Title: Optimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors,
Abstract: This paper uses model symmetries in the instrumental variable (IV) regression
to derive an invariant test for the causal structural parameter. Contrary to
popular belief, we show there exist model symmetries when equation errors are
heteroskedastic and autocorrelated (HAC). Our theory is consistent with
existing results for the homoskedastic model (Andrews, Moreira and Stock(2006}
and Chamberlain (2007}), but in general uses information on the structural
parameter beyond the Anderson-Rubin, score, and rank statistics. This suggests
that tests based only the Anderson-Rubin and score statistics discard
information on the causal parameter of interest. We apply our theory to
construct designs in which these tests indeed have power arbitrarily close to
size. Other tests, including other adaptations to the CLR test, do not suffer
the same deficiencies. Finally, we use the model symmetries to propose novel
weighted-average power tests for the HAC-IV model.