Enhancing Treatment Effect Prediction on Privacy-Protected Data: An Honest Post-Processing Approach

Abstract

As firms increasingly rely on customer data for personalization, concerns over privacy and regulatory compliance have grown. Local Differential Privacy (LDP) offers strong individual-level protection by injecting noise into data before collection. While effective for safeguarding privacy, LDP can severely degrade data utility. This paper examines its impact on an important marketing practice: personalized interventions through Conditional Average Treatment Effect (CATE) prediction. We show that LDP introduces model-dependent bias and variance distortions in CATE estimates, which vary across covariates and can impair treatment prioritization, reduce predictive accuracy, and lead to inefficient resource allocation. Existing correction methods from the measurement error literature are often inadequate in high-dimensional, privacy-constrained settings where flexible models are used. To address these challenges, we propose a model-agnostic post-processing approach that refines CATE predictions while preserving LDP guarantees. Our method leverages an unbiased but noisy proxy for the true CATE and applies an iterative boosting procedure to better align predictions with this proxy. A major challenge is the high approximation error of the proxy variable due to LDP noise, which can lead to overfitting in standard post-processing. To mitigate this, we introduce an honest algorithm that combines sample splitting with a novel subgroup cross-learning technique to prevent overfitting. Through simulation studies and real-world marketing applications, we show that our method significantly improves both CATE prediction and treatment prioritization under LDP protection. Our findings offer a practical solution for organizations seeking to balance personalization and privacy, positioning post-processing as a powerful tool in navigating the privacy–utility trade-off.

Keywords: targeted intervention, conditional average treatment effect estimation, differential privacy, honest estimation, post-processing

JEL Classification: C51, C52, C53, C93, M31