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

[Tirthankar Chakravarty <tirthankar.lists@gmail.com>]

"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!
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