Compositional Synthetic Controls
Abstract
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.
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BibTeX
@misc{boussim2026compositional,
title = {{Compositional Synthetic Controls}},
author = {Onil Boussim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.16991},
eprint = {2607.16991},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16991},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Compositional Synthetic Controls
AU - Onil Boussim
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2607.16991
UR - https://arxiv.org/abs/2607.16991
AB - 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.
ER -