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From |
Austin Nichols <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 14 Jan 2013 10:36:38 -0500 |

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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Regression Discontinuity Designs with rd package and binary outcome***From:*Jeffrey Wooldridge <jmwooldridge60@gmail.com>

**References**:**st: Regression Discontinuity Designs with rd package and binary outcome***From:*gregor.hochschild@gmx.de

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