Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period (2201.06898v4)

Abstract: We propose difference-in-differences 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.