Re: st: Regression discontinuity with interrupted time series

[Joshua Mitts <joshua.mitts@yale.edu>]

Hi Austin,

Thank you for taking the time to reply in such depth.  Let me try to
clarify--I don't think I explained very clearly.  I'm using a fuzzy RD
design with a numeric cutoff that determines eligibility for the
program.  Treatment is taken by compliers at time t.  I measure
subjects at repeated intervals prior to and following treatment.  The
assumptions of non-manipulability of assignment variable,
monotonicity, and exclusion are valid at time t.

I could stay in the world of traditional RD and observe differences at
t+5 minus t-5.  But that seems unduly restrictive.  If I assume a
linear trend and could somehow control for autocorrelation, the
additional outcomes at t+1, t+2, etc. would seem to provide useful
data.  These are, after all, affected by the treatment at time t too.
ITS says I can compare trends pre- and post-treatment (with control
group providing counterfactual over time), and RD gives local
randomization with a non-manipulable arbitrary cutoff.  It seems there
has to be a way to combine these, e.g., regress change in pre- to
post- trend on treatment dummy (w/eligibility instrument) weighted by
proximity to numeric cutoff at time t.

Thanks again,
Josh

On Wed, Mar 6, 2013 at 4:51 PM, Austin Nichols <austinnichols@gmail.com> wrote:
>
> 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
> >
> > [1] Somers, Maree-Andre, Pei Zhu, Robin Jacob, and Howard Bloom. 2009.
> > Combining Regression Discontinuity Analysis and Interrupted
> > Time-Series Analysis. Grant #R305D090009. Washington, DC: Institute of
> > Education Sciences, U. S. Department of Education.
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