Re: st: RE: Why not always specify robust standard errors?

["Rodrigo A. Alfaro" <raalfaroa@gmail.com>]

Hi all,

I downloaded the paper from http://www.stat.berkeley.edu/~census/mlesan.pdf, 
guessing that is a reliable version. It seems for me that for nonlinear 
model Maarten is right. In english, models like Logit or Probit are 
complicated to justified with robust standard error when the researcher is 
not sure of the underlying model. But for linear models, in particular the 
OLS proposed in the beginning of the discussion I think that there is not 
too much problem (Just for fun: it is interesting to note that each of these 
\hat e(i)^2 are not consistent but the weighted average by x's is). In the 
OLS, whatever is the underlying model, the standard asymptotic approach 
gives us that the t-stats are asymptotically normal. As pointed in the 
paper, probably the finite sample t is not close to a t-student. In 
conclusion, it seems to me reasonable to apply robust to OLS regarding that 
doing that you could lose efficiency and other measures availables (like 
AIC, BIC, R2, etc) under the case of the model does not have 
heteroscedasticity. I hope that the researcher does not get a strongly 
different answer, if so I will take a second look of the specification of 
the model, at the end heteroscedasticity is a signal of our ignorance of 
true process.

But my original motivation of writing this email is the following. Consider 
that the model in study cannot be estimated by OLS, due to some endogeneity 
of the regressors. Are you still applying robust anyway? some of the 
discussion has been analyzed by Baum, Schaffer and Stillman in their paper 
about -ivreg2-. The analyze the problem of choosing between IV and GMM (two 
steps). I took the analysis starting from the fact of the researcher will 
"click" (or type) the robust option anyway. It is clear that robustness does 
not work in frameworks where the estimator itself is seriously biased. For 
example, when the degree of overidentification and the degree of endogeneity 
are large none of these estimators are reliables, giving as well very 
imprecise standard errors and making the inference completly wrong. Loosely 
speaking it seems to me that others problems in the model such as quality 
and number of instruments are more relevant than the heteroskedascity 
itself.

I hope to get a lot of replies :-)
Rodrigo.





----- Original Message ----- 
From: "Richard Williams" <Richard.A.Williams.5@ND.edu>
To: <statalist@hsphsun2.harvard.edu>
Sent: Tuesday, February 13, 2007 5:59 PM
Subject: RE: st: RE: Why not always specify robust standard errors?



> At 12:26 PM 2/13/2007, Maarten Buis wrote:
> > If you think your model is correct then it makes no sense to use robust
> > standard errors. Note that the model assumes no heteroscedasticity in
> > the population, so the fact that we always find some heteroskedasticity
> > in our samples is no argument. You could test it of course, but since
> > we are now in ``purist land'' we would have serious troubles with
> > performing tests based on the model that was subsequently selected,
> > since now our conclusions are based on a sequence of tests...
> Thanks Maarten.  I'm no doubt betraying my statistical ignorance here, but 
> is that the correct definition of "correct?"  i.e. does "correct" mean no 
> heteroskedasticity?  Or is no hetero just a requirement for OLS to be the 
> optimal method for estimating the model?  It seems to me that a model 
> could be correct in that Y is a linear function of the Xs and all relevant 
> Xs are included.  The additional requirement of homoskedastic errors is a 
> requirement for OLS estimates to be BLUE.  But, if errors are 
> heteroskedastic, we can use another method, like WLS.  Or, we can content 
> ourselves with using robust standard errors which do not require that the 
> errors be iid.
>
> In any event, in practice probably every model will be at least a little 
> mis-specified and/or have error terms that aren't perfectly iid.  So, why 
> not always use robust?  One potential problem, I think, is that robust 
> standard errors tend to be larger.  Perhaps unnecessarily relaxing the iid 
> assumption has similar effects to including extraneous variables - 
> estimates will remain unbiased but adding unnecessary junk to the model 
> can cause standard errors to go up.
>
> You know, this is one of the problems with using Stata.  I never used to 
> have these kinds of problems with SPSS, because SPSS doesn't let you 
> estimate robust standard errors!
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
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