Papers › Learning Treatment Effects in Panels with General Intervention Patterns
Learning Treatment Effects in Panels with General Intervention Patterns
Vivek F. Farias, Andrew A. Li, Tianyi Peng
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 Oᵢⱼ := M^*ᵢⱼ + Eᵢⱼ + 𝒯ᵢⱼ Zᵢⱼ where 𝒯ᵢⱼ are unknown, heterogenous treatment effects. The problem requires we estimate the average treatment effect τ^* := ∑ᵢⱼ 𝒯ᵢⱼ Zᵢⱼ / ∑ᵢⱼ Zᵢⱼ. The synthetic control paradigm provides an approach to estimating τ^* when Z places support on a single row. This paper extends that framework to allow rate-optimal recovery of τ^* 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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