Regression Discontinuity with Multiple Running Variables Allowing Partial Effects

In regression discontinuity (RD), a running variable (or "score") crossing a cutoff determines a treatment that affects the mean-regression function. This paper generalizes this usual "one-score mean RD" in three ways: (i) considering multiple scores, (ii) allowing partial effects due to each score crossing its own cutoff, not just the full effect with all scores crossing all cutoffs, and (iii) accommodating quantile/mode regressions. This generalization is motivated by (i) many multiple-score RD cases, (ii) the full-effect identification needing the partial effects to be separated, and (iii) informative quantile/mode regression functions. We establish identification for multiple-score RD (MRD), and propose simple estimators that become "local difference in differences" in case of double scores. We also provide an empirical illustration where partial effects exist.