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# Re: st: Local Linear Regression for Regression Discontinuity Designs

 From Alex Olssen To statalist@hsphsun2.harvard.edu Subject Re: st: Local Linear Regression for Regression Discontinuity Designs Date Mon, 23 May 2011 23:40:14 +1200

```Dear Andreas,

Estimation of the local linear regression model can be implemented by
OLS (restricting the subset of observations appropriately) IF you are
of -rd- only allows estimation based on the triangular kernel - which
is optimal for boundary estimation - see the references in Imbens and
Lemieux 2009.

As an aside, it would have been tremendously helpful if you had posted
some example code with your question.

I compared OLS with dummies, lpoly, and an older version of Austin
Nichol's -rd- and got the same result in each case (all used the
rectangular kernel)
I tried again tonight but even after using the triangular kernel I
couldn't quite get the results from manual -lpoly- to match those of
Austin Nichol's -rd-

I present an example using the auto dataset - just to show the code.

* test rd
sysuse auto, clear
ren price y
gen x = length - 193
gen z = (x >= 0)
gen z_x = z*x

reg y x if x > -10 & x < 0
reg y x if x >= 0 & x < 10
reg y x z z_x if x > -10 & x < 10
* OLS with dummies produces the same result as
* OLS on either side when the same bandwidths are used

lpoly y x if x < 0, deg(1) ker(rec) bwidth(10) gen(L) at(x) nogr
lpoly y x if x >= 0, deg(1) ker(rec) bwidth(10) gen(R) at(x) nogr
gen diff = R - L
su diff if x == 0
* OLS with dummies produces the same result as
* local linear regression when the rectangular kernel is used

* note Austin Nichol's rd only allows use of the traingle kernel
* which is boundary optimal - see references in Imbens and Lemieux 2009
lpoly y x if x < 0, deg(1) ker(tri) bwidth(10) gen(L2) at(x) nogr
lpoly y x if x >= 0, deg(1) ker(tri) bwidth(10) gen(R2) at(x) nogr
gen diff2 = R2 - L2
su diff2 if x == 0
rd y x, deg(1) bwidth(10)

Perhaps Austin could comment on the difference?  I expect I have made
an oversight somewhere.

Kind regards,

Alex

On 23 May 2011 01:20, andreas nordset <andreas.nordset@gmail.com> wrote:
> Dear Statalist members,
>
> in a context in which individuals are eligible for a treatment if and
> only if they are aged above 50, I would like to implement a Regression
> Discontinuity Design to estimate the effect of the treatment on
> several outcomes, i.e. the difference between the average outcome just
> above the threshold and the average outcome just below the threshold,
> where these averages must be estimated.
>
> My impression is that the standard way of doing this is to use "Local
> Linear Regression".
>
> My understanding is that I can hence obtain the Reduced-Form effect by
> simply estimating:  -reg outcome D50 age D50_age if
> inrange(age,50-h,50+h)-
> where D50 is a dummy for being aged above 50, D50_Age is the
> interaction of that dummy with age, and h is the bandwidth.
> Equivalently, I would obtain the Wald estimates with:  -ivreg2 outcome
> age D50_age (treatment=D50) if inrange(age,50-h,50+h)-.
> Put differently, my understanding of "Local Linear Regression" is to
> estimate simple linear OLS regressions, but a separate line on each
> side and only "locally", i.e. using only observations from the
> interval (50-h,50+h).
>
> Yet when I do so, I obtain estimates that differ from those obtained
> using Austin Nichol's -rd- command that apparently uses the -lpoly-
> command for local linear regression. Does that mean that my
> understanding of LLR is incorrect, maybe because some more
> sophisticated weighting of observations is needed? In your view, is
> such a more sophisticated procedure needed, and if so what would be
> the problems with my very simple procedure?
>
> *
> *   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/
>

*
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```