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

From   Jen Zhen <>
Subject   Re: st: re: RD with covariates: With Frisch-Waugh Theorem? What are the SEs?
Date   Mon, 18 Apr 2011 15:17:18 +0200


thanks a lot for your reply!
And apologies for not giving the link for Fuji-Imbens-Kalyanaraman's
-rdob- command--I had mistakenly assumed that giving the authors'
names would suffice.

Furthermore, my reference to the Frisch-Waugh Theorem was only an idea
based on what one learns in graduate school about OLS regressions, but
I am unfortunately not aware of any existing applications to an RD
context and therefore not sure whether such an application is in fact

Now: Your comment that -rdob- does in general provide SEs also in the
presence of further covariates has prompted me to search further why
it did not do so in my case (I just got a "."):

I turned out that this happened whenever the outcome variable was
missing for some observations.
I had not initially thought of this, because other estimation
commands, like Stata's -reg-, would just estimate the respective
equation using only the non-missing observations, and also because the
same problem had not arisen when I did not include covariates.
But now that I have found out about this, dropping all observations
for which my outcome is not observed does seem to solve the problem.

So thanks again for your help and best regards,

On Sun, Apr 17, 2011 at 10:04 PM, Ariel Linden, DrPH
<> wrote:
> 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
> 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 <>
> 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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