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

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: Regression Discontinuity, with treatment effects that vary with an endogenous covariate? Date Sun, 4 Jul 2010 09:35:46 -0400

```Jen Zhen <jenzhen99@gmail.com> :
inc is endogenous, so your model does not support causal inference
using the RD assumptions--if you can't identify coef D and E
plausibly, then you have problems--maybe you can find an instrument
for inc and switch to an IV formulation?

Nothing stops you mechanically from stratifying on inc and running
-rd- within subsamples, but you have conceptual problems with
interpretation, IMHO.

PS. the Statalist FAQ exhorts you to specify where software comes from
(e.g. -rd- from SSC).

On Sun, Jul 4, 2010 at 6:13 AM, Jen Zhen <jenzhen99@gmail.com> wrote:
> 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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