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Fixed-Effects Analysis: Question regarding interaction term

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I am conducting a fixed-effects analysis with a three-wave panel data set. I am regressing wage on participation in an educational training program. However, I am also interested if the Impact of participation changes dependent on the voluntariness of participation. So: xtreg wage participation##voluntary covariates, fe vce (cluster id).

This is my Problem: Only if someone participates in treatment, they are asked if they are participating voluntarily or are forced to do so. So it lookes s.th. like this:
id wave Treatment (yes=1) voluntary (yes=1)
1 1 0* (missing)
1 2 1 1
1 3 1 1
2 1 0 (missing)
2 2 0 (missing)
2 3 1 0
*I have excluded everyone who already participated in wave 1, because I cannot calculate a before-and-after estimator for them.

I think that a fixed-effects analysis needs a transition from zero to one in any case, also for an interaction term and that this is why, if I try to conduct an analysis, Stata tells me that I have "no observations". I looked it up, and there definitely are cases, so it is not a problem of too many missings. However, I do not have any transition in my data from voluntary== 0 to voluntary == 1.

I thought about changing the missings of the "voluntary"-variable prior to the participation into zero's.

sort id wave
replace voluntary = 0 if voluntary[_n+1] !=.

So it looks like this:
id wave Treatment (yes=1) voluntary (yes=1) | old variable voluntary (yes=1) | new variable
1 1 0 (missing) 0
1 2 1 1 1
1 3 1 1 1
2 1 0 (missing) (missing)
2 2 0 (missing) 0
2 3 1 1 0
But I am unsure whether that might wreck my control group (though I wouldn't know why, since I just change the missings prior to participation) or if there any other problems with it.



I am very interested in your feedback. Or maybe you have any other idea on how to tackle that problem? Thank you very much in advance!

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