The later the better? A novel approach to estimating the effect of school starting age on ADHD and academic skills

Abstract

School entry is an important life transition where early disadvantages may have consequences for children’s educational trajectory. This paper provides important evidence on the production of disadvantages by the education system using a novel approach to school starting age (SSA) which is not biased by parental resources or prior dis-advantages. By using due date from the Medical Birth Registry of Norway (MBRN) as an instrumental variable for SSA, and register data covering the entire Norwegian population, I show that a one-year increase in SSA led to a 59 per cent lower risk of being diagnosed with ADHD and significantly higher national test scores in 5^th and 9^th grade. Additionally, this study finds that 10.1 per cent of births are shifted from the week before the school entry cut-off to the week after. Parents with higher educational attainment are significantly more likely to shift births across the cut-off, providing a cautionary note to studies attempting to estimate causal effects of SSA using month or date of birth. Overall, this study provides important evidence one way in which inequalities are produced by the education system and how socioeconomically advantaged parents may act to mitigate these risks.

Entry into formal schooling is a key life transition and an optimal entry may set children on productive pathways where additional resources and advantages are accumulated across the life course (Dannefer, 2003; DiPrete and Eirich, 2006). This transition is often governed by rules that determine the age at which children begin. In most cases, this is based on the child’s birthday and an arbitrarily set cut-off date, where children born before this date are expected to enter school in one year, and children born after enter in the next. This creates a discontinuity around the cut-off date, where children born just before the threshold are nearly a year younger when they enter school compared to the children born just days, or weeks, later. As education is a cumulative process, early experiences within the education system may be important determinants of future outcomes and early disadvantages in school may”lock in” students to certain educational trajectories which have important implications for later school performance and educational outcomes (Breen and Jonsson, 2005; DiPrete and Eirich, 2006).

The accumulation of (dis)advantages across the life course begins at a young age and early childhood experiences can set individuals on positive or negative educational trajectories (Dannefer, 2003; DiPrete and Eirich, 2006). Rather than a linear process, however, this accumulation of (dis)advantages is altered by the interaction of individuals, their parental resources, and the system itself (Dannefer, 2003). In the case of negative early educational experiences such as young school start, parents of higher socioeconomic status may act to compensate for these disadvantages to ensure fewer negative consequences on later academic achievement. This idea, put forth by Bernardi (2014) and Bernardi and Grätz (2015), is referred to as compensatory advantage. Under this theory, parents with higher socioeconomic status may invest additional resources to compensate for the negative effects of their child entering school at a younger age (Bernardi, 2014). This idea is related to the theory of effectively maintained inequality (EMI), by Lucas (2001), which suggests that advantaged parents will utilize their resources to obtain and maintain advantages for their children. For example, higher socioeconomic status families may use their resources to obtain a qualitative advantage in education by avoiding the disadvantages related to young school starting age (SSA). This could be done by ‘redshirting’, or postponing school entry, for their child born before the school entry cut-off, or by shifting the birth of their child to avoid a birth date before the cut-off in the case of strict school entry rules.

This article contributes to the existing literature on SSA in two ways. First, it provides important evidence for the production of disadvantages by the education system using a novel approach which is not biased by selection or early disadvantages prior to school entry. To do this, I use one’s due date estimated through ultrasound examination as an instrumental variable (IV) for SSA to estimate its impact on ADHD diagnosis and academic skills. This method avoids bias due to both ‘redshirting’ and the sorting of children’s birth dates by parents of higher socioeconomic status, which may bias estimates obtained through a regression discontinuity design (RDD). A small number of previous studies have used due date as an instrumental variable, for either belonging to peer groups on a digital platform or as a measure of maternity ward congestion (Bensnes, 2021; Jiang and Zhu, 2022). However, this is the first application of due date as an IV for SSA.

Second, this article contributes to understanding whether and to what extent births are shifted across the school entry cut-off in Norway. Few studies have quantified the shifting of births with regard to the school entry cut-off, with the majority of previous studies based in the East Asian context (Dickert-Conlin and Elder, 2010; Shigeoka, 2015; Huang, Zhang and Zhao, 2020; Kim, 2021; Valdés and Requena, 2023; González and Dip, 2024). The Norwegian setting provides an interesting context to examine the shifting of births relative to the school entry cut-off. Norway has a strict school enrolment system which is comparable to the enforcement of school entry in Japan and South Korea, two countries which previous studies have found a significant proportion of births shifted to the week following the cut-off date (Shigeoka, 2015; Kim, 2021). This is in contrast to findings from the United States, where researchers found no evidence of shifting births across the school entry cut-off and where school enrolment age is much more flexible (Dickert-Conlin and Elder, 2010). However, the educational culture in Japan and South Korea is in many ways quite different from that in Norway. For example, the academic pressure on both parents and children may increase the perceived returns to delaying birth for parents who value academic achievement (Shigeoka, 2015). I also examine whether parents of certain characteristics are more likely to shift the birth than others. Parents of higher socioeconomic status may be especially concerned with avoiding the academic disadvantages associated with a young SSA and may act to avoid this disadvantage, as suggested by EMI (Lucas, 2001).

Background

Previous literature

Previous research into the increased prevalence of ADHD among relatively younger students have put forth two main hypotheses. The most popular explanation is the oversupply hypothesis, where the increased prevalence is due to a misinterpretation of developmentally appropriate behaviour as symptoms of ADHD (Diefenbach et al., 2022). Due to the age difference between children within a school cohort being up to 11 months, the youngest children in the school cohort are often developmentally less mature compared to their peers and are more likely to exhibit inattentive, impulsive, and hyperactive behaviours. Teachers may naturally compare these students to their school peers rather than to those of the same chronological age. This may lead to an increased probability for the relatively youngest to be referred to special education services and for teachers to suggest parents seek ADHD or specific learning disorder diagnostics (Balestra, Eugster and Liebert, 2020; Arrhenius et al., 2021). There could also be a converse effect where relatively older students are under-diagnosed as they are compared with peers who are often less developmentally mature, and thus actual symptoms of ADHD may be overshadowed by their relatively greater developmental maturity.

