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Debt arithmetic rests on two schedules: how much the primary balance improves when debt rises, and how far the interest a government pays exceeds its economy’s growth. This article estimates how both move with differential ageing, a country’s departure from the OECD-wide ageing path within a year, on 33 OECD economies over 1985 to 2024. The response of the primary balance to debt shows no detectable gradient in differential ageing: point estimates bracket zero, and 90% intervals exclude changes of more than about half the response per ten dependency points. Future ageing predicts current fiscal behaviour, and the combined gradient stays within that bound. The differential part of the fall in the primary balance is indistinguishable from zero. The interest-growth differential widens with differential ageing on gross interest, by about two points per ten dependency points, an imprecise association whose point estimate is zero net of receipts. Carried to 2050 as conditional scenarios with their joint uncertainty, the gradients leave every margin intact in most draws when only ageing beyond the OECD path counts; extrapolated to total projected ageing beyond the observed range, they exhaust the historical response for five members, a count from none to ten across specifications.
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Wen et al. (2026) studied this question.
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