  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. However, such estimators are not robust to heterogeneous treatment
effects in general; 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. 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
Desch\^enes and Greenstone (2012).
