Doubly Robust Proximal Synthetic Controls

TL;DR

This paper introduces two novel nonparametric methods for synthetic control analysis, leveraging proximal causal inference and covariate shift, with a doubly robust estimator that improves treatment effect estimation accuracy.

Contribution

It develops two new identification formulas and estimators for synthetic controls, incorporating covariate shift and proximal causal inference, including a doubly robust estimator.

Findings

The proposed methods perform well in simulations.

Application to vaccine data demonstrates practical utility.

The doubly robust estimator is consistent under model misspecification.

Abstract

To infer the treatment effect for a single treated unit using panel data, synthetic control methods construct a linear combination of control units' outcomes that mimics the treated unit's pre-treatment outcome trajectory. This linear combination is subsequently used to impute the counterfactual outcomes of the treated unit had it not been treated in the post-treatment period, and used to estimate the treatment effect. Existing synthetic control methods rely on correctly modeling certain aspects of the counterfactual outcome generating mechanism and may require near-perfect matching of the pre-treatment trajectory. Inspired by proximal causal inference, we obtain two novel nonparametric identifying formulas for the average treatment effect for the treated unit: one is based on weighting, and the other combines models for the counterfactual outcome and the weighting function. We introduce the concept of covariate shift to synthetic controls to obtain these identification results conditional on the treatment assignment. We also develop two treatment effect estimators based on these two formulas and the generalized method of moments. One new estimator is doubly robust: it is consistent and asymptotically normal if at least one of the outcome and weighting models is correctly specified. We demonstrate the performance of the methods via simulations and apply them to evaluate the effectiveness of a Pneumococcal conjugate vaccine on the risk of all-cause pneumonia in Brazil.