The four scales, and what each says a child is worth
Four scales cover most of the practical ground — the OECD lists the
first three among the most commonly used, and the fourth is the one the US
government actually runs on. They were built by different institutions, for
different countries, using different methods — and they give
different answers.
OECD-modified (Eurostat) 1.00.50.3 (under 14)
Old OECD / “Oxford” 1.00.70.5
Square root √(household size) — no age distinction——
US Census SPM (adults + 0.5 × children)^0.7—0.5, before the exponent
The OECD-modified scale, adopted by Eurostat in the late
1990s, assigns 1.0 to the first adult, 0.5 to each additional person aged
14 or over, and 0.3 to each child under 14. The older
“Oxford” scale — which the OECD had
floated in 1982 for countries without one of their own — is more
generous to extra bodies: 1.0, then 0.7 per additional adult and 0.5 per
child. The square root scale, used in recent OECD
cross-country comparisons, throws out age entirely and simply divides by
the square root of household size, so a household of four is assumed to
need twice what one person needs.
Sources: Glossary:
Equivalised disposable income, Eurostat; and
The
OECD Approach to Measuring Income Distribution and Poverty, Förster
& Mira d’Ercole, OECD.
The American entry is the most interesting for our purposes. The US Census
Bureau’s Supplemental Poverty Measure uses a
three-parameter scale, and its formula for a two-parent
family is:
(adults + 0.5 × children) count the adults in full, each child as half — the folk rule, exactly
raised to the power 0.7 the economy-of-scale term: bigger households get a discount for sharing
Single-parent families get their own version — (adults + 0.8 × first child + 0.5 × other children)^0.7 — and households of one or two adults with no children use (adults)^0.5 instead. The 0.70 exponent sits inside the 0.65–0.75 range recommended by the National Academy of Sciences panel.
Source: Supplemental
Poverty Measure: Technical Documentation, U.S. Census Bureau —
which is also where the official measure’s own approach is described:
it adjusts thresholds by family size, number of children and adults, and
whether the householder is 65 or older, a different mechanism. The SPM is a
supplement, not a replacement: it
“does
not replace the official poverty measure” (Fox & Burns,
The Supplemental Poverty Measure: 2020, U.S. Census Bureau).
Look closely at that first term. Inside the parentheses, the US
Census Bureau’s Supplemental Poverty Measure counts a child as exactly
half an adult. The group-chat rule is not a folk corruption of the
expert one — on that parameter, it is the expert one. What
the folk rule drops is everything to the right: the exponent that then
discounts the whole household for sharing. (Because the exponent is
non-linear, 0.5 is an input, not the child’s finished weight —
and a single parent’s first child enters at 0.8 instead.)