Learning Treatment Effects in Panels with General Intervention Patterns

TL;DR

This paper extends synthetic control methods to estimate average treatment effects in panel data with complex intervention patterns, providing theoretical guarantees and demonstrating improved performance over existing methods.

Contribution

It introduces a novel framework for rate-optimal treatment effect estimation in general intervention patterns, expanding beyond the traditional single-row support assumption.

Findings

First theoretical guarantees for general intervention patterns

Significant empirical improvements over existing estimators

Effective in both synthetic and real-world datasets

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 $O_{ij} := M^*_{ij} + E_{ij} + \mathcal{T}_{ij} Z_{ij}$ 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.