Difference-in-Differences for Continuous Treatments and Instruments with Stayers *
50 Pages Posted: 4 Mar 2022 Last revised: 12 Mar 2024
Date Written: January 18, 2022
Abstract
We propose difference-indifferences estimators in designs where the treatment is continuously distributed at every period, as is often the case when one studies the effects of taxes, tariffs, or prices. We assume that between consecutive periods, the treatment of some units, the switchers, changes, while the treatment of other units remains constant. We show that under a placebo-testable parallel-trends assumption, averages of the slopes of switchers' potential outcomes can be nonparametrically estimated. We generalize our estimators to the instrumental-variable case. We use our estimators to estimate the price-elasticity of gasoline consumption.
Keywords: differences-in-differences, continuous treatment, two-way fixed effects regressions, heterogeneous treatment effects, panel data, policy evaluation, instrumental variable JEL Codes: C21, C23
JEL Classification: C21, C23
Suggested Citation: Suggested Citation