Synthetic Design: An Optimization Approach to Experimental Design with Synthetic Controls
This work addresses experimental design challenges for researchers using synthetic controls, offering incremental improvements over existing methods.
The paper tackles the problem of optimally designing experiments with pre-treatment data by proposing methods to select treated units and weights, showing improvements in mean squared error and statistical power over randomized trials in simulations using US Bureau of Labor Statistics data.
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 methods for choosing the set of treated units in conjunction with the weights. 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 approaches 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 mean squared error and statistical power when compared to simple and commonly used alternatives such as randomized trials.