reg vs areg, apparent inconsistent behaviour?

[dimitris karletsos]

I cannot understand why the coefficient on weight is the same in reg and areg in A), but they are not the same in B).

sysuse auto, clear
gen car_id = _n

* A)
reg price weight length i.mpg
areg price weight length, absorb(mpg)

* B)
reg price weight length i.car_id
areg price weight length, absorb(car_id)

[Sarah Edgington]

Model B cannot be estimated as written. You are including 75 variables in a model with 74 observations (73 values of car_id + weight + length). In order to estimate the model, Stata leaves out some variables and gives you a message it's due to collinearity.
Notice that reg and areg leave out different variables, which is why the models are not comparable.

[Carlo Lazzaro]

Dimitris:
as an aside to Sarah's helpfule reply, codes under B) are actually not cross-sectional regressions: there's no variation in -car_id-.
See also:

. g wave=1

. xtset car_id wave

Panel variable: car_id (strongly balanced)
 Time variable: wave, 1 to 1
         Delta: 1 unit

. xtreg price weight length, fe
note: weight omitted because of collinearity.
note: length omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =         74
Group variable: car_id                          Number of groups  =         74

R-squared:                                      Obs per group:
     Within  =      .                                         min =          1
     Between =      .                                         avg =        1.0
     Overall =      .                                         max =          1

                                                F(0,0)            =       0.00
corr(u_i, Xb) =      .                          Prob > F          =          .

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |          0  (omitted)
      length |          0  (omitted)
       _cons |   6165.257          .        .       .            .           .
-------------+----------------------------------------------------------------
     sigma_u |  2949.4959
     sigma_e |          .
         rho |          .   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(73, 0) = .                          Prob > F =      .

. xtreg price weight length, re
insufficient observations
r(2001);

.