Race to the top? Relative age and student achievement

Elizabeth U. Cascio 06 September 2008

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The share of US six year olds in first grade fell from 96% in 1968 to 84% in 2005. In a recent paper, David Deming and Susan Dynarksi (2008) estimate that only a third of this decline is explained by increases in the minimum school entry ages established by US states. The rest is thought to be due to teachers deeming more children unready to progress from kindergarten to first grade and to more parents choosing to delay their child’s entrance into school (“red shirting”).

Anecdotally, parent hold children back to give them an edge in the early years – ensuring that they are among the oldest students in the class rather than the youngest. Being old or mature relative to one’s classmates can matter for achievement over the long term if elementary school children are tracked early on the basis of skill, which is strongly correlated with age when children are young. Placement in the top academic track can be self-reinforcing, since it may tackle more advanced material and move more quickly through a given curriculum. At the same time, older school entrants might become relatively more motivated for school or self-confident because of their relative standing in the class. Importantly, the result is “zero-sum”: when older students gain, younger students lose, becoming less engaged with school, being placed on lower tracks, etc. In principle, this can create an unsustainable “race to the top”.1

Is there any evidence that such a race is rational? To date, most empirical research in this area has estimated the net effect on achievement of being older at school entry and thus failed to identify the effects of “relative age” separately from those of biological or chronological age, which are highly correlated (Bedard and Dhuey 2006).

In the US, study of this issue is complicated due to the lack of information on respondents’ classmates in the survey data. In a recent paper, Diane Whitmore Schanzenbach and I (2007) address this identification problem using data from a social experiment. We find no evidence that being older than one’s kindergarten classmates raises test scores or the likelihood of taking a test to gain entry to a four-year college. Quite the contrary, being relatively old at the start of school may slow the acquisition of human capital.

The study

The experiment that underlies our work is Project STAR (Student-Teacher Achievement Ratio), which was designed to estimate the effects of class size on achievement.2 In fall 1985, approximately 6000 kindergartners and 330 teachers in 79 schools in the US state of Tennessee were assigned by lottery to one of three types of classes – small (with target enrollment of 13-17 students), regular (with target enrollment of 22-25 students), and regular with a full-time teacher’s aide. Data are available on class assignment and on test scores through eighth grade, as well as grade repetition and whether each participant took a college-entrance exam.

The design of Project STAR thus allows us to observe children who entered school at the same age but had kindergarten classmates with different ages on average. While such an exercise is feasible with other data, Project STAR helps to ensure that the variation in relative age is close to random. Indeed, while participants were not explicitly randomly assigned to classrooms, the data exhibit the “balance” on observed characteristics that we would expect from an experiment. On average, the characteristics of a child’s peers are not predictable on the basis of his or her own characteristics. In a non-experimental setting, by contrast, concerned parents may lobby to have their children placed in kindergarten classrooms where they would be relatively old.

More generally, parents exercise some choice over when their children start school, and school entrants who are older at school entry may have different abilities in addition to being more mature than those who are younger. To isolate the effects of maturity, we base our estimates on variation in kindergarten entry ages due to the local school-entry cut-off of September 30. Thus, we predict a child born on September 30 to have started school in the academic year he turned five, but a child born October 1 to have started school in September of the following academic year. We predict school entry ages of a child’s peers – and hence relative maturity – in the same way.

The impact of relative age

Our findings are potentially surprising. Children assigned to classrooms where they were relatively old – or where their classmates were on average young – performed worse on tests than children of the same age assigned to classrooms where they were relatively young. The effects of relative age at the start of school on test scores shrink over time, but persist through eighth grade, well after the experiment ended and participants found themselves in different classrooms, if not different schools altogether. Holding constant age, children who were relatively old in their kindergarten classrooms were also more likely to have repeated a grade by eighth grade and less likely to have taken a college entrance exam by the end of high school.

What might explain these findings? One interpretation is that older peers are better behaved peers or better teachers themselves, making time in the kindergarten classroom – a foundation for subsequent learning – more productive for a child regardless of his age. If learning expectations changed little in the face of transitory variation across classrooms in the age distributions of students, the scope for a positive peer effect (or a “perverse” relative age effect) may have been particularly large in our data. Consistent with this idea, Todd Elder and Darren Lubotsky (2005) have recently found that having older peers in the same grade because of a higher minimum age at school entry increases the likelihood of being retained or diagnosed with a learning disability, and while it raises test scores, it does so by less than we find. A higher minimum age at school entry might be associated with higher expectations of students, as the maturity of the average child in all classrooms rises.

This discussion highlights the fact that it is impossible to separate the effect of relative age from the spillover that comes from having older peers in the models described above. We therefore explore the robustness of our conclusions by estimating models where we measure relative age non-linearly (e.g., with a child’s rank in his kindergarten classroom age distribution) and control directly for both own and average classmate age. Here, we do uncover some evidence that being relatively young among one’s classmates at the start of school increases the likelihood of repeating a grade, suggesting that teachers do assess a child’s school readiness in relation to other children in a classroom, not using some absolute standard. However, our estimates still suggest that moving a child from a classroom where he would be the oldest to one where he would be the youngest would lower the likelihood of being retained on net. The estimates also suggest that there is no positive impact of being relatively old on test scores or college exam test-taking.

Implications

Our findings provide little support for the hypothesis that being relatively old at the start of school is beneficial. They support a growing consensus that test score differentials between older and younger school entrants have little to do with what happens in school. 3

If not beneficial, why do so many US kids today start their school careers “below grade”? At this point, the answer is not clear. However, the phenomenon is startling once one considers the other potential downsides – for educational attainment, earnings, and tax contributions to social insurance programs – of starting school late.

References

Bedard, Kelly and Elizabeth Dhuey. 2006. “The Persistence of Early Childhood Maturity: International Evidence of Long-Run Age Effects.The Quarterly Journal of Economics 121(4) (November) pp. 1437-1472.

Cascio, Elizabeth U. and Diane Whitmore Schanzenbach. 2007. “First in the Class? Age and the Education Production Function.” NBER Working Paper 13663.

Deming, David and Susan Dynarski. 2008. “The Lengthening of Childhood.Journal of Economic Perspectives 22(3): 71-92.

Elder, Todd E. and Darren H. Lubotsky. 2008. “Kindergarten Entrance Age and Children’s Achievement: Impacts of State Policies, Family Background, and Peers,” Forthcoming, The Journal of Human Resources.

Footnotes

1 See, for example, Gootman, Elissa. “Preschoolers Grow Older as Parents Seek an Edge,” The New York Times 19 October 2006.

2 For more discussion of Project STAR and subsequent studies based on it, see Schanzenbach, Diane Whitmore. 2007. “What Have Researchers Learned From Project STAR?” Brookings Papers on Education Policy, 2006/07, pp. 205-228.

3 In particular, a new generation of research has arisen attempting to disentangle the contributions of age at test and age at school entry, which vary one-for-one in cross-sectional data, to the reduced-form age differential in achievement. Elder and Lubotsky (2008) present suggestive evidence of the importance of age at test, showing that the age gradient in test performance is steeper for children from families were investments prior to school are greater. For other countries, there is more direct evidence. For example, in Norway, data are available where age at school entry and age at test do not vary one-for-one. A recent analysis of these data concludes that age at test has the greater impact on test performance.

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Topics:  Education

Tags:  test scores, school starting age, children

Assistant Professor of Economics, Dartmouth College