Event-Studies with a Continuous Treatment

Abstract

This paper builds on the identification results and estimation tools for continuous difference-in-difference designs in Callaway, Goodman-Bacon, and Sant'Anna (2024) to discuss aggregation strategies for event studies with continuous treatments. Estimates from continuous designs are functions of the treatment dosage/intensity variable. Nonparametric plots of these functions show heterogeneity across doses but not heterogeneity over time. Event-study-type plots of aggregated parameters achieve the opposite. We describe how partially aggregating across treatment doses and event time can lead to readable yet nuanced figures that reflect how causal effects evolve over time, potentially in different parts of the treatment dose distribution.