Estimating treatment effects with a unified semi-parametric difference-in-differences approach

2025-06-13

AI Summary

Traditional difference-in-differences (DID) methods rely on the mean-level parallel trends assumption, which is inadequate for skewed outcome distributions. Moreover, identifying heterogeneous treatment effects—such as quantile, probability, or Mann–Whitney effects—requires separate, often incompatible, parallel trends assumptions, leading to fragmented modeling and conceptual inconsistency. This paper proposes a unified semiparametric DID framework grounded in a latent-variable cumulative probability model (CPM). By formulating the parallel trends assumption on the expectation of the latent variable, our approach enables simultaneous identification of average, quantile, probabilistic, and Mann–Whitney treatment effects under a single, coherent assumption. The method integrates latent-variable modeling, CPM estimation, and DID inference, ensuring robustness and supported by asymptotic theory. Simulation studies confirm consistency and robustness across data-generating processes. Empirically, applying the framework to Medicaid expansion reveals a statistically significant increase in baseline CD4 count among HIV-positive individuals at treatment initiation, with highly concordant estimates across all effect types.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Distributed Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The difference-in-differences (DID) approach is widely used for estimating causal effects with observational data before and after an intervention. DID is traditionally used to assess an average treatment effect among the treated after making a parallel trends assumption on the means of the outcome. With skewed outcomes, a transformation is often needed; however, the transformation may be difficult to choose, results may be sensitive to the choice, and parallel trends assumptions are made on the transformed scale. More recent DID methods estimate alternative treatment effects, such as quantile treatment effects among the treated, that offer a different understanding of the impact of a treatment and may be preferable with skewed outcomes. However, each alternative DID estimator requires a different parallel trends assumption. We introduce a new DID method that is capable of estimating average, quantile, probability, and novel Mann-Whitney treatment effects among the treated with a single unifying parallel trends assumption. The proposed method uses a semi-parametric cumulative probability model (CPM). The CPM is a linear model for a latent variable on covariates, where the latent variable results from an unspecified transformation of the outcome. Our DID approach makes a universal parallel trends assumption on the expectation of the latent variable conditional on covariates. Hence, our method overcomes challenges surrounding outcomes with complicated, difficult-to-model distributions and avoids the need for separate assumptions and/or approaches for each estimand. We introduce the method; describe identification, estimation, and inference; conduct simulations evaluating its performance; and apply it to real-world data to assess the impact of Medicaid expansion on CD4 cell count at enrollment among people living with HIV.

Problem

• Estimates diverse treatment effects with one parallel trends assumption
• Addresses skewed outcomes without needing outcome transformation
• Unifies DID methods for average, quantile, and probability effects

Innovation

• Unified semi-parametric difference-in-differences approach
• Single parallel trends assumption for multiple effects
• Latent variable model with unspecified outcome transformation