re: st: RDD robustness check: Controlling for covariates?

["Ariel Linden, DrPH" <ariel.linden@gmail.com>]

Hi Jen,

If I understand your question correctly, you want to see if the coefficient
of the treatment assignment variable changes when you control for a
covariate? If that is what you are asking, I'd say that the covariate must
be span both sides of the cutoff. I can't imagine a scenario where you are
trying to adjust/control for something that occurs to only the treated, or
to only the controls. After all, the regression discontinuity design is
intended to mirror a randomized controlled trial (albeit in observational
data). So, just like in an RCT, you would control for baseline
characteristics across both treatment and control groups. 

On another, but related, topic, you should conduct a test to see if that
covariate is "balanced" (again, as you would in an RCT). This is easily
done. You simply replace the outcome variable with the covariate and leave
the rest of the regression model as is. If the covariate is balanced, then
we'd expect to see confidence intervals cross zero (and an insignificant p
value)...

I suggest you give a look at Austin Nichol's -rd- program (findit rd) as
well as read the section on RD in his paper: Nichols, Austin. 2007.  Causal
Inference with Observational Data. Stata Journal 7(4): 507-541.

I hope this helps

Ariel 

Date: Mon, 13 Feb 2012 17:23:46 +0100
From: Jen Zhen <jenzhen99@gmail.com>
Subject: st: RDD robustness check: Controlling for covariates?

Dear list members,

just as a robustness check (not for the main estimates) for a
regression discontinuity design, I'd like to test whether results
change when I control for a covariate.

However, I'm unsure whether I should just control for the covariate in
the same way on both sides of the threshold, or whether I need to
allow the effect of the covariate to vary between the two sides, i.e.
should I use

- - reg outcome T forcingvar T_forcingvar covar -
or
- - - reg outcome T forcingvar T_forcingvar covar T_covar-  ?

Thanks so much and best regards,
JZ

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