Replicate areg results with reg

[Josh Errickson]

I'm trying to understand how `areg` works. I'm attempting to replicate it - I'm able to get the expected coefficients, but different standard errors. What am I missing?

. sysuse auto, clear
(1978 automobile data)

. drop if missing(rep78)
(5 observations deleted)

.
.
. reg mpg weight gear_ratio i.rep78

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(6, 62)        =     21.31
       Model |  1575.97621         6  262.662702   Prob > F        =    0.0000
    Residual |  764.226686        62  12.3262369   R-squared       =    0.6734
-------------+----------------------------------   Adj R-squared   =    0.6418
       Total |   2340.2029        68  34.4147485   Root MSE        =    3.5109

------------------------------------------------------------------------------
         mpg | Coefficient  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
             |
       rep78 |
          2  |  -.3828844   2.784787    -0.14   0.891    -5.949594    5.183825
          3  |  -.5204951   2.568204    -0.20   0.840    -5.654262    4.613272
          4  |  -.7514522   2.633873    -0.29   0.776     -6.01649    4.513585
          5  |   2.036937   2.740728     0.74   0.460      -3.4417    7.515574
             |
       _cons |   34.20089   7.387405     4.63   0.000     19.43367     48.9681
------------------------------------------------------------------------------

. 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 | Coefficient  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

.
. foreach var of varlist mpg weight gear_ratio {
  2.     egen mean`var' = mean(`var'), by(rep78)
  3.     egen mean`var'overall = mean(`var')
  4.     gen `var'c = `var' - mean`var' + mean`var'overall
  5.     drop mean`var' mean`var'overall
  6. }

. reg mpgc weightc gear_ratioc

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(2, 66)        =     44.33
       Model |  1026.56042         2  513.280211   Prob > F        =    0.0000
    Residual |  764.226699        66  11.5791924   R-squared       =    0.5732
-------------+----------------------------------   Adj R-squared   =    0.5603
       Total |  1790.78712        68  26.3351047   Root MSE        =    3.4028

------------------------------------------------------------------------------
        mpgc | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     weightc |  -.0051031   .0008922    -5.72   0.000    -.0068845   -.0033217
 gear_ratioc |   .9014782   1.517369     0.59   0.554    -2.128047    3.931004
       _cons |   34.05889   6.839212     4.98   0.000     20.40396    47.71382
------------------------------------------------------------------------------

[Andrew Musau]

In your manual case, the degrees of freedom (dof) used to compute the standard errors are wrong whereas areg corrects for this. With demeaning, you need to adjust the dofs as the means have been subtracted.

[Mike Murphy]

The standard errors in regs 1 & 2 are exactly the same for the coefficients of interest, only the constant is different- see the discussion in the technical note in the areg helpfile.