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

[John Antonakis <john.antonakis@unil.ch>]

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.

__________________________________________

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Faculty of Business and Economics (HEC)
Department of Organizational Behavior
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On 12.10.2010 22:10, Austin Nichols wrote:
> In that case, I strongly disagree with your advice--you are
> constraining the slope of pretest to be the same on both sides of the
> discontinuity, and not using any concept of a bandwidth around the
> cutoff; local linear regression is the standard approach, not linear
> regression.  Further, if you mean to subtract the mean of the
> assignment variable when you say "pretest is mean-centered" then the
> coefficient on group does not measure the jump in outcomes at the
> cutoff unless the cutoff happens to be right at the mean of pretest.
>
> On Tue, Oct 12, 2010 at 8:50 AM, John Antonakis<john.antonakis@unil.ch>  wrote:
> > Hi Austin:
> >
> > Using the "classical" RDD design, "group" is the treatment indicator;
> > pretest is the "cutoff" measure for assignment to group.
> >
> > Best,
> > On 12.10.2010 03:34, Austin Nichols wrote:
> > > John --
> > > I don't understand your advice here at all--is group supposed to be a
> > > treatment indicator?  Is pretest an assignment variable or a control
> > > variable?
> > > Prashant --
> > > One can of course write a wrapper -program- containing several
> > > estimators and -bootstrap- the whole thing, which then allows testing
> > > across estimators--the -rd- package on SSC is no exception to that
> > > general rule, but make sure you set the bandwidth exogenously if you
> > > are using local linear regression as -rd- does.  Also -findit ivqte-
> > > for one approach to quantile TE, and note that RD can be seen as a
> > > version of IV; see refs cited in -help rd-.
> > >
> > > On Mon, Oct 11, 2010 at 3:04 AM, John Antonakis<john.antonakis@unil.ch>
> > >   wrote:
> > > > Hi:
> > > >
> > > > You could use -suest-.  For example, suppose you have the following basic
> > > > specification (where pretest is mean-centered, to set the intercept to
> > > > the
> > > > cut-off value):
> > > >
> > > > y = b0 + b1*pretest + b2*group + e
> > > >
> > > > Estimate the model for each group, e.g.,
> > > >
> > > > reg y pretest group if boys==1
> > > > est store boys
> > > > reg y pretest group if boys==0
> > > > est store girls
> > > > suest boys girls
> > > >
> > > > Now you can do cross-equation tests, e.g.,
> > > >
> > > > test [boys_mean]group = [girls_mean]group
> > > >
> > > > Hope this helps.
> > > > John.
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