Re: st: Difference-in-Difference on panel data without treatment and control group distinction

[Nils Braakmann <nilsbraakmann@googlemail.com>]

Dear Eirik,

as far as I see it, you don't really have a DiD-design, not even in
the pooled OLS case. The crucial point in a DiD is that you have (a)
two groups that can be distinguished before and and after treatment
and (b) the treatment hits only one group in the second period. The
control group is then used to purge common influences of time. Note
that this only works because you have both time series variation
(before and after treatment) and cross-sectional variation (treatment
vs. control group). In your scenario where the financial crisis
essentially hits everyone, you don't really have a control group (so
no cross sectional variation), which means that all you are left with
is the time series variation. Basically, all you can do is looking at
before-after-comparisons. The usual problem with this approach is that
you can't really seperate the effect of the treatment from the effect
of time (or more specifically, the effect of other variables that are
correlated with time, but are themselves not an outcome of the
treatment), i.e. the fact that you're looking at observations at two
different points in time. In fact, I don't see much potential to set
this up as a DiD-design as there is no group (I can think of) that is
not affected by the financial crisis. Apart from that, I would use
fixed-effects and look at within firm(?) comparisons (accepting that
the claim to causality is quite weak in these estimates). Maybe one
could have a look at the literature on testing for structural breaks
to find some inspiration, but this is not really my field of
experience.

Hope this helped.
Best
Nils

On Thu, Apr 1, 2010 at 1:33 PM, Eirik Egeland Nerheim
<Eirik.Nerheim@stud.nhh.no> wrote:
> Dear Reader,
>
> I am writing a termpaper (MSc level) on financial accounts' effect on
> equity pricing. My independent variable is market capitalization at
> close price the market day accounts are released to the public.
> Explanatory variables are various accounting data such as EBIT, cash
> flow measures, debt to equity at period end and total assets to control
> for firm size. All observations are quarterly.
>
>
> I am interested in finding out the difference in coefficient estimates
> from before till after the financial crisis. With pooled OLS, the
> difference in difference (DD) estimate is easily obtained and checked by
> including a dummy that indicates if the observations are before or after
> the financial crisis was a fact, and an interaction variable (time dummy
> * explanatory variable):
>
>
> y = a + b * timedummy + c *explanatory variables + d*interaction + u
>
>
> However, I am unsure whether this is the correct approach to use with my
> panel data. We can assume that all corporations were affected by the
> financial crisis, so there is no control or treatment group: only
> observations before and after.
>
>
> In my static panel data model, i.e. only with contemporaneous
> explanatory variables, I have used economic reasoning and a Hausman test
> to conclude that a fixed-effects (FE) model is a better model than
> random-effects (RE). Running the model y = a + b*controls + u with FE,
> once for observations before the financial crisis and once for those
> after, I get two  estimates whose difference does not equal the
> d-paramater if I run the model
>
>
> y = a + b * timedummy + c *explanatory variables + d*interaction + u
>
>
> with FE, which was the case with OLS.
>
>
> Can I still trust the estimate of d when using FE? Should I rather be
> using another technique to obtain the difference in coefficient
> estimates?
>
>
> Yours,
> Eirik E. Nerheim
>
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