Can I use Robust fixed effect model for omitted variables, heteroskedasticity, and autocorrelation

[Elle Nguyen]

I have panel data, at first I run linear regression model (as below), do some tests and notice my model has omitted variables, heteroskedasticity, and autocorrelation problem. If I choose another model like FEM/REM/Robust FEM, will these problem be solved? Or can you please suggest me how to deal with these problem?
Thank you!

. xtset code year
panel variable:  code (strongly balanced)
time variable:  year, 2010 to 2019
delta:  1 unit

.
. regress wins_ROA wins_ATO winsor_SIZE TANG LEV

Source         SS                 df          MS                     Number of obs   =    5,010
                                                                              F(4, 5005)      =    646.79
Model       5.59435539         4      1.39858885            Prob > F        =    0.0000
Residual   10.8225265       5,005   .002162343            R-squared       =    0.3408
                                                                              Adj R-squared   =    0.3402
Total        16.4168819       5,009   .003277477            Root MSE        =    .0465

    
wins_ROA         Coef.         Std. Err.        t        P>t        [95% Conf.    Interval]
    
wins_ATO        .0188105   .0008743      21.52    0.000     .0170965    .0205244
winsor_SIZE    .0072232    .0004905      14.73     0.000     .0062616    .0081849
TANG             -.0181619   .0030956      -5.87     0.000    -.0242307    -.012093
LEV                -.1497816   .0031995     -46.81    0.000    -.1560541    -.1435092
_cons             -.0718411   .0127784      -5.62     0.000    -.0968924    -.0467898
    

. estat ovtest

Ramsey RESET test using powers of the fitted values of wins_ROA
Ho:  model has no omitted variables
F(3, 5002) =      9.20
Prob > F =      0.0000

. estat hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Ho: Constant variance
Variables: fitted values of wins_ROA

chi2(1)      =   840.19
Prob > chi2  =   0.0000

[Carlo Lazzaro]

Elle:
what strikes me is that you -xtset- your panel dataset (and this is correct) but then you went -regress- (which is not that clear, especially without -vce(cluster panelid)- standard errors.
I would recommend you to consider -xtreg-.

[Elle Nguyen]

Thanks for your quick reply Carlo. I follow your advice and run the model using xtreg, but there still exist omitted variable bias, heteroskedasticity and autocorrelation problem after running Ramsey, xttest3, and xtserial. What can I do to treat this? Will using vce(robust) or cluster(id) fix the problem?

 xtreg ROA LEV TANG ATO SIZE, fe

Fixed-effects (within) regression               Number of obs     =      5,010
Group variable: code                            Number of groups  =        501

R-sq:                                           Obs per group:
     within  = 0.1281                                         min =         10
     between = 0.2612                                      avg =       10.0
     overall = 0.2010                                        max =         10

                                                                     F(4,4505)         =     165.53
corr(u_i, Xb)  = -0.0997                                  Prob > F          =     0.0000

------------------------------------------------------------------------------
         ROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         LEV |  -.1477405   .0082955   -17.81   0.000    -.1640037   -.1314773
        TANG |  -.0707758   .0078355    -9.03   0.000    -.0861373   -.0554143
         ATO |   .0353984   .0026366    13.43   0.000     .0302293    .0405675
        SIZE |   .0101497   .0019722     5.15   0.000     .0062833    .0140161
       _cons |  -.1521152   .0535431    -2.84   0.005    -.2570859   -.0471446
-------------+----------------------------------------------------------------
     sigma_u |  .05344546
     sigma_e |  .05432783
         rho |  .49181334   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(500, 4505) = 8.45                   Prob > F = 0.0000

[Carlo Lazzaro]

Elle:
1) as far as heteroskedasticity and epsilon autocorrelation are concerned, simply use non-default standard errors (-robust- or -vce(cluster clusterid)-);
2) -estat ovtest- is not supported by -xtreg-. Hence, to investigate model misspecification, you should use a procedure based on fitted values and their squared term, as reported in -linktest- entry, Stata .pdf manual.

[Elle Nguyen]

I've never used manual command for omitted variable test before so can you please check if mine is right or not?

predict fit, xbu

.
. gen fit_2=fit^2

.
. gen fit_3=fit^3

.
. gen fit_4=fit^4
.
. xtreg ROA LEV TANG ATO SIZE fit_2 fit_3 fit_4, fe
 test fit_2 fit_3 fit_4

 ( 1)  fit_2 = 0
 ( 2)  fit_3 = 0
 ( 3)  fit_4 = 0

       F(  3,  4502) =   23.60
            Prob > F =    0.0000

[Carlo Lazzaro]

Elle:
Using -xb- vs -xbu- probably does not make any difference, because they differ by a panel-specific constant (ui).
That said, as per your augmented regression, there an apparent misspecification issue.

[Elle Nguyen]

Thank you for your clarification! It helps me a lots.

[Jeff Wooldridge]

A few comments. First, RESET is not an omitted variables test. It is a functional form test that may, accidentally, sometimes detect omitted variables. Second, you should not include ui^ in the RESET test as its asymptotic properties are unknown. Only xb. But even then, you are not detecting omitted variables. You should try some squares and interactions of the x variables. Third, you should include year fixed effects and use vce(robust) in obtaining your standard errors. If you use fixed effects with year fixed effects and then try some nonlinear functional forms that's about all you can do -- unless you have an instrumental variable for your key explanatory variable.

[Elle Nguyen]

Thank you Jeff, it seems like I have to check my model again.