st: RD Optimal Bandwidth Algorithm sensitive to scaling?

[Stata Chris <statachris@gmail.com>]

Dear list members,

I am using Austin Nichols' -rd-
(http://ideas.repec.org/c/boc/bocode/s456888.html) command,
as well as the related -rdob- by Fuji-Imbens-Kalyanaraman-Fuji
(http://www.economics.harvard.edu/faculty/imbens/software_imbens)

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
http://www.nber.org/papers/w14726 ) 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,
Chris
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