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st: re: RD with covariates: With Frisch-Waugh Theorem? What are the SEs?


From   "Ariel Linden, DrPH" <ariel.linden@gmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: re: RD with covariates: With Frisch-Waugh Theorem? What are the SEs?
Date   Sun, 17 Apr 2011 13:04:50 -0700

Jen,

First off, the rules of engagement for the statalist is that the poster
provide clear details about what they are referring to, in this case, you
did not reference where you found rdob, rd, or provide a reference to the
Frisch-Waugh Theorem in the context of regression discontinuity.

rdob (found at
http://www.economics.harvard.edu/faculty/imbens/software_imbens) does
provide SE's, whether or not you include covariates.

rd (findit -rd-) uses -lpoly- as its base (run separately for left and right
of the cutoff). Indeed, -lpoly- does not accept covariates. However, you can
get SE's from the model as well as bootstrap rd to get bootstrapped
estimates (read the help file for rd). Conversely, you could run linear
regressions manually on either side of the cutoff, limited to the local
neighborhood under study, and add covariates as necessary, or you could run
the standard regression model traditionally used in rd (see Lee and Lemieux
"Regression discontinuity designs in economics" Journal of Economic
Literature, June 2010, pp 281-355 for a comprehensive discussion on all
these approaches). 

As for the Frisch-Waugh Theorem, you did not provide a reference, so unless
we all know what the specific context is (or validity of the approach you
are suggesting) we cannot be helpful.

Ariel

Date: Sat, 16 Apr 2011 12:05:03 +0200
From: Jen Zhen <jenzhen99@gmail.com>
Subject: st: RD with covariates: With Frisch-Waugh Theorem? What are the
SEs?

Dear Statalist members,

I would like to implement a Regression Discontinuity Design in which I
control for additional covariates so as to reduce the amount of noise.
And I need to know the SEs of my estimate.

Imbens-Kalyanaraman's -rdob- does not give me SEs once I add covariates, and
Austin Nichol's -rd- does not seem to allow for covariates.

So I'm wondering whether, following the Frisch-Waugh Theorem, I can just
first -reg- outcome and forcing variable on my set of additional covariates,
and then just do the -rd- or -rdob-using the residuals of the two
regressions? But will I then automatically get the correct SEs, or do I need
to make some adjustment?

Any advice on this would be much appreciated.

Best regards,
JZ


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