Exact Nonparametric Inference for a Binary Endogenous Regressor

This paper describes a randomization-based estimation and inference procedure for the distribution or quantiles of potential outcomes with a binary treatment and instrument. The method imposes no parametric model for the treatment effect, and remains valid for small n, a weak instrument, or inference on tail quantiles, when conventional large-sample methods break down. The method is illustrated using simulations and data from a randomized trial of college student incentives and services.