Areg and xtreg giving different results

[Deni Mazrekaj]

Unfortunately, my data is confidential so I cannot post it here, but I ran three different regressions with an unbalanced panel dataset of individuals over 20 months.

areg hoursworked age, a(ID)

Then I demeaned hoursworked and age by ID and ran:

reg hoursworkeddemeaned agedemeaned

These two regressions provided the same coefficients.

But then I did

xtset ID

xtreg hoursworked age, fe

I have got very similar coefficients but not exactly the same, there was a slight difference.

Anyone knows why something like this would occur? I thought these approaches were equivalent.

[Andrew Musau]

You can post the regression results, possibly excluding the variable names. The coefficients should be identical, but the standard errors may differ due to different degrees of freedom adjustments.

[Carlo Lazzaro]

Deni:
the following approaches give back the same results for the coefficients that are shared among the three regressions (-age- is the only one that the three codes have in common):

use "https://www.stata-press.com/data/r17/nlswork.dta"

. xtreg ln_wage age if idcode<=3, fe

Fixed-effects (within) regression               Number of obs     =         39
Group variable: idcode                          Number of groups  =          3

R-squared:                                      Obs per group:
     Within  = 0.3795                                         min =         12
     Between = 0.6496                                         avg =       13.0
     Overall = 0.1214                                         max =         15

                                                F(1,35)           =      21.40
corr(u_i, Xb) = -0.2960                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0307608   .0066489     4.63   0.000     .0172629    .0442588
       _cons |   .8796702   .1939752     4.53   0.000     .4858795    1.273461
-------------+----------------------------------------------------------------
     sigma_u |  .30623358
     sigma_e |  .25645513
         rho |  .58777837   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(2, 35) = 17.07                      Prob > F = 0.0000

. areg ln_wage age if idcode<=3, abs(idcode)

Linear regression, absorbing indicators             Number of obs     =     39
Absorbed variable: idcode                           No. of categories =      3
                                                    F(1, 35)          =  21.40
                                                    Prob > F          = 0.0000
                                                    R-squared         = 0.5552
                                                    Adj R-squared     = 0.5171
                                                    Root MSE          = 0.2565

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0307608   .0066489     4.63   0.000     .0172629    .0442588
       _cons |   .8796702   .1939752     4.53   0.000     .4858795    1.273461
------------------------------------------------------------------------------
F test of absorbed indicators: F(2, 35) = 17.073              Prob > F = 0.000

. reg ln_wage age i.idcode if idcode<=3

      Source |       SS           df       MS      Number of obs   =        39
-------------+----------------------------------   F(3, 35)        =     14.57
       Model |   2.8738157         3  .957938567   Prob > F        =    0.0000
    Residual |  2.30192326        35  .065769236   R-squared       =    0.5552
-------------+----------------------------------   Adj R-squared   =    0.5171
       Total |  5.17573896        38  .136203657   Root MSE        =    .25646

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0307608   .0066489     4.63   0.000     .0172629    .0442588
             |
      idcode |
          2  |  -.3831397   .1049083    -3.65   0.001    -.5961148   -.1701645
          3  |  -.6053814   .1044625    -5.80   0.000    -.8174516   -.3933112
             |
       _cons |   1.230398   .1900956     6.47   0.000     .8444837    1.616313
------------------------------------------------------------------------------

.