A L-infinity Norm Synthetic Control Approach

TL;DR

This paper introduces an L-infinity norm regularized synthetic control method that balances the robustness of dense weighting schemes with the flexibility of traditional sparse approaches, supported by theoretical and empirical validation.

Contribution

It proposes a novel L-infinity regularization for synthetic control, combining the strengths of DID and traditional SC, with an efficient algorithm and theoretical guarantees.

Findings

Enhanced robustness to control unit selection.

Improved finite-sample performance in simulations.

Theoretical asymptotic properties established.

Abstract

This paper reinterprets the Synthetic Control (SC) framework through the lens of weighting philosophy, arguing that the contrast between traditional SC and Difference-in-Differences (DID) reflects two distinct modeling mindsets: sparse versus dense weighting schemes. Rather than viewing sparsity as inherently superior, we treat it as a modeling choice simple but potentially fragile. We propose an L-infinity-regularized SC method that combines the strengths of both approaches. Like DID, it employs a denser weighting scheme that distributes weights more evenly across control units, enhancing robustness and reducing overreliance on a few control units. Like traditional SC, it remains flexible and data-driven, increasing the likelihood of satisfying the parallel trends assumption while preserving interpretability. We develop an interior point algorithm for efficient computation, derive asymptotic theory under weak dependence, and demonstrate strong finite-sample performance through simulations and real-world applications.