This paper considers inference for parameters defined by moment inequalities and equalities. The parameters need not be identified. For a specified class of test statistics, this paper establishes the uniform asymptotic validity of subsampling, <italic>m</italic> out of <italic>n</italic> bootstrap, and “plug-in asymptotic”...

In the linear instrumental variables model with possibly weak instruments we derive the asymptotic size of testing procedures when instruments locally violate the exogeneity assumption. We study the tests by Anderson and Rubin (1949, <italic>The Annals of Mathematical Statistics</italic> 20, 46–63), Moreira...

This paper considers inference based on a test statistic that has a limit distribution that is discontinuous in a parameter. The paper shows that subsampling and <italic>m</italic> out of <italic>n</italic> bootstrap tests based on such a test statistic often have asymptotic size—defined as the limit of exact size—that is...

This paper investigates the asymptotic size properties of a two-stage test in the linear instrumental variables model when in the first stage a Hausman (1978) specification test is used as a pretest of exogeneity of a regressor. In the second stage, a simple hypothesis about a component of the...