Checking for multicollinearity, omitted variable bias, and homoskedasticity in panel data.

[Nick Baradar]

Dear All,

I am currently running a panel data fixed effects regression in Stata and I aim to identify potential issues such as multicollinearity, omitted variable bias, and homoskedasticity/heteroskedasticity. However, commands like vif, estat imtest, and hettest appear to be inappropriate for panel data regressions. I attempted to use these commands after running xtreg regression, but Stata indicated that these tests are not applicable. I would greatly appreciate your advice on which commands to use in this scenario.

Thank you very much in advance!

[Carlo Lazzaro]

Nick:
are those assignment-related questions?

[Nick Baradar]

Carlo Lazzaro, I appreciate your sarcasm. However, if you're curious, feel free to check my other posts to confirm that I've moved past the age for assignments.

[Carlo Lazzaro]

Nick:
no sarcasm at all. Usually this kind of posts have that origin, as they give the (wrong in your case) impression that the original poster is not interested in skimming through the Stata manual and/or related literature/reference, but is longing to receive a set on answers to plug in the assignment form.
That said:
1) Multicollinearity: see -estat vce, corr- after -xtreg,fe-;
2) heterosledasticity: see community-contributed module -xttest3-;
3) omitted variable bias: replicate -linktest. procedure by hand:

. use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage c.age##c.age, fe vce(cluster idcode)

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, 4709)        =     507.42
corr(u_i, Xb) = 0.0440                          Prob > F          =     0.0000

                             (Std. err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0539076    .004307    12.52   0.000     .0454638    .0623515
             |
 c.age#c.age |  -.0005973    .000072    -8.30   0.000    -.0007384   -.0004562
             |
       _cons |    .639913   .0624195    10.25   0.000     .5175415    .7622845
-------------+----------------------------------------------------------------
     sigma_u |   .4039153
     sigma_e |  .30245467
         rho |  .64073314   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict fitted, xb
(24 missing values generated)

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

. xtreg ln_wage fitted sq_fitted , fe vce(cluster idcode)

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, 4709)        =     523.09
corr(u_i, Xb) = 0.0467                          Prob > F          =     0.0000

                             (Std. err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      fitted |   2.569185   .7085064     3.63   0.000     1.180181    3.958189
   sq_fitted |    -.47432   .2153021    -2.20   0.028    -.8964128   -.0522272
       _cons |  -1.290258    .580562    -2.22   0.026    -2.428431   -.1520844
-------------+----------------------------------------------------------------
     sigma_u |    .403403
     sigma_e |  .30238578
         rho |  .64025357   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 


. test sq_fitted

 ( 1)  sq_fitted = 0

       F(  1,  4709) =    4.85
            Prob > F =    0.0276

As the -test- outcome rejects the null, the model is misspecified.