Difference-in-Differences Estimators with Continuous Treatments and No Stayers
4 Pages Posted: 19 Feb 2024
Date Written: February 8, 2024
Abstract
Many treatments or policy interventions are continuous in nature. Examples include prices, taxes or temperatures. Empirical researchers have usually relied on two-way fixed effect regressions to estimate treatment effects in such cases, see e.g. Deschênes and Greenstone (2012). However, such estimators are not robust to heterogeneous treatment effects in general (De Chaisemartin and D’Haultfoeuille, 2020); they also rely on the linearity of treatment effects. We propose estimators for continuous treatments that do not impose those restrictions, and that can be used when there are no stayers: the treatment of all units changes from one period to the next. This is for instance the case when the treatment is precipitations or temperatures: for instance, temperatures of all US counties change, if ever so slightly, between two consecutive years. We start by extending the nonparametric results of de Chaisemartin et al. (2023) to cases without stayers. We also present a parametric estimator, and use it to revisit Deschênes and Greenstone (2012).
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