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.

翻译：本文从权重设计的哲学视角重新阐释了合成控制（SC）框架，认为传统SC与双重差分法（DID）之间的差异反映了两种不同的建模思路：稀疏权重方案与密集权重方案。我们并不将稀疏性视为固有优势，而是将其视为一种建模选择——虽简洁但可能脆弱。我们提出了一种L-∞正则化的SC方法，该方法融合了两种方法的优点。与DID类似，它采用更密集的权重方案，将权重更均匀地分配到控制单元中，从而增强稳健性并减少对少数控制单元的过度依赖。与传统SC类似，它保持了灵活性和数据驱动特性，在保持可解释性的同时提高了满足平行趋势假设的可能性。我们开发了一种高效计算的内点算法，在弱依赖条件下推导了渐近理论，并通过仿真和实际应用展示了其优异的有限样本性能。