Let say I have a really simple model $y=x+controls+u$, x is the treatment and is endogenous dummy variable, and z is an instrument variable for x. I want to test the casual relationship between x and y(effect of treatment). I have tested that z is corrected with x, it increased people who are treated, it is also likely to be exogenous.
However, the problem is, I suspect that z will also increase the effect of treatment. That is, it not only affect y through increasing x, but also increase x’s effect. Also, z probably has nothing to do with people who aren’t treated, and it doesn’t affect y for the whole samples(not much people are treated).
Under this situation, will the instrument be invalid? I only took introductory econometrics, I guess maybe it is some sort of heteroscedasticity?