Joint Covariate Balancing for Difference-in-Differences with Missing Outcome Evolutions

We propose a joint covariate balancing estimator for the average treatment effect on the treated (ATT) in a difference-in-differences (DID) design when the outcome evolution, rather than a specific outcome level, is missing at random (MAR). The proposed estimator combines treatment and response into one indicator and calibrates the two group-based density ratios directly. Point estimation therefore requires only two nuisance working models, and inference adds two linear projections, giving four in total, whereas a factorized implementation of the efficient influence function requires five: one treatment probability, two response probabilities, and two outcome-evolution models. The estimator is automatically self-normalized and attains the semiparametric efficiency bound for the coarsened data model when all working models are correctly specified. Furthermore, we show that the proposed estimator is doubly robust for both consistency and inference. The simulation results support componentwise robustness and confirm the efficiency result when all nuisance models are correctly specified, while highlighting substantial small-sample limitations under low response probabilities. An all-correct design further shows that the efficiency ordering relative to an estimator using the always-observed outcome level can reverse.