Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period

Clément de Chaisemartin, Xavier D'Haultfoeuille, F\'elix Pasquier and Gonzalo Vazquez-Bare

Papers from arXiv.org

Abstract: We propose new difference-in-difference (DID) estimators for treatments continuously distributed at every time period, as is often the case of trade tariffs, or temperatures. We start by assuming that the data only has two time periods. We also assume that from period one to two, the treatment of some units, the switchers, changes, while the treatment of other units, the stayers, does not change. Then, our estimators compare the outcome evolution of switchers and stayers with the same value of the treatment at period one. Our estimators only rely on parallel trends assumptions, unlike commonly used two-way fixed effects regressions that also rely on homogeneous treatment effect assumptions. Comparing switchers and stayers with the same period-one treatment is important: unconditional comparisons of switchers and stayers implicitly assume constant treatment effects over time. With a continuous treatment, switchers cannot be matched to stayers with exactly the same period-one treatment, but comparisons of switchers and stayers with the same period-one treatment can still be achieved by non-parametric regression, or by propensity-score reweighting. We extend our results to applications with no stayers, more than two time periods, and where the treatment may have dynamic effects.

Date: 2022-01, Revised 2023-07
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Working Paper: Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period (2022)
Working Paper: Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period (2022)
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