  We develop a framework for difference-in-differences designs with staggered
treatment adoption and heterogeneous causal effects. We show that conventional
regression-based estimators fail to provide unbiased estimates of relevant
estimands absent strong restrictions on treatment-effect homogeneity. We then
derive the efficient estimator addressing this challenge, which takes an
intuitive "imputation" form when treatment-effect heterogeneity is
unrestricted. We characterize the asymptotic behavior of the estimator, propose
tools for inference, and develop tests for identifying assumptions. Our method
applies with time-varying controls, in triple-difference designs, and with
certain non-binary treatments. We show the practical relevance of our results
in a simulation study and an application. Studying the consumption response to
tax rebates in the United States, we find that the notional marginal propensity
to consume is between 8 and 11 percent in the first quarter - about half as
large as benchmark estimates used to calibrate macroeconomic models - and
predominantly occurs in the first month after the rebate.
