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

["Ariel Linden. DrPH" <ariel.linden@gmail.com>]

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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