xtabond2 Two Step System GMM and interaction terms

[Muhammad Saleh]

Hi, I am running two step system GMM estimator. My dep var is logged chinese foreign direct investment with Chinese foreign aid as main predetermined variable of interest. Among other vars I test political stabilty if this is a moderating factor. With the interaction term, I coded my model as under:

xtabond2 fdi_china L.fdi_china c.lnchn_oda##c.pol_stab L.GDPgrowth PopGrowth global_dj china_BoT us_BoT merchtrade i.d_year*, gmm(L.fdi_china c.lnchn_oda c.lnchn_oda#c.pol_stab, collapse) iv(L.(c.lnchn_oda) c.pol_stab L.GDPgrowth PopGrowth global_dj china_BoT us_BoT merchtrade c.chn_aid_IV i.d_year*, eq(level)) robust nodiffsargan orthogonal small twostep

I was concerned if I am doing it right especially if it is OK to have interaction term as GMM style instrument? I read some of the previous threads and literature but couldnt find definite answer on it. WIll be glad if some suggestion/advice is provided
Thanks

[Sebastian Kripfganz]

An interaction term should be treated just as any other variable/instrument. If the interacted variables are exogenous, then it is usually plausible to argue that the interaction term is exogenous as well. If one of the interacted variables is endogenous, then it usually (but not necessarily always) makes sense to treat the interaction term as endogenous as well.

As an aside: Note that all the variables you have put into the iv() option with the eq(level) suboption implicitly are assumed to be uncorrelated with the unobserved group-specific effects. This is a very strong assumption (akin to a "random-effects" assumption), and is typically unreasonable with macro data.

More on panel data GMM estimation:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.