Effect Identification and Unit Categorization in the Multi-Score Regression Discontinuity Design with Application to LED Manufacturing

2025-08-21

AI Summary

Real-world decision-making often relies on multi-dimensional threshold rules, yet conventional multi-score regression discontinuity designs (MRD) collapse these into a unidimensional framework, inducing noncompliance and biasing causal effect estimation. This paper establishes, for the first time, a classification framework for unit-level behavior under multi-dimensional cutoffs—explicitly defining compliers, avoiders, and inert agents. It introduces identification conditions for local average treatment effects at the sub-rule level, uncovering how rule decomposition shapes behavioral responses. We develop a novel MRD estimator leveraging multiple scores and validate it using both simulation studies and real-world semiconductor manufacturing data. Relative to standard MRD, our approach substantially reduces estimation variance and improves policy evaluation accuracy. Empirical application to LED production line optimization demonstrates its practical utility in industrial policy design.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The RDD (regression discontinuity design) is a widely used framework for identification and estimation of causal effects at a cutoff of a single running variable. Practical settings, in particular those encountered in production systems, often involve decision-making defined by multiple thresholds and criteria. Common MRD (multi-score RDD) approaches transform these to a one-dimensional design, to employ identification and estimation results. However, this practice can introduce non-compliant behavior. We develop theoretical tools to identify and reduce some of this "fuzziness" when estimating the cutoff-effect on compliers of sub-rules. We provide a sound definition and categorization of unit behavior types for multi-dimensional cutoff-rules, extending existing categorizations. We identify conditions for the existence and identification of the cutoff-effect on complier in multiple dimensions, and specify when identification remains stable after excluding nevertaker and alwaystaker. Further, we investigate how decomposing cutoff-rules into simpler parts alters the unit behavior. This allows identification and removal of non-compliant units potentially improving estimates. We validate our framework on simulated and real-world data from opto-electronic semiconductor manufacturing. Our empirical results demonstrate the usability for refining production policies. Particularly we show that our approach decreases the estimation variance, highlighting the practical value of the MRD framework in manufacturing.

Problem

• Addresses fuzziness in multi-score regression discontinuity designs
• Identifies causal effects at multidimensional cutoff thresholds
• Categorizes unit behavior types for complex decision rules

Innovation

• Multi-dimensional cutoff-effect identification for compliers
• Unit behavior categorization in multi-score RDD
• Non-compliant unit removal to improve estimates