Dear all,

I am trying to estimate an interaction term between two continuous variables in a PPML model, namely:

Code:
β1 (ln⁡(1+ RDijt-1)×GNIit)
where RD is an index of regulatory distance ranging from 0 to 100, and GNI stands for Gross National income. Also, i stands for exporter, j for importer and t for year. The dependent variable (gvc_total) is export from country i to country j in year t. While we expect RD to have a negative effect on export (hence, a negative coefficient), the opposite is true for the moderator GNIit
The coefficient of the interaction term is the one of the output below:

Code:
  asdoc ppmlhdfe gvc_total c.lag1_lnRD_imputed##c.GNIcap_exp lag1_lntariffs lag1_RT
> A ln_dist $dummy_list if exp!=imp, a(exp_sector_time imp_sector_time) vce(cluster 
> pair_sector_id) replace nest label cnames(overall GVC participation) dec(3) add(RE
> SET Test, 0.000, AVE, 0.000) d
(dropped 5066 observations that are either singletons or separated by a fixed effect
> )



HDFE PPML regression                              No. of obs      =    657,981
Absorbing 2 HDFE groups                           Residual df     =     68,928
Statistics robust to heteroskedasticity           Wald chi2(13)   =    8276.65
Deviance             =  15296318.24               Prob > chi2     =     0.0000
Log pseudolikelihood = -8466648.213               Pseudo R2       =     0.9144

Number of clusters (pair_sector_id)=    68,929
                         (Std. Err. adjusted for 68,929 clusters in pair_sector_id)
-----------------------------------------------------------------------------------
                  |               Robust
        gvc_total |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
lag1_lnRD_imputed |  -.1589669   .0238908    -6.65   0.000    -.2057921   -.1121417
       GNIcap_exp |          0  (omitted)
                  |
             
c.ln⁡(1+ RDijt-1)#|
     c.GNIit |   .0029432   .0005393     5.46   0.000     .0018863    .0040001
                  |
   lag1_lntariffs |  -.1669346   .0197142    -8.47   0.000    -.2055738   -.1282954
         lag1_RTA |   .1113005   .0355856     3.13   0.002      .041554    .1810471
          ln_dist |  -.8107724   .0216022   -37.53   0.000    -.8531119   -.7684329
           contig |   .3042479   .0290538    10.47   0.000     .2473036    .3611922
    comlang_ethno |   .1456843   .0371045     3.93   0.000     .0729608    .2184078
           comcol |   -.229223   .1156892    -1.98   0.048    -.4559697   -.0024762
         comrelig |  -.0529728   .0549299    -0.96   0.335    -.1606336    .0546879
            col45 |   .0751228   .0871865     0.86   0.389    -.0957595    .2460052
 comleg_posttrans |   .2575868   .0244418    10.54   0.000     .2096817    .3054919
transition_lega~e |  -.1042719   .0398606    -2.62   0.009    -.1823973   -.0261465
          sibling |  -.1060025    .079126    -1.34   0.180    -.2610867    .0490817
            _cons |   13.01029   .1793332    72.55   0.000      12.6588    13.36178
-----------------------------------------------------------------------------------

Absorbed degrees of freedom:
---------------------------------------------------------+
     Absorbed FE | Categories  - Redundant  = Num. Coefs |
-----------------+---------------------------------------|
 exp_sector_time |     12087           0       12087     |
 imp_sector_time |     11655         210       11445     |
---------------------------------------------------------+
I would have two questions:
1) Is it correct to create an interaction between a logged (RD) and non-logged (GNI) variable when implementing a PPML estimator?
2) Since GNI is not logged, do I need to transform the coefficient of the interaction in order to interpret it?

Looking forward to your feedback and comments.
Thank you in advance for your time