Another possible explanation is the stress-related hypothesis. As school entry is considered a significant life transition, this is often associated with large socio-emotional and cognitive demands. Children are also required to adapt to these demands quickly after beginning school. Due to their relatively lower levels of developmental maturity, the youngest children in the school cohort may not be able to effectively adapt to this situation, which could lead to increased stress levels and peer difficulties resulting in either the development or heightening of hyperactive and inattentive behaviours (Diefenbach et al., 2022).

Previous research has shown a clear association between SSA and ADHD in childhood. A majority of studies have found this association regardless if measured through diagnosis, treatment, or symptoms and across countries with varying entry cut-off dates (Evans, Morrill and Parente, 2010; Karlstad et al., 2017). In Norway, Karlstad et al. (2017) examine the association between month of birth and ADHD diagnosis and treatment. The researchers find that boys born in the 3 months before the school entry cut-off had a 1.4 times higher probability of receiving ADHD medication compared to those born in the 3 months after the cut-off, for girls the probability was 1.8 times higher (Karlstad et al., 2017). Others have argued that utilizing exact date of birth rather than birth month provides a more robust estimate as this avoids bias due to selective conception. In the U.S., Evans, Morrill and Parente (2010) find that being born after the cut-off resulted in a decrease in the likelihood of receiving an ADHD diagnosis of 2.1 percentage points when using exact date of birth and a RDD.

Young school starting age has also been shown to be associated with poorer school performance (Fredriksson and Öckert, 2009; Solli, 2017). When looking at relative age effects within school cohort in Norway, Solli (2017) finds that the oldest students significantly outperform younger students in terms of GPA, with the difference as large as 20 per cent of a standard deviation. One’s school starting age may impact their school performance through various mechanisms which are often difficult to disentangle. Relatively older children may perform better in school due to entering school at a developmentally more optimal age (Kaila, 2017). Alternatively, being relatively older than one’s peers could have beneficial effects on school performance through increased confidence, or they may perform better on school assessments simply because they are chronologically older at the time of the exam (Kaila, 2017). This difference in overall age-at-test has previously been shown to be the most likely explanation for the school performance disparities, and is supported by studies finding smaller effects at older ages (Black, Devereux and Salvanes, 2011).

Much of the previous literature has either utilized month or date of birth to attempt to identify causal effects of SSA on either ADHD or school performance. However, this relies on the idea that parents cannot manipulate either the month or date of birth to fall on either side of the school entry cut-off, assuming that date of birth is ‘as-good-as randomly assigned’ and thus the resulting estimates provide a causal effect of SSA on a range of outcomes, such as school performance or ADHD risk. For example, Hoogerheide, Kleibergen and van Dijk (2007, p. 79) state that”This is a plausible assumption, as one’s birthday is unlikely to be correlated with personal attributes other than age at school entry”, and McCrary and Royer (2011, p.3) state ”This assumption is plausible a priori, since parents are unlikely to strategically plan the exact date of birth of their child”. While this is a testable assumption, and many previous studies both examine the plausibility of this assumption in their context and utilize robustness tests to check whether their results are sensitive to shifts in birth timing, a growing body of evidence suggests caution in assuming the randomness of date of birth a priori (Shigeoka, 2015; Huang, Zhang and Zhao, 2020; Kim, 2021; González and Dip, 2024).

The purpose of using date of birth rather than actual SSA has been to avoid bias due to delayed school entry, or ‘redshirting’. There are many potential reasons why parents may wish to delay their child’s birth until after the school entry cut-off. Parents may wish to delay their child’s school start until they are older and more developmentally prepared for the demands of school. Such redshirting is unlikely to be randomly distributed, but rather relates to characteristics of both the parents and the child. While utilizing date of birth may avoid biases induced by both selective conceptions and delayed school entry, this method is still sensitive to selection bias through the shifting of births around the cut-off (Balestra, Eugster and Liebert, 2020; Bjerke et al., 2022). However, few studies have looked into the potential shifting of birth dates in response to the school entry rule. In Japan, Shigeoka (2015) finds that about 7 per cent of births are shifted from the week before the school entry cut-off (April 2^nd) to the week after. Like in Norway, school entry age is strictly enforced in Japan, increasing the incentives to manipulate the date of birth, as there are few opportunities to delay school start after birth (Shigeoka, 2015).

In South Korea, Kim (2021) finds that 42 per cent of births were moved from the last week of December to the first week of January when the school entry cut-off was January 1^st. The large share of births shifted likely results from two motives according to the author: first, due to the Confucian age culture, parents have an incentive to move the birth until after the new year for their children to have the same Korean age as those in their school cohort, and second, parents also value the academic advantages of the relatively oldest children in a cohort (Kim, 2021). Mothers who are more socioeconomically advantaged were most likely to shift the birth date and boy births were more likely to be shifted than girl births (Kim, 2021). González and Dip (2024) found evidence of births being shifted from the 7 days prior to the school entry cut-off into the 7 days after in Argentina, with boy births more likely to be shifted. In China, Huang, Zhang and Zhao (2020) find that parents are able to shift the date of birth, however, they are more likely to bring the birth forward to before the cut-off, as opposed to results for Japan and South Korea. The authors state that this is mostly likely due to the preference among parents for their child to begin school early, as this is believed to improve their academic prospects and school performance (Huang, Zhang and Zhao, 2020).

