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, NBER Technical Working Paper 199). The class
of tests covered by this admissibility result
contains the Anderson and Rubin (1949,
Annals of Mathematical Statistics
20, 46–63) 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, Econometrica 71,
1027–1048) belongs to the closure of (i.e., can be
interpreted as a limiting case of) the class of
tests covered by our admissibility result.