The effect of age at school entry on college admission and earnings: A regression-discontinuity approach

Matta, Rafael; Ribas, Rafael P.; Sampaio, Breno; Sampaio, Gustavo R. Article The effect of age at school entry on college admission and earnings: A regression-discontinuity approach IZA Journal of Labor Economics Provided in Cooperation with: IZA – Institute of Labor Economics Suggested Citation: Matta, Rafael; Ribas, Rafael P.; Sampaio, Breno; Sampaio, Gustavo R. (2016) : The effect of age at school entry on college admission and earnings: A regression-discontinuity approach, IZA Journal of Labor Economics, ISSN 2193-8997, Springer, Heidelberg, Vol. 5, Iss. 9, pp. 1-25, https://doi.org/10.1186/s40172-016-0049-5 This Version is available at: https://hdl.handle.net/10419/152373 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ IZA Journal of Labor Economics Matta et al. IZA Journal of Labor Economics (2016) 5:9 DOI 10.1186/s40172-016-0049-5 ORIGINAL ARTICLE Open Access The effect of age at school entry on college admission and earnings: a regression-discontinuity approach Rafael Matta1, Rafael P. Ribas1, Breno Sampaio2* and Gustavo R. Sampaio2 *Correspondence: [email protected] 2Department of Economics, Universidade Federal de Pernambuco, Rua dos Economistas, Cidade Universitaria, 50740-590 Recife Pernambuco, Brazil Full list of author information is available at the end of the article Abstract This paper provides evidence of the effect of age at school entry on college admission and earnings. It does so by exploiting a number of features in the application process to one of the major flagship universities in Brazil. By comparing applicants with different ages at school entry depending on whether they were born on December 31 or on January 1, our estimates show that applicants who delayed first-grade enrollment present higher aptitude test scores and probability of admission. Our results further suggest that advantaged applicants also earn more early in their careers. JEL Classification: I21, J24 Keywords: School starting age, School achievement, College admission, Aptitude test score 1 Introduction The perception that maturity plays an important role in school learning has encouraged parents and teachers to delay children’s first-grade enrollment. As a consequence, there has been a significant increase in the age at school entry in countries such as the USA (Deming and Dynarski 2008). In fact, there is strong evidence that older pupils tend to outperform their younger classmates in early grades (Bedard and Dhuey 2006; Puhani and Weber 2007; McEwan and Shapiro 2008; Justin 2009). However, there is also evidence that this difference declines over time and disappears in the long run, having no positive effect on adult outcomes (Elder and Lubotsky 2009; Mühlenweg and Puhani 2010). Some studies even find that entering school later reduces educational attainment, by increasing high school dropout rates, and decreases lifetime earnings, by reducing experience in the labor market (Angrist and Krueger 1991; 1992; Dobkin and Ferreira 2010; Black et al. 2011).1Nonetheless, the positive effects in early grades may be persistent in a system where students are tracked early into different schools or classes (Allen and Barnsley, 1993; Fredriksson and Öckert 2014). Given the weak and still disputable evidence of its long-term effects, our study presents and discusses the consequences of a delayed school entry on the admission of college applicants and on their subsequent earnings. We exploit the admission process to one of the major flagship universities in Brazil, which selects candidates strictly based on an entrance exam. In addition to its high quality and reputation, Universidade Federal de © 2016 The Author(s). Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 2 of 25 Pernanbuco (UFPE) is a public university and does not charge tuition fees. As a result, practically all high school graduates in the state of Pernambuco apply to this institution as their first choice. This circumstance makes our study unique because candidates who are not accepted by this university cannot easily enroll at another equally good institution.2 Moreover, Brazil does not have a tracking system that could explain the persistence of early disadvantages. At the same time, the country also has one of the highest rates of grade retention in the world (Bruns et al. 2012).3Thus, this system might diminish the disadvantage felt by younger pupils, who are more likely to repeat a grade. We compare college applicants whose age differences at school entry are exogenously determined by whether they were born on December 31 or on January 1, along with the minimum-age rule enforced by primary schools in Brazil. Our analysis, however, should not be interpreted as the long-term effect on the probability of first graders going to college. Instead, we estimate the effect of delaying school entry on high school graduates aiming to join an elite institution. Our regression-discontinuity (RD) design shows that, among boys, delaying school entry by 1 year increases the admission test score by 0.5 standard deviations (sds) and the probability of college admission by 15 percentage points (p.p.). Importantly, due to the higher repetition rates among early entrants, the age difference between students born on December 31 and those born on January 1 practically disappears by the time they graduate from high school. Therefore, the effect on college admission cannot be attributed to