A Non-Bipartite Matching Framework for Difference-in-Differences with General Treatment Types

2025-11-26

AI Summary

Traditional difference-in-differences (DID) methods are restricted to binary treatments and struggle to generalize to continuous or ordinal treatments. This paper proposes a non-binary matching DID framework that avoids strong parametric assumptions and does not rely on “stayers” (units with invariant treatment status). The method constructs an optimal non-binary bipartite graph matching design to enable precise comparison of heterogeneous treatment trajectories while balancing covariates, thereby supporting nonparametric, finite-population causal inference for arbitrary treatment types. Its key innovations include: (i) introducing randomization-based design conditions and (ii) defining a sample-average DID ratio, circumventing outcome model specification and the ideal control-unit assumption. Empirical evaluations demonstrate robustness and substantially improved estimation efficiency on real-world data, significantly broadening the applicability of DID in observational studies.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Difference-in-differences (DID) is one of the most widely used causal inference frameworks in observational studies. However, most existing DID methods are designed for binary treatments and cannot be readily applied to non-binary treatment settings. Although recent work has begun to extend DID to non-binary (e.g., continuous) treatments, these approaches typically require strong additional assumptions, including parametric outcome models or the presence of idealized comparison units with (nearly) static treatment levels over time (commonly called ``stayers'' or ``quasi-stayers''). In this technical note, we introduce a new non-bipartite matching framework for DID that naturally accommodates general treatment types (e.g., binary, ordinal, or continuous). Our framework makes three main contributions. First, we develop an optimal non-bipartite matching design for DID that jointly balances baseline covariates across comparable units (reducing bias) and maximizes contrasts in treatment trajectories over time (improving efficiency). Second, we establish a post-matching randomization condition, the design-based counterpart to the traditional parallel-trends assumption, which enables valid design-based inference. Third, we introduce the sample average DID ratio, a finite-population-valid and fully nonparametric causal estimand applicable to arbitrary treatment types. Our design-based approach that preserves the full treatment-dose information, avoids parametric assumptions, does not rely on the existence of stayers or quasi-stayers, and operates entirely within a finite-population framework, without appealing to hypothetical super-populations or outcome distributions.

Problem

• Extends difference-in-differences to non-binary treatments without strong parametric assumptions
• Eliminates reliance on stayers or quasi-stayers with static treatment levels over time
• Enables design-based causal inference for general treatment types within finite populations

Innovation

• Non-bipartite matching balances covariates and treatment trajectories
• Design-based inference replaces parallel-trends assumption
• Fully nonparametric estimand for arbitrary treatment types