Thanks Kit--I am aware of the problem regarding system-wide estimators
and the fact that a misspecification in one part of the model may bias
another part of the model; in fact, I always compare 2sls estimates
(which I refer to as a "safe-bet" estimator) to those of a systems
estimator (e.g., 3sls or ML). However, there is the efficiency problem
on the one hand; on the other, how does one do single-equation
estimation with in the context of a non-recursive system. Again, here
is the example:
Eq1: y = x1 + x2 + z
Eq2: x1 = m1 + m2 + x2 + z
Eq3: x2 = n1 + n2 + x1 + z
Eq4: m1 = q1 + q2 + z
Eq5: m2 = p1 + p2 + z
The predicted value of x2 enters in Eq. 2; however, the predicted value
of x1 enters in Eq. 3. So, how does one go about estimating this
non-recursive model using a single-equation estimator?
Thanks,
John.
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University of Lausanne
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On 06.02.2010 13:39, Kit Baum wrote:
On Feb 6, 2010, at 2:33 AM, John wrote:
What if the system is non-recursive (with feedback loops) and with
multiple equations, e.g.,
y = x1 + x2 + z
x1 = m1 + m2 + x2 + z
x2 = n1 + n2 + x1 + z
m1 = q1 + q2 + z
m2 = p1 + p2 + z
Here one would need reg3, but how would one ensure consistency of
standard errors (in the presence of heteroskedasticity), apart from
bootstrapping (and Roodman's -cmp- would not here as it is only for
recursive systems)?
No, you don't _need_ reg3. A systems estimator is never needed unless you want to impose constraints across equations on the coefficients. There is nothing wrong with limited-information (single-equation) estimation of each equation in turn. A systems estimator can provide efficiency; but on the other hand any misspecification means that every equation's coefficients can become inconsistent if one equation is flawed.
Kit Baum | Boston College Economics & DIW Berlin | http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming | http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata | http://www.stata-press.com/books/imeus.html
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