Compositional Synthetic Controls
Abstract
This paper develops a synthetic control estimator for compositional outcomes, vectors of shares generated by an underlying categorical process. Derived from a random utility model with interactive fixed effects on relative systematic utilities, the estimator maps compositions to log-odds, where the standard convex hull condition identifies the counterfactual as a convex combination of donor log-odds. Equivalently, it recovers the Fr\'{e}chet barycenter under the Aitchison metric, the canonical geometry of the simplex (the non-linear space of shares) using a single set of weights across all categories. I also developed a placebo inference procedure based on the Aitchison distance. An application to Pennsylvania's electricity generation mix following the Alternative Energy Portfolio Standard uncovers a large and persistent compositional shift: natural gas exceeds its counterfactual by nearly 60 percentage points by 2022, while renewables lose relative ground.
Cite
@article{arxiv.2607.16991,
title = {Compositional Synthetic Controls},
author = {Onil Boussim},
journal= {arXiv preprint arXiv:2607.16991},
year = {2026}
}