Primary Submission Category: Synthetic Control Method
On the Assumptions of Synthetic Control Methods
Authors: Claudia Shi, Dhanya Sridhar, Vishal Misra, David Blei,
Presenting Author: Claudia Shi*
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