Contrary to these studies, Dickert-Conlin and Elder (2010) and Valdés and Requena (2023) do not find any evidence of shifting of birth dates around the school entry cut-off in the United States or Spain, or any systematic differences in maternal characteristics around the cut-off. The lack of evidence for birth shifting in the U.S. may be related to the flexibility of school entry and the relatively common practice of ‘redshirting’ among advantaged families (Dickert-Conlin and Elder, 2010). It is unknown whether parents in Norway shift the timing of births in response to the school entry cut-off, and whether this differs by parental characteristics.

The Norwegian context

Compulsory education consists of 10 years of schooling with children enrolling in August of the calendar year they turn six and graduating the calendar year they turn 16. Compulsory schooling is not tied to a minimum school leaving age such as in the United States, but rather mandated to 10 years length, thus resulting in the same length of schooling regardless of the time of year which children are born. The age at which a child enrols into compulsory school is enforced relatively strictly in Norway with the cut-off date set at January 1^st. During compulsory school, students are taught the same curriculum and grade retention is not practiced; this allows students to progress through grades regardless of academic performance and students do not receive ‘failing’ grades in courses or exams (Borodankova and Coutinho, 2011). Through strict enforcement of the age at school enrolment and automatic grade promotion, all students within a school cohort complete compulsory school at the same time.

If parents wish to enrol their child either a year earlier or later than their predetermined enrolment date, they must apply to the municipality for permission. Approval of this application requires an expert assessment carried out by the Educational Psychology Services specifying that the child is not developmentally ready to begin compulsory schooling, or conversely that the child is socially, cognitively, and developmentally ready to begin school early. This is a holistic assessment which includes a pedagogic report from the child’s kindergarten, observation of the child in kindergarten, a skills test, as well as conversations with the parents, kindergarten teachers, and the child. This strict enforcement leads to low overall non-compliance rates with 2 per cent of children receiving late or early school start (Cools, Schøne and Strøm, 2017). Despite high compliance rates, early and late school start is highly linked to month of birth and gender, as boys born in December are more likely to receive a delayed school start and girls born in January are more likely to receive an early school start (Cools, Schøne and Strøm, 2017).

Data, measures, and methods

Due date, school starting age, ADHD risk, and academic skills

The study population includes all individuals born in Norway between 1999 and 2007 to two Norwegian-born parents and who were alive and living in Norway between the ages of 7 and 16 or to the last available year (2021). A small number of individuals missing information on the 5^th grade national tests (< 1 per cent) and due date from ultrasound examination (< 4 per cent) were excluded, leaving the analytical sample at 392,311 individuals. All pregnant individuals are offered a routine ultrasound examination during the second trimester which is used to set a due date based on foetal measurements (Gjessing, Grøttum and Eik-Nes, 2007). Although this is a voluntary examination, over 98 per cent of pregnant individuals attend (Reinar et al., 2014). The due date is then set independently from the last menstrual period (LMP) based on the ultrasound examination. In the event that the due date based on the LMP and the ultrasound examination differ greatly, further follow-up may be recommended. Individual level data was obtained through linkage of five population based registers using unique personal identifiers. Data for this sample come from the Medical Birth Registry of Norway (MBRN) which supplies information on due date through ultrasound examination, the Norwegian Population Register and the National Education Database from Statistics Norway, which provide information on background and family characteristics, national test scores and parental educational attainment, and the National Health Insurance Scheme (KUHR) and National Patient Register (NPR) which contains information on visits and diagnoses from general practitioners and specialist physicians, respectively.

Data on SSA was obtained using the year of the individuals’ 5^th grade national test and their birth month. As automatic grade promotion is mandated through compulsory education individuals are not retained before reaching 5^th grade (Borodankova and Coutinho, 2011). ADHD diagnoses were measured at ages 7 to 15, due to data restrictions, and for the analyses on academic skills the students’ national test scores in math and reading in 5^th and 9^th grade are used. Figure A1 in Appendix A shows the share of children and adolescents registered with an ADHD diagnosis across ages and split by gender. The majority of diagnoses are concentrated among ages 7 to 11, with very few diagnoses in the ages before school start. Detailed information on the variables is provided in Appendix B.

Birth shifting

The main analyses on birth timing includes all individuals born in Norway between 1995 and 2018 to two Norwegian-born parents (N = 1,073,442). Individual level data on date of birth along with child and parental characteristics was obtained through linkage of two population based registers using unique personal identifiers. The Norwegian Population Register which supplied information on background and family characteristics and exact date of birth, and the National Education Database which provided information on parental educational attainment.

The proportion of births shifted is also analysed by birth type; spontaneous, induction, and caesarean-section. Due to data restrictions, exact date of birth cannot be linked in these analyses. Thus, results present the share of births shifted from December to January by birth type using month of birth. The information on birth type and month of birth is provided by MBRN.

Empirical strategy

To estimate the effect of SSA on ADHD diagnosis and academic skills, I use the due date of the individual as an instrument for SSA as opposed to exact date of birth. Utilizing due date as determined by ultrasound rather than date of birth circumvents the bias induced by parents shifting births around the cut-off, as there should be no incentive for parents to manipulate the due date. Detailed information on the due date instrument is provided in Appendix C.

