Distributed lag model with interactions

#1
Hello everyone!

I am currently investigating panel data. I want to conduct a poisson regression including (finite) distributed lag technique for my independent vairables (1, 2 and 3 year lag). Additionally I want to include an interaction effect (moderation). I am unsure as to how I correctly model my regression.

My DV Patents should be explained by IV Numberofmergers, for example one, two and three years prior the observations of the patents, respectively. My moderator term will be R&DintensityxNumberofmergers. Also I want to control for the variable ln_emp as well as for the dummy variables YearEffective and AcquirorPrimarySICCode.
I am unsure as to where to use the lagged variables. Would I lag the controls twice as well? and would it make sense to lag both variables in the interaction term?

Does anyone have suggestions for a reasonable regression model?

these are some of my thoughts, in Stata codes:

a. Every Variable lagged three times
xtpoisson patents cl.ln_xrdintensity##cl.Numberofmergers cl2.ln_xrdintensity##cl2.Numberofmergers cl3.ln_xrdintensity##cl3.Numberofmergers l.ln_emp l2.ln_emp l3.ln_emp i.YearEffective i. AcquirorPrimarySICCode

b. interaction terms lagged three times, but control variable "ln_emp" only lagged once
xtpoisson patents cl.ln_xrdintensity##cl.Numberofmergers cl2.ln_xrdintensity##cl2.Numberofmergers cl3.ln_xrdintensity##cl3.Numberofmergers l.ln_emp i.YearEffective i. AcquirorPrimarySICCode

c. Only "Numberofmergers" lagged twice in interaction term, "ln_emp" only lagged once
xtpoisson patents c.ln_xrdintensity##cl.Numberofmergers c.ln_xrdintensity##cl2.Numberofmergers c.ln_xrdintensity##cl3.Numberofmergers l.ln_emp i.YearEffective i. AcquirorPrimarySICCode
.
.
.
and so on.



Maybe someone can help me out on this one.

Best regards

Christopher