Fixed effect Regression

[Larissa Staal]

Hello,

I am new to Stata and Econometrics.
What kind of assumptions should be tested for using FE?
I already checked the normality of residuals and since it is not normally distributed, I took the Log.
This changes the results of my analysis. Is it needed to take the log?
Also, I read something about stationarity (xtserial), and my results are significant. How to resolve this?


Could someone give me some recommendations?

Thanks in advance!

[Carlo Lazzaro]

Larissa:
welcome to this forum.
1) and 2) there's no need to log if the only reason for that is non-normality of the residual distribution. Conversely, if you detect heteroskedastcity and/or autocorrelation you can safely invoke -robust- or -vce(cluster panelid)- (unlike -regress-, they do the very same job under -xtreg-) to deal with these nuisances. That said, with such a limited number of panels the non-default standard errors can be inaccurate. Hence, you have to compare the standard errors under the deafult and non-default assumptions.
3) With a short panel dataset (N>T) you should not worry about stationarity.
4) in your second code you logged in both side of your regression equation. Beware that this way you have log-linear model for some variables and a log-log one for other variables: their interpretation is pretty different.
5) I would test whether the functional form of your regressand is correctly specified, just mimicking the following toy-example:

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage c.age##c.age, fe

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1087                                         min =          1
     Between = 0.1006                                         avg =        6.1
     Overall = 0.0865                                         max =         15

                                                F(2,23798)        =    1451.88
corr(u_i, Xb) = 0.0440                          Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0539076   .0028078    19.20   0.000     .0484041    .0594112
             |
 c.age#c.age |  -.0005973   .0000465   -12.84   0.000    -.0006885   -.0005061
             |
       _cons |    .639913   .0408906    15.65   0.000     .5597649    .7200611
-------------+----------------------------------------------------------------
     sigma_u |   .4039153
     sigma_e |  .30245467
         rho |  .64073314   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23798) = 8.74                 Prob > F = 0.0000

. predict fitted, xb
(24 missing values generated)

. g sq_fitted=fitted^2
(24 missing values generated)

. xtreg ln_wage fitted sq_fitted, fe

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1092                                         min =          1
     Between = 0.1033                                         avg =        6.1
     Overall = 0.0881                                         max =         15

                                                F(2,23798)        =    1457.96
corr(u_i, Xb) = 0.0467                          Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      fitted |   2.569185    .476861     5.39   0.000     1.634507    3.503863
   sq_fitted |    -.47432   .1440324    -3.29   0.001    -.7566326   -.1920074
       _cons |  -1.290258   .3930351    -3.28   0.001    -2.060631   -.5198837
-------------+----------------------------------------------------------------
     sigma_u |    .403403
     sigma_e |  .30238578
         rho |  .64025357   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23798) = 8.72                 Prob > F = 0.0000

. test sq_fitted

 ( 1)  sq_fitted = 0

       F(  1, 23798) =   10.84
            Prob > F =    0.0010

.

Since the outcome of -test- on the -sq_fitted- reaches statistical significance, the model is misspecified (that is, it needs more predictors and/or interactions to give afair and true view of the data generating process).