As described in Roodman (2006:11-12) the choice of relying on the Hansen's J
or Sargan's test of overidentifying restrictions depends on whether you
suspect non-sphericity in the errors (e.g. in the case of heteroscedastic
errors). Sargan's statistic is a special case of Hansen's J under the
assumption of homoscedasticity. Therefore, for robust GMM the Sargan test
statistic is inconsistent.
Nonetheless, both these tests have low power if your model includes a very
large set of excluded instruments, so you might want to also investigate the
"difference-in-Sargan tests of exogeneity of instrument subsets".
Best,
Johan Hellstrom
---------------
Roodman, D. (2006). How to do xtabond2: An introduction to "Difference" And
"System" Gmm in stata, Working Paper No. 103: Center for global development.
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