Targeted Function Balancing

TL;DR

This paper presents Targeted Function Balancing (TFB), a covariate balancing framework that improves treatment effect estimation by balancing functions of covariates based on outcome regression models, challenging traditional imbalance avoidance.

Contribution

TFB introduces a novel approach to covariate balancing that leverages outcome regression models and their variance, enabling more efficient and flexible treatment effect estimation.

Findings

TFB effectively balances covariates using outcome regression functions.

Leaving some covariate imbalance can increase efficiency without bias.

The framework is compatible with various regression estimators like KRLS, LASSO, and BART.

Abstract

This paper introduces Targeted Function Balancing (TFB), a covariate balancing weights framework for estimating the average treatment effect of a binary intervention. TFB first regresses an outcome on covariates, and then selects weights that balance functions (of the covariates) that are probabilistically near the resulting regression function. This yields balance in the regression function's predicted values and the covariates, with the regression function's estimated variance determining how much balance in the covariates is sufficient. Notably, TFB demonstrates that intentionally leaving imbalance in some covariates can increase efficiency without introducing bias, challenging traditions that warn against imbalance in any variable. Additionally, TFB is entirely defined by a regression function and its estimated variance, turning the problem of how best to balance the covariates into how best to model the outcome. Kernel regularized least squares (KRLS), the LASSO, and Bayesian Additive Regression Trees (BART) are considered as regression estimators. With KRLS, TFB contributes to the literature of kernel-based weights. As for the LASSO, TFB uses the regression function's estimated variance to prioritize balance in certain dimensions of the covariates, a feature that can be greatly exploited by choosing a sparse regression estimator. With BART, we demonstrate that TFB can apply regression estimators that do not have linear representations. The R Package tfb implements TFB.