Hello everyone,

I am trying to run a gravity model with the inclusion of an interaction term composed of three variables. My dependent variable is gvc_total, which is the bilateral penetration in the global value chain of an exporter in the domestic economy of an importer. The interaction term is c.lag1_lnRD_imputed##i.exp_developing##i.income_cl assification_imp. lag1_lnRD_imputed corresponds to the bilateral difference in year t-1 in domestic regulation between two countries (exp and imp), exp_developing is a dummy variable equals to 1 if the exporter is a developing country and income_classification_imp is a categorical variable with three classes, in which importers are classified as 2 (low-income), 3 (middle-income) and 4 (high-income). I would like to see whether higher levels of bilateral regulatory differences have a higher impact on developing countries and how this is differentiated according to the income level of the importer.
This is a sample of my data:

Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input str5(exp imp) double year float(gvc_total lag1_lnRD_imputed exp_developing income_classification_imp)
"ARG" "AUS" 2005    .4810562         . 1 4
"ARG" "AUS" 2006    .7095908  3.080612 1 4
"ARG" "AUS" 2007    3.686711 3.0960314 1 4
"ARG" "AUS" 2008   2.6161735  3.040033 1 4
"ARG" "AUS" 2009   2.3592985 2.9926226 1 4
"ARG" "AUS" 2010     2.80107  2.946606 1 4
"ARG" "AUS" 2011   4.7547293  2.920012 1 4
"ARG" "AUS" 2012   4.7634377  2.899041 1 4
"ARG" "AUS" 2013   4.5947137 2.8946085 0 4
"ARG" "AUS" 2014    5.387508 2.8502626 1 4
"ARG" "AUS" 2015    4.823783 2.8395286 1 4
"ARG" "AUS" 2005 .0025410315         . 1 4
"ARG" "AUS" 2006  .003603552  3.080612 1 4
"ARG" "AUS" 2007  .005169975 3.0960314 1 4
"ARG" "AUS" 2008  .005921311  3.040033 1 4
"ARG" "AUS" 2009    .6192643 2.9926226 1 4
"ARG" "AUS" 2010  .007792954  2.946606 1 4
"ARG" "AUS" 2011  .010513017  2.920012 1 4
"ARG" "AUS" 2012  .009914982  2.899041 1 4
"ARG" "AUS" 2013    .4977893 2.8946085 0 4
"ARG" "AUS" 2014  .008768263 2.8502626 1 4
"ARG" "AUS" 2015  .007165529 2.8395286 1 4
"ARG" "AUS" 2005    .7004743         . 1 4
"ARG" "AUS" 2006   1.2754846  3.080612 1 4
"ARG" "AUS" 2007   .14972857 3.0960314 1 4
"ARG" "AUS" 2008     .596966  3.040033 1 4
"ARG" "AUS" 2009   .45553005 2.9926226 1 4
"ARG" "AUS" 2010    .5267684  2.946606 1 4
"ARG" "AUS" 2011   .01068677  2.920012 1 4
"ARG" "AUS" 2012   13.515596  2.899041 1 4
"ARG" "AUS" 2013    .0933937 2.8946085 0 4
"ARG" "AUS" 2014   .06100044 2.8502626 1 4
"ARG" "AUS" 2015    2.423828 2.8395286 1 4
"ARG" "AUS" 2005   .03694565         . 1 4
"ARG" "AUS" 2006  .013627814  3.080612 1 4
"ARG" "AUS" 2007   .02500085 3.0960314 1 4
"ARG" "AUS" 2008  .036339752  3.040033 1 4
"ARG" "AUS" 2009  .014212865 2.9926226 1 4
"ARG" "AUS" 2010   .02837868  2.946606 1 4
end
and this is the code with the output


