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Re: st: Regression discontinuity with interrupted time series


From   Joshua Mitts <joshua.mitts@yale.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Regression discontinuity with interrupted time series
Date   Thu, 7 Mar 2013 16:00:59 -0500

Hi all,

Thank you all so much for the responses.  Austin, your comments were
very helpful and I greatly appreciate it.

William, I do not have a link to a paper, unfortunately.  My citation
was to a research project on this issue for which MDRC received a
~$450k DOE grant in 2009
(http://ies.ed.gov/funding/grantsearch/details.asp?ID=754).
Apparently, the results have not yet been circulated publicly in
written form.  When that happens, maybe it will shed more light on
these types of scenarios.

Best,
Josh

On Thu, Mar 7, 2013 at 3:46 PM, William Buchanan
<william@williambuchanan.net> wrote:
>
> I have tried to find the paper that Joshua referenced in the initial query
> and had little luck.  I found another paper written by one of those authors
> citing the paper referenced by Joshua.  Perhaps it would be helpful if
> Joshua could provide a link to find the paper that he referenced so others
> can get a better idea of what he is trying to do?
>
>
> On Mar 7, 2013, at 11:20 AM, 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...
> >
> > Ariel
> >
> > Date: Wed, 6 Mar 2013 16:51:24 -0500
> > From: Austin Nichols <austinnichols@gmail.com>
> > Subject: Re: st: Regression discontinuity with interrupted time series
> >
> > Joshua Mitts <joshua.mitts@yale.edu>:
> > You need to be a lot more clear about your scientific model of the
> > data generating process.  I have not read the cited paper, but I am
> > doubtful about the marriage of RD and ITS. The point of RD is that
> > outcomes of observations on either side of the cutoff are identical on
> > average except for treatment status so the jump in outcomes at the
> > cutoff is the effect of treatment; that is not true if you think
> > treatment has some dynamic impacts, or in other words the effect of
> > treatment increases (or decreases) in the assigment variable, so that
> > you do not want the instantaneous impact of treatment at the cutoff,
> > but some effect away from the cutoff.  Imagine it this way: you have
> > an announcement event that affects stock prices at noon but you do not
> > want to compare stock prices at one minute after noon to noon because
> > you think the event actually changes the time path of investment and
> > you want changes in market valuation over some period until the
> > announced policy change takes place.  This is no longer a good
> > situation for RD if you are thinking about comparing across time. You
> > can still use the dummy for above the cutoff at time t as a dummy for
> > treatment in periods after t, but the comparison will not have the
> > clean RD interpretation (where the counterfactual is essentially
> > observed if the data is dense around the cutoff) if you are using time
> > as an assignment variable. Can you assume linear trends before and
> > after time t? You can define time as time minus t so that the constant
> > is the jump in mean outcomes at t, and the dummy for above the cutoff
> > is the instrument for treatment; if they are perfectly collinear you
> > have a "sharp" design but you may want to also estimate a change in
> > trend after t for the treatment group, for which you may need an
> > additional instrument--the key here is how the cutoff is defined.  Is
> > the variable that is compared to the cutoff subject to manipulation?
> > Changing over time? Only examined at time t?  If you have an assigment
> > variable that is not time, you are back in the world of RD, and you
> > may be better off with a long difference in outcomes (reducing
> > problems due to measurement error in fixed effect models), e.g. y at
> > t+5 minus y at t-5, regressed on treatment in the usual RD manner.
> >
> > On Wed, Mar 6, 2013 at 11:00 AM, Joshua Mitts <joshua.mitts@yale.edu>
> > wrote:
> >> Hi,
> >>
> >> How can I combine regression discontinuity with interrupted time
> >> series analysis in Stata?  I have repeated observations of an outcome
> >> variable for ~180 units over time, an intervention at time t at a
> >> cutoff value, and more repeated observations post-intervention.  With
> >> ordinary RD, I can only measure the outcome individually at t+1, t+2,
> >> etc.  It seems this is an active area of research[1], but I'm not sure
> >> how to implement it in Stata.  Any suggestions would be greatly
> >> appreciated.
> >>
> >> Thank you,
> >> Josh
> >>
> >> --
> >> Joshua Mitts
> >> Yale Law School '13
> >> joshua.mitts@yale.edu
> >
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