differences in age at the test but rather to learning disadvantages that persist over time. For girls, the effect at early ages is weaker and not persistent on average.4 According to Elder and Lubotsky (2009), two potential mechanisms could explain why later entrants outperform their peers. One is that greater maturity at school entry improves children’s learning ability at primary school and this effect persists over time. The other is that starting school later implies more human capital accumulated from parenting. To the extent that well-educated parents provide more human capital accumulation at home, the relationship between school-entry age and future outcomes should be weaker for the children of less-educated parents. We find, however, that the effect of delaying school entry on test scores is stronger among candidates with less parental education. If parents do not have a college degree, the enrollment delay increases the admission test score of boys by 0.73–0.86 sds and of girls by 0.14–0.57 sds. These findings imply that the difference in college admission scores comes from candidates’ learning ability at primary school, rather than from previously accumulated knowledge. Our findings are consistent with the ideas that learning disadvantages at an early age have a persistent impact on adults (Cunha and Heckman 2007; Cunha et al. 2010) and that grade retention is not an effective way to remedy this distortion (Manacorda 2012). We also conduct a number of tests to shore up our conclusions. First, we confirm the strength of our instrument by showing that children born on January 1 and on December 31 are indeed more likely to be the oldest and the youngest in the first grade, respectively. Second, our results do not seem to be driven by birthday manipulation. If parents planned ahead so that their children were born after New Year’s Eve, then the density of birthdays would be discontinuous around this day. Using the density test proposed by McCrary (2008), however, we show that there is no significant discontinuity between December 31 and January 1. Similarly, parents of children born on New Year’s Day have essentially the same income and education levels as parents of children born on New Year’s Eve. Thus, Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 3 of 25 our results are unlikely to be driven by parental background or birthday manipulation; they certainly derive only from the minimum-age rule. Finally, we verify whether the difference found in college admission rates is carried into the labor market. Unfortunately, we have only data of candidates’ employment in their 20s, which are not enough to estimate lifetime earnings. Nevertheless, among poorer candidates, we find that men born on January 1 earn about 20 % more at the age of 25 than if they were born on December 31. For female candidates, the difference in earnings is not significant, but being born a day later increases by 4–14 % the probability of graduating from college and working by the age of 25. These results are consistent with the hypothesis that delaying school entry increases the lifetime earnings of poorer candidates. The remainder of this paper is organized as follows. Section 2 describes the four sources of data used to estimate the effects on college admission, first-grade enrollment, and adult earnings. Section 3 discusses our empirical strategy based on an RD design. Section 4 presents our main findings, as well as several tests that confirm the consistency of these findings. Our conclusions are presented in Section 5. 2Data 2.1 College application data The main source of data used in this study is the admission exam taken by candidates for the Universidade Federal de Pernambuco (UFPE), which is a flagship university in the Northeast of Brazil.5The vast majority of its undergraduate students used to be admitted through an exam, called the vestibular, which was held only once a year.6This exam has two rounds and evaluates students in the following subjects: mathematics, Portuguese, a foreign language (English, French, or Spanish), literature, history, geography, physics, chemistry, and biology. In the first round, every candidate takes one test per subject and the score is the average of all these tests. The results of this eliminate about 40 % of the candidates, who do not go to the next round. The second-round exam comprises Portuguese, a foreign language, and the three other subjects specifically required for the future program.7The final score is a weighted average of the firstand second-round scores. Finally, each program admits those candidates with the best final scores until all the places are taken. Up to 2013, the final test score was the only admission criterion, so a candidate could not leapfrog others with better scores.8On average, about 10 % of the original candidates per program were admitted. The dataset consists of the application details of 216,771 candidates between 2002 and 2005. However, most of the candidates take the exam more than once. Apart from not being admitted in previous years, some of them retake the exam because they want to switch majors or even institutions. To analyze high school graduates, our sample is restricted to those who graduated from high school in the year that they took the exam. Although failed candidates can retake the exam, we are interested in the cases in which they are immediately admitted to an elite school. Either delaying college admission or going to another institution is considered