binary interaction and regression discontinuity

[Jimmy Wang]

My goal is to examine whether the effect of X₁ on Y will be moderated by a binary variable D. So the regression is in this simple form:

Y=b₀+b₁X₁+b₂X₁*D + b₃D + e

But one complicating factor is that D in my study is a function of X₁ itself; namely, D=1 when X₁-X₂>=0 and D=0 otherwise (where X₂ is another level-1 variable).

In other words, I hypothesize that the effect of X₁ will vary, depending on whether D is 1 or 0. This looks to me a bit similar to the regression discontinuity design but not exactly the same, as the difference of Y in the neighborhood of the discontinuity point isn't my research focus.

Can I use the above regression (namely, estimated b₁, b₂, b₃) to test my research hypothesis? Is there any potential concern?

Thank you.

[Dave Airey]

Are you worried about a regression singularity or unacceptable VIFs?

[Jimmy Wang]

Are you worried about a regression singularity or unacceptable VIFs?

Not really. The regression outputs didn't show anything unusual.

I asked mainly because I couldn't find textbook examples/papers similar to what I'm doing, and fear that this design
may have theoretical problems that I'm not aware of.

Any thought?

Thank you.