Are “Nearly Exogenous Instruments” reliable?
Daniel Berkowitz, Mehmet Caner, Ying Fang
#002091 20131014 (published)
We show that when instruments are nearly exogenous, the two stage least squares t-statistic unpredictably over-rejects or under-rejects the null hypothesis that the endogenous regressor is insignificant and Anderson–Rubin test over-rejects the null. We prove that in the limit these tests are no longer nuisance parameter free.

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