ex post T and C for DD

Mel asks:

Question: My understanding of a difference in difference model is that
the two groups should exist before a policy takes affect (e.g. two
states, companies, school districts).  I was studying the impact of a
policy on an outcome where the two groups did not exist until the
policy went into effect and everyone was eligible for the policy all
at once.  There was no staggered implementation.  Because of this I
thought to use a lagged dependent variable model to study the impact
of the taking advantage of the new program offered through the policy.
 DVt1= Program + DVt-1 + error.  This model would at least allow me to
control for the separate groups in time two.  I recently saw someone
publish on my topic but they used a difference in difference model.
They assigned the program status which in reality could only occur in
t1 after the policy went into affect to the same people in t-1 when
the program did not exist. I did not think this was correct, thus I am
writing for clarification.

thanks for your question Mel

check out the classic training evals by Ashenfelter (1978) and Ashenfelter
and Card (1985).  They compare pre and post for trainees and controls.
They don't know who is a trainee until "period 2." Once training status
is known, however, it's easy to reach back (in a panel) for pre-treatment
obs for both groups.  

Is this a credible identification strategy?
Probably not as good as being able to make an ex ante T and C distinction,
but sometimes ok.
well, when is this ok . . .
Check out the originals and find out!  These classics do a great job of
explaining why and when this sort of DD makes sense . . .

JA