Vivek F. Farias, Andrew A. Li, Tianyi Peng
arXiv 5 Jun 2021 · Statistics — Machine Learning · 5 citations (OpenAlex)
arXiv:2106.02780 · PDF · DOI · OpenAlex · Extracted main text
The problem of causal inference with panel data is a central econometric question. The following is a fundamental version of this problem: Let $M^*$ be a low rank matrix and $E$ be a zero-mean noise matrix. For a `treatment' matrix $Z$ with entries in ${0,1}$ we observe the matrix $O$ with entries $O_{ij} := M^*_{ij} + E_{ij} + \mathcal{T}_{ij} Z_{ij}$ where $\mathcal{T}_{ij} $ are unknown, heterogenous treatment effects. The problem requires we estimate the average treatment effect $\tau^* := \sum_{ij} \mathcal{T}_{ij} Z_{ij} / \sum_{ij} Z_{ij}$. The synthetic control paradigm provides an approach to estimating $\tau^*$ when $Z$ places support on a single row. This paper extends that framework to allow rate-optimal recovery of $\tau^*$ for general $Z$, thus broadly expanding its applicability. Our guarantees are the first of their type in this general setting. Computational experiments on synthetic and real-world data show a substantial advantage over competing estimators.
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arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Heterogeneous Treatment Effects in Panel Data | 0.928 | 25 | 6 |
| 2 | Inference for Low-rank Completion without Sample Splitting with Application to Treatment Effect Estimation | 0.405 | 1 | 1 |
| 3 | 2401.13665 | 0.405 | 1 | 1 |