Exact Inference for a Weak Instrument, a Small Sample, or Extreme Quantiles

Abstract

This paper describes a randomization-based inference procedure for the distribution or quantiles of potential outcomes for 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.

Keywords: randomization inference, permutation inference, finite sample, instrumental variables, treatment effects

JEL Classification: C12, C14, C30