Re: st: RE: RE: eivreg and deming

[John Antonakis <john.antonakis@unil.ch>]

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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