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Synthetic Design: An Optimization Approach to Experimental Design with Synthetic Controls
Nick Doudchenko · Khashayar Khosravi · Jean Pouget-Abadie · Sébastien Lahaie · Miles Lubin · Vahab Mirrokni · Jann Spiess · guido imbens

Tue Dec 07 08:30 AM -- 10:00 AM (PST) @ None #None

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.

Author Information

Nick Doudchenko (Google)
Khashayar Khosravi (Google Research)
Jean Pouget-Abadie (Google)
Sébastien Lahaie (Google Research)
Miles Lubin (Google)
Vahab Mirrokni (Google Research)
Jann Spiess (Stanford University)
guido imbens (Stanford University)

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