Yiping Lu, Jiajin Li, Lexing Ying, Jose Blanchet
arXiv 28 Nov 2022 · Econometrics · 1 citations (OpenAlex)
arXiv:2211.15241 · PDF · DOI · OpenAlex · Extracted main text
The optimal design of experiments typically involves solving an NP-hard combinatorial optimization problem. In this paper, we aim to develop a globally convergent and practically efficient optimization algorithm. Specifically, we consider a setting where the pre-treatment outcome data is available and the synthetic control estimator is invoked. The average treatment effect is estimated via the difference between the weighted average outcomes of the treated and control units, where the weights are learned from the observed data. {Under this setting, we surprisingly observed that the optimal experimental design problem could be reduced to a so-called phase synchronization problem.} We solve this problem via a normalized variant of the generalized power method with spectral initialization. On the theoretical side, we establish the first global optimality guarantee for experiment design when pre-treatment data is sampled from certain data-generating processes. Empirically, we conduct extensive experiments to demonstrate the effectiveness of our method on both the US Bureau of Labor Statistics and the Abadie-Diemond-Hainmueller California Smoking Data. In terms of the root mean square error, our algorithm surpasses the random design by a large margin.
appendix boundary found by appendix_command · 50% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Abadie, Alberto, Zhao, Jinglong (2021) Synthetic controls for experimental design | 1.000 | 17 | 4 | 100% |
| 2 | Doudchenko, Nick, Khosravi, Khashayar, Pouget-Abadie, Jean, Lahaie,… (2021) Synthetic Design: An Optimization Approach to Experimental Design with Synthetic Controls | 1.000 | 17 | 3 | 100% |
| 3 | Abadie, Alberto, Diamond, Alexis, Hainmueller, Jens (2010) Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program | 1.000 | 10 | 4 | 100% |
| 4 | Xu, Yiqing (2017) Generalized synthetic control method: Causal inference with interactive fixed effects models | 1.000 | 7 | 4 | 100% |
| 5 | Athey, Susan, Bayati, Mohsen, Doudchenko, Nikolay, Imbens, Guido, Kh… (2021) Matrix completion methods for causal panel data models | 1.000 | 6 | 3 | 100% |
| 6 | Singer, Amit (2011) Angular synchronization by eigenvectors and semidefinite programming | 0.961 | 9 | 4 | 89% |
| 7 | Zhong, Yiqiao, Boumal, Nicolas (2018) Near-optimal bounds for phase synchronization | 0.874 | 9 | 4 | 67% |
| 8 | Ferman, Bruno (2021) On the properties of the synthetic control estimator with many periods and many controls | 0.811 | 4 | 2 | 100% |
| 9 | Morgan, Kari Lock, Rubin, Donald B (2012) Rerandomization to improve covariate balance in experiments | 0.811 | 4 | 2 | 100% |
| 10 | Liu, Huikang, Yue, Man-Chung, Man-Cho So, Anthony (2017) On the estimation performance and convergence rate of the generalized power method for phase synchronization | 0.717 | 19 | 4 | 37% |
Showing the top 10 of 60 scored citations.