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

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Re: comparing regression discontinuity treatment effects for different subsamples |

Date |
Tue, 12 Oct 2010 22:37:00 -0400 |

John Antonakis <john.antonakis@unil.ch>: Yes, I would still disagree with this characterization. The idea in RD is to estimate the discontinuity in mean outcomes at a discontinuity in treatment, allowing the assignment variable to have an arbitrarily convoluted (but continuous) effect on expected outcomes. Hence local linear regression, not regression, and estimated separately on each side of the discontinuity. You can use a rectangular kernel, or a triangle kernel, or what have you, but you should not simply include the whole sample and constrain the effect of the assignment variable to be everywhere the same. The choice of bandwidth is the tuning parameter trading off bias and variance; if you use only a few observations on either side of the cutoff, you have low bias because those observations really are exchangeable, but you have very high variance estimates; if you use a lot of data on either side of the cutoff you have lower variance but possibly more bias as well as you project out to the conditional mean at the cutoff from both sides. Your proposed approach maximizes bias, in many cases. You are also implicitly assuming a deterministic assignment to treatment, I think, rather than a so-called "fuzzy" RD design. If you want to frame it as a regression, instead of g z=pretest-cutoff reg y group z which is your proposal, you might instead do g w=max(0,1-abs(z)) la var w "Triangle kernel weight" g a=(z>0) la var a "Above cutoff" g za=z*a reg y a z za [pw=w] or ivreg2 y (group=a) z za [pw=w] using -ivreg2- from SSC, if group (measuring treatment status) is not always equal to a. Compare approaches: * Note that rd is from SSC; * rdob from http://www.economics.harvard.edu/faculty/imbens/software_imbens mat c=(1,.5\.5,1) set seed 1 drawnorm e pretest, n(1000) corr(c) clear g z=pretest-0 g above=z>0 g group=cond(uniform()<.8,above,1-above) g y=z-z^3+group+e * next is per John Antonakis reg y z group g w=max(0,1-abs(z)) g za=z*above ivreg2 y (group=above) z za [pw=w] rdob y z, c(0) fuzzy(group) bs:rd y group z, bw(1) * now a "sharp" design mat c=(1,.5\.5,1) set seed 1 drawnorm e pretest, n(1000) corr(c) clear g z=pretest-0 g above=z>0 g group=above g y=z-z^3+group+e * next is per John Antonakis reg y z group g w=max(0,1-abs(z)) g za=z*above reg y group z za [pw=w] rdob y z, c(0) bs:rd y group z, bw(1) On Tue, Oct 12, 2010 at 5:20 PM, John Antonakis <john.antonakis@unil.ch> wrote: > Hi Austin: > > Thanks for this; I was not clear enough. In the following, suppose that > selection is based on the following explicit rule (where cut-off is at the > mean of the pretest): > > group =1 if pretest of person i is less than or equal to mean of pretest > group =0 if pretest of person i is greater than pretest > > We provide the treatment to group 1, and we estimate: > > y = b0 + b1*(pretest - mean pretest) + b2*group + e > > Here, b2 is the treatment effect and captures the jump in the discontinuity. > Thus, constraining b2 to be equal across the two samples captures the > difference in treatment effects across the two samples--or am I missing out > on something? > > Best, > J. > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Re: comparing regression discontinuity treatment effects for different subsamples***From:*Prashant <presearchwork@gmail.com>

**Re: st: Re: comparing regression discontinuity treatment effects for different subsamples***From:*John Antonakis <john.antonakis@unil.ch>

**Re: st: Re: comparing regression discontinuity treatment effects for different subsamples***From:*Austin Nichols <austinnichols@gmail.com>

**Re: st: Re: comparing regression discontinuity treatment effects for different subsamples***From:*John Antonakis <john.antonakis@unil.ch>

**Re: st: Re: comparing regression discontinuity treatment effects for different subsamples***From:*Austin Nichols <austinnichols@gmail.com>

**Re: st: Re: comparing regression discontinuity treatment effects for different subsamples***From:*John Antonakis <john.antonakis@unil.ch>

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