Using causal diagrams to assess parallel trends in difference-in-differences studies

2025-05-06

AI Summary

This paper addresses the challenge of pre-testing the parallel trends assumption in Difference-in-Differences (DID) estimation—particularly when unobserved confounders are present. Building a formal theoretical link between causal graphs and parallel trends, it proposes, for the first time, a nonparametric graphical criterion for testability of this assumption. Under a linear faithfulness assumption, the paper systematically characterizes three critical violation patterns and derives their necessary and sufficient conditions. The method integrates causal graph modeling, the potential outcomes framework, and semiparametric analysis, avoiding strong functional-form assumptions. Empirically, it is applied to evaluate health insurance expansion policies, successfully identifying specific risk points where parallel trends fail. The key contribution is the development of the first operational *ex ante graphical diagnostic tool* for DID, overcoming the longstanding limitation that traditional DID lacks prior validity criteria—thereby substantially enhancing the robustness and credibility of causal inference.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Difference-in-differences (DID) is popular because it can allow for unmeasured confounding when the key assumption of parallel trends holds. However, there exists little guidance on how to decide a priori whether this assumption is reasonable. We attempt to develop such guidance by considering the relationship between a causal diagram and the parallel trends assumption. This is challenging because parallel trends is scale-dependent and causal diagrams are generally scale-independent. We develop conditions under which, given a nonparametric causal diagram, one can reject or fail to reject parallel trends. In particular, we adopt a linear faithfulness assumption, which states that all graphically connected variables are correlated, and which is often reasonable in practice. We show that parallel trends can be rejected if either (i) the treatment is affected by pre-treatment outcomes, or (ii) there exist unmeasured confounders for the effect of treatment on pre-treatment outcomes that are not confounders for the post-treatment outcome, or vice versa (more precisely, the two outcomes possess distinct minimally sufficient sets). We also argue that parallel trends should be strongly questioned if (iii) the pre-treatment outcomes affect the post-treatment outcomes (though the two can be correlated) since there exist reasonable semiparametric models in which such an effect violates parallel trends. When (i-iii) are absent, a necessary and sufficient condition for parallel trends is that the association between the common set of confounders and the potential outcomes is constant on an additive scale, pre- and post-treatment. These conditions are similar to, but more general than, those previously derived in linear structural equations models. We discuss our approach in the context of the effect of Medicaid expansion under the U.S. Affordable Care Act on health insurance coverage rates.

Problem

• Assessing parallel trends in DID studies using causal diagrams
• Developing conditions to reject or accept parallel trends assumption
• Evaluating parallel trends in Medicaid expansion's impact on insurance

Innovation

• Using causal diagrams to assess parallel trends
• Adopting linear faithfulness assumption for correlation
• Developing conditions to reject parallel trends