Code:
.  asdoc ppmlhdfe gvc_total c.lag1_lnRD_imputed##i.exp_developing##i.income_clas
> sification_imp lag1_lntariffs lag1_RTA ln_dist $dummy_list if exp!=imp, a(exp_
> sector_time imp_sector_time) vce(cluster pair_sector_id) replace nest cnames(o
> verall GVC participation) dec(3) add(RESET Test, 0.000, AVE, 0.000)
(dropped 5066 observations that are either singletons or separated by a fixed ef
> fect)

(legend: p: exact partial-out   s: exact solver   h: step-halving   o: epsilon b
> elow tolerance)
Converged in 16 iterations and 53 HDFE sub-iterations (tol = 1.0e-08)

HDFE PPML regression                              No. of obs      =    657,981
Absorbing 2 HDFE groups                           Residual df     =     68,928
Statistics robust to heteroskedasticity           Wald chi2(21)   =    8540.75
Deviance             =  15224547.31               Prob > chi2     =     0.0000
Log pseudolikelihood = -8430762.747               Pseudo R2       =     0.9148

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_i~d |  -.1894304   .0315448    -6.01   0.000    -.2512571   -.1276038
1.exp_devel~g |          0  (omitted)
              |
exp_develop~g#|
           c. |
lag1_lnRD_i~d |
           1  |   .4557452   .1341563     3.40   0.001     .1928036    .7186868
              |
income_cla~mp |
           2  |          0  (omitted)
           3  |   1.418432   .3873059     3.66   0.000     .6593261    2.177537
           4  |          0  (omitted)
              |
income_cla~mp#|
           c. |
lag1_lnRD_i~d |
           2  |   -.014681   .0655308    -0.22   0.823    -.1431191     .113757
           3  |  -.4596913   .1467517    -3.13   0.002    -.7473193   -.1720632
           4  |   .1397922   .0333796     4.19   0.000     .0743694    .2052151
              |
exp_develop~g#|
income_cla~mp |
         0 3  |          0  (empty)
         1 2  |   .8923923   .4241467     2.10   0.035     .0610801    1.723704
         1 3  |          0  (omitted)
         1 4  |   1.512856   .3679944     4.11   0.000     .7916001    2.234111
              |
exp_develop~g#|
income_cla~mp#|
           c. |
lag1_lnRD_i~d |
         0 3  |          0  (empty)
         1 2  |  -.3549914   .1515992    -2.34   0.019    -.6521204   -.0578624
         1 3  |          0  (omitted)
         1 4  |  -.4380782   .1400441    -3.13   0.002    -.7125596   -.1635969
              |
lag1_lntari~s |  -.1761927   .0182922    -9.63   0.000    -.2120447   -.1403407
     lag1_RTA |    .136915   .0368821     3.71   0.000     .0646273    .2092026
      ln_dist |  -.8003638   .0218646   -36.61   0.000    -.8432176     -.75751
       contig |   .3244154   .0291999    11.11   0.000     .2671846    .3816462
comlang_ethno |   .1493362   .0364861     4.09   0.000     .0778247    .2208477
       comcol |  -.2656031   .1177075    -2.26   0.024    -.4963055   -.0349006
     comrelig |  -.0009697   .0558059    -0.02   0.986    -.1103473    .1084079
        col45 |   .1237388   .0835462     1.48   0.139    -.0400087    .2874862
comleg_post~s |   .2450281    .024703     9.92   0.000      .196611    .2934452
transition_~e |  -.1048861    .039355    -2.67   0.008    -.1820204   -.0277517
      sibling |  -.1014199   .0794286    -1.28   0.202    -.2570972    .0542573
        _cons |   12.48745   .2074874    60.18   0.000     12.08079    12.89412
-------------------------------------------------------------------------------

I would have two questions:
1) in this case, the red-output states that the impact of regulatory differences is higher for developing economies (than for developed economies which is the baseline) when the importer is high-income( 4) and low-income as well (2). Is that interpretation correct?

2) I saw that in this context the postestimation analysis usually includes a plot with margins, would you also recommend further post-estimation analysis?

I am sorry for the length of the question, I hope to see some interesting comments and ideas anyway.
Thank you in advance for your time.