Estimating Treatment Effects on Proportions with Synthetic Controls

2026/05/21 by Konstantin Bogatyrev, Lukas F. Stoetzer

paper · doi:10.1017/pan.2026.10046

Abstract

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.

Citations

• Refining Gamson: The Isometric Log-Ratio Transformation and Portfolio Proportionality in Multiparty Governments
• The Electoral Effects of State-Sponsored Anti-LGBTQ Measures
• Geographies of discontent: Public service deprivation and the rise of the far right in Italy
• Navigating Potential Pitfalls in Difference-in-Differences Designs: Reconciling Conflicting Findings on Mass Shootings’ Effect on Electoral Outcomes
• Using Multiple Outcomes to Improve the Synthetic Control Method
• Causal Models for Longitudinal and Panel Data: A Survey
• Causal Panel Analysis under Parallel Trends: Lessons from a Large Reanalysis Study
• Causal Panel Analysis under Parallel Trends: Lessons from a Large Reanalysis Study
• Simulating Party Shares
• Pretest with Caution: Event-Study Estimates after Testing for Parallel Trends
• What's Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature
• What’s trending in difference-in-differences? A synthesis of the recent econometrics literature
• Revisiting Event Study Designs: Robust and Efficient Estimation
• Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects
• A Practical Guide to Counterfactual Estimators for Causal Inference with Time-Series Cross-Sectional Data
• Synthetic Difference in Differences
• The Augmented Synthetic Control Method
• Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models
• Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program
• The Statistical Analysis of Compositional Data.
• Bootstrap Methods: Another Look at the Jackknife

Related

• On the Assumptions of Synthetic Control Methods
• Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration
• Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models
• Synthetic Controls with Staggered Adoption
• On the Misspecification of Linear Assumptions in Synthetic Control