When using a RDD, selective conception is controlled for through the linear date of birth term and the treatment effect is estimated by measuring the size of the discontinuity across the cut-off. However, when the due date as an instrument for SSA, this selective conception is no longer controlled for, which may introduce bias into the estimates if too large of a bandwidth is used. To avoid this bias, the bandwidth must be small enough that births cannot be sorted through strategic conception. For example, if a bandwidth of ± 30 days is used, covering most of December and January, it would be possible for parents to plan conception to avoid a due date in December and instead plan for a birth date in January. However, when using a bandwidth of ± 15 days, it is theoretically unlikely that parents would be able to systematically plan to avoid a due date in late December and instead plan to have a birth date in early January. Previous research has shown that around 88 per cent of births occurred within ± 2 weeks of the ultrasound due date, leading to a natural uncertainty in the actual date of birth when relying on due date (Majola et al., 2021). Thus, I utilize only observations with a due date within ± 15 days of January 1^st to avoid bias induced by strategic conception. The equation for the first stage regression between due date and SSA then becomes:

$${\displaystyle \begin{array}{l}{\displaystyle SSA={\delta }_0+{\delta }_{1}DueDate+{\delta }_{Y}YoDD+ϵ}\end{array}}$$

(1)

Where DueDate is a linear term measuring the distance of the due date in days from January 1^st restricted to ± 15 days around the cut-off, YoDD is the year of the due date recentered from July to June to account for time trends, and ϵ is the residual. The predicted values are then used to estimate the second stage regression:

$$\text{You can't use 'macro parameter character \#' in math mode}$$

(2)

Where Y is the outcome of interest, β₁ is the second stage coefficient of interest which estimates the effect of a one-year increase in SSA encompassing the compound effect of being older in absolute (age-at-entry) and relative terms (within a school cohort), SŜA is the predicted value of SSA from the first stage equation using the DueDate linear term instrument, YoDD is the year of the due date, recentered from July to June, and ϵ is the residual. The two-stage least squares (2SLS) regression is used as the main specification, with estimates from ordinary least squares (OLS) regression provided for comparison.

Next, I turn to the shifting of births around the school entry cut-off. To quantify the shifting of births, I utilize recentered births around January 1^st. To find the number and share of births shifted within each specified window around the cut-off, I follow the approach by Gans and Leigh (2009). The regression equation estimated is:

$${\displaystyle \begin{array}{lll}{\displaystyle Y_{dy}=}& \alpha +{\beta }_{1}Januar{y}_{dy}+{\beta }_{Y}Yo{B}_t+{\beta }_{Y}Do{W}_t& +{\beta }_{Y}Holida{y}_t+{ϵ}_{dy}\end{array}}$$

(3)

Where Y_dy is the number of births for day d in recentered year y, January_dy is a dummy variable taking the value of one the birthday d occurs after December 31^st in each year y. YoB_t are year of birth fixed effects, recentered from July to June, accounting for differing time trends in the number of births, DoW_t are day of week fixed effects, Holiday_t are public holiday fixed effects, and ϵ_dy is the residual. The coefficient of interest is β₁ which provides a measure of the daily number of births shifted after December 31^st controlled for weekday, holiday, and yearly trends. If β₁ is equal to zero, this would indicate that births occur randomly around the cut-off, while if the coefficient is positive this would indicate the number of daily births shifted into January and conversely if it is negative it would indicate the number of daily births shifted into December. When Y_dy is replaced with the log number of births, β₁ is used to capture the share of births moved within the corresponding window. To examine potential heterogeneous responses by child and parental characteristics, subgroup analyses by child’s gender and birth order, and parental education level were completed using equation 3. All analyses were conducted using R version 4.1.2 (R Core Team, 2021). The ‘ivDiag’ package for R was used for calculating the IV estimates (Lal and Xu, 2023).

Results

The effect of school starting age on ADHD diagnosis and academic skills

In Table 1, I present the results for the effect of SSA on the probability to receive an ADHD diagnosis along with the first stage estimate for observations with a due date ± 15 days around January 1^st. The first stage estimate in column (2) shows that a one day later due date leads to an average increase in SSA of 0.0280 years, or 10.2 days. This first stage relation is then used to estimate SŜA, as the later the individual’s due date, the more likely that individual is to be born after the cut-off date and thus begin school at a later age.

Table 1

School starting age and ADHD diagnosis

	OLS Regression	IV-2SLS
	(1)	(2) 1st stage	(3) 2nd stage
Variables	ADHD diagnosis	SSA	ADHD diagnosis
SŜA	-0.0171*		-0.0366*
Due Date	(0.0040)	0.0280*	(0.0076)
[− 15, 15]		(0.0003)
Term year fixed effects	Yes	Yes	Yes
F-test of instrument	-	-	9,175.82
Risk (%)	-27.6	-	-58.8
N	19,083	19,083	19,083

Note. Year of term recentered to run from July to June. Robust standard errors in parentheses. Robust first stage F statistic. Sample includes only observations with a due date of ± 15 days around January 1^st. Sample includes those with a due date between 1999 and 2004.

^*P < 0.001

Columns (1) and (3) show the estimated effect of a one year increase in SSA on the probability of receiving an ADHD diagnosis. The effect is estimated using OLS and IV regressions, respectively. Using the naïve OLS regression, a one-year increase in SSA is associated with a decrease in ADHD diagnosis probability of 1.71 percentage points, or 28 per cent. However, once SSA is instrumented with due date, results from the IV estimate show that a one-year increase in SSA resulted in a decrease in the probability to receive a diagnosis of ADHD of 3.66 percentage points, or a 59 per cent reduction in risk. Additionally, the null hypothesis of a weak instrument is rejected as the F-test is larger than 10.

