This paper considers the finite sample distribution of the 2SLS estimator and derives bounds on its exact bias in the presence of weak and/or many instruments. We then contrast the behavior of the exact bias expressions and the asymptotic expansions currently popular in the literature, including...

We derive nonparametric sharp bounds on average treatment effects with an instrumental variable (IV) and use them to evaluate the effectiveness of the Job Corps (JC) training program for disadvantaged youth. We concentrate on the population average treatment effect (ATE) and the average...

In econometrics some nonparametric instrumental regression models and nonparametric demand models with endogeneity lead to nonlinear integral equations with unknown integral kernels. We prove convergence rates of the risk for the iteratively regularized Newton method applied to these problems....

We provide simple tests for selection on unobserved variables in the Vytlacil-Imbens-Angrist framework for Local Average Treatment Effects. The tests allow researchers not only to test for selection on either or both of the treated and untreated outcomes, but also to assess the magnitude of the...

This paper examines a general class of inferential problems in semiparametric and nonparametric models defined by conditional moment restrictions. We construct tests for the hypothesis that at least one element of the identified set satisfies a conjectured (Banach space) "equality" and/or (a...

This paper develops characterizations of identified sets of structures and structural features for complete and incomplete models involving continuous and/or discrete variables. Multiple values of unobserved variables can be associated with particular combinations of observed variables. This can...