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st: constant in -xtreg (yes, again!)


From   jean-luc morin-chesnel <jeanluc.morinchesnel@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: constant in -xtreg (yes, again!)
Date   Tue, 3 Dec 2013 21:48:18 +0100

Dear all,

First, let me tell you that I have read
http://www.stata.com/support/faqs/statistics/intercept-in-fixed-effects-model/

many, many times.

Still I am puzzled and maybe you can help me. The faq states that "
xtreg, fe reports have simply been reformulated so that the reported
intercept is the average value of the fixed effects."

However, I do not see where this result is shown on the page. It
appears that Stata estimates the model

 yit  - yi  + y  =  a + (xit  - xi  + x)b + (eit  - ei  + v) + e

under the constraint that v=0 (the sum of the fixed effects v_i)

Could someone explain me why a=the average of the fixed effects v_i?
Is this an obvious result?
I am mistaken somewhere?


Next, by looking at the example I tried to recover the constant
reported in -xtreg from the regression with dummy variables. Am I
correct to compute

7.545455 (constant of the fe estimator) =( 4 + (4-2.5) + (4+4.333) +
(4+10.333))/4
                                                          7.0415
                                                          (the average
of the fixed effects in the regression dummy specification)
?



Many thanks!!!
JL
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