costly for candidates because it implies less lifetime earnings. In addition, we exclude all candidates who finished high school on adult education programs and those with a large age-grade distortion. Because we are interested in the effect of delaying primary school entrance at 6 years of age, we keep only candidates who are 18.5 years or younger—i.e., those who spent at most 12 years at school. These candidates either delayed their school entry for at most 1 year Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 4 of 25 or repeated at most one grade. Due to this age restriction, we can still separate the reason for delaying high school graduation by using the date of birth as an instrumental variable. For older candidates, their age can be explained by more combinations of entry delay and grade repetition so that the instrument becomes exponentially weaker. The final sample has 45,261 observations, evenly split between 2002 and 2005 and between the various birth cohorts. A birth cohort is defined as a group of candidates born between July 1 and June 30th of the following year. It is worth stressing that almost half the candidates do not take the second-round exam. Moreover, since some majors are more competitive than others, the second-round exam is different not only in terms of subjects but also in terms of difficulty. Accordingly, we use only the first-round scores to compare the performance of candidates. This score is also standardized every year based on the mean and standard deviation of all candidates. Table 1 presents some descriptive statistics. In our sample, the percentage of admitted candidates is 9.7 %, which is slightly lower than the overall percentage of 10.3 %. However, the average test score of first-time candidates is 0.22 sds greater than the overall mean score. These differences may be explained by the fact that first-time candidates usually apply for more competitive programs, so their probability of admission is lower even though their average score is higher. 2.2 Primary and high school data To support our evidence and identification strategy, we also use data from PNAD, Brazil’s National Household Survey, from 1992 to 2005, and from the 2001 National Basic Education Assessment System (SAEB). The purpose of the PNAD data is to answer the following questions: (1) Are children born more frequently before or after January 1? (2) Do children born on January 1 have to delay their entrance to primary school? (3) Does the age gap in the first grade remain until they graduate from high school? All these questions are addressed before we move to our main results. Nonetheless, the PNAD sample cannot be automatically compared to the college application sample, mainly because only 23 % of children in Brazil graduate from high school by the age of 18. If we consider the children of parents who have at least high school education, then this rate jumps to almost 70 %. Accordingly, in addition to restricting the PNAD sample to children in the Northeast region who were born between July 1984 and June 1989, we also reweight it so that it mimics the same parental education as the sample of college candidates above. In practice, we apply the following sample weight in our analyses: wnew i=wold i Pr PE =pei|College Application Data Pr PE =pei|PNAD where wold iistheoriginalsampleweightfromPNADandpe iis the parental education value of child i. While the probability on the numerator is estimated using the college application data, the denominator is estimated using PNAD. The new sample weight, wnew i,isalsorescaledsothatithasthesamemeanandstandarddeviationaswold i,not generating artificial outliers. Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 5 of 25 Table 1 Descriptive statistics All samples Born in July–Dec. Born in Jan.–June Mean Std. dev. Mean Std. dev. Mean Std. dev. Admitted 0.097 0.296 0.095 0.294 0.099 0.298 First-round score 0.223 0.880 0.186 0.890 0.256 0.878 Age 17.78 0.431 17.91 0.465 17.64 0.341 Born in January–June 0.489 0.500 0.000 0.000 1.000 0.000 Female 0.591 0.492 0.583 0.493 0.599 0.490 Father’s education Middle school 0.163 0.369 0.163 0.370 0.162 0.369 High school 0.382 0.486 0.378 0.485 0.385 0.487 College 0.351 0.477 0.349 0.477 0.354 0.478 Mother’s education Middle school 0.140 0.347 0.145 0.352 0.136 0.342 High school 0.393 0.488 0.388 0.487 0.398 0.489 College 0.383 0.486 0.376 0.484 0.389 0.488 Household income 5–10 MWs 0.294 0.456 0.294 0.456 0.294 0.456 11–15 MWs 0.119 0.323 0.116 0.320 0.121 0.326 16–20 MWs 0.081 0.273 0.081 0.273 0.081 0.273 >20 MWs 0.103 0.304 0.105 0.307 0.101 0.301 Private high school 0.709 0.454 0.700 0.458 0.719 0.450 Private primary/middle school 0.717 0.451 0.704 0.457 0.731 0.444 Living in Pernambuco 0.959 0.197 0.960 0.195 0.958 0.200 Living in the Northeast 0.985 0.122 0.985 0.122 0.985 0.122 Birth cohort 1985–1986 0.326 0.469 0.326 0.469 0.327 0.469 1986–1987 0.345 0.475 0.348 0.476 0.342 0.474 Year 2003 0.327 0.469 0.271 0.444 0.258 0.438 2004 0.332 0.471 0.279 0.449 0.258 0.437 2005 0.247 0.431 0.173 0.379 0.227 0.419 Employed at 25 years old 0.488 0.500 0.494 0.500 0.482 0.500 Employed and graduated at 25 0.186 0.389 0.184 0.387 0.187 0.390 Annual earnings (R$) if employed 19,784 22,026 19,903 22,710 19,655 21,267 Number of observations 45,261 23,133 22,128 The sample of candidates for undergraduate programs at UFPE is restricted to those who graduated from high school in the year that they took the college entrance exam and were under 18.5 years old. The first-round score is standardized, with mean zero and variance one, with respect to the whole set of candidates taking the exam at the same time. Annual earnings are deflated to December 2006 level using the National Consumer Price Index (INPC) MW current minimum wage The purpose of the SAEB data is to verify the positive selection in our sample of college applicants. Its survey asks whether students want to continue or stop studying after graduation. This allows us to look not only at performance but also at high school students’ decision to pursue higher education as a function of their month of birth. 