Direct Bias-Correction Term Estimation for Propensity Scores and Average Treatment Effect Estimation

2025/09/26 by Kato, Masahiro · 7 citations
#Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2509.22122

Abstract

This study considers the estimation of the average treatment effect (ATE). For ATE estimation, we estimate the propensity score through direct bias-correction term estimation. Let \(X_i, D_i, Y_i)\_i=1ⁿ be the observations, where X_i ∈ ℝ^p denotes p-dimensional covariates, D_i ∈ \0, 1\ denotes a binary treatment assignment indicator, and Y_i ∈ ℝ is an outcome. In ATE estimation, the bias-correction term h₀(X_i, D_i) = (1[D_i = 1])/(e₀(X_i)) - (1[D_i = 0])/(1 - e₀(X_i)) plays an important role, where e₀(X_i) is the propensity score, the probability of being assigned treatment 1. In this study, we propose estimating h₀ (or equivalently the propensity score e₀) by directly minimizing the prediction error of h₀. Since the bias-correction term h₀ is essential for ATE estimation, this direct approach is expected to improve estimation accuracy for the ATE. For example, existing studies often employ maximum likelihood or covariate balancing to estimate e₀, but these approaches may not be optimal for accurately estimating h₀ or the ATE. We present a general framework for this direct bias-correction term estimation approach from the perspective of Bregman divergence minimization and conduct simulation studies to evaluate the effectiveness of the proposed method.

Citations

• A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression
• Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression
• Direct Debiased Machine Learning via Bregman Divergence Minimization
• Automatic Debiased Machine Learning for Covariate Shifts
• Augmented balancing weights as linear regression
• Estimation based on nearest neighbor matching: from density ratio to average treatment effect
• RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests
• Automatic Debiased Machine Learning via Riesz Regression
• Telescoping Density-Ratio Estimation
• Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation
• Adapting Neural Networks for the Estimation of Treatment Effects
• Automatic Debiased Machine Learning of Causal and Structural Effects
• Automatic Debiased Machine Learning of Causal and Structural Effects
• Approximate Residual Balancing: De-Biased Inference of Average Treatment\n Effects in High Dimensions
• Covariate Balancing Propensity Score by Tailored Loss Functions
• Doubly Robust Estimation in Missing Data and Causal Inference Models
• Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score
• Calibration Estimators in Survey Sampling
• The central role of the propensity score in observational studies for causal effects
• A Generalization of Sampling Without Replacement from a Finite Universe
• Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies

Cited by

• Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates via Generalized Riesz Regression
• Riesz Regression As Direct Density Ratio Estimation
• A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression
• Bridging the Gap between Empirical Welfare Maximization and Conditional Average Treatment Effect Estimation in Policy Learning
• genriesz: A Python Package for Automatic Debiased Machine Learning with Generalized Riesz Regression
• Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression
• Direct Debiased Machine Learning via Bregman Divergence Minimization

Related

• Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score
• When is the estimated propensity score better? High-dimensional analysis and bias correction
• Optimal Covariate Balancing Conditions in Propensity Score Estimation
• Double propensity-score adjustment: A solution to design bias or bias due to incomplete matching
• Propensity Score Weighting and Trimming Strategies for Reducing Variance and Bias of Treatment Effect Estimates: A Simulation Study