Compositional Synthetic Controls

When applying synthetic control to compositional outcomes (budget, vote shares), researchers commonly minimize Euclidean distances between raw shares. I propose constructing synthetic controls in Aitchison geometry, using centered log-ratio coordinates to select donor weights and form counterfactuals. This approach respects proportional comparisons and is exactly invariant to common multiplicative changes in relative odds. Under a multinomial-choice model, its weights summarize similarity in relative utility indices. Monte Carlo simulations, including a CES allocation model, show that this method performs better when relative incentives determine shares. An application to U.S. school finance demonstrates that this choice can alter reported inference.