The Mode Treatment Effect

TL;DR

This paper introduces the concept of mode treatment effect in program evaluation, proposing estimation methods and analyzing their asymptotic properties, highlighting differences from traditional mean and median effects.

Contribution

It fills the gap by defining, estimating, and deriving asymptotic properties of the mode treatment effect using kernel and machine learning methods.

Findings

Estimators follow asymptotic normality with slower convergence rates.

Mode treatment effect estimation differs from mean and median in convergence behavior.

Provides theoretical foundation for future empirical applications.

Abstract

Mean, median, and mode are three essential measures of the centrality of probability distributions. In program evaluation, the average treatment effect (mean) and the quantile treatment effect (median) have been intensively studied in the past decades. The mode treatment effect, however, has long been neglected in program evaluation. This paper fills the gap by discussing both the estimation and inference of the mode treatment effect. I propose both traditional kernel and machine learning methods to estimate the mode treatment effect. I also derive the asymptotic properties of the proposed estimators and find that both estimators follow the asymptotic normality but with the rate of convergence slower than the regular rate $\sqrt{N}$, which is different from the rates of the classical average and quantile treatment effect estimators.