Estimating Treatment Effects on Proportions with Synthetic Controls

Abstract Synthetic control methods are widely used for causal inference in case studies and panel data settings, often applied to model counterfactuals for proportional outcomes. However, conventional synthetic control methods are designed for univariate outcomes, leading researchers to model counterfactuals for each proportion separately. We make the case for jointly estimating synthetic controls across multiple compositional outcomes. Using the same weights for each proportion establishes a constant control comparison, improving comparability while adhering to compositional constraints on treatment effects. We illustrate the benefits of the method through a simulation and two applications to recent empirical studies. This implementation integrates naturally with a wide range of synthetic control approaches, providing interpretable estimates for compositional panel data common in political science.