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First-differences panel model and interaction term

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Dear all,

I'm currently having a problem with interaction terms in a first-differences model in a panel context. In my research, I'd like to analyze the effect of announcements on firms' returns on minutely basis. But now I want to take into account the interest expressed about each firm (proxied by search queries).

My variables are:
minute the minute considered
companyID the ID of the company considered
announcement a dummy variable which is 1 if an announcement is currently made at this minute and 0 otherwise - but an announcement has often a length of more than one minute
return the return of the respective company "companyID" at minute "minute"
interest the interest expressed about the respective company "companyID" at minute "minute"
Now I'd like to calculate this with my first-differences model with an interaction term between my dummy "announcement" and my continous variable "interest".
But I'm unsure which way to use, as I see three possibilities here:
  1. Treat all variables the same and just use first differences of each:
    Code:
    reg d.return d.(interest announcement interest#announcement), vce(cluster companyID)
    Which is equivalent to generate the interaction first and use its difference:
    Code:
    gen interestXannouncement = interest*announcement
    	reg d.return d.(interest announcement interestXannouncement), vce(cluster companyID)
  2. Generate the differences first and use their interaction:
    Code:
    gen Dinterest = d.interest
    	gen Dannouncement = d.announcement
    	reg d.return d.(interest announcement) Dinterest#Dannouncement, vce(cluster companyID)
  3. Generate the difference only of the continous variable "interest" and keep the time dummy as it is:
    Code:
    gen Dinterest = d.interest
    	reg d.return d.(interest announcement) Dinterest#announcement, vce(cluster companyID)
#1 was my first approach because it is just the transfer from my fixed effects panel regression (xtreg, fe). My search on Statalist then pointed me to #2. But after some time of thinking I'm highly unsure now if #1 and #2 make sense at all in my case. As I have my time-dummy "announcement" which would be in these cases always 0 except at the beginning and end of the announcement timespan. This could be avoided with #3.

Could anyone give me a hint how to decide between these three approaches? Or is any (or all) of them nonsense per se?
Any help is greatly appreciated. Thanks in advance!

Regards
Levin (using Stata 14.1)

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