Choosing A Headline Estimand from Matching, DID, and Hybrid Designs: A Minimax-Regret Approach

2026-06-18

AI Summary

This study addresses the challenge in panel data causal inference that the identifying assumptions of difference-in-differences (DID), matching (M), and their hybrid (DIDM) are non-nested, leaving researchers without a principled basis for selecting a primary estimator. The paper proposes a unified selection framework grounded in the minimax-regret criterion and demonstrates that, under a broad class of loss functions, the estimand associated with DIDM achieves minimax-regret optimality. Consequently, it recommends DIDM as the headline estimator, with conventional DID and matching estimates serving as robustness bounds. Both theoretical analysis and empirical applications validate the efficacy of this approach, leading to a practical reporting guideline: prioritize DIDM while presenting DID and matching results as boundary checks.

Abstract

Researchers using panel data to estimate causal effects routinely choose among three approaches to using past outcomes: difference-in-differences (DID), conditioning on lagged outcomes (matching, M), and a hybrid that does both (DIDM). The corresponding identifying assumptions are non-nested, leaving little guidance on which to report. We give conditions under which the corresponding estimands are ordered, with DIDM bracketed between matching and DID. This makes DIDM the minimax-regret choice among the three under a broad class of loss functions. We recommend reporting DIDM as the headline estimate, with matching and DID as bounds. We illustrate in applications.

Problem

• causal inference
• panel data
• difference-in-differences
• matching
• minimax regret

Innovation

• minimax regret
• difference-in-differences
• matching
• hybrid design
• causal inference