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We develop a concept of weak identification in linear IV models where
the number of instruments
can grow at the same rate or slower than the sample size. We propose a
jackknifed version of
the classical weak identification-robust Anderson-Rubin (AR) test
inference based on the jackknifed AR is valid even under
heteroscedasticity. The feasible version of
this statistic uses a novel variance estimator. The test has uniformly
correct size and good power properties.
Lastly, we develop a pre-test for weak identification that is related to
the size property of a Wald test based on Jackknife Instrumental
Variable Estimator (JIVE). This new pre-test is valid under
heteroscedasticity and with many instruments.