Is e(r2_a) the adjusted within R-squared in xtreg, fe?

[Alex Mai]

Dear statalist,

I have run a fixed-effects regression by xtreg, fe r, and then use ereturn list to produce adjusted R-square. I find that e(r2) is the same as e(r2_w), the within R-squared. So may I ask if e(r2_a) is just the adjusted within R-squared?

Thank you very much!

[Carlo Lazzaro]

Alex:
yes it is, but it differs in decimal digits from e(r2_w), as you can see from the following toy-example:

. xtreg ln_wage age, fe r

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.1026                                         min =          1
     between = 0.0877                                         avg =        6.1
     overall = 0.0774                                         max =         15

                                                F(1,4709)         =     884.05
corr(u_i, Xb)  = 0.0314                         Prob > F          =     0.0000

                             (Std. Err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0181349   .0006099    29.73   0.000     .0169392    .0193306
       _cons |   1.148214   .0177153    64.81   0.000     1.113483    1.182944
-------------+----------------------------------------------------------------
     sigma_u |  .40635023
     sigma_e |  .30349389
         rho |  .64192015   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. ereturn list

scalars:
               e(r2_w) =  .1025747671254915
               e(rank) =  1
               e(Tbar) =  6.053078556263269
               e(Tcon) =  0
              e(g_min) =  1
              e(g_avg) =  6.053078556263269
              e(g_max) =  15
                e(N_g) =  4710
            e(sigma_u) =  .4063502328846532
               e(corr) =  .0313506604859547
               e(r2_o) =  .0773811195932452
               e(r2_b) =  .0876851602614176
            e(sigma_e) =  .3034938911233301
              e(sigma) =  .5071775366817735
                e(rho) =  .6419201461924331
                  e(p) =  3.4442776666e-178
               e(df_m) =  0
               e(df_b) =  1
                  e(F) =  884.0510055602717
               e(ll_0) =  -5426.929832151553
                 e(ll) =  -3884.175784681907
                e(tss) =  6516.690152088633
               e(df_a) =  4709
               e(r2_a) =  .1025432873572554
                e(rss) =  2192.091189848528
                e(mss) =  250.5537342607759
               e(rmse) =  .2772974866348904
                 e(r2) =  .1025747671254915
               e(df_r) =  4709
                  e(N) =  28510
            e(N_clust) =  4710

[Alex Mai]

Alex:
yes it is, but it differs in decimal digits from e(r2_w), as you can see from the following toy-example:

Dear Carlo,

Many thanks!

[Alvaro Ramos]

Dear Alex, how are you.
I stumbled in this thread by accident, but I would like to ask you.
What is the purpose of the r next to the ",fe" at the end of your command?

[Carlo Lazzaro]

Alvaro:
welcome to this forum.
-r- is the abbreviation of -robust- (ie, cluster-robust standard error).
Interestingly, while you can invoke it via -robust- or -vce(cluster clusterid)- in -xtreg- (as both these options do the very same job, that is taking heteroskedasticity and/or autocorrelation into account), in -regress- the -robust- option takes heteroskedasticity only into account, whereas -.vce(cluster clusterid- does the same with autocorrelation of the epsilon.