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

 From Jen Zhen To statalist@hsphsun2.harvard.edu Subject Re: st: Regression Discontinuity, with treatment effects that vary with an endogenous covariate? Date Sun, 4 Jul 2010 12:13:38 +0200

```Thanks for the reply, Austin!

No, prior earnings do not jump at the cutoff. So the point is not to
"control" for unbalancedness of any covariates between treatment and
control group, for as far as I've been able to check these are all
continuous at the cut-off.
It's more that I expect that within those treated (right of the
cutoff) there will  be a difference between those with higher and
those with lower prior income.

So if I run
Y = A + B*(tenure) + C*(Dummy for Tenure>=T) + D*(Dummy for
Tenure>=T)*(inc) + E*(inc) + u,
wouldn't that allow me to obtain different treatment effects depending
on the value of inc?

Many thanks and all best,
JZ

PS: I was of course referring to the "-rd- command written for Stata"
(that should be the right way to put it?), as opposed to "Stata's -rd-
command". Apologies for the imprecise formulation.

On Sat, Jul 3, 2010 at 3:42 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> The RD design uses the jump in expected benefits at the tenure cutoff
> to identify a causal effect at one particular value of tenure; if
> there were a jump also in prior earnings at that cutoff, it would
> invalidate the design.  So, no, you can't include an interaction.
> Also note that Stata has no -rd- command (ssc describe rd).
>
> On Sat, Jul 3, 2010 at 5:13 AM, Jen Zhen <jenzhen99@gmail.com> wrote:
>> 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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