The bias in the OLS specification likely can be explained by characteristics which are both associated with age at school start and ADHD diagnosis risk. There may be systematic differences in the children born right before and right after the cut-off, and there are also likely differences in those who receive an early or later school start. These two mechanisms may bias the OLS estimate in different directions and are likely working simultaneously, for example if those born before the cut-off are negatively selected, this may upwardly bias the estimates. However, if those who are more likely to receive a late school start are also less likely to have advantaged parents, this may downwardly bias the OLS estimates. In Norway, children of parents with lower education are more likely to ‘redshirt’ and less likely to receive an early school start compared to those with higher educated parents (Cools, Schøne and Strøm, 2017). Although this is contrary to the patterns of redshirting in other countries, in Norway, low socioeconomic children are overrepresented among those who receive a delayed school start (Cools, Schøne and Strøm, 2017). Therefore, a simple OLS regression for age at school start and risk of ADHD diagnosis will lead to biased results, and avoiding this bias through the IV regression provides a causal effect of SSA on the risk of ADHD diagnosis.

Table 2 presents the results for the effect of SSA on academic skills using the 5^th and 9^th grade math and reading national test scores. The results show that a one-year increase in SSA led to an increase in national test score of 0.37 standard deviations for math and reading. The effect is slightly attenuated in the 9^th grade scores, where a one-year increase in SSA resulted in an increase of 0.18 and 0.24 standard deviations for the math and reading test scores, respectively. Overall, the OLS regression estimates under-estimate the effect, similarly to the results for ADHD diagnosis. As prior literature has often used month or date of birth along with a regression discontinuity design to estimate the causal effect of SSA, Appendix D estimates this effect on both ADHD diagnosis and academic skills using OLS regression, RDD, and 2SLS regression with month and date of birth along with the due date IV, to compare the effect estimates from these different methods. Results show that the RD estimate for ADHD diagnosis appears to be downwardly biased compared to the IV estimate. However these effect estimates are not statistically significantly different. When it comes to academic skills, the RD estimates appear to over-estimate the effect of SSA. However, again these effect estimates are not statistically significantly different. Subgroup analyses by gender and parental education for both ADHD and national test scores are presented in Appendix E. I find no statistically significant differences in the effect of SSA on ADHD or academic skills by gender or parental education.

Table 2

School starting age and academic skills

		OLS regression	IV-2SLS
		(1)	(2)	(3)
			1st stage	2nd stage
National Test	Variables	Test score	SSA	Test score
5th Grade: Math	SŜA Due Date [− 15,15]	0.349* (0.014)	0.0267* (0.0002)	0.370* (0.026)
	F-test of instrument	-	-	13,374.1
	N	27,926	27,926	27,926
5th Grade: Reading	SŜA Due Date [− 15,15]	0.335* (0.014)	0.0267* (0.0002)	0.365* (0.026)
	F-test of instrument	-	-	13,229.3
	N	27,615	27,615	27,615
9th Grade: Math	SŜA Due Date [− 15,15]	0.168* (0.014)	0.0267* (0.0002)	0.179* (0.026)
	F-test of instrument	-	-	13,469.8
	N	27,639	27,639	27,639
9th Grade: Reading	SŜA Due Date [− 15,15]	0.174* (0.013)	0.0266* (0.0002)	0.239* (0.025)
	F-test of instrument	-	-	13,361.5
	N	27,693	27,693	27,693

Note. Year of term recentered to run from July to June. Adjusted for term-year fixed effects. Robust standard errors in parentheses. Robust first stage F statistic. Sample includes only observations with a due date of ± 15 days around January 1^st.

^*P < 0.001

Nonrandom sorting of birth timing

In the following section, I examine the extent to which births near the cut-off are shifted and whether this varies by certain characteristics. Figure 1 presents the average daily births recentered around the cut-off date using pooled daily births from 1995–2018 birth cohorts. This figure shows a clear preference for January births, with the average number of daily births in December varying between 100–110 births before a clear drop near the cut-off and a quick increase in early January and a stable trend of around 115–125 daily births throughout the rest of the month. Some of the large drops seen in the week before January 1^st are likely a result of the Christmas holidays. However, December 31^st is not a national holiday in Norway while January 1^st is, despite this, the number of births drops sharply on the last day of December and increases sharply on January 1^st, before continuing to increase into the early days of the new year. This is likely as result of births being postponed from the final days of December across the cut-off and into the first days of January.

Figure 1

Mean daily births around cut-off date

Note. Pooled daily births from 1995–2018 birth cohorts. Date of birth recentered around January 1st cut-off.

Table 3 provides the estimates of the degree to which births are moved across the cut-off after controlling for weekends, holidays, and yearly trends. In Panel A of Table 3 the number of births each day is the dependent variable, and the window of births is progressively widened from 7 days before and after the cut-off to ± 60 days. Following Gans and Leigh (2009), the number of births moved is calculated by dividing the January coefficient by 2 (as one birth moved results in one less birth in December and one additional birth in January) and then multiplying this by the number of days in the window. Similarly, the share of births shifted calculated by dividing the January coefficient by 2 before converting the log points into percentage points. When comparing the week before January 1^st to the week after, a total of 74 births were shifted across the cut-off within the window. As the bandwidth around the cut-off is widened, the number of births moved increases to 433 births, however the January coefficient falls from 21.10 births per day in the ± 7 days around the cut-off to 14.44 births per day in the ± 60 days around January 1^st.