2.3 Employment data To estimate the effect of birthday on candidates’ employment and earnings, we match their application to UFPE with employment records from Relação Anual de Informação Sociais (RAIS) from the Brazilian Ministry of Labor and Employment, MTE. RAIS Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 6 of 25 presents comprehensive individual information on occupations, demographic characteristics, and earnings of all registered employees in Brazil. By law, every private or public-sector employer must report this information every year. When available, the matching is based on the candidate’s social security number. Otherwise, it is based on the candidate’s name, gender, and date and place of birth. Using RAIS data from 2009 to 2012, when the candidates were 25 years old, we are able to find 49 % of them. That is, at least 49 % of the UFPE first-time candidates in 2002–2005 were formally employed at the age of 25. However, only 19 % (39 % of the employed) had already graduated from college (see Table 1). On average, those who are employed receive almost R$20,000 a year, which corresponds to 4.7 minimum wages in 2006. Earnings are deflated to the December 2006 level using the National Consumer Price Index (INPC). 3 Empirical strategy In this section, we explain the empirical strategy we adopt to identify the causal effect of early maturity on test scores after high school, college admission, and adult earnings. In our context, early maturity means delaying the start of primary school and then being one of the oldest pupils in the first grade. Since parents do not randomly take such a decision and we cannot observe when the college candidates started primary school, we use the candidates’ birthday as an instrumental variable. In particular, we compare candidates born on December 31 with those born a day later, on January 1, using a regression-discontinuity (RD) design. In Brazil, the law required children to enroll in first grade in the year they turn seven.9 Moreover, most schools did not admit children to the first grade unless they were turning seven that year. Thus, children born on December 31 could start primary school when they are still 6 years old. However, other children born a day later could not start the first grade in the same year because they are still a day away from turning six on December 31. Let Yibe student i’s achievement after high school—e.g., as shown in their aptitude test score, college admission, employment, and earnings. Although the minimum-age rule is supposed to affect our outcome of interest through several channels, such as maturity when applying for college and learning ability during primary school, these channels do not offset each other. Thus, consider the following reduced-form model: Yi=τI(Bi≥0)+g(Bi)+εi,(1) where Biis student i’s birthday, which is equal to zero on January 1 and negative (positive) before (after) this date, gis a nonparametric function, and εiis a random term. While function gcaptures the systematic relationship between the birth date and the outcome of interest, coefficient τrepresents the discontinuity in this relationship around January 1. That is, τis the effect of being born on January 1 rather than December 31. To interpret τas the effect of the minimum-age policy, first we need the age constraint to be binding—i.e., some parents want their children to start school but they cannot do so due to their age. This condition is verified by estimating the school enrollment rate, Ei, around age six, as follows: Ei=τEI(Bi≥0)+gE(Bi)+εE,i.(2) If τE= 0, then the age constraint makes children born on January 1 delay their school start for a year. Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 7 of 25 The fundamental assumption in identifying τand τEis that parents do not manipulate their child’s birthday. Parents may choose whether their child is born before or after January 1 and this choice could be related to parenting skills. In a RD design, the manipulation of the running variable is an issue only if it happens locally around the cutoff. If parents prefer January 1 to December 31, or vice versa, we should observe a significant difference in birthday densities between these two dates. Accordingly, we verify the assumption of no manipulation using McCrary’s (2008) test. As we estimate Eqs. (1) and (2), the effect of delaying school entry on future outcomes, β, can be calculated using the Wald estimator: ˆ β=ˆτ ˆτE .(3) All equations are estimated using triangular kernel functions. The optimal bandwidth is chosen according to the procedures of Calonico et al. (2014) and Imbens and Kalyanaraman (2012). Robust standard errors are calculated as described by Calonico et al. (2014). 