Re: st: Regression Discontinuity Designs with rd package and binary outcome

[Austin Nichols <austinnichols@gmail.com>]

Philippe Van Kerm asked me that same question in 2008, and in the
absence of any new insight, my answer is the same. The -rd- design can
be thought of (and estimated) as a local IV model (-ivreg- with
weights emphasizing obs close to the cutoff), where a binary treatment
is instrumented by a dummy D for "Z>0 (assignment var above the
cutoff)" while controlling for Z and DZ. It might make sense to
estimate local logits in many cases, for the first stage since
treatment is binary, or the second stage when the outcome is binary.
But logits and IV do not mix well. You can write out a GMM form of
local probits or logits or estimate a reweighted bivariate probit, but
while the linear model works well in most cases even when variables
are binary, the other models require functional form assumptions and
may often introduce bias where the local linear model had negligible
bias.

There are cases that need special treatment, where the linear model
does not work well, but then you have to switch to another model, and
give up on -rd- which is designed around linear models only.
Currently, there is only one fix for a failure of the linear model in
-rd-, when predictions for mean treatment at the cutoff lie outside
the feasible range (where you might want another link function) but
the fix is just to switch to local mean smoothing (a zero degree
polynomial), not to a logit or another model.

On Sun, Jan 13, 2013 at 6:26 PM,  <gregor.hochschild@gmx.de> wrote:
> Hi,
>
> I am using a Regression Discontinuity Designs and Austin Nichols's rd command to estimate the effect of some outcome y on a treatment D, which is defined by a cutoff point c in some continuous variable x. My outcome variable y is binary. This is a pretty common situation for RDD. E.g. the classical incumbency advantage example often uses "winning in the next election" as one of the outcome variables (e.g. Lee and Lemieux 2010).
>
> Here is my question: I never read something about linear vs. logistic regression in the RDD literature (or the distribution of the outcome variable in general). Linear (or polynomial) local regressions are commonly used such as `lpoly` in the rd package. Why not some local logistic regression?
>
> Thanks!
>
>
>
> Lee, David S., and Thomas Lemieux. 2010. “Regression Discontinuity Designs in Economics.” Journal of Economic Literature 48:281–355.
>
> rd package
> http://ideas.repec.org/c/boc/bocode/s456888.html

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