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st: Pooling several discontinuities: Use observations twice?


From   Jen Zhen <jenzhen99@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Pooling several discontinuities: Use observations twice?
Date   Mon, 6 Dec 2010 20:17:53 +0100

Dear all,

here's an interesting question:

I have a setup in which the assigned treatment size increases (by
different amounts) every 2 years of age.

What I've done so far is to regress my outcome on the assigned
treatment applicable to the respective age interval, while controlling
for a spline in age. But I'm wondering what I would gain anything from
somehow aligning all discontinuities, so that I could then do a more
standard Regression Discontinuity Design? At least I could then plot
the discontinuity in a more intuitive way. So I'm pondering how to
best implement this.

For simplicity, say I have 4 age intervals, with assignment jumps
between intervals 1/2, 2/3 and 3/4. Then observations in brackets 1
and 4 will in any case be used only once. But I'm thinking that
observations from brackets 2 and 3 can give me 2 pieces of
information, namely once what it's like to be to the right of
respectively the 1st and the 2nd threshold, and once what it's like to
be to the right of respectively the 2nd and the 3rd threshold. So I'm
thinking of giving each observation from those intermediate brackets a
twin using the -expand- command, and then assign each first twin to
the next trheshold to its left and each second twin to the next
threshold to its right. Then I want to compute for each observation
the distance to its repsective threshold, and then just run a single
regression of my outcome on the assigned treatment (I don't observe
actual treatments) along with a flexible function of the distance from
the threshold. I'm wondering however whether and if so how I will need
to adjust standard errors if I use many observations twice, to make
sure I do not overstate the amount of information I have? Or would you
counsel to use each observation from an intermediate bracket only
once, assigning those left of the bracket's median to the left
threshold, and those right of the median to the right threshold?

Thanks and all best,
JZ
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