adjusted R-squared using area versus reghdfe

[Yi Chen]

Dear Statalist community,

I have a model that controls for many fixed effects and clustered standard errors by one of the controlled fixed effects. I found reghdfe gives me very different adjusted R-squared when clustering standard errors vs. not clustering standard errors. But areg gives the same adjusted R-squared regardless of clustering or not clustering standard errors. I'd like to ask:

1. Should we generally trust the adjusted R-squared from reghdfe when controlling for several fixed effects and also clustering at a level that is controlled as fixed effects?
2. Does anyone know how areg estimate adjusted R-squared? I didn't find it in the areg manual.

Thank you.

[Carlo Lazzaro]

Yiqun:
welcome to this forum.
1) as the community-contributed command (as you're kindly requested to detail; please see the FAQ on this and other posting-related topics. Thanks) -reghdfe- focuses on within variation, you should consider -within R-sq- (just like you would do with -xtreg,fe-).
2) areg estimate adjusted R-squared as -regress- does.

[Yi Chen]

Thanks a lot Carlo. I'd like to ask if the adjusted R-squared estimated by areg would be different between clustering vs. not clustering standard errors at a level that is also absorbed as fixed effects?

[Carlo Lazzaro]

Yi:
no, it isn't, as you can easily prove yourself via the following toy-example:

. use  http://www.stata-press.com/data/r16/auto2.dta
(1978 Automobile Data)

. help areg

. areg mpg weight gear_ratio, absorb(rep78)

Linear regression, absorbing indicators         Number of obs     =         69
Absorbed variable: rep78                        No. of categories =          5
                                                F(   2,     62)   =      41.64
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6734
                                                Adj R-squared     =     0.6418
                                                Root MSE          =     3.5109

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0051031   .0009206    -5.54   0.000    -.0069433    -.003263
  gear_ratio |    .901478   1.565552     0.58   0.567    -2.228015    4.030971
       _cons |   34.05889   7.056383     4.83   0.000     19.95338     48.1644
------------------------------------------------------------------------------
F test of absorbed indicators: F(4, 62) = 1.117               Prob > F = 0.356

. areg mpg weight gear_ratio, absorb(rep78) vce(cluster foreign)

Linear regression, absorbing indicators         Number of obs     =         69
Absorbed variable: rep78                        No. of categories =          5
                                                F(   1,      1)   =          .
                                                Prob > F          =          .
                                                R-squared         =     0.6734
                                                Adj R-squared     =     0.6418
                                                Root MSE          =     3.4829

                                (Std. Err. adjusted for 2 clusters in foreign)
------------------------------------------------------------------------------
             |               Robust
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0051031   .0009415    -5.42   0.116    -.0170654    .0068592
  gear_ratio |    .901478   2.589644     0.35   0.787    -32.00307    33.80602
       _cons |   34.05889   11.25922     3.02   0.203     -109.003    177.1208
------------------------------------------------------------------------------

.

[Yi Chen]

Thanks a lot Carlo.