We consider a panel data setting in which one observes measurements of units over time, under different interventions. Our focus is on the canonical family of synthetic control methods (SCMs) which, after a pre-intervention time period when all units are under control, estimate counterfactual outcomes for test units in the post-intervention time period under control by using data from donor units who have remained under control for the entire post-intervention period. In order for the counterfactual estimate produced by synthetic control for a test unit to be accurate, there must be sufficient overlap between the outcomes of the donor units and the outcomes of the test unit. As a result, a canonical assumption in the literature on SCMs is that the outcomes for the test units lie within either the convex hull or the linear span of the outcomes for the donor units. However despite their ubiquity, such overlap assumptions may not always hold, as is the case when, e.g., units select their own interventions and different subpopulations of units prefer different interventions a priori. We shed light on this typically overlooked assumption, and we address this issue by incentivizing units with different preferences to take interventions they would not normally consider. Specifically, we provide a SCM for incentivizing exploration in panel data settings which provides incentive-compatible intervention recommendations to units by leveraging tools from information design and online learning. Using our algorithm, we show how to obtain valid counterfactual estimates using SCMs without the need for an explicit overlap assumption on the unit outcomes.

我们提出了一种在面板数据设置中激励探索的合成控制方法，通过利用信息设计和在线学习的工具，为单位提供适用的干预建议，从而在不需要明确的单位结果重叠假设的情况下获得有效的对照估计。

激励感知的合成对照：通过激励式探索实现准确的反事实估计