interpreting the interaction coefficient in the instrumental variable Poisson model (ivpoisson)

[morel john]

Hello Dear Statalists,

I have a question about interpreting the interaction coefficient in the instrumental variable Poisson model (ivpoisson).

I regress bilateral import on migration shares, GDP, distance, regional trade agreement, language, landlocked, border, colonial ties, and common currency.

I add an interaction between migration shares and currency dummy to see if migration has a higher impact on bilateral trade if the country pair are in a currency union.

code:

 ivpoisson gmm imports_imf (sh_immig sh_emig sh_immig_cur sh_emig_cur = sh_lag_immig  sh_lag_emig sh_lag_immig_cur sh_lag_emig_cur) lngdp_od lndistw border rta comlang_off sibling comcur landlocked, vce(robust) igmm wmatrix(cluster pairid) multiplicative

1. imports: bilateral imports ;
2. sh_immig: immigration as share of destination country population; sh_emig is emigration as share of origin country population ;
3. sh_lag_immig : lag value of immigration share; same for sh_lag_emig ;
4. sh_immig_cur : interaction between immigration share and currency dummy, same for sh_emig_cur ;
5. sh_lag_immig_cur: interaction between lag value of migration share and currency dummy;
6. lngdp_od: the log of gross domestic product ;
7. lndistw: log of the distance
8. Border, rta, comlang, comcur, sibling and landlocked are dummies for having a : common border, regional trade agreement, common language, common currency, colonial ties and being landlocked.

In the command, we have in brackets : ( endogenous variable = instruments ). Since migration is considered as endogenous, I also consider the interaction as endogenous variable, and then use the interaction between lag value of migration and currency dummy as instrument.

In the regression results, both immigration and emigration share are positively signed, currency is also positive, but the interactions between migration shares and currency are negative.

This make no sense. I think i miss something about the interpretation or i do not compute the right way.

Thanks for the help !

Best regards,

Morel