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Re: st: Generated regressor problem


From   Robert Duval <rduval@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Generated regressor problem
Date   Wed, 3 Aug 2005 12:57:56 -0400

Actually none seem to be correct.

The 1st claim: If your generated regressor is consistent then your
parameter estimate over the generated regressor in your final
regression should be consistent too (of course as long as the model in
that second exercise is correctly specified). I guess this is the only
sense in which that phrase can be interpreted.

2nd & 3rd claim: No. Once you have genrated regressors all the
inference estimtes are wrong if not adjusted to incorporate the extra
variance coming from the generated regressor term. Although this
adjustment has been found to be small for the non-generated regressors
in some empirical applications, still no theoretical rule will save
you from having to adjust the whole matrix of variance-covariance. (in
other words how can you be sure that your case is one of these cases
where it doesn't make much of a difference without making the
adjustment?). Furthermore, I've seen empirical exercises where the
adjustment makes a big difference precisely on the inference over the
parameter of the generated regressor.


Maybe you want to look at Wooldrige's "Econometrics Analysis of
Cross-section and panel data" to see the general formulas in the
context of M-estimation.

best
robert

On 8/3/05, mq102@york.ac.uk <mq102@york.ac.uk> wrote:
> I am using the conditional variance from a GARCH(1,1) model as a regressor
> (supposed to be a measure of uncertainty) in another regression.
> If I undestand correctly, this may create a problem of generated regressors
> (Pagan, 1984): inference in the generated regression is generally not valid.
> 
> I have to confess that Pagan's paper is too difficult for me, but I could
> not find a manual plainly explaining the nature of the problem and the
> possible solutions.
> 
> Looking at other (applied) papers, I found the following solutions (not
> necessarily consistent each other):
> -if the generaring regression is correctly specified, don't worry (nice
> solution, my favourite!)
> -Hypothesis testing on the coefficient of the generated regressor is always
> valid, but you can not test hypotheses on the other variables in the
> generated regression
> -in general, you can use Newey and West standard errors and carry out
> inference in the generated regression.
> 
> Which is the correct one?
> Thanks for any help you can provide.
> 
> Mario
> 
> 
> University of York
> Department of Economics and Related Studies
> Heslington
> York YO10 5DD
> United Kingdom
> email: mq102@york.ac.uk
> 
> 
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