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# RE: st: Diff-in-diff: how to account for treatment intensity, rather than just a treatment dummy?

 From Cameron McIntosh To STATA LIST Subject RE: st: Diff-in-diff: how to account for treatment intensity, rather than just a treatment dummy? Date Sun, 12 Aug 2012 22:15:28 -0400

```The following may also be of interest:

Crown, W.H. (2010). There's a reason they call them dummy variables: a note on the use of structural equation techniques in comparative effectiveness research. Pharmacoeconomics, 28(10), 947-955.

Cam

> Date: Sun, 12 Aug 2012 15:20:59 -0700
> Subject: Re: st: Diff-in-diff: how to account for treatment intensity, rather than just a treatment dummy?
> From: tirthankar.lists@gmail.com
> To: statalist@hsphsun2.harvard.edu
>
> "Second, if I do not find another way than to break the treatment
> variable D into 10 dummies, does anyone know how I could recover the
> mean ATT and its standard error? I guess I would need to weight the 10
> different ATTs that I got, but what should be the weights? How about
> number of treated observations in each treatment group?"
>
> The process you want is described in Imbens' 2000 Biometrika paper
> which proposes the Generalised Propensity Score [GPS]
> dx.doi.org/10.1093/biomet/87.3.706
> See page 708.
>
> T
>
> On Sun, Aug 12, 2012 at 2:36 PM, John Carey <johncarey196@gmail.com> wrote:
> > Hi everyone!
> >
> > I have been working on a difference-in-differences strategy, and I was
> > hoping someone could clarify an important point for me.
> >
> > In the beginning, the treatment I am working on was not a dummy. It is
> > a discrete variable ("D") which ranges from 1 to 10 when observations
> > are treated, and equals 0 otherwise. For the sake of simplicity, I
> > turned it into a dummy, equal to 1 when the discrete variable is
> > strictly positive, and equal to 0 otherwise. That way, I was able to
> > use a few common diff-in-diff models (OLS regression and psmatch2).
> > Also, I should specify that I only have 2 periods (pre-treatment, and
> > post-treatment).
> >
> > However, I have been doing research about how to account for treatment
> > intensity, because I would like to take into account the fact that
> > being treated with 10 is not the same as being treated with 1.
> >
> > For now, I have created 10 dummies for each of the possible values of
> > the treatment variable, and I have run 10 different regressions (1
> > against 0; 2 against 0; 3 against 0...). However, it is not easy to
> > get a full picture with that process. First, I have very few treated
> > observations for some of the treatment values, and therefore inference
> > is an issue. Second, I have not found an easy way to compare the
> > treatment effects to each other, since I have compared each of them to
> > getting 0 unit of treatment.
> >
> > Therefore, here are two questions ;)
> >
> > First, do you know of any way to account for treatment intensity
> > without breaking the treatment variable into 10 dummies? Ideally, I
> > would like to be able to run one regression which would take it all
> > into account. Some sort of weighted ATT.
> > For instance, do you think it is possible to use a regular OLS
> > diff-in-diff equation, plug the treatment variable as a discrete
> > variable (as opposed to a dummy), and include as many group fixed
> > effects and there are treatment values? I would be tempted to write it
> > like this:
> > Yit = a + b[T=t1] + c1[D=1] + c2[D=2] + ... + c10[D=10] + d[T=t1]*[D] + e
> > In that equaltion, I would let [D] range from 0 to 10, and d would be
> > the ATT. Do you think that makes sense?
> >
> > Second, if I do not find another way than to break the treatment
> > variable D into 10 dummies, does anyone know how I could recover the
> > mean ATT and its standard error? I guess I would need to weight the 10
> > different ATTs that I got, but what should be the weights? How about
> > number of treated observations in each treatment group? I thought
> > about doing that, but I stopped because the fact that treatment was
> > not randomly allocated made me think otherwise.
> >
> > Thank you everyone for your help, and I wish you a great week!
> > *
> > * 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/
> *
> * For searches and help try:
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> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/

*
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```