Isotonic propensity score matching

TL;DR

This paper introduces an isotonic regression-based one-to-many matching estimator for average treatment effect, leveraging monotonicity assumptions to improve efficiency, robustness, and validity over existing methods.

Contribution

It develops a novel matching estimator using isotonic regression for propensity scores, addressing key issues like efficiency and robustness in treatment effect estimation.

Findings

Improves efficiency and robustness of matching methods.

Provides a uniformly consistent isotonic estimator.

Enhances bootstrap validity for treatment effect estimation.

Abstract

We propose a one-to-many matching estimator of the average treatment effect based on propensity scores estimated by isotonic regression. This approach is predicated on the assumption of monotonicity in the propensity score function, a condition that can be justified in many economic applications. We show that the nature of the isotonic estimator can help us to fix many problems of existing matching methods, including efficiency, choice of the number of matches, choice of tuning parameters, robustness to propensity score misspecification, and bootstrap validity. As a by-product, a uniformly consistent isotonic estimator is developed for our proposed matching method.