Children Costs in a One-Adult Household: Empirical Evidence from the UK

• Model. Extends collective consumption models with assignable goods to one-adult households, with separate sharing rules and shadow prices for mothers and fathers.
• Evidence. Provides the first estimates of children’s resource shares in single-parent households of a high-income country. Existing evidence concerns Côte d’Ivoire (Bargain, Donni & Kwenda, 2014), Argentina (Echeverria et al., 2019) and Jamaica (Bose-Duker et al., 2021).
• Test of external validity. The model, data and assignable good are those of Bargain, Donni & Hentati (2022) for couples, so the two sets of estimates are directly comparable.
• Policy. The literature on the two-child limit documents its effect on income and poverty (González & Trommlerová, 2023; Chzhen & Bradshaw, 2025; Stewart et al., 2025). This paper asks whether intra-household allocation itself justifies conditioning support on family size.

Surveys record spending by household, not by person, so what a single parent spends on a child is never observed. Adult clothing is the exception as it is recorded for the person who wears it.

If having a child changes a parent’s budget but not his or her taste for clothing, childless single adults with the same characteristics show how clothing spending varies with the resources one has for oneself. A single parent’s clothing then reveals the resources the parent keeps. The rest is the child’s share.

Example. Childless single women spend £9.46 a week on their own clothing; single mothers with one child spend £7.53, although their total budget is larger, £136 against £117 (Table 2, 1987 pounds). The model attributes 14.7% of the mother’s resources to the child (Table 4), about £20 a week at that budget.

A single parent cares about his or her own consumption and about the child’s. As sole decision-maker, the parent’s choices are efficient by construction, and children have no bargaining power. The household differs from a childless adult in two ways: a sharing rule $\varphi$⁠, the share of total expenditure $y$ the parent keeps, and a Barten price $\pi$ on non-clothing consumption, which captures the gains from sharing goods such as housing and heating.

The parent therefore behaves like a childless adult with budget $\varphi y$ and prices adjusted for joint consumption:

where $\omega$ is the clothing budget share, $p$ the price of clothing and $g$ the clothing demand of a childless adult. The child’s share $1-\varphi$ measures the cost of children.

One difficulty remains because $\varphi$ and $\pi$ enter the same demand equation. Proposition 1 gives sufficient conditions to distinguish them. The benchmark uses decade indicators to shift adult clothing demand through fashion, norms, and relative prices, while excluding these indicators from the sharing rule and the scale-economies equation. These indicators are relevant in the data, with joint tests yielding $p=0.034$ for women and $p=0.011$ for men (Table 1). Alternative specifications impose independence from expenditure, independence from prices, or a multiplicative effect of family size.

The clothing budget share is quadratic in log expenditure, estimated separately for men and women and jointly on childless adults and single parents:

Single adult demand (equation 14).

For parents, $\omega$⁠, $p$ and $y$ are replaced by $\omega/\varphi$⁠, $p/\pi$ and $\varphi y/\pi$⁠. The sharing rule is logistic in parental characteristics, children’s characteristics (number, age, sex composition), log prices and log expenditure. The Barten price depends on expenditure and $\sqrt{n}$⁠.

Parent demand (equation 15).

Sharing rule (equation 16) and alternative family-size restriction (17).

Economies of scale (equation 18).

Unified estimating equation (19).

View specifications, PDF pages 10–13.

Estimation is by nonlinear iterated two-stage least squares, with total income instrumenting total expenditure. Resource shares are evaluated at sample means (delta method) and as averages of individual predictions (Monte Carlo).

• Surveys. Harmonized Family Expenditure Survey, Expenditure and Food Survey and Living Costs and Food Survey, 1978–2022.
• Sample. Single adults aged 18–55, childless or living with biological children aged 0–15: 24,748 women (10,924 childless, 13,824 mothers) and 15,634 men (14,059 childless, 1,575 fathers) (Tables 3–4).
• Goods and prices. Men’s and women’s clothing as assignable goods; all other non-durables as a composite; national annual price indices, with relative clothing prices falling sharply until about 2009 (Figure 8).
• Descriptive pattern. Parents’ own clothing falls with each child, from £7.53 to £6.29 and £5.15 for mothers and from £4.34 to £3.56 and £2.02 for fathers, while total expenditure does not (Table 2).

Standard errors are reported in parentheses.

Main findings

• External validity. For single mothers, the child’s share (14.7%) is close to the couple benchmark (14.2%).
• Gender. The share is higher for single fathers (22.2%), but the difference with mothers is not statistically significant, whether evaluated at the mean or averaged over households (Table 12).
• Family size. The total share for children rises with each child, less than proportionally. Across the expenditure distribution, per-child shares do not differ significantly by family size, except among low-expenditure single fathers (Figure 1).
• Equivalence scales. The OECD-modified scale implies a 23% share for one child, above the estimate for single mothers.
• Robustness. Results hold when identification relies on regional rather than temporal variation, without economies of scale, and with childless comparison groups matched to parents (Tables 5 and 13).