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

From   Roger Harbord <>
Subject   Re: st: ivreg2 C-statistic with liml & robust options
Date   Tue, 22 Feb 2005 19:09:18 -0000

--On 22 February 2005 16:18 +0000 Mark Schaffer <> wrote:


Date sent:      	Tue, 22 Feb 2005 15:59:26 -0000
From:           	Roger Harbord <>

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-

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?

Best wishes,

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

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