Table 3

Sorting of birth timing

Window	(1) ±7 days	(2) ±15 days	(3) ±30 days	(4) ±60 days
A: Number of births
January	21.10*	15.21*	14.65*	14.44*
	(1.47)	(0.99)	(0.63)	(0.46)
Births shifted within window (n)	74	114	220	433
Adj. R2	0.77	0.70	0.73	0.71
B: Log number of births
January	0.193*	0.140*	0.133*	0.128*
	(0.014)	(0.009)	(0.006)	(0.004)
Share shifted within window	10.1 per cent	7.2 per cent	6.9 per cent	6.6 per cent
Adj. R2	0.76	0.71	0.74	0.72
Observations	336	720	1,440	2,862

Note. Adjusted for year of birth (redefined as running from July to June), weekday, and holiday fixed effects. Robust standard errors in parentheses. Number of daily births come from pooled 1995–2018 birth cohorts and sample includes births within the specified window around the school entry cut-off date. January is a dummy variable for whether or not a birth date is after December 31^st. The number of births moved is calculated as W × β/2 where W is the number of days in the window. The share of births shifted is calculated as exp(β/2)-1. Observations are days per year.

^*P < 0.001

Looking at the share of births shifted in Panel B of Table 3, 10.1 per cent of births are moved across the cut-off within one week before to one week after January 1^st. Within ± 15 days, I estimate that 7.2 per cent of births that would have occurred in the last two weeks of December are shifted to the first two weeks of January, controlling for holidays, weekends, and yearly trends. The majority of shifting appears to occur around within 15 days on either side of the cut-off, while the share moved gradually decreases when expanding the window from 15 to 60 days. This is consistent with the idea that parents may be able to delay the birth up to a certain point, after which a different form of non-random sorting, selective conception, plays a more important role. Appendix F presents the results for the period from 1950–2018. Results show that while the largest shifting of births occurs in the most recent cohorts, this is not an entirely new phenomenon.

Cesarean-sections and inductions

Results for the share of births moved from December to January by birth type are presented in Table 4. Due to data restrictions, results by birth type are presented for all December and January births rather than by exact date, therefore the average number of births via caesarean-section or induction by day cannot be used to analyse the proportion shifted within a given window. Results show that for spontaneous births, i.e. those born without induction or caesarean-section, approximately 5 per cent of births are moved from December to January. A larger magnitude of births born via induction are moved at around 7 per cent and this is statistically significantly different from the share of spontaneous births moved. Overall, nearly 8 per cent of births from caesarean-section are moved from December to January. However, when the caesarean births are classified by whether they were emergent or elective, I find a smaller portion of emergent caesarean births moved at 4.2 per cent and no significant difference to spontaneous births, while 12.4 per cent of elective caesarean births are moved from December to January. Since this analysis includes all births in December and January, the sorting of births presented here is likely due to two mechanisms, strategic conception and shifting of deliveries. The estimates for births via spontaneous or emergent caesarean-section are most likely resulting from the first mechanism; strategic conception, whereas the estimates for inductions and elective caesarean-sections are likely a combination of both mechanisms. The sorting of induced births likely results from both mechanisms as there is varying indications for the use of inductions in Norway which may reflect both more ‘emergent’ indications such as preeclampsia and more ‘planned’ indications such as postterm pregnancy. Thus, the more emergent inductions would not likely be shifted from December to January, whereas there is more flexibility in planning inductions due to postterm pregnancy, which may allow for shifting births from the end of December to the beginning of January. Appendix G presents the descriptive characteristics of births via spontaneous, induction, and caesarean-section.

Table 4

Nonrandom sorting by birth type

	(1)	(2)	(3)Cesarean-Section	(4)	(5)
	Spontaneous	Induction	Overall	Emergent	Elective
Log number of births
January	0.103**	0.141**	0.152**	0.083**	0.234**
	(0.008)	(0.010)	(0.013)	(0.019)	(0.013)
Share shifted from December to January	5.3 per cent	7.3 per cent	7.9 per cent	4.2 per cent	12.4 per cent
Adj. R2	0.94	0.98	0.92	0.85	0.94
P-value for difference	-	0.002*	<0.001**	0.305	<0.001**
Observations	48	48	48	48	48

Note. Adjusted for year of birth (redefined as running from July to June). Robust standard errors in parentheses. Number of monthly births come from pooled 1995–2018 birth cohorts and sample includes all births in December and January across the cut-off. January is a dummy variable for whether or not a birth occurs in January. The share of births moved is calculated as exp(β/2)-1. P-values for difference between the share moved for each birth type compared to spontaneous births. Observations are months per year.

^*P < 0.01

^**P < 0.001

Heterogeneous responses

As shown, there appears to be a relatively large share of births shifted across the cut-off, the majority of which is concentrated around the week before and the week after January 1^st. To further understand these shifts in birth timing, I examine the potential heterogeneous responses by exploiting the characteristics of the parents and the children. Table 5 examines shifts in births by parental educational attainment. Births to higher educated mothers and fathers are more often shifted across the cut-off, with 7.8 per cent of births to mothers and 8.2 per cent of births to fathers with an upper secondary education or higher moved, compared to 5.4 per cent of births to mothers and 4.5 per cent of births to fathers with less than an upper secondary education. The differences are statistically significant at the 5 per cent and 1 per cent levels, respectively. Additional analyses by child characteristics are presented in Appendix H. There is no statistically significant difference by the child’s gender, however, second-borns and later are significantly more often shifted (9.3 per cent) compared to first-borns (4.6 per cent).

