Before revision:  It is linked to the asymptotic behavior in measure of differentially private estimators. We demonstrate that particular instances of regression discontinuity design and average treatment effect may be problematic for inference with differential privacy because their estimators can only be ensured to converge weakly with their asymptotic limit remaining random and, thus, may not be estimated consistently.
After revision:  It is naturally characterized by the concepts from the random sets theory. We show that particular instances of regression discontinuity design and average treatment effect may be problematic for inference with differential privacy because their estimators can only be ensured to converge weakly with their asymptotic limit remaining random and, thus, may not be estimated consistently.