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


From   "Martin Weiss" <martin.weiss1@gmx.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: AW: Why is the adj. R-squared lower with time FE than with time & firm FE?
Date   Tue, 29 Sep 2009 15:18:27 +0200

<> 

" 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 is added, and that the adjusted R2 penalizes you for an additional
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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