-squared rises to 0.916... How is this possible and what is the role of the between R-squared in this case?
```
Ida

Zitat von Martin Weiss <martin.weiss1@gmx.de>:

```
```
<>

" 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."

It all depends on whether you are talking about the adjusted R2 or not. Note
in the example that R2 does indeed increase, even when a meaningless
covariate, with the penalty exceeding the increase in the unadjusted R2...

***
clear*
set obs 10000
set seed 123456
gen x=rnormal()
gen eps=rnormal()
gen noise = rnormal(0,10)

gen y =1+5*x+eps

qui reg y x
di in red e(r2) " " e(r2_a)
qui reg y x noise
di in red e(r2) " " e(r2_a)
***

HTH
Martin

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von
itchiftc@rumms.uni-mannheim.de
Gesendet: Dienstag, 29. September 2009 14:28
An: statalist@hsphsun2.harvard.edu
Betreff: st: Why is the adj. R-squared lower with time FE than with time &
firm FE?

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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```
```

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