The top-order zonal polynomials <italic>C</italic>(<italic>A</italic>), and top-order invariant polynomials <italic>C</italic>_null_,…,<italic>null</italic> (<italic>A</italic>₁, …, <italic>A</italic>) in which each of the partitions of <italic>k</italic>, <italic>i</italic> = 1, …, <italic>r</italic>, has only one part, occur frequently in multivariate distribution theory, and econometrics — see, for example, Phillips (1980, <italic>Econometrica</italic>...

This paper studies the asymptotic validity of the Anderson–Rubin (<italic>AR</italic>) test and the <italic>J</italic> test for overidentifying restrictions in linear models with many instruments. When the number of instruments increases at the same rate as the sample size, we establish that the conventional <italic>AR</italic> and <italic>J</italic> tests are...