We propose a method based on optimal transport theory for causal inference in classical treatment and control study designs. Our approach sheds a new light on existing approaches and generalizes them to settings with high-dimensional data. The implementation of our method leverages recent advances in computational optimal transport to produce an estimate of high-dimensional counterfactual outcomes. The benefits of this extension are demonstrated both on synthetic and real data that are beyond the reach of existing methods. In particular, we revisit the classical Card & Krueger dataset on the effect of a minimum wage increase on employment in fast food restaurants and obtain new insights about the impact of raising the minimum wage on employment of full- and part-time workers in the fast food industry.

翻译：我们提出了一种基于传统治疗和控制研究设计中因果推断的最佳运输理论方法。我们的方法为现有方法提供了新的视角,并将这些方法概括到具有高维数据的环境。我们的方法的实施利用了计算最佳运输的最新进展,得出了高维反事实结果的估计。这一扩展的好处既体现在合成数据,也体现在现有方法所不具备的实际数据上。特别是,我们重新审视了传统卡片和克鲁格数据集,该数据集涉及提高最低工资对快餐餐馆就业的影响,并获得了关于提高最低工资对快速食品业全时和非全时工人就业的影响的新见解。