Re: st: Estimating firm level data on regional level data using a within estimator.

[Maarten buis <maartenbuis@yahoo.co.uk>]

--- On Sun, 6/6/10, John Antonakis wrote:
> The assumptions of the estimators must be met. If the
> assumptions of the random effects estimator are not met, and
> if the Hausman test shows that the estimator is not
> consistent then the researcher has to bite the bullet! 
> It is the same thing as estimating a regression model where
> you know that x correlates with the disturbance and yet you
> go ahead and estimate the model in any case. The coefficient
> of x could be higher, lower, or of a different sign. What is
> the use to society to report estimates that one knows to be
> inconsistent?

Inconsistent and bias critically depends on what you want
to know: linear regression and random effects will give you a 
consistent estimate on how the averages differ between groups.
So a statement that estimate XYZ is inconsistent or biased is 
meaningless unless you first specify (explicitly or implicitly)
what it is that you exactly want to know. Fixed effects estimators
are controlling for all unobserved variables that are constant
on the higher level unit. However, you often do _not_ want to 
controll for all variables, e.g. intervening variables. Since
fixed effects indiscrimately controlls for all higher level
variables, the fixed effects regression will be a inconsistent
estimate for a large (probably the largest) subset of parameters
of interest. On the other hand, fixed effects do not control for 
all unobserved variables you might want to control for, in 
particular those that aren't constant on the higher level. So
again there are a large set of parameters of interest for which
fixed effects are inconsistent. 

In essence the only way to reliably controll for unobserved 
variables is to observed them. Even a randomized experiment will 
only work if the paremeter of interest is a linear combination 
of means (and I am ignoring the problem of external validity). 
All this is not to deny that randomized experiments and fixed 
effects regression are useful tools in ones statistical 
toolbox, but they are just that, a tool with advantages and 
disadvantages. 

I am being a bit hard, I guess this has more to do with my 
frustration with some of the recent converts in my discipline. 
As is often the case, the recent converts are the worst 
fundamentalists. My impression is that in many cases where 
people in my discipline use fixed effects regression those 
people have no idea what they want to controll for (other 
than that they want to control for "everything"), which to 
me means that those estimates are exactly meaningless. 
Anyhow, as I said, my frustration is with people who abuse
a method they don't understand, and obviously none of this 
applies to you. So don't take any of this personally.

-- Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------


      

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