Nick Doudchenko, Google

• Title: Optimal Design of Experiments in Panel-Data Settings

• Abstract: We investigate the optimal design of experimental studies that have pre-treatment outcome data available. The average treatment effect is estimated as the difference between the weighted average outcomes of the treated and control units. A number of commonly used approaches fit this formulation, including the difference-in-means estimator and a variety of synthetic-control techniques. We propose several different novel estimators and motivate the choice between them depending on the underlying assumptions the researcher is willing to make. Observing the NP-hardness of the problem, we introduce a mixed-integer programming formulation which selects both the treatment and control sets and unit weightings. We prove that these proposed estimators lead to qualitatively different experimental units being selected for treatment. We use simulations based on publicly available data from the US Bureau of Labor Statistics that show improvements in terms of the mean squared error of the estimates and statistical power when compared to simple and commonly used alternatives such as randomized trials.