Ulric B. and Evelyn L. Bray Social Sciences Seminar

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.