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

Philipp Alexander Schwarz, Oliver Schacht, Sven Klaassen, Johannes Oberpriller, Martin Spindler

arXiv 21 Aug 2025 · Statistics — Methodology

arXiv:2508.15692 · PDF · DOI · OpenAlex · Extracted main text

Abstract

RDD (Regression discontinuity design) is a widely used framework for identifying and estimating causal effects at the cutoff of a single running variable. In practice, however, decision-making often involves multiple thresholds and criteria, especially in production systems. Standard MRD (multi-score RDD) methods address this complexity by reducing the problem to a one-dimensional design. This simplification allows existing approaches to be used to identify and estimate causal effects, but it can introduce non-compliance by misclassifying units relative to the original cutoff rules. We develop theoretical tools to detect and reduce "fuzziness" when estimating the cutoff effect for units that comply with individual subrules of a multi-rule system. In particular, we propose a formal definition and categorization of unit behavior types under multi-dimensional cutoff rules, extending standard classifications of compliers, alwaystakers, and nevertakers, and incorporating defiers and indecisive units. We further identify conditions under which cutoff effects for compliers can be estimated in multiple dimensions, and establish when identification remains valid after excluding nevertakers and alwaystakers. In addition, we examine how decomposing complex Boolean cutoff rules (such as AND- and OR-type rules) into simpler components affects the classification of units into behavioral types and improves estimation by making it possible to identify and remove non-compliant units more accurately. We validate our framework using both semi-synthetic simulations calibrated to production data and real-world data from opto-electronic semiconductor manufacturing. The empirical results demonstrate that our approach has practical value in refining production policies and reduces estimation variance. This underscores the usefulness of the MRD framework in manufacturing contexts.

Citation extraction

appendix boundary found by appendix_command · 79% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

Showing the top 10 of 44 scored citations.