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Re: Re: st: Regression discontinuity with interrupted time series


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: Re: st: Regression discontinuity with interrupted time series
Date   Thu, 7 Mar 2013 16:03:08 -0500

Ariel <ariel.linden@gmail.com>:
I would not go that far.  I suggested one way forward that I thought
would be easy to interpret, and one that was harder to interpret, but
there are others.  The OP seems to want a packaged solution marrying
RD and ITS, based on e.g.
 http://ies.ed.gov/funding/grantsearch/details.asp?ID=754
but I suspect a more nuanced approach will be easier to swallow both
for the applied researcher and his readers.

Another way forward is to note the connection of a trend difference to
the "regression kink" design.

My concern was that the OP has one instrument and may want to estimate
two impacts: a difference in level at time t and a difference in trend
for time>=t. One can adopt a control function approach or use the
interaction of the instrument A (for "above the cutoff") with t as a
second instrument, which was my second suggestion for a way forward.
The key there is that At is zero for all time before the intervention,
and is used as an instrument for Tt, so that term is picking up the
change in trend (the discontinuous jump in dy/dt, not the
discontinuous jump in y).


On Thu, Mar 7, 2013 at 2:20 PM, Ariel Linden. DrPH
<ariel.linden@gmail.com> wrote:
> Austin is absolutely right here. For an interesting historical perspective,
> RD and ITSA originated from the same basic idea. That is, find a continuous
> x-variable and define a cutoff. In the case of ITSA, the x-variable is
> "time" and we are interested in both the "step" (first month of the
> intervention), and the "trend" (of all the months after the start of the
> intervention). In RD, the x-variable is also continuous, but here we care
> only about the average effect determined by the local values on either side
> of the cutoff.
>
> Given this general perspective, it seems an oddity to combine the two
> methods, since they require a x-variable which is going to differ, and a
> cutoff, which is going to differ. It seems as if you'd be referring to a
> sub-group analysis in which the subgroupings were decided at one level of
> the analysis and then compared at the next level (e.g., right side of the
> cutoff on the RD analysis, then analyzed at the time cutoff on the ITSA)...
>
> It is difficult to imagine how this could be done in any valid fashion...
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