Is children’s free school meal ‘eligibility’ a good proxy for family income?

Abstract

Family income is an important factor associated with children’s educational achievement. However, key areas of UK research (for example, on socially segregated schooling) and policy (for example, the allocation of funding to schools) rely on children’s free school meal (FSM) ‘eligibility’ to proxy family income. This article examines the relationship between children’s FSM ‘eligibility’ and equivalent net household income in a nationally representative survey of England (the Family Resources Survey). It finds that children ‘eligible’ for FSM are much more likely than other children to be in the lowest income households. However, only around one‐quarter to one‐half of them were in the lowest income households in 2004/5. This is principally because the receipt of means‐tested benefits (and tax credits) pushes children eligible for FSM up the household income distribution. The implications for key areas of research and policy are discussed.

Acknowledgements

This article has benefitted from discussions with Rebecca Allen, John Micklewright and Nikos Tzavidis. This research was funded by the Department for Education and Skills in the UK.

Notes

1. This is well known. In particular, McMahon and Marsh (1999) reported that around 20% of children entitled to FSM do not take them up.

2. The (before housing costs) McClements equivalence scale equals 0.61 for the head of household, 0.39 for a spouse, 0.46 for a non‐spouse second adult, 0.42 for a third adult, 0.36 for each subsequent adult, 0.09 for each dependent child aged 0–1, 0.18 for each dependent child aged 2–4, 0.21 for each dependent child aged 5–7, 0.23 for each dependent child aged 8–10, 0.25 for each dependent child aged 11–12, 0.27 for each dependent child aged 13–15 and 0.36 for each dependent child aged 16 or over. The equivalence value for a household is the sum of the scales for that household. For example, the equivalence value for a household containing a couple with a 4 year‐old and a 14 year‐old child is 1.45 (= 0.61 + 0.39 + 0.18 + 0.27). The equivalent household income is the household income divided by the equivalence value. The main findings of this article are not significantly affected by equivalisation. They are also not significantly affected by measuring household income before rather than after housing costs.

3. Figure 1 shows kernel density functions. Kernel density estimation is a non‐parametric way of estimating the probability density function of a random variable. Kernel density functions are a generalisation and improvement over histograms. Histograms are not smooth, depend on the end points of bins and depend on the width of bins. The first two problems can be alleviated by using kernel density estimators. Compared to histograms, kernel density estimators are smooth and have no end points. However, kernel density estimators do depend on bandwidth (which is equivalent to a histogram’s width of bins).

4. The first assumption is likely to be a relatively good approximation. The second assumption might not hold if IS and IB‐JSA receipt, and hence eligibility for FSM, is under‐reported in the FRS. However, our findings are robust to relaxing this assumption.

5. The percentage of children eligible for but not claiming FSM = 2.0%.

6. The percentage of children eligible for and claiming but not taking up FSM = 5.7%.

7. The upper bound on the percentage of children eligible for and claiming FSM not in the lowest income families accounted for by explanation 2 is the maximum percentage of children eligible for and claiming FSM ranked 18.4–100 in the distribution of family income after means‐tested benefits and tax credits but ranked 1–18.4 in the distribution of family income before means‐tested benefits and tax credits divided by the minimum percentage of children ranked 16.4–100 in the distribution of family income after means‐tested benefits and tax credits given that maximum. The lower bound on the percentage of children eligible for and claiming FSM not in the lowest income families accounted for by explanation 2 is the minimum percentage of children eligible for and claiming FSM ranked 18.4–100 in the distribution of family income after means‐tested benefits and tax credits but ranked 1–18.4 in the distribution of family income before means‐tested benefits and tax credits divided by the maximum percentage of children ranked 16.4–100 in the distribution of family income after means‐tested benefits and tax credits given that minimum. Upper and lower bounds on the percentage of children eligible for and claiming FSM not in the lowest income families accounted for by explanations 1 and 3 are calculated similarly.

8. Bias in the regression including FSM ‘eligibility’ is zero if two conditions hold (Wooldridge, 2002, pp. 61–67). First, in a regression of the dependent variable on the independent variables, and both family income and FSM ‘eligibility’, the coefficient on FSM ‘eligibility’ is zero. In other words, family income, not FSM ‘eligibility’, affects the dependent variable. Second, family income is partially uncorrelated with the independent variable of interest once FSM ‘eligibility’ is included in the regression.