Asking about how to choose between OLS and fixed effec

[hussein bataineh]

Hi please I'm doing research in investigating the impact of chief sustainability officer on financial performance. my data is panel data from 2004 -2022, actual different research is using different approach, OLS, Fixed effect, random effect. i know now that we use Husman test determining whether to use between fixed effect and random effect,


i want to know if there is a test to determine whether OLS is appropriate and how we can run it please.??

[Andrew Musau]

The test for poolability is the F-test of joint significance of the firm dummies. This is provided automatically at the foot of the table if you use xtreg.

webuse grunfeld, clear
xtset company year
xtreg invest mvalue kstock, fe
regress invest mvalue kstock i.company
testparm i.company

Res.:

. xtreg invest mvalue kstock, fe

Fixed-effects (within) regression               Number of obs     =        200
Group variable: company                         Number of groups  =         10

R-squared:                                      Obs per group:
     Within  = 0.7668                                         min =         20
     Between = 0.8194                                         avg =       20.0
     Overall = 0.8060                                         max =         20

                                                F(2,188)          =     309.01
corr(u_i, Xb) = -0.1517                         Prob > F          =     0.0000

------------------------------------------------------------------------------
      invest | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      mvalue |   .1101238   .0118567     9.29   0.000     .0867345    .1335131
      kstock |   .3100653   .0173545    17.87   0.000     .2758308    .3442999
       _cons |  -58.74393   12.45369    -4.72   0.000    -83.31086     -34.177
-------------+----------------------------------------------------------------
     sigma_u |  85.732501
     sigma_e |  52.767964
         rho |  .72525012   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 188) = 49.18                     Prob > F = 0.0000

. 
. regress invest mvalue kstock i.company

      Source |       SS           df       MS      Number of obs   =       200
-------------+----------------------------------   F(11, 188)      =    288.50
       Model |   8836465.8        11  803315.073   Prob > F        =    0.0000
    Residual |  523478.114       188  2784.45805   R-squared       =    0.9441
-------------+----------------------------------   Adj R-squared   =    0.9408
       Total |  9359943.92       199  47034.8941   Root MSE        =    52.768

------------------------------------------------------------------------------
      invest | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      mvalue |   .1101238   .0118567     9.29   0.000     .0867345    .1335131
      kstock |   .3100653   .0173545    17.87   0.000     .2758308    .3442999
             |
     company |
          2  |   172.2025   31.16126     5.53   0.000     110.7319    233.6732
          3  |  -165.2751   31.77556    -5.20   0.000    -227.9576   -102.5927
          4  |    42.4874   43.90987     0.97   0.334    -44.13197    129.1068
          5  |  -44.32013   50.49225    -0.88   0.381    -143.9243    55.28406
          6  |   47.13539   46.81068     1.01   0.315    -45.20629    139.4771
          7  |   3.743212   50.56493     0.07   0.941    -96.00433    103.4908
          8  |   12.75103   44.05263     0.29   0.773    -74.14994      99.652
          9  |  -16.92558   48.45326    -0.35   0.727    -112.5075    78.65636
         10  |   63.72884   50.33023     1.27   0.207    -35.55572    163.0134
             |
       _cons |  -70.29669   49.70796    -1.41   0.159    -168.3537    27.76035
------------------------------------------------------------------------------

. 
. testparm i.company

 ( 1)  2.company = 0
 ( 2)  3.company = 0
 ( 3)  4.company = 0
 ( 4)  5.company = 0
 ( 5)  6.company = 0
 ( 6)  7.company = 0
 ( 7)  8.company = 0
 ( 8)  9.company = 0
 ( 9)  10.company = 0

       F(  9,   188) =   49.18
            Prob > F =    0.0000

.

If the test statistic is significant, a fixed effects model is preferred over a pooled model.