Three's a crowd: Identification challenges in the triple difference model with spillover effects

2026-01-22

AI Summary

This study addresses the challenge that conventional triple-difference (DDD) models fail to simultaneously identify treatment and spillover effects when spillovers contaminate the control group. To resolve this issue, the authors propose a dual triple-difference framework that restructures the identification assumptions and spillover architecture, thereby formally characterizing the conditions under which both effects are identifiable—a contribution not previously achieved in the literature. Theoretical analysis establishes the identification validity of the proposed approach, while Monte Carlo simulations and an empirical application to special economic zones in Italy demonstrate its robustness and accuracy in practical settings. This new framework enables consistent estimation of both direct treatment and spillover effects even in the presence of cross-group contamination.

Technology Category

Game Theory and Economic Paradigms: Mechanism DesignSearch and Optimization: Mixed Discrete/Continuous SearchMultiagent Systems: Mechanism Design

Application Category

User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systemsGraph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphsWeb Mining and Content Analysis: Content-based information diffusion

Abstract

The paper studies identification in triple-difference designs when spillover effects contaminate one or more control groups. We show that, under conventional identifying assumptions, the triple-difference model fails to identify both the treatment effect and the spillover effect under such interference. To overcome this limitation, we propose an alternative specification, the double-triple-difference model, and explicitly formalize identifying assumptions and spillover structures required for consistent identification of both effects. We derive formal identification results and assess the performance of the proposed model through Monte Carlo simulations. An empirical application evaluating a Special Economic Zone in Italy is provided.

Problem

• triple difference
• spillover effects
• identification
• interference
• control groups

Innovation

• triple difference
• spillover effects
• identification
• double-triple-difference
• causal inference