Placebo Discontinuity Design

2025-07-16

AI Summary

Standard regression discontinuity designs (RDD) often fail when running variables are strategically manipulated, violating the key continuity assumption for potential outcomes and undermining causal identification. This paper proposes a local instrumental variable (LIV) approach leveraging placebo treatments and placebo outcome variables: within the discontinuity neighborhood, pseudo-treatments and pseudo-outcomes are constructed, and their discontinuities serve as local instruments to decompose the conventional RDD estimator into an unbiased main term and a bias-correction term. The method dispenses with strong continuity assumptions, relying instead on local comparability of placebo variables and identifiability of the manipulation structure. We establish consistency and robust inference for the proposed estimator. Simulations and empirical applications demonstrate accurate causal effect recovery even under substantial manipulation. By relaxing foundational RDD assumptions, this work extends the applicability of RDD to settings with strategic behavior and provides a novel tool for social policy evaluation.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Causal Learning

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Standard regression discontinuity design (RDD) models rely on the continuity of expected potential outcomes at the cutoff. The standard continuity assumption can be violated by strategic manipulation of the running variable, which is realistic when the cutoff is widely known and when the treatment of interest is a social program or government benefit. In this work, we identify the treatment effect despite such a violation, by leveraging a placebo treatment and a placebo outcome. We introduce a local instrumental variable estimator. Our estimator decomposes into two terms: the standard RDD estimator of the target outcome's discontinuity, and a new adjustment term based on the placebo outcome's discontinuity. We show that our estimator is consistent, and we justify a robust bias-corrected inference procedure. Our method expands the applicability of RDD to settings with strategic behavior around the cutoff, which commonly arise in social science.

Problem

• Identifies treatment effect despite violation of continuity assumption
• Introduces local instrumental variable estimator for RDD
• Expands RDD applicability to settings with strategic behavior

Innovation

• Leverages placebo treatment and outcome
• Introduces local instrumental variable estimator
• Adjusts for discontinuity with placebo outcome