Table 5

Heterogeneous responses: shifts in birth timing

	Mother’s education level			Father’s education level
	(1) Upper secondary or higher		(2) Less than upper secondary	(3) Upper secondary or higher		(4) Less than upper secondary
A: Number of births January	12.69***		2.49***	12.87***		2.12***
	(0.82)		(0.45)	(0.81)		(0.45)
Births shifted within window (n)	95		19	97		16
Adj. R2	0.57		0.83	0.56		0.77
B: Log number of births January	0.151***		0.105***	0.157***		0.087***
	(0.010)		(0.020)	(0.010)		(0.019)
Share shifted within window	7.8 per cent		5.4 per cent	8.2 per cent		4.5 per cent
Adj. R2	0.58		0.78	0.57		0.73
P-value for difference		0.036*			0.001**
Mean daily births	83		26	81		27
Observations	720		720	720		720

Note. Adjusted for year of birth (redefined as running from July to June), weekday, and holiday fixed effects. Robust standard errors in parentheses. Number of daily births come from pooled 1995–2018 birth cohorts and sample includes births within ± 15 days around the school entry cut-off date. January is a dummy variable for whether or not a birth date is after December 31^st. The number of births moved is calculated as W × β/2 where W is the number of days in the window (i.e. 15). The share of births shifted is calculated as exp(β/2)-1. Observations are days per year.

^*P < 0.05

^**P < 0.01

^***P < 0.001

Overall, the results on birth shifting point to systematic differences in the parental characteristics of children born in the last 15 days of December compared to those born in the first 15 days of January, after the school entry cut-off date. The births shifted across the cut-off are most often second or higher births and are more significantly more often born to higher educated mothers and fathers. In addition, the highest proportion of birth shifted from December to January occurred via elective cesarean-section, where the largest share occurs in mothers above 30 and second-borns or later. These results show, therefore, that the assumption that exact date of birth is randomly distributed across the school entry cut-off does not hold. This shifting of births provides evidence for the presence of endogenous sorting of births, of which would invalidate the main assumption of the RDD.

Discussion and conclusions

This study presents a novel approach to SSA by utilizing expected due date to provide estimates of the effect of SSA on ADHD diagnosis risk and academic skills, which circumvents issues related to sorting of births near the cut-off. Results for ADHD show that a one-year increase in SSA resulted in a decrease in the likelihood of receiving a diagnosis by 3.66 percentage points, or 58.8 per cent. In Norway, a previous study on school starting age and ADHD using month of birth found a 1.5 times increase in the risk of receiving a diagnosis of ADHD for boys and 1.8 times higher risk for girls when comparing those born between October and December compared to those born January through March (Karlstad et al., 2017).

For academic skills, results show that a one-year increase in SSA resulted in an increase in test scores of about 0.36 standard deviations for 5^th grade math and reading. In 9^th grade, the effect was slightly attenuated, where a one-year increase in SSA led to a 0.19 and 0.25 standard deviations higher score for math and reading, respectively. Previous studies have similarly found an attenuation in the effect of SSA on school performance over time, a finding that supports the idea that differences in school performance by school starting age are most likely driven by the difference in age-at-test (Fredriksson and Öckert, 2009; Black, Devereux and Salvanes, 2011). While the effect appears to be attenuated over time, the results still find a significant academic advantage of older SSA in 9^th grade, when students are turning 14 years old. However, while the national test scores do not have any consequences for the students’ subject grades, if this effect of SSA is also present within exam grades, this could have a longer-lasting impact on the students’ future educational trajectory. In Norway, students apply for upper secondary education at age 16 using their GPA from lower secondary school. Therefore, the academic advantage of SSA could result in educational inequalities in later education if students who enter school at a younger age are disadvantaged when applying for upper secondary school and beyond, consistent with the cumulative (dis)advantage theory (Dannefer, 2003; DiPrete and Eirich, 2006).

This study also examined the shifting of birth timing in response to the school entry cut-off in Norway. Results showed that as much as 10.1 per cent of births are moved from the week prior to the school entry cut-off to the week after. Higher educated parents were significantly more likely to shift births from the end of December to the beginning of January. Few previous studies have examined birth timing and the school entry cut-off. The findings for Norway are contrary to what was found by Dickert-Conlin and Elder (2010) and Valdés and Requena (2023) in the United States and Spain, where researchers found no evidence of birth timing shifting or heterogeneous responses among mothers to the school entry cut-off. However, in the U.S. it is much more common for parents to delay their child’s school entry, and the school entry age is much more flexible in this regard as compared to the Norwegian system (Dickert-Conlin and Elder, 2010). In Spain, redshirting is much less common, however childcare involves a substantial cost which may outweigh the potential benefits of an older school starting age for parents (Valdés and Requena, 2023). Overall, the findings from this study on birth timing present a cautionary note to the large body of research utilizing month and date of birth as an exogenous instrument for SSA. These findings reveal that for the recent cohorts in Norway, being born after the school entry cut-off is positively correlated with certain parental and child characteristics and that parents can strategically determine the date of birth even within a few days of the cut-off. Therefore these findings provide a caveat for utilizing date of birth as an instrument for SSA, as depending on the context this may not meet the requirements for an exogenous instrument.

Additionally, the evidence of shifting by parental educational attainment provides important insights into one way in which parents of higher socioeconomic status may use their resources to secure and maintain advantages for their children. These findings support the theory of effectively maintained inequality, where advantaged families will act in ways that obtain a qualitative or quantitative advantage in their child’s education (Lucas, 2001). This sheds light on one mechanism in which despite equality in access to a certain educational level across socioeconomic position, inequalities in education are maintained and perpetuated across generations through the attainment of qualitative ad- vantages, such as an older SSA (Lucas, 2001). In subgroup analyses by parental education (Appendix E), however, I find no statistically significant difference in the effect of SSA on ADHD diagnosis or academic skills between those with high and low parental education. Therefore, these analyses do not provide evidence of a compensatory advantage for the negative consequences of a younger SSA. These findings are supported by Grätz and Wiborg (2022) who do not find evidence of a compensatory advantage for academic performance, but only with regards to educational choice in the Norwegian context.

