A Supplementary materials

A.1 Conditional MSE of the treatment effect estimator The expression for the conditional mean squared error used in Section 2 can be derived as follows. 's as the only source of randomness in the above expression and assuming that they are Abadie et al., 2010), or the assumption that treatment periods are themselves chosen at random and In this section we present the exact mixed-integer programming formulations that can be used for solving the proposed models in one of the available academic or commercial solvers. SCIP (Gamrath et al., 2020) which can handle mixed-integer nonlinear programs (MINLP's) with We need two additional observations to formulate the problem as a quadratic objective with linear constraints. 's can be carried inside the The problem becomes more complicated when there is no constraint on the number of treated units. In this section we provide a proof of Theorem 1. A B null which is independent of the index l .