= Solution
If sex predicts apprenticeship uptake, extreme UTC sex ratios create both <confounding> and weak overlap. Matching only the aggregate percentage of boys may leave no genuinely comparable control, and an additive distance can hide a large imbalance in this influential variable. Sex may also be an <effect modifier>, so the UTC effect can differ across these unusual compositions. One should enforce close sex-ratio balance and estimate sex-specific effects before standardizing them to the intended policy population.
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