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Re: st: ivreg2 and estimation under autocorrelation


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, "Ryan D. Edwards" <redwards@hsph.harvard.edu>
Subject   Re: st: ivreg2 and estimation under autocorrelation
Date   Mon, 21 Feb 2005 23:30:50 +0000 (GMT)

Ryan,

I think it's the spirit of the approach to autocorrelation that you're
missing.  As you note, OLS is unbiased in the presence of autocorrelation,
as is IV (making some assumptions).  ivreg2 with bw() reports standard
errors that allow for asymptotically correct inference with OLS in the
presence of autocorrelation of almost arbitrary form (you need to make some
assumptions about how quickly it dies out via the bw option).

If you use the gmm option together with bw(), the coefficients will change.
 Here, ivreg2 will report coefficient estimates that are efficient in the
presence of autocorrelation of almost arbitrary form (again, you need to
make some asumptions about how quickly it dies out) as well as standard
errors that are correct.

The approach is more akin to the approach to heteroskedasticity that the
standard Stata robust and cluster options allow with many different
estimators.  ivreg2 with the robust option reports the same coefficients as
without, but the SEs are correct in the presence of arbitrary
heteroskedasticity; ivreg2 with robust and gmm reports coefficients that are
efficient in the presence of arbitrary heteroskedasticity as well as correct
SEs.  Contrast this with feasible GLS, where you model the
heteroskedasticity explicitly.  If you model it correctly, you'll get
estimates that are more efficient than those reported by ivreg2, even with
the gmm option; if you model it incorrectly, you'll get estimates that
aren't even consistent, let alone efficient.  It's the standard
robustness-vs-efficiency tradeoff.

Hope this helps.

Cheers,
Mark

Quoting "Ryan D. Edwards" <redwards@hsph.harvard.edu>:

> The last time I wanted to estimate a time-series model in the presence of
> autocorrelation and endogenous RHS variables, I used TSP, which had a
> nifty AR() command for essentially doing Stata's "prais" or old "corc"
> command with instrumental variables.  I see that Baum, Schaffer, and
> Stillman have expertly provided the Stata community with a new
> version of ivreg2, which I think can correct the var-covar matrix for
> heteroscedasticity and for autocorrelation.
> 
> My concern is that ivreg2 may be getting the standard errors right but not
> necessarily the coefficient estimates, at least not in the way traditional
> corrections for autocorrelation typically do.  I'm concerned because in
> the phillips.dta example discussed in the helpfile, the parameter
> estimates do not change when the bw() option is used.  That is,
> 
> . ivreg2 cinf unem
> . ivreg2 cinf unem, bw(3)
> . ivreg cinf unem
> . reg cinf unem
> 
> all yield exactly the same coefficient estimates.  (The standard errors
> are a little different across most but not all of these.)  By contrast, if
> we run
> 
> . prais cinf unem
> 
> we obtain different estimates and standard errors.  I was under the
> impression that this outcome is to be expected after correcting for
> autocorrelation.  While OLS is technically unbiased, because the direction
> of bias is unknown and therefore should be zero on average, in practice
> autocorrelation acts as an omitted variable, moving the estimates in one
> direction or another, even though it is unknown ex ante.  So it would be
> odd to see the estimates remain exactly the same after autocorrelation
> were corrected for.
> 
> Am I wrong to be concerned?  Or am I perhaps missing the spirit of the
> autocorrelation correction in ivreg2?  Is there a different Stata
> algorithm that does what I'm looking for?
> 
> Ryan D. Edwards, Ph.D.
> redwards@hsph.harvard.edu
> Postdoctoral Fellow in the Study of Aging, RAND Corporation
>  and Visiting Scientist, 2004-2005
> Department of Population and International Health
> Harvard School of Public Health
> 
> *
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> *   http://www.stata.com/support/statalist/faq
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> 



Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3294
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
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