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Compositional Synthetic Controls

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  • Onil Boussim

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.

Suggested Citation

  • Onil Boussim, 2026. "Compositional Synthetic Controls," Papers 2607.16991, arXiv.org.
    • Handle: RePEc:arx:papers:2607.16991
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    File URL: https://arxiv.org/pdf/2607.16991
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