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Re: st: ivreg2 C-statistic with liml & robust options


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   Roger Harbord <roger.harbord@bristol.ac.uk>
Subject   Re: st: ivreg2 C-statistic with liml & robust options
Date   Tue, 22 Feb 2005 19:22:28 +0000 (GMT)

Roger,

Quoting Roger Harbord <roger.harbord@bristol.ac.uk>:

> --On 22 February 2005 16:18 +0000 Mark Schaffer
> <M.E.Schaffer@hw.ac.uk> wrote:
> 
> > Roger,
> >
> > Date sent:      	Tue, 22 Feb 2005 15:59:26 -0000
> > From:           	Roger Harbord <roger.harbord@bristol.ac.uk>
> >
> >> If I use -ivreg2- with both the -liml- and -robust- options i get
> LIML
> >> point estimates with heteroskedasticity-robust standard errors
> (very
> >> nice, my thanks to Baum, Schaffer & Stillman).
> >>
> >> But if i use the -orthog()- option to test the endogeneity of a
> >> regressor, the resulting C-statistic doesn't appear to change
> >> depending on whether or not I use the -robust- option. However it
> does
> >> change with use of -robust- if i use 2SLS instead of LIML. (i
> have
> >> ivreg2 version 2.0.06 from SSC)
> >>
> >> Does this mean that the C-statistic given by -orthog()- is
> ignoring
> >> the -robust- option  when I use LIML? If so is there an
> alternative?
> >
> > Well spotted.
> >
> > With IV, the C-stat without -robust- is based on two Sargan
> > statistics.  Add -robust-, and the C-stat is based on two Hansen
> J
> > statistics.  These two Hansen Js come from two GMM estimations. 
> That
> > is, there is no difference between the C-stat reported for IV
> with
> > -robust- and the C-stat reported for two-step GMM with the -gmm-
> > option.
> >
> > The C-stat for LIML is based on the Anderson-Rubin statistic
> (the
> > LIML analog of the Sargan statistic).  The -robust- analog of the
> C-
> > stat would be based on the robust analog of the Anderson-Rubin
> > statistics.  These in turn would come from the robust analog of
> LIML,
> > which is continuously-updated GMM (aka "CUE").  The current
> version
> > of ivreg2 doesn't implement CUE, but we have a beta version that
> > does.  If you're really keen on trying it out, I can send it to
> you.
> >
> 
> Many thanks for the rapid and very helpful response, Mark. The beta
> version 
> of ivreg2 sounds really interesting, but i don't think i'm in a
> position to 
> beta-test it as i'm still getting to grips with this area myself and
> i'd 
> rather stick to generally-accepted methods for analyses as the whole
> idea of 
> IV is unfamiliar in my field.
> 
> Based on what you say i think i'll go back to IV (2SLS) with the
> -robust- 
> option for estimation and endogeneity tests and use LIML only as a
> 
> sensitivity analysis for the point estimates as one way of checking
> for weak 
> instrument problems (in addition to examining the 1st-stage F).
> Anything 
> beyond that is going to get too difficult to explain for one
> thing... I've 
> got evidence of heteroskedasticity so don't want to use an
> endogeneity test 
> based on LIML that doesn't account for it. While using LIML for estimation 
> but Hansen Js for endogeneity testing could appear inconsistent. My
> reading 
> of Baum, Schaffer & Stillman is that IV with the -robust- option is less 
> likely to run into problems of weak instruments/small samples than GMM, 
> though at the expense of losing efficiency. Is that correct?

At least half is.  IV is less likely to have problems with small samples
(because GMM uses estimates of 4th moments, and these can require big
samples to be decent estimates).  I don't recall seeing anything, though,
about IV being less prone to weak instrument problems than (2-step) GMM. 
But this literature is expanding rapidly, and maybe there's something out
there that discusses this.

Cheers,
Mark

> Best wishes,
> Roger.
> 
> C. F. Baum, M. E. Schaffer, and S. Stillman. Instrumental
> variables
> and GMM: Estimation and testing. Stata Journal 3 (1):1-31, 2003.
> 
> -- 
> Roger Harbord
> Department of Social Medicine, University of Bristol
> http://www.epi.bris.ac.uk
> 
> 



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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