Panel Data: Pooled OLS vs Fixed Effect

[GwanSeon Kim]

Dear Experts,

I have an unbalanced panel data as below:

If I have data above, what model I should use between Pooled OLS and Fixed Effect model.

Are there any specific tests I can conduct to choose the correct model?

Thank you so much for helping.

[Andrew Musau]

If you run xtreg,fe, you obtain this information from the foot of the regression table (highlighted in red below).

. webuse grunfeld
. xtreg invest mvalue kstock,fe

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

R-sq:                                           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 |      Coef.   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

If this test is significant, i.e., that all firm effects are equal to 0, you reject poolability and opt for the fixed effects model. Here is the intuition using least squares dummy variables (LSDV) regression which is equivalent to fixed effects.

. 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 |      Coef.   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
------------------------------------------------------------------------------

The difference between pooled OLS and LSDV (fixed effects) are the firm dummies taking values 2-10 above. If pooled OLS is preferred over fixed effects, then this implies that the dummies are jointly not significant (or are jointly equal to zero). We can perform this test using the testparm command in Stata as below:

. 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

Doing this, we get the same test statistic as obtained under xtreg. Therefore, fixed effects is preferred in this instance.

[Samantha Robertson]

I have a question which corresponds to the question raised above. For this reason I do not use a new thread.

The sample is comparable to that of "grunfeld", however the panel is unbalanced and comprises singletons with respect to firms. Less than 1% of the observations are singletons.

When I run a fixed effects regression with

xtreg y x i.year, fe

for the

F test that all u_i=0

I get

 Prob > F = 0.0000

.
Thus, using firm fixed effects is recommended.

However, when I first drop all missing values of the variables used in the regression, drop the singletons using the code

bysort firmid: drop if _N==1

and then run

xtreg y x i.year, fe

I get the same coefficients and t-stats except for the intercept

but

I get a large p-value for the

F test that all u_i=0

I understand that for the F-Test, F(v₁,v₂), v₁ decreases when singletons are removed manually before conducting the regression but I did not expect that whether singletons are dropped before xtreg is used or not makes a difference with regard to the decision whether to use firm fixed effects or not.

Does -xtreg- not consider singletons for the F test that all u_i=0?

Should I then use fixed effects or not?

[Carlo Lazzaro]

Samantha:
there's an upward issue: why removing singletions (and making-up your data) when Stata can handle both balanced and unbalanced panel datasets?