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Re: st: Difference in Difference vs. Fixed Effects


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Difference in Difference vs. Fixed Effects
Date   Wed, 2 Oct 2013 07:41:51 -0400

Dear Joerg,

If your outcome variable has values only between 0 and 1, ordinary
regression may not be appropriate.  Please tell us more about the
nature of your outcome variable.

Are your treatment and control groups observational (i.e., not the
result of randomized assignment)?  Please tell us more about that
aspect of your data.

The fixed-effects model does not remove only the effect of treatment.
It removes the effects of all potential confounders, both observed and
unobserved, that do not vary with time.  The book by Fitzmaurice,
Laird, and Ware (2011) has an accessible discussion of fixed-effects
and random-effects models, and it should be possible to find other
relevant articles and books.

David Hoaglin

Fitzmaurice GM, Laird NM, Ware JH (2011). Applied Longitudinal
Analysis, second edition.  Wiley.

On Wed, Oct 2, 2013 at 2:26 AM, Joerg Lang <joerglang0@gmail.com> wrote:
> Dear Stalist users,
>
> currently writing my Master thesis and working with
> Stata 12, I have the following problem.
>
> I have a dataset on two time periods (2010 and 2012) and two groups
> (treatment and control). There is no treatment in the baseline and the
> treatment group uptakes the treatment between 2010 and 2012. The uptake is
> non-random.
> Now, I want to estimate the impact in a difference in difference design.
> At first, I estimate the following model:
>  y b0+b1Time+b2Treatment+b3Time*Treatment+u
>
> using the -reg command:
>
> -reg y time treatment time*treatment, cluster (h1)
>
> while y is the outcome variable that is between 0 and 1 and h1 is the
> household identifier. I use the cluster option to account for the problem
> of serial correlation. In a second estimation I also include some other
> covariates.
>
> I always thought that this setting and a setting with fixed effects
> yield exactly the same result as long as one has only two points in time
> (in my case 2010 and 2012).
>
> However, estimating the same model with:
>
> - xtreg y Time Treatment Time*Treatment, fe vce(cluster h1)
>
> gives slightly different results. The difference increases when including
> more covariates, which are the same in both cases. As well, there is no
> variation in the households. Thus, the same households and the same
> variables are used in both estimations.
> Obviously, treatment is omitted in the xtreg case since it does not vary
> between time.
> However, I think that this should not change anything.
> My question is:
>  Is my model correctly specified or did I overlook something?
> And, if my estimation is correct: Why this difference? Is this "normal"? If
> so, what does it tell me then, i.e. what is the reason for it?
>
> Since I have already been stuck with this problem for quite a while, any
> help or literature suggestions  would be very much appreciated.  Hope
> this question is not too trivial for you.
>
> Best regards,
>
> Joerg
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