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

["Eirik Egeland Nerheim" <Eirik.Nerheim@stud.nhh.no>]

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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