This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of...

We propose a method to explore the causal transmission of an intervention through two endogenous variables of interest. We refer to the intervention as a catalyst variable. The method is based on the reduced-form system formed from the conditional distribution of the two endogenous variables...

Instrumental variables (IVs) are a commonly used technique for causal inference from observational data. In practice, the variation induced by IVs can be limited, which yields imprecise or biased estimates of causal effects and renders the approach ineffective for policy decisions. We confront...

In instrumental variable studies, missing instrument data are very common. For example, in the Wisconsin Longitudinal Study, one can use genotype data as a Mendelian randomization–style instrument, but this information is often missing when subjects do not contribute saliva samples or when the...

This paper describes a method for carrying out non-asymptotic inference on partially identifi ed parameters that are solutions to a class of optimization problems. The optimization problems arise in applications in which grouped data are used for estimation of a model's structural parameters....