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st: RD Optimal Bandwidth Algorithm sensitive to scaling?

From   Stata Chris <>
Subject   st: RD Optimal Bandwidth Algorithm sensitive to scaling?
Date   Fri, 15 Jul 2011 15:45:27 +0200

Dear list members,

I am using Austin Nichols' -rd-
( command,
as well as the related -rdob- by Fuji-Imbens-Kalyanaraman-Fuji

Now I've discovered that the optimal bandwidth chosen and hence the
resulting estimates are sensitive to the scaling of the outcome variable.
To demonstrate this, I make use of an example discussed in this context
in an earlier post:

sysuse auto, clear
gen Price = price/1000
gen z = length - 193
rd price z
rd Price z

As you can check, when I use as outcome the price in 1000 dollars
("Price") rather than in dollars ("price"), I get a different bandwidth
and hence a very different estimate,
whereas I think I would wish to get the previous estimate just divided
by 1000.

This does not seem a very desirable property to me, but I'm not sure
where in the optimal bandwidth algorithm (see ) this comes from
and whether it would be possible to avoid this. Probably some of you
can say more about this?

Thanks and best regards,
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