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

[Cameron McIntosh <cnm100@hotmail.com>]

And more directly related to the GPC method that Tirthankar suggested, I would recommend:

Moodie, E.E.M., & Stephens, D.A. (2012). Estimation of dose–response functions for longitudinal data using the generalised propensity score.  Statistical Methods in Medical Research, 21(2), 149-166.

Cam

----------------------------------------
> From: cnm00@@hotmail.com
> To: statalist@hsphsun..harvard.edu
> Subject: RE: st: Diff-in-diff: how to account for treatment intensity, rather than just a treatment dummy?
> Date: Sun, 2 Aug 012 2::5::8 -400<
>
> The following may also be of interest:
>
> Crown, W.H. (010)). There's a reason they call them dummy variables: a note on the use of structural equation techniques in comparative effectiveness research. Pharmacoeconomics, 8((0)), 47--55..
>
> Cam
>
> > Date: Sun, 2 Aug 012 5::0::9 -700<
> > 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@hsphsun..harvard.edu
> >
> > "Second, if I do not find another way than to break the treatment
> > variable D into 0 dummies, does anyone know how I could recover the
> > mean ATT and its standard error? I guess I would need to weight the 0<
> > 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' 000 Biometrika paper
> > which proposes the Generalised Propensity Score [GPS]
> > dx.doi.org/0..093//biomet/7....06<
> > See page 08..
> >
> > T
> >
> > On Sun, Aug 2,, 012 at ::6 PM, John Carey <johncarey96@@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 to 0 when observations
> > > are treated, and equals otherwise. For the sake of simplicity, I
> > > turned it into a dummy, equal to when the discrete variable is
> > > strictly positive, and equal to otherwise. That way, I was able to
> > > use a few common diff-in-diff models (OLS regression and psmatch)).
> > > Also, I should specify that I only have 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 0 is not the same as being treated with ..
> > >
> > > For now, I have created 0 dummies for each of the possible values of
> > > the treatment variable, and I have run 0 different regressions (<
> > > against ;; against ;; against ....). 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 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 0 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=t]] + c[[D=]] + c[[D=]] + ... + c0[[D=0]] + d[T=t]]*[D] + e
> > > In that equaltion, I would let [D] range from to 0,, 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 0 dummies, does anyone know how I could recover the
> > > mean ATT and its standard error? I guess I would need to weight the 0<
> > > 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!
> > > *
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