Dear Users,

I am working on a balanced panel with 50 countries observed over 19 years. My main dependent variable is I(1) while my main independent variable is I (0).
Both are indicated in the following output as FDI and I. All control variables are a mixture of I(0) and I(1) and I found evidence of heteroscedasticity, first-degree autocorrelation and cross-sectional dependence.

I had initially planned to use a systems GMM estimator, but it assumes that all variables be stationary at levels. In order to deal with the problem of mixed stationarity among variables, I saw this post where Jeff Wooldridge recommended Driscoll-Kraay approach to overcome the challenge while transforming all non-stationary variables by taking their first differences.

I have followed the recommendation but I am not confident of my output since I am neither an advanced user nor have advanced knowledge of econometrics. Here is the advice I need:

1) Can I proceed to present these results? I am a bit hesitant because three-year dummies are dropped from the estimations (I can't explain why) and the coefficients of some year dummies are strongly significant.
2) Would it be acceptable if I proceed with a GMM estimation but difference non-stationary variables to meet the expectations?

Code:
 xtscc D.FDI D.L.FDI D.GDP D.TRADE D.AID D.EXR NATR I yr*, fe lag(4)

Code:
Regression with Driscoll-Kraay standard errors   Number of obs     =       850
Method: Fixed-effects regression                 Number of groups  =        50
Group variable (i): ID                           F( 23,    16)     =     26.24
maximum lag: 4                                   Prob > F          =    0.0000
                                                 within R-squared  =    0.0983

------------------------------------------------------------------------------
             |             Drisc/Kraay
    __00000K |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         FDI |
         LD. |   .1090312   .0662507     1.65   0.119    -.0314141    .2494765
             |
         GDP |
         D1. |    .138741    .048443     2.86   0.011     .0360463    .2414356
             |
       TRADE |
         D1. |   .1310995   .0549137     2.39   0.030     .0146876    .2475114
             |
         AID |
         D1. |   .0026035   .0089651     0.29   0.775    -.0164017    .0216087
             |
         EXR |
         D1. |  -.0031345   .0046832    -0.67   0.513    -.0130624    .0067935
             |
        NATR |   .0106743   .0047457     2.25   0.039     .0006138    .0207348
           I |   .0403172   .0088159     4.57   0.000     .0216284     .059006
        yr_1 |          0  (omitted)
        yr_2 |          0  (omitted)
        yr_3 |   .1163223   .0201306     5.78   0.000     .0736473    .1589972
        yr_4 |   .0697446   .0124469     5.60   0.000     .0433584    .0961308
        yr_5 |   .0908792   .0127773     7.11   0.000     .0637926    .1179658
        yr_6 |  -.0163546   .0109941    -1.49   0.156    -.0396611    .0069519
        yr_7 |   .0911496    .019723     4.62   0.000     .0493386    .1329605
        yr_8 |   .2674504   .0130407    20.51   0.000     .2398053    .2950956
        yr_9 |          0  (omitted)
       yr_10 |   .1628334   .0207781     7.84   0.000     .1187858     .206881
       yr_11 |   .0933184   .0102961     9.06   0.000     .0714916    .1151453
       yr_12 |   .1116583   .0118736     9.40   0.000     .0864873    .1368293
       yr_13 |   .0524463    .011628     4.51   0.000      .027796    .0770966
       yr_14 |   .0866192    .016139     5.37   0.000      .052406    .1208325
       yr_15 |   .0087971    .015348     0.57   0.574    -.0237391    .0413334
       yr_16 |   .0385855   .0230498     1.67   0.114    -.0102777    .0874488
       yr_17 |   .0549583   .0204628     2.69   0.016      .011579    .0983375
       yr_18 |   .0504483   .0166365     3.03   0.008     .0151805    .0857162
       yr_19 |   .0005665   .0153748     0.04   0.971    -.0320266    .0331596
       _cons |   .0093688    .027222     0.34   0.735    -.0483392    .0670768
------------------------------------------------------------------------------


Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input double(FDI GDP TRADE AID EXR NATR I)
8.1252975 24.726702 4.1409704 19.113628  4.320946 3.1907837 -1.395516
8.4100485  24.72592 4.0725812 19.108112  4.346594 3.0786939 -1.010776
8.6228029 24.762064 4.1131238 19.041902 4.3780425 3.0803736 -.6260364
8.7314687 24.940803  4.129113 19.292978 4.3489219 3.1500927 -.4944898
8.8645602 25.169731 4.1851091 19.574318 4.2775081 3.2198058 -.1928248
end