Abstract: We consider treatment-effect estimation with a two-periods panel, where units are untreated at period one, and receive strictly positive doses at period two. First, we consider designs with some quasi-untreated units, with a period-two dose local to zero. We show that under a parallel-trends assumption, a weighted average of slopes of units' potential outcomes is identified by a difference-in-difference estimand using quasi-untreated units as the control group. We leverage results from the regression-discontinuity-design literature to propose a nonparametric estimator. Then, we propose estimators for designs without quasi-untreated units. Finally, we propose a test of the homogeneous-effect assumption underlying two-way-fixed-effects regressions.

Abstract: The distribution of treatment effects is a relevant, yet generally unknown, parameter for impact evaluation and policy choice. Randomized experiments reveal the average treatment effect, but not the dispersion of treatment effects around the mean. In this paper, I propose bounds on the variance of the treatment effect based on the semidefinite completion of the correlation matrix of potential outcomes and baseline covariates. I prove properties of the identified set, consistency of the set estimator and asymptotic validity of the corresponding confidence interval. Compared to only using the marginal distributions of potential outcomes, baseline covariates considerably refine the identified set. Nonetheless, inference may be adversely affected by covariates that are irrelevant in some well-defined sense. I revisit Cueva et al. (2024), who use Fréchet-Hoeffding inequalities to bound the variance of treatment effect, and find that confidence intervals based on the proposed bounds are generally tighter.

Abstract: I propose an event study extension of Synthetic Difference-in-Differences (SDID) estimators. I show that, in simple and staggered adoption designs, estimators from Arkhangelsky et al. (2021) can be disaggregated into dynamic treatment effect estimators, comparing the lagged outcome differentials of treated and synthetic controls to their pre-treatment average. Estimators presented in this note can be computed using the sdid_event Stata package.

Abstract: The command did_multiplegt_dyn can be used to estimate event-study effects in complex designs with a potentially non-binary and/or non-absorbing treatment. This paper starts by providing an overview of the estimators computed by the command. Then, simulations based on three real datasets are used to demonstrate the estimators' properties. Finally, the command is used on four real datasets to estimate event-study effects in complex designs. The first example has a binary treatment that can turn on an off. The second example has a continuous absorbing treatment. The third example has a discrete multivalued treatment that can increase or decrease multiple times over time. The fourth example has two, binary and absorbing treatments, where the second treatment always happens after the first.