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Re: st: RE: RE: eivreg and deming


From   John Antonakis <john.antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: RE: eivreg and deming
Date   Tue, 01 Jun 2010 23:16:51 +0200

Sorry about that....for the benefit of those who don't know the terms, by endogenous, I mean that the modeled independent variable correlates with the error term of the y equation. By exogenous I mean randomly varying (and does not correlate with the error term). Measurement error is a special case of endogeneity where x is actually exogenous; however, because of measurement error it correlates with the error term (thus rendering it endogenous). For those who wish to know more, here is a snippet from one of my papers where I explain this in more detail:

Suppose we intend to estimate the following model, where we intend to observe is a latent variable, x*:

y=b0+b1x*+e

However, instead of observing x*, which is exogenous and a theoretically “pure” or latent construct, we observe instead a not-so-perfect indicator or proxy of x*, which we call x (assume that x* is the IQ of leader i). This indicator consists of the true component (x*) in addition to an error term (u) as follows (see Cameron & Trivedi, 2005; Maddala, 1977):

x=x*+u, or
x*=x-u

Now substituting the above into the first equation gives:

y=b0+b1(x-u)+e

Expanding and rearranging the terms gives:

y=b0+b1x+(e-b1u)

As is evident, the coefficient of x will be inconsistent given that the full error term, which now includes measurement error too, is correlated with x. Note that measurement error in the y variable does not bias coefficients and is not an issue because it is absorbed in the error term of the regression model. Variables that are correlated with the problematically-measured variable will also be affected if the bias is not removed from x. By constraining the residual to (1-reliability)*Variance of x (Bollen, 1989), we can purge x from endogeneity bias.

Ref:
Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley. Cameron, A. C., & Trivedi, P. K. (2005). Microeconometrics: Methods and applications. New York: Cambridge University Press.
Maddala, G. S. (1977). Econometrics. New York: McGraw-Hill.

Best,
J.

____________________________________________________

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:
http://www.hec.unil.ch/people/jantonakis

Personal page:
http://www.hec.unil.ch/jantonakis
____________________________________________________



On 01.06.2010 22:23, Nick Cox wrote:
Here as elsewhere I note that the exogenous-endogenous terminology is
one widely used by economists and not one that is natural or even
familiar to many of us outside economics. That aside, I do agree that
-eivreg- is a method not requiring instrumental variables which could be
used so long as you have a good idea about reliability. Nick n.j.cox@durham.ac.uk
John Antonakis

One example where eivreg is perfectly legitimate to use: IQ is mostly exogenous (determined by genes); so, if we have a non-so-perfect proxy of IQ, we can estimate its reliability (empirically via test-retest or via internal consistency) and thus "purge" the endogeneity bias due to measurement error. This is much easier to do and more defensible than trying to instrument IQ. I would be hard pressed to find a good instrument for IQ.

On 01.06.2010 19:43, Nick Cox wrote:

Compared with what? is a flip but nevertheless I suggest also a fair
answer.
I can't comment on Tony's specifics here -- as there aren't any! --
but
I guess that many people feel queasy in this territory because
deciding
on a proper treatment of situations in which all variables are subject
to error is very demanding. There are so many things to be specified
about error structure.
StataCorp's own feelings appear mixed too: there is a bundle of good
stuff at http://www.stata.com/merror that is semi-official (my
description not theirs!).
By the way, many economists and econometricians seem fixated on using
instrumental variables in this situation, but such methods don't
exhaust
the possibilities. Nick n.j.cox@durham.ac.uk
Lachenbruch, Peter

At a seminar not long ago, an eminent statistician commented that EIV
was not very useful and led to more problems (he didn't specify what
they were) that it was worth.  Anyone else have similar experience?

Risto.Herrala@bof.fi

I need to do errors in variables regression, where the errors are
heteroscedastic. A Stata user has programmed a 'deming' ado -file for
this purpose. Does anyone have experience of its use?

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