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Re: st: Re: How to correct standard errors of a 2sls performed by

From   John Antonakis <>
Subject   Re: st: Re: How to correct standard errors of a 2sls performed by
Date   Sat, 06 Feb 2010 14:04:06 +0100

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?



Prof. John Antonakis, Associate Dean Faculty of Business and Economics
Department of Organizational Behavior
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   |
                              An Introduction to Stata Programming  |
   An Introduction to Modern Econometrics Using Stata  |

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