Semiparametric Estimation of Treatment Effects in Randomized Experiments

TL;DR

This paper introduces new semiparametric methods for estimating treatment effects in randomized experiments, especially suited for large samples, heavy-tailed outcomes, and small effects, with efficient estimators and novel interpretations.

Contribution

It develops efficient semiparametric estimators for treatment effects under broad conditions, extending existing models to include asymmetry and providing new theoretical bounds.

Findings

Derived the semiparametric efficiency bound for treatment effects.

Proposed efficient estimators with interpretative insights.

Extended Huber's model to asymmetric cases.

Abstract

We develop new semiparametric methods for estimating treatment effects. We focus on settings where the outcome distributions may be thick tailed, where treatment effects may be small, where sample sizes are large and where assignment is completely random. This setting is of particular interest in recent online experimentation. We propose using parametric models for the treatment effects, leading to semiparametric models for the outcome distributions. We derive the semiparametric efficiency bound for the treatment effects for this setting, and propose efficient estimators. In the leading case with constant quantile treatment effects one of the proposed efficient estimators has an interesting interpretation as a weighted average of quantile treatment effects, with the weights proportional to minus the second derivative of the log of the density of the potential outcomes. Our analysis also suggests an extension of Huber's model and trimmed mean to include asymmetry.