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st: Dynamic panel data with dynamic and endogenous regressor


From   Misha Spisok <misha.spisok@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Dynamic panel data with dynamic and endogenous regressor
Date   Tue, 15 Jun 2010 13:43:33 -0700

Hello, Statalist,

My question, in short, is, "What model (and corresponding Stata
command) is appropriate for dynamic panel data with an endogenous
regressor (i.e., an endogenous regressor besides the lagged dependent
variable) that is itself dynamic?"

For example, suppose I am interested in the effect of x on y, but x
itself is endogenous (and, of course, y_i,t-1 is as well) and modeled
dynamically.

y_it = b0 + b1*y_i,t-1 + b2*x_i,t-1 + e_it

with, as usual, e_it = m_i + n_it

Something like this could be handled, as I understand, by -xtabond-,
-xtabond2-, -xtdpd-, among other commands.

But if also,

x_it = c0 + c1*x_i,t-1 + c2*y_i,t-1 + u_it

with, similar to the above, u_it = g_i + v_it

so that y_i,t-1 is enogenous along with x.

Without instruments "waiting in the wings," are the
Arellano-Bond/Blundell-Bond/Arellano-Bover style instruments
sufficient?

If so, can this be implemented in, e.g., -xtabond-, -xtabond2-, -xtdpd-, etc.?

Or is this best done with Stata's -gmm- command?

If one does, however, have an instrument, say z, for x (or, say, w,
for y) does this change anything?

This strikes me as "merely" system GMM that has, beyond the system of
levels and differences of y with the "usual" instruments, an
additional system of levels and differences of x with the "usual"
instruments (plus, ideally(?), some more instruments).

I apologize for any lack of clarity or misuse of terminology; I'm
happy to be corrected.

Alos, if someone can suggest some references, I would appreciate it;
the treatments that I have found don't cover this case.

Thank you for your time.

Best,

Misha
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