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st: new paper on instrument proliferation risk in difference, system GMM
I have just posted a short working paper elaborating on some points in
my earlier "How to Do xtabond2" about the dangers of generating too many
instruments in difference and system GMM. In a nutshell, the estimators
can generate results that are at once valid yet appear valid because of
a falsely reassuring Hansen J test of joint instrument validity. What
makes the problem insidious is that instrument proliferation can easily
occur *by default*. The paper makes no new theoretical contribution,
referring to documentation of these problems already in the literature.
xtabond2 largely mimics Stata's xtabond and Doornik, Arellano, and
Bond's DPD package in its default assumptions about which (and how many)
instruments to generate. Nevertheless, as the author of xtabond2, I feel
some responsibility for the frequency with which (I fear) these
estimators are being misapplied.
I illustrate the risks with reference to two papers on economic growth
determinants, Forbes (2000) on income inequality and Levine, Loayza, and
Beck (LLB, 2000) on financial sector development. I find that endogenous
causation proves hard to rule out in both papers. The practical lesson
is about the need to test results for robustness to substantial
reduction in the instrument count.
"A Short Note on the Theme of Too Many Instruments" is at
http://www.cgdev.org/content/publications/detail/14256/.
Motivated by the process of writing this paper, I've modified xtabond2
so that it reports both the Sargan and Hansen tests of overid
restrictions for one-step, robust estimation, as well as two-step
estimation. The Sargan test is not robust--not consistent in the process
of non-spherical errors--but unlike the Hansen test it is not greatly
weakened by a high instrument count. So it seemed better to still report
the Sargan even when the Hansen is the asymptotically correct one. Type
"ssc install xtabond2, replace" for the latest.
--David
David Roodman
Center for Global Development
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