Would -xtscc- solve serial auto correlation and heteroskedasticity in a panel data?

[Patrick James Lim]

I am running Stata 13 and working on a panel data.
Panel variable has about 200 entries(countries) and 10 years from 2006 to 2016 Although I have missing observations in between.

. xtset
       panel variable:  Country (unbalanced)
        time variable:  Year, 2006 to 2016
                delta:  1 year

I tested for serial correlation using -xtserial- and based on the results, I'm assuming there's serial correlation.

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,      63) =    274.750
           Prob > F =      0.0000

Also, I tested for heteroskedasticity using -lrtest-

. lrtest hetero ., df (69)

Likelihood-ratio test                                 LR chi2(69) =    850.41
(Assumption: . nested in hetero)                      Prob > chi2 =    0.0000

. est replay hetero

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Model hetero
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        heteroskedastic
Correlation:   no autocorrelation

Estimated covariances      =        70          Number of obs      =       621
Estimated autocorrelations =         0          Number of groups   =        70
Estimated coefficients     =         8          Obs per group: min =         1
                                                               avg =  8.871429
                                                               max =        11
                                                Wald chi2(7)       =  26671.07
Log likelihood             = -47.08043          Prob > chi2        =    0.0000

----------------------------------------------------------------------------------
        lnGDPppp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
    Billionaires |   .0027389   .0001044    26.23   0.000     .0025342    .0029436
       RuleofLaw |   .0047183     .00032    14.74   0.000     .0040911    .0053454
      GovFreedom |   .0050105   .0006552     7.65   0.000     .0037264    .0062946
       TradeOpen |   .0160248   .0005429    29.52   0.000     .0149608    .0170888
WealthInequality |  -.0073895   .0006478   -11.41   0.000    -.0086593   -.0061198
    Unemployment |  -.0228004   .0011183   -20.39   0.000    -.0249923   -.0206085
           lnPop |   .7194886    .005653   127.28   0.000      .708409    .7305682
           _cons |    13.4601   .1186022   113.49   0.000     13.22764    13.69256
----------------------------------------------------------------------------------

I'm not quite sure how to interpret the output, but I'm assuming too that it is heteroskedastic, or am I wrong?

If it is indeed heteroskedastic. Would using xtscc to regress my data solve both problems?
I searched for ways to solve said problems and I came across a post suggesting that it does indeed.
If not, is there a better way to handle this?

Lastly, are there any more tests I should do to make sure that my model output will be reliable?
Thank you.

[Carlo Lazzaro]

Patrick:
you're dealing with a large N, small T panel dataset.
Clustering the standard errors on -panelid- manages heteroskedasticity and/or autocorrelation.

[Patrick James Lim]

Thank you so much! Now it's clear.