Optimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors

This paper uses model symmetries in the instrumental variable (IV) regressionto derive an invariant test for the causal structural parameter. Contrary topopular belief, we show there exist model symmetries when equation errors... [ view full 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.