Before revision:  In addition, our proposed methodology accommodates linear and nonlinear specifications, allows for treatment effect heterogeneity, and can be applied with either panel or repeated cross section data . We establish the asymptotic distribution of our proposed doubly robust estimators , and propose a computationally simple bootstrap procedure to conduct asymptotically valid inference. Our inference procedures directly account for multiple testing, and are therefore suitable in situations where researchers are interested in the effect of a given policy on many different outcomes. We demonstrate the relevance of our proposed policy evaluation tools in two different applications .
After revision:  In addition, our proposed methodology accommodates linear and nonlinear specifications, allows for treatment effect heterogeneity, and can be applied with either panel or repeated cross-section data are available, and show that our proposed estimators attain the semiparametric efficiency bound when the working models are correctly specified. Finally, by paying particular attention to the estimation method used to estimate the nuisance parameters, we show that one can sometimes construct doubly robust DID estimators for the ATT that are also doubly robust for inference. Simulation studies and an empirical application illustrate the desirable finite-sample performance of the proposed estimators. Open-source software for implementing the proposed policy evaluation tools in two different applications .