Learning Treatment Effects in Panels with General Intervention Patterns

Code

• github.com/TianyiPeng/Causal-Inference-Code
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Abstract

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 + T_ij Z_ij where T_ij are unknown, heterogenous treatment effects. The problem requires we estimate the average treatment effect ^* := _ij T_ij Z_ij / _ij Z_ij. The synthetic control paradigm provides an approach to estimating ^* when Z places support on a single row. This paper extends that framework to allow rate-optimal recovery of ^* 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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