Synthetic control methods are widely used for policy evaluation, but most existing approaches rule out interference among units, compromising validity when such effects are present. We develop a framework that accommodates contaminated donor pools and unknown interference patterns through two stages: factor-model adjustment for unobserved confounding, followed by robust regression in which direct and interference effects appear as a sparse outlier component. We study two asymptotic regimes. When the number of units is fixed and at least half are unaffected by interference, high-breakdown robust regression yields consistent identification of valid controls and asymptotically normal inference. When the number of units diverges, we allow for sparse large and dense weak interference, with robust M-estimation remaining valid even when the post-intervention period is short. Unlike existing approaches requiring prespecification of valid controls or parametric modeling of interference, our framework relies only on coarse sparsity information and enables formal inference on both direct and interference effects. We assess the proposed methods through simulations and two empirical applications. An analysis of the US embassy relocation to Jerusalem reveals significant interference effects on conflict outcomes in Jordan, and an analysis of Beijing's air pollution policy uncovers spatial interference patterns consistent with prevailing wind directions.

翻译：合成控制方法被广泛用于政策评估，但现有方法大多排除了单元间的干扰效应，当此类效应存在时会损害估计的有效性。我们提出了一个框架，通过两个阶段处理受污染的供体池和未知的干扰模式：首先通过因子模型调整未观测混杂因素，随后进行稳健回归，其中直接效应和干扰效应以稀疏异常值成分的形式呈现。我们研究了两种渐近机制。当单元数量固定且至少一半单元不受干扰影响时，高崩溃点的稳健回归能够一致识别有效控制组并提供渐近正态的统计推断。当单元数量发散时，我们允许存在稀疏强干扰和稠密弱干扰，即使干预后时期较短，稳健M估计仍保持有效。与现有方法需要预先指定有效控制组或对干扰进行参数化建模不同，我们的框架仅依赖粗略的稀疏性信息，并能对直接效应和干扰效应进行正式统计推断。我们通过模拟研究和两个实证应用评估了所提方法。对美国使馆迁往耶路撒冷的分析揭示了该事件对约旦冲突结果的显著干扰效应，而对北京空气污染政策的分析则发现了与盛行风向一致的空间干扰模式。