Re: st: St : Regression discontinuity with Dichotomous dependent variable

[Nick Sanders <sandersn@stanford.edu>]

Well noted - my use of reg assumed a sharp discontinuity, and a more correct
specification would have said "a local linear regression with rectangular weights" and added a bandwidth range (e.g., if running > -band & running < band). One might also consider adding clustering on the running variable (a la Lee and Card 2008).

Lee, David S. and David Card, Regression Discontinuity Inference with Specification Error, Journal of Econometrics, 127 (2008)


On Jan 3, 2012, at 3:17 PM, Austin Nichols <austinnichols@gmail.com> wrote:

> Nick Sanders <sandersn@stanford.edu>:
> Not so; you would need weights defined by the kernel with a given
> bandwidth to make it a local linear regression.  Also, if treatment is
> not deterministically determined by the running variable, i.e.
> assignment is "fuzzy" as they say, you need ivregress not regress.
> 
> The ref given by Cameron McIntosh from July 14, 2011 pertains more to
> -biprobit- and its relatives.
> 
> On Tue, Jan 3, 2012 at 4:05 PM, Nick Sanders <sandersn@stanford.edu> wrote:
>> I bow to those with greater knowledge, but I imagine one could simply specify (assuming the treatment occurs if the running variable is greater than the cutoff):
>> 
>> gen pastcut = running > cut
>> gen runXpast = running * pastcut
>> 
>> reg outcome running pastcut runXpast
>> 
>> which is just a local linear regression (without covariates) and the coefficient on pastcut is interpretable as the impact of the treatment.
>> 
>> While there is a risk a predicted value might fall outside 0 and 1, I think that is generally accepted as ignorable unless you face many unusual values.
>> 
>> On Jan 3, 2012, at 2:52 PM, Cameron McIntosh <cnm100@hotmail.com> wrote:
>> 
>>> I think this deck might be helpful:
>>> Nichols, A. (July 14, 2011). Causal inference for binary regression. http://www.stata.com/meeting/chicago11/materials/chi11_nichols.pdf
>>> 
>>> Cam
>>> ----------------------------------------
>>>> Date: Tue, 3 Jan 2012 12:41:32 -0800
>>>> From: ayman.farahat@yahoo.com
>>>> Subject: Re: st: St : Regression discontinuity with Dichotomous dependent variable
>>>> To: statalist@hsphsun2.harvard.edu
>>>> 
>>>> HI Nick
>>>> This is exactly correct. I am not sure about the polynomial.
>>>> 
>>>> Also, while it is possible to model a 0/1 as a continuous with OLS, there is the risk that i would get values outside the 0/1 range.
>>>> Thanks
>>>> Ayman
>>>> 
>>>> 
>>>> 
>>>> 
>>>> ________________________________
>>>> From: Nick Sanders
>>>> To: "statalist@hsphsun2.harvard.edu"
>>>> Sent: Tuesday, January 3, 2012 11:19 AM
>>>> Subject: Re: st: St : Regression discontinuity with Dichotomous dependent variable
>>>> 
>>>> Hello Ayman,
>>>> 
>>>> If I understand, you have a 0,1 variable as your outcome and a continuous running variable. You can do this with standard OLS and it is the classic RD setup. Perhaps your concern is the polynomial choice in the running variable (independent)?
>>>> 
>>>> On Jan 3, 2012, at 1:10 PM, Ayman Farahat  wrote:
>>>> 
>>>>> Hello;
>>>>> 
>>>>> I am working on evaluating a treatment effect. The treatment assignment is based on a regression model that assigns a continuous score. Subjects that have a score greater than the cutoff are treated while those below are not treated. So it fits the RD design framework.
>>>>> 
>>>>> However, the dependent variable is not a continuous response but rather a dichotomous variable; did the subject perform a certain action. I am using Austin Nichol's excellent RD package. However, the package assumes that the dependent variable is continuous and uses a polynomial to fit a local regression.
>>>>> 
>>>>> Is there a way to extend RD to include dichotomous dependent variables?
>>>>> Thanks
>>>>> Ayman
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