Untangling Partial Treatment Effects When Multiple Scores Determine Eligibility

What the Paper Asks

This paper by Jin-Young Choi and Myoung-Jae Lee asks how researchers can recover causal effects in regression discontinuity (RD) settings when treatment assignment depends on more than one running variable (score), and when crossing different cutoffs may produce distinct, partial effects rather than a single “all-or-nothing” jump.

Why This Matters

Standard RD methods assume one score and identify a single mean jump at a cutoff. But many applied settings use multiple eligibility criteria (multiple scores), and policy impact can be generated by each score independently. Failing to separate these partial effects can blur identification and mislead substantive conclusions about who benefits from a policy and why.

How the Authors Approach It

• The paper generalizes the usual one-score mean RD in three directions: (i) multiple running variables, (ii) allowance for partial effects from each score crossing its cutoff (not only the full effect when all cutoffs are crossed), and (iii) extension to quantile and mode regression functions, not just mean outcomes.
• The authors develop identification arguments that show when and how each partial effect is separately recoverable in a multiple-score RD (MRD) setup.
• They propose simple, implementable estimators. In the special case of two running variables, these estimators take the form of a “local difference-in-differences,” facilitating intuitive implementation and interpretation.

Main Results

• Formal identification conditions for MRD are established, clarifying the assumptions needed to disentangle individual score effects from the joint effect.
• Estimators are provided for mean, quantile, and mode RD parameters under the multiple-score framework, with the double-score case linked explicitly to a local diff-in-diff estimator.

Empirical Illustration

An empirical example demonstrates a context where partial effects are present and where the proposed MRD approach isolates the contributions of individual scores, illustrating the practical importance of the decomposition for causal inference and policy interpretation.

The paper supplies a practical and theoretically grounded toolkit for applied researchers facing multi-criteria eligibility rules and contributes to more nuanced causal analysis in RD designs.