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...

This paper establishes consistency of least squares estimators in (i) a multiple regression model with integrated regressors and explosive, non-mixing errors, and (ii) a dynamic linear regression model with regressors and errors that may have infinite variances. In the former context, the...

This paper presents conditions under which a quadratic form based on a <italic>g-</italic>inverted weighting matrix converges to a chi-square distribution as the sample size goes to infinity. Subject to fairly weak underlying conditions, a necessary and sufficient condition is given for this result. The result...

The least squares estimator for the linear regression model is shown to converge to the true parameter vector either with probability one or with probability zero. In the latter case, it either converges to a point not equal to the true parameter with probability one, or it diverges with...