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RE: RE : Heteroskedasticity and fixed effects (was: st: RE: Re: Weak instruments)


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: RE : Heteroskedasticity and fixed effects (was: st: RE: Re: Weak instruments)
Date   Thu, 17 Jul 2008 16:21:34 -0400

Richard Williams wrote:

>>I might have a slightly different take: If a test for hetero comes up 
positive, don't just assume that means that you should use wls or 
robust standard errors or whatever.  [snip]<<

I agree. Heteroscedasticity can be a sign of a lot of things. This is
why I recall a nice warning about on "White-washing" your VCE mentioned
in Peter Kennedy's excellent A Guide to Econometrics. 

I recall a case in some multinomial discrete choice data from a
linguistics experiment I analyzed where there was clear
heteroscedasticity. It turned out that it went away once a very large
outlier was removed from the dataset. When we checked, the outlier was
explainable in terms of the stimulus in that cell of the experiment. The
stimulus word was "thanks", which is ambiguous about whether it's
singular or plural due to the -s ending. Finding outliers in complex
models can be very tricky. 

Of course, heteroscedastiticy also often arises due to a
misspecification of the error term. For instance, if you use OLS in the
presence of a ceiling or floor effect, you often "need" either an
interaction term or suffer from heteroscedasticity or both. In fact, you
simply have the wrong model and need to get one that can accommodate the
ceiling or floor effect, of which there are several. 

Nonetheless, robust standard errors and related methods such as
bootstrapping and jackknifing can be quite useful. A lot of times
there's just some "crud" in your data for which you won't ever find a
model. The variables you would need to measure are unavailable, either
because nobody gathered them or because they simply can't be gathered. A
model-based solution such as random effects isn't going to work---maybe
you simply don't have the information on the clustering. It would be a
shame for analysis to stop because someone decides to go unreasonably
purist. (I'm invoking the spirit of Tukey here.) Robust VCE and the like
can let you get more reasonable standard errors in the presence of crud.
But you should be honest about what you did, most importantly with
yourself. 

JV


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