  In this paper we study estimation of and inference for average treatment
effects in a setting with panel data. We focus on the setting where units,
e.g., individuals, firms, or states, adopt the policy or treatment of interest
at a particular point in time, and then remain exposed to this treatment at all
times afterwards. We take a design perspective where we investigate the
properties of estimators and procedures given assumptions on the assignment
process. We show that under random assignment of the adoption date the standard
Difference-In-Differences estimator is is an unbiased estimator of a particular
weighted average causal effect. We characterize the proeperties of this
estimand, and show that the standard variance estimator is conservative.
