On the Assumptions of Synthetic Control Methods

TL;DR

This paper critically examines the assumptions behind synthetic control methods, reformulating the causal inference problem at a more granular level to clarify conditions for valid causal estimation and suggest improved data usage strategies.

Contribution

It introduces a fine-grained model for synthetic control, deriving conditions for causal identification and providing insights into the origins of linearity assumptions.

Findings

Clarifies the source of linearity in SC methods

Provides conditions for non-parametric causal identification

Suggests new data selection strategies for SC applications

Abstract

Synthetic control (SC) methods have been widely applied to estimate the causal effect of large-scale interventions, e.g., the state-wide effect of a change in policy. The idea of synthetic controls is to approximate one unit's counterfactual outcomes using a weighted combination of some other units' observed outcomes. The motivating question of this paper is: how does the SC strategy lead to valid causal inferences? We address this question by re-formulating the causal inference problem targeted by SC with a more fine-grained model, where we change the unit of the analysis from "large units" (e.g., states) to "small units" (e.g., individuals in states). Under this re-formulation, we derive sufficient conditions for the non-parametric causal identification of the causal effect. We highlight two implications of the reformulation: (1) it clarifies where "linearity" comes from, and how it falls naturally out of the more fine-grained and flexible model, and (2) it suggests new ways of using available data with SC methods for valid causal inference, in particular, new ways of selecting observations from which to estimate the counterfactual.