st: Regression Discontinuity, with treatment effects that vary with an endogenous covariate?

[Jen Zhen <jenzhen99@gmail.com>]

Dear Statalisters,

I would like to estimate the treatment effect on unemployment duration
of receiving a lump-sum cash transfer.
The individuals in my dataset receive some dollar amount iff their
tenure exceeds some threshold value, so I considered using a
Regression Discontinuity Design.

One issue though is that the amount is the same regardless of
individuals' prior monthly earnings, however my intuition tells me
that, if there is an effect, its size should depend on prior earnings,
with the effect being larger the more earnings months are being
replaced by the payment, i.e. the lower prior monthly earnings. Prior
earnings are of course an endogenous variable.

So I am wondering whether it would make sense to use a RD design, and
add to the treatment dummy for being above the threshold also an
interaction of that dummy with prior earnings, so as to allow the
treatment effect to vary (presumably negatively) with prior wages?
If so, is there a way to do this using Stata's -rd- command?

Any advice is much appreciated.

Thanks and best regards,
JZ
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