A1283
Title: Estimating effects of time-varying continuous-treatment in regression discontinuity designs
Authors: Shoichiro Nagasaka - Doshisha University (Japan) [presenting]
Yutaka Kano - Doshisha University (Japan)
Abstract: The purpose is to study statistical causal inference when treatment assignment is made based on a threshold, treatment intensity is continuous, and effects evolve over time. Building on regression discontinuity designs (RDD), it is noted that continuous-treatment approaches, including the framework of a prior study, identify effects at the cutoff but do not explicitly model temporal dynamics. A time-varying continuous-treatment RDD is introduced that preserves identification from the running variable crossing a known cutoff yet allows treatment to vary across time. Estimation combines kernel-weighted local methods tailored to dynamic settings, local quantile regression to recover distributional impacts that may shift, and local linear regression to estimate average responses with reduced boundary bias near the threshold. Together, these estimators accommodate continuous dosage, exploit local smoothness, and trace time-dependent treatment response patterns. Assumptions for identification and consistency are stated, bandwidth selection is discussed, and it is shown how the approach nests the standard RDD as a special case. Monte Carlo studies and empirical evidence demonstrate practical relevance, including sensitivity to bandwidth and kernel choices. Code and replication materials are released. Applications include clinical and economic panels with evolving policies and thresholds measured repeatedly over time across units and periods.
