A Two-stage Inference Procedure for Sample Local Average Treatment Effects in Randomized Experiments

TL;DR

This paper introduces a two-stage inference method for accurately estimating the sample local average treatment effect in randomized experiments with non-compliance, accounting for instrument strength and experimental design variations.

Contribution

It develops a novel two-stage procedure that ensures correct coverage of the sample LATE, adaptable to different experimental designs and regression adjustments.

Findings

Method achieves asymptotically correct coverage rates.

Finite sample performance validated through extensive simulations.

Applied successfully to voter encouragement experiment data.

Abstract

In a given randomized experiment, individuals are often volunteers and can differ in important ways from a population of interest. It is thus of interest to focus on the sample at hand. This paper focuses on inference about the sample local average treatment effect (LATE) in randomized experiments with non-compliance. We present a two-stage procedure that provides asymptotically correct coverage rate of the sample LATE in randomized experiments. The procedure uses a first-stage test to decide whether the instrument is strong or weak, and uses different confidence sets depending on the first-stage result. Proofs of the procedure is developed for the situation with and without regression adjustment and for two experimental designs (complete randomization and Mahalaonobis distance based rerandomization). Finite sample performance of the methods are studied using extensive Monte Carlo simulations and the methods are applied to data from a voter encouragement experiment.