Quantifying Causal Effects via Temporal Regression Discontinuity Designs with Time-Varying Effects

Music City Center 

Regression discontinuity (RD) designs exploit locally random sorting across a treatment threshold in a running variable to estimate intervention effects. When the running variable is temporal (e.g., time or age), treatment is assigned at a time threshold, and all units eventually receive it, distinguishing Temporal Regression Discontinuity (TRD) from cross-sectional RD. While constant post-treatment effects are often assumed, complex processes in fields like environmental science and public health make this unrealistic. Instead, treatment effects evolve over time. To address this, we propose a flexible Gaussian process-based approach to detect and quantify time-varying effects with few assumptions. Our framework introduces an effect function to capture post-treatment dynamics and provides conditions to extract effect magnitude and duration via its derivative. We also develop a robust statistical test for time-varying effects. Simulations demonstrate our method's superiority over OLS and local regression in TRD settings. Finally, we apply our method to evaluate the impacts of a major transport intervention on air quality.

Temporal Regression Discontinuity Design

Time-varying Effect

Gaussian process regression

Causal Analysis 

Section on Nonparametric Statistics