Greetings, I'm facing some doubts regarding the solution of Driscoll-Kraay to account for the standard errors of the estimators with the phenomena of cross-section dependence.

From what I've read in the article of Hoechle of the Stata Journal (2007) when cross-sectional dependence is occurring the best approach is to estimate the regression model with the Driscoll-Kraay robust standard errors. I have a Panel with large T and small N, according to that article it can be implemented.

Here I ask, by using these Driscoll-Kraay errors in the regression, the cross-sectional dependence has been accounted? as Hoeckle states in his exercise with financial data. However, one should re-test for cross-sectional dependence after using the regression with the Driscoll-Kraay standard errors? or it's non-sense since the estimation has already taken into consideration and if it was before it's going to be after.

Assume I used a Distributed-LAG pooled OLS and get this using the CD test given by xtcd2 result.

Code:
Pesaran (2015) test for weak cross-sectional dependence.
Residuals calculated using predict, residuals.
(96 missing values generated)
H0: errors are weakly cross-sectional dependent.
CD = 44.557
p-value = 0.000
So in this context I reject null and accept the errors of the pooled have a strong cross sectional dependence.

Now I perform the regression with Driscoll-Kraay errors like:

Code:
xtscc Change_Index L.Change_Index L2.Change_Index L3.Change_Index L4.Change_Index L5.Change_Index L6.Change_Index L7.Change_Index L8.Change_Index L9.Change_Index L10.Change_Index L11.Change_Index L12.Change_Index L13.Change_Index L14.Change_Index L15.Change_Index L16.Change_Index L.Ex_Rate_Change L2.Ex_Rate_Change L3.Ex_Rate_Change L4.Ex_Rate_Change L5.Ex_Rate_Change L6.Ex_Rate_Change L7.Ex_Rate_Change L8.Ex_Rate_Change L9.Ex_Rate_Change L10.Ex_Rate_Change L11.Ex_Rate_Change L12.Ex_Rate_Change L13.Ex_Rate_Change L14.Ex_Rate_Change L15.Ex_Rate_Change L16.Ex_Rate_Change L.GOLD_Change L2.GOLD_Change L3.GOLD_Change L4.GOLD_Change L5.GOLD_Change L6.GOLD_Change L7.GOLD_Change L8.GOLD_Change L9.GOLD_Change L10.GOLD_Change L11.GOLD_Change L12.GOLD_Change L13.GOLD_Change L14.GOLD_Change L15.GOLD_Change L16.GOLD_Change L.PLATINUM_Change L2.PLATINUM_Change L3.PLATINUM_Change L4.PLATINUM_Change L5.PLATINUM_Change L6.PLATINUM_Change L7.PLATINUM_Change L8.PLATINUM_Change L9.PLATINUM_Change L10.PLATINUM_Change L11.PLATINUM_Change L12.PLATINUM_Change L13.PLATINUM_Change L14.PLATINUM_Change L15.PLATINUM_Change L16.PLATINUM_Change L.SILVER_Change L2.SILVER_Change L3.SILVER_Change L4.SILVER_Change L5.SILVER_Change L6.SILVER_Change L7.SILVER_Change L8.SILVER_Change L9.SILVER_Change L10.SILVER_Change L11.SILVER_Change L12.SILVER_Change L13.SILVER_Change L14.SILVER_Change L15.SILVER_Change L16.SILVER_Change  L.WTI_Change L2.WTI_Change L3.WTI_Change L4.WTI_Change L5.WTI_Change L6.WTI_Change L7.WTI_Change L8.WTI_Change L9.WTI_Change L10.WTI_Change L11.WTI_Change L12.WTI_Change L13.WTI_Change L14.WTI_Change L15.WTI_Change L16.WTI_Change  L.BRENT_Change L2.BRENT_Change L3.BRENT_Change L4.BRENT_Change L5.BRENT_Change L6.BRENT_Change L7.BRENT_Change L8.BRENT_Change L9.BRENT_Change L10.BRENT_Change L11.BRENT_Change L12.BRENT_Change L13.BRENT_Change L14.BRENT_Change L15.BRENT_Change L16.BRENT_Change   country_1 country_2 country_3 country_4 country_6 Cont_Change, ase
And the results of the xtcd2 test show this:

Code:
xtcd2
Pesaran (2015) test for weak cross-sectional dependence.
Residuals calculated using predict, residuals.
(96 missing values generated)
H0: errors are weakly cross-sectional dependent.
CD = 44.557
p-value = 0.000
I got the exact same results of strong cross-sectional dependence, however, the robust standard errors with the DK are way different from the OLS.

My ultimate question is that If I should worry that the Pesaran test after regression with robust errors of driscoll-Kraay is a concern? or it doesn't matter since the estimators are already taking this existence and increasing the values to give valid statistics regarding each parameter.