Muhummad Amjad, Vishal Misra, Devavrat Shah, Dennis Shen
arXiv 15 May 2019 · Statistics — Methodology · 1 citations (OpenAlex)
arXiv:1905.06400 · PDF · DOI · OpenAlex · Extracted main text
When evaluating the impact of a policy on a metric of interest, it may not be possible to conduct a randomized control trial. In settings where only observational data is available, Synthetic Control (SC) methods provide a popular data-driven approach to estimate a "synthetic" control by combining measurements of "similar" units (donors). Recently, Robust SC (RSC) was proposed as a generalization of SC to overcome the challenges of missing data high levels of noise, while removing the reliance on domain knowledge for selecting donors. However, SC, RSC, and their variants, suffer from poor estimation when the pre-intervention period is too short. As the main contribution, we propose a generalization of unidimensional RSC to multi-dimensional RSC, mRSC. Our proposed mechanism incorporates multiple metrics to estimate a synthetic control, thus overcoming the challenge of poor inference from limited pre-intervention data. We show that the mRSC algorithm with $K$ metrics leads to a consistent estimator of the synthetic control for the target unit under any metric. Our finite-sample analysis suggests that the prediction error decays to zero at a rate faster than the RSC algorithm by a factor of $K$ and $\sqrt{K}$ for the training and testing periods (pre- and post-intervention), respectively. Additionally, we provide a diagnostic test that evaluates the utility of including additional metrics. Moreover, we introduce a mechanism to validate the performance of mRSC: time series prediction. That is, we propose a method to predict the future evolution of a time series based on limited data when the notion of time is relative and not absolute, i.e., we have access to a donor pool that has undergone the desired future evolution. Finally, we conduct experimentation to establish the efficacy of mRSC on synthetic data and two real-world case studies (retail and Cricket).
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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 | Muhammad Amjad, Devavrat Shah, and Dennis Shen (2018) Robust synthetic control self | 1.000 | 12 | 5 | 100% |
| 2 | A. Abadie, A. Diamond, and J. Hainmueller (2010) Synthetic control methods for comparative case studies: Estimating the effect of californiaâs tobacco control program | 1.000 | 6 | 3 | 100% |
| 3 | A. Abadie, A. Diamond, and J. Hainmueller (2011) Synth: An r package for synthetic control methods in comparative case studies | 1.000 | 6 | 3 | 100% |
| 4 | A. Abadie and J. Gardeazabal (2003) The economic costs of conflict: A case study of the basque country | 1.000 | 5 | 3 | 100% |
| 5 | Bradley Efron and Carl Morris (1977) Stein's paradox in statistics | 0.737 | 3 | 2 | 100% |
| 6 | Muhammad J Amjad (2018) Sequential Data Inference via Matrix Estimation: Causal Inference, Cricket and Retail self | 0.585 | 3 | 1 | 100% |
| 7 | Anish Agarwal, Devavrat Shah, Dennis Shen, and Dogyoon Song (2019) On robustness of principal component regression self | 0.511 | 3 | 2 | 33% |
| 8 | Christina Lee (2017) Latent Variable Model Estimation via Collaborative Filtering | 0.511 | 2 | 1 | 100% |
| 9 | Donald B. Rubin Paul R. Rosenbaum (1983) The central role of the propensity score in observational studies for causal effects | 0.511 | 2 | 1 | 100% |
| 10 | Donald B. Rubin (1973) Matching to remove bias in observational studies | 0.511 | 2 | 1 | 100% |
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