What you have is a simultaneous equation system (SEM). A SEM can be estimated equation by equation by single equation methods (2SLS, LIML, ...)
In your system, the endogenous variables are y, x1, x2, m1, m2. The exogenous variables are n1, n2, q1, q2, p1, p2.
In your first stage, you would estimate each of the endogenous variables on all of the exogenous variables
In your second stage, you use the predicted values of the endogenous variables to replace the endogenous variables on the right hand side of each equation.
This means that you can estimate Eq2 by 2SLS, specifying all of the exogenous variables above as instruments. m1 and m2 would be the included exogenous, and the others would be the excluded exogenous
Idem for Eq3
Eq4 and Eq5 can be estimated by OLS
Eric de Souza
College of Europe
BE-8000 Brugge (Bruges)
Belgium
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of John Antonakis
Sent: 06 February 2010 14:04
To: [email protected]
Subject: Re: st: Re: How to correct standard errors of a 2sls performed by
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.
____________________________________________________
Prof. John Antonakis, Associate Dean
Faculty of Business and Economics
Department of Organizational Behavior
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
Faculty page:
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Personal page:
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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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