Distributionally Robust Treatment Effect

TL;DR

This paper introduces a distributionally robust estimator for treatment effect prediction that accounts for distributional shifts using Wasserstein neighborhoods, providing bounds and inference methods.

Contribution

It proposes a novel Wasserstein-based distributionally robust approach for treatment effect estimation under partial identification and heterogeneity.

Findings

The estimator preserves the sign of the average treatment effect.

It shrinks estimates toward zero depending on heterogeneity.

The paper establishes consistency and asymptotic normality of bounds.

Abstract

Using only retrospective data, we study the problem of predicting treatment effects for the same treatment/policy implemented in a different location or time period. We propose a distributionally robust estimator that minimizes the worst-case mean squared error for the prediction of treatment effect over a class of distributions defined by a Wasserstein neighborhood around the source distribution. Because the joint distribution of potential outcomes is unidentified, the problem is inherently one of partial identification. We characterize the sharp upper and lower bounds of the minimax optimizer by exploiting the Fr\'echet class of distributions consistent with the marginal distributions of potential outcomes. The resulting predictor preserves the sign of the average treatment effect under the source distribution but is shrunk toward zero, with the degree of shrinkage depending on the extent of treatment effect heterogeneity. We establish consistency and asymptotic normality of the bound estimators, develop a two-step inference procedure, and discuss the choice of the robustness parameter.