While this article utilizes a novel approach in using due date to provide causal estimates for the effect of SSA on ADHD diagnosis and academic skills, it is not without limitations. First, the IV design provides estimates of the local average treatment effect (LATE), which provides information on the effect of SSA for individuals with a due date around the school entry cut-off. Thus, these estimates may have limited generalizability to those farther away from the cut-off. Second, these findings, both on the effect of SSA and the results for birth shifting, may not be generalizable to other contexts outside Norway. The school entry system in Norway is quite strict and therefore the findings may not be generalizable to other systems with more flexibility, such as Denmark. Additionally, Norway is a social democracy with generous welfare policies for families and children, including near full coverage of subsidized early childhood education. Thus, the equality of educational and pre-school opportunities which Norway provides likely influence the results, and may not be generalizable to other contexts (Esping-Andersen, 2005).

Despite these limitations, these findings have implications for future research as well as educational and health policies. As this study shows, parents seem to be aware of and respond to the school entry cut-off with regards to their child’s birth date. More socioeconomically advantaged parents appear to be particularly capable of manipulating the birth date, even within a very close window. This has implications for future research utilizing this discontinuity in SSA, as using month or date of birth may still result in biased estimates if this systematic sorting of births occurs. Simply controlling for such systematic sorting on observables is not a viable solution, as sorting along these dimensions also makes sorting on unobserved characteristics a likely scenario. Researchers should take care in examining whether this shifting of birth dates occurs in their context, and take the appropriate measures to avoid this potential source of bias. In some contexts, the availability of data on due dates for large populations may be limited, in which case applying the method suggested in this paper may not be a feasible option.

An important consideration is whether this birth shifting could have negative implications for the children’s health. Previous studies examining the impact of birth shifting on child outcomes have found an increase in birth weight and gestational age among those shifted, but no evidence of effects on adverse outcomes such as infant mortality (Gans and Leigh, 2009; Shigeoka, 2015).

Previous studies in Denmark have not shown an association between SSA and ADHD (Dalsgaard et al., 2014; Pottegård, Hallas and Zoe¨ga, 2014). This may be due to the much more flexible school entry system compared to Norway, where children born close to the cut-off date are much more likely to delay school start by one year (Pottegård, Hallas and Zoe¨ga, 2014). Practitioners diagnosing ADHD and those referring children for ADHD diagnostics should be aware of the potential risk of misclassification when comparing relatively young children to older peers. Additionally, the results point to an academic advantage of older SSA that persists into lower secondary school. This could have consequences for students’ educational trajectory as students use grades obtained in lower secondary school when applying for upper secondary school. Given the evidence of higher educated parents utilizing their resources to avoid the disadvantages of younger SSA for their children, the effect of SSA on ADHD diagnosis and academic skills also points how educational inequalities by parental socioeconomic status can be produced by mechanisms within the education system. In Norway, policymakers wishing to reduce the educational and health disparities could consider introducing a more flexible school entry system, where particularly vulnerable and less developmentally mature children, for example those born close to the cut-off and from more disadvantaged backgrounds, are allowed to delay school enrolment. Overall, this study provides important insights into one way inequalities are produced by the education system, and one way in which socioeconomically advantaged parents mitigate the potential risks for their children.

Kathryn Christine Beck is a Doctoral Research Fellow at the Centre for Fertility and Health at the Norwegian Institute of Public Health and the Department of Sociology and Human Geography at the University of Oslo. Her research interests include educational and social inequalities and mental health among youth. In her current doctoral thesis, she studies the social and health consequences of experiences in the Norwegian education system. Her work has been published in the journals Demography, BMJ Open and Child Development.

Kathryn Christine Beck is a Doctoral Research Fellow at the Centre for Fertility and Health at the Norwegian Institute of Public Health and the Department of Sociology and Human Geography at the University of Oslo. Her research interests include educational and social inequalities and mental health among youth. In her current doctoral thesis, she studies the social and health consequences of experiences in the Norwegian education system. Her work has been published in the journals Demography BMJ Open and Child Development.

Acknowledgements

Thank you to the participants of the 29^th Norwegian Epidemiological Association (NOFE) conference for their helpful comments and for sharing their insight. I would also like to particularly thank Martin Flatø and Torkild Hovde Lyngstad for their highly valuable inputs on the article. The article has also benefited from comments from seminar participants at the Nordic Institute for Studies in Innovation, Research and Education (NIFU). This study was approved by the Regional Committees for Medical and Health Research Ethics (REK) in Norway (#2018/434). Data from the Norwegian Patient Registry has been used in this publication. The interpretation and reporting of these data are the sole responsibility of the authors, and no endorsement by the Norwegian Patient Registry is intended nor should be inferred.

Funding

This work was supported by the Research Council of Norway through its ground-breaking research funding scheme (Lost in transition? Uncovering social and health consequences of sub-optimal transitions in the education system, project No. 314562). This work was partly supported by the Research Council of Norway through its Centres of Excellence funding scheme, project number 262700.

Data availability

The register data underlying this article can be accessed by application to the Regional Committee for Medical and Health Research Ethics in Norway, Statistics Norway, the Norwegian Institute of Public Health, and the Norwegian Directorate of Health. The ethical approval for this article does not open for storage of data on an individual level in repositories or journals. The analytic code necessary to reproduce the analyses presented in this paper is publicly accessible, and can be found at https://github.com/KathrynChristineBeck/TheLaterTheBetter.