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This paper considers the problem of conducting inference on the regression coefficient in a bivariate regression model with a highly persistent regressor. Gaussian power envelopes are obtained for a class of testing procedures satisfying a conditionality restriction. In addition, the paper proposes feasible testing procedures that attain these Gaussian power envelopes whether or not the innovations of the regression model are normally distributed.

This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by Andrews, Moreira, and Stock (2004). The class of tests covered by this admissibility result contains the Anderson and Rubin (1949) test. Thus, there is no conventional statistical sense in which the Anderson and Rubin (1949) test "wastes degrees of freedom". In addition, it is shown that the test proposed by Moreira (2003) belongs to the closure of (i.e., can be interpreted as a limiting case of) the class of tests covered by our admissibility result. Keywords: Instrumental Variables, Regression, Inference. JEL Classifications: C13, C14, C30, C51, D4, J24, J31.

This paper derives asymptotic power envelopes for tests of the unit root hypothesis in a zero-mean AR(1) model. The power envelopes are derived using the limits of experiments approach and are semiparametric in the sense that the underlying error distribution is treated as an unknown infinitedimensional nuisance parameter. Adaptation is shown to be possible when the error distribution is known to be symmetric and to be impossible when the error distribution is unrestricted. In the latter case, two conceptually distinct approaches to nuisance parameter elimination are employed in the derivation of the semiparametric power bounds. One of these bounds, derived under an invariance restriction, is shown by example to be sharp, while the other, derived under a similarity restriction, is conjectured not to be globally attainable.