The Evolution of SES Gradients in Skills in the School Years: Evidence from the US and the UK

1. The Evolution of SES Gradients in Skills in the School Years: Evidence from the US and the UK Katherine MagnusonUniversity of Wisconsin-Madison Jane WaldfogelColumbia University & London School of Economics Elizabeth WashbrookUniversity of Bristol Royal Statistical Society, 4th April 2011 We gratefully acknowledge funding from the Russell Sage Foundation’s CRITA project. Waldfogel and Washbrook also gratefully acknowledge funding from the Sutton Trust. We also thank YouGeon Lee for excellent research assistance with the ECLS-K data.

2. Introduction • Many studies have shown sizeable SES disparities in skills at school entry in both the US and the UK, but less is known about whether these gaps hold constant, widen or diminish as children move through the school years. • Do schools play an equalizing or disequalizing role? Does this differ • Across the two countries? • Across schooling stages (e.g. the primary/secondary transition in the UK?) • Does the evolution of disparities in socio-emotional skills mirror that of more commonly studied academic achievement outcomes?

3. Aims • Aim: Systematically compare the mean differences in outcomes at ages 4 to 14 between different socio-economic groups along a number of dimensions. • How does the gradient differ: • By outcomes: academic achievement (reading and maths) versus socio-emotional behaviour (internalizing and externalizing symptoms) • By measure of SES: parental education or family income • By the outcome metric: absolute values versus standardized scores • In size at a given age and in changes over time • In the US versus the UK

4. Repeated cross-sections are often used in this context for practical data reasons. But studies of this type have a number of drawbacks. Academic outcomes by SEP quintile from three cohort studies Figure 1.2. in Alissa Goodman and Paul Gregg (eds) Poorer children educational attainment: How important are attitudes and behaviour? Joseph Rowntree Foundation, March 2010.

5. Methodological issues • Missing data • Non-random attrition in the longitudinal sample may lead to biases when making statements about population averages (and differently for the two countries). • Non-response affects not only who is observed in the sample, but also • The estimated outcome variance used to norm the scores at each age • The boundaries used to define quantiles of income or an SES index

6. Methodological issues • Raw vs standardized scores • Why standardize? • To allow comparison of outcomes measured in different metrics • z-scores give estimates of effect sizes (intuitive sense of magnitudes) • But what do we really care about? • Typically children’s academic skills show increasing variance over the course of development, which is removed by standardization. • A standard deviation difference at 16 may equate to much larger disparities in the skills that matter for future success than a standard deviation gap at 7. • The two methods may lead to different characterizations of whether gaps are widening or narrowing with age.

7. Datasets and assessments

8. Assessment ages

9. Non-response in ALSPAC The mechanisms leading to missing data differ strongly for academic achievement and behavioural outcomes. Core ALSPAC cohort = 13,988 children alive at 1 year. Key Stage outcomes are available for all children in English state schools, even if they left the study. Just 7% were never observed in state school from 7 to 14; but only 66% were always in a state school. Requiring EA reduces this further to 53%. SDQ outcomes require parental completion of a postal questionnaire at 5 dates. 28% have complete records, 68% have at least 2 out of 5. Non-response is non-monotonic. Parental education comes from a single questionnaire in pregnancy; income from at least one of two questionnaires at 33 and 47 months.

10. Multiple imputation • The ice command in Stata was used to impute values for the full 13,988 cohort five times. Standard errors of all estimates are adjusted to the process. • Additional variables used in the imputation: • Cohort year, month of birth, gender, mother’s age and its square, birth weight, non-white dummy (98%+ observed) • Parental education, FSM and SEN status at age 11 (85%+) • Family structure, family income at 33 & 47m, nursery attendance, family income at 85m, 97m & 11y • Additional SDQ sub-scores reported by parents at 47 months and by teachers in Years 3 and 6.

11. Math imputation results, by education Numbers in red calculated wholly or partly from imputed values

12. Externalizing behaviour imputation results, by education Numbers in red calculated wholly or partly from imputed values

13. Income quintile boundaries, by sample Numbers in red calculated wholly or partly from imputed values

14. The effects of imputation on estimated SES gradients in Maths Black lines are 95% CIs

15. The effects of imputation on estimated SES gradients in Externalizing behaviour Black lines are 95% CIs

16. UK Raw Achievement Scores

17. UK Standardized Achievement Scores

18. US Raw Achievement Scores

19. US Standardized Achievement Scores

20. Summary of standardized achievement gaps High – Low gaps in mean z-scores (ISCED 5A/6 vs ISCED 2; top vs bottom income quintile groups)

21. UK Raw Behavior Scores

22. UK Standardized Behavior Scores

23. US Raw Behavior Scores

24. US Standardized Behavior Scores

25. Summary of standardized behavior gaps High – Low gaps in mean z-scores (ISCED 5A/6 vs ISCED 2; top vs bottom income quintile groups)

26. Conclusions We find evidence of widening academic achievement gaps in the UK between 7 and 14, with greater widening after age 11. This holds for maths and reading, for income and education, and for raw and standardized scores. We hypothesize this is related to greater sorting at the secondary than the primary level. The US results are more sensitive to the choice of raw or standardized scores. Raw scores reveal constant gaps in the first years of schooling, with widening thereafter. Standardized scores reveal gaps that narrow in the first years of schooling, then return to their original values by age 14. Either way, the rapid growth in inequality of outcomes in the UK after age 11 does not appear to hold in the US in the same way.

27. Conclusions Cross-national comparisons on gradients in behaviour must be tentative due to measurement differences across the surveys. However, the results suggest that social gradients are much smaller in socio-emotional outcomes than in academic achievement. We find little evidence of systematic widening or narrowing of behaviour gradients during the school years in either country. Careful thought needs to be given to the methodological details of constructing even the simplest descriptive statistics in work that compares outcomes over time and across countries!