4 Results Our results are divided into five parts. First, we show that our instrument (i.e., being born on or after January 1) is indeed exogenous and not subject to parents’ choice. Second, we confirm that the minimum-age rule for primary school has been enforced in Brazil and that this instrument is strong enough to predict school-entry age. In Sections 4.3 and 4.4, we present our main results and discuss potential mechanisms through which schoolentry age is related to college admission. Finally, we show some evidence for the effect on employment and earnings by the time candidates turn 25. 4.1 Is the date of birth endogenous? Before we move to the main results, we should check whether parents choose that their child’s birthday occurs before or after January 1. If they perceived the child would perform better among younger peers, they might plan her birthday to be after New Year’s Eve. In this case, other characteristics related to parenting skills could also drive our results. To verify this issue, we perform two different tests. First, we test for birthday manipulation using McCrary’s test. McCrary (2008) proposes an estimator for the discontinuity in the density function around the cutoff (January 1) of the running variable (the birthday). His test is implemented as a Wald test in which the density is continuous under the null hypothesis. Second, we verify whether being born before or after January 1 is related to parental education. Here we assume that the parent’s education is a good proxy for parenting. The more educated parents are, the higher the investment made in their child’s education. The first graph on the left of Fig. 1 shows that first-time college candidates are more likely to be born on January 1 than on December 31. However, this difference can be the result not only of parental choice but also of performance at school. If students born on December 31 perform worse in school, then they are also less likely to finish high school and apply for college. The second graph on the right confirms that there is no significant difference in the population over the probability of being born before or after January 1. Namely, if we look at the whole cohort of children born at much the same time, living Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 8 of 25 = 0.099*** (0.033) 0 .001 .002 .003 .004 Jan 1-180 -150 -120 -90 -60 -30 30 60 90 120 150 180 Birthday College Candidates = 0.041 (0.067) 0 .001 .002 .003 .004 Jan 1-180 -150 -120 -90 -60 -30 30 60 90 120 150 180 Birthday Population Fig. 1 Distribution of birthdays and the McCrary density test. This figure shows the histograms of birthdays with the bin width equal to 10 days. The center of the graphs is zero, which represents January 1. The first graph on the left is the distribution of birthdays of UFPE first-time candidates between 2002 and 2005. The second graph on the right (PNAD data) is the distribution of birthdays of children born between July 1984 and June 1988, living in the state of Pernambuco, and with similar parental education to that of the UFPE candidates. θis McCrary’s (2008) estimator for log density discontinuity, with standard errors in parentheses. *** represent statistical significance at the 1 % level in the same state, and with similar parental education, there is no evidence of birthday manipulation. As a result, the discontinuity found among college candidates can be ascribed to school performance, which can potentially lower our causal estimate. That is, if the missing children applied for college at the right age, they would perform worse than those who do actually apply, lowering the average score below the cutoff. To provide evidence of this positive selection in our sample, we present in Fig. 2 two conditional density estimates of the SAEB score for high school graduates in the state of Pernambuco. One considers the sample of students who are 18.5 years or younger (dashed line)—mimicking our sample—and the other considers those older than 18.5 years (solid Pr(willing to study)=.62 Pr(willing to study)=.77 0 .5 1 1.5 2 2.5 density 5.2 5.4 5.6 5.8 6 6.2 log(score) small age−grade distortion large age−grade distortion Fig. 2 School graduates, willingness to study, and positive selection. This figure shows two density estimates of the SAEB score for high school graduates in the state of Pernambuco. One is from a sample of students who are 18.5 years or younger (dashed line) and the other is from those older than 18.5 years (solid). This figure also displays the conditional percentage of students that answered “yes” when asked about their willingness to continue studying after high school Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 15 of 25 age and future outcomes should be stronger for the former’s children. Namely, the effect on aptitude test scores would be proportional to parental education. Nevertheless, we find the opposite. The gap between candidates born in late December and early January is higher among those with less parental education. Table 5 shows that the birthday effect on the test scores of boys is between 0.16 and 0.21 sds if their parents do not have a college degree and between 0.04 and 0.19 sds if at least one of them does. If we divide these estimates by the effect on first-grade enrollment, we find that delaying the school start increases by 0.73–0.86 sds the average test scores in the former group. Even for girls, the effect becomes significant if we look only at the group with less parental education. In this group, being born on January 1 increases by 0.08– 0.11 sds the average test score. As a consequence, delaying school entry increases their average test score by 0.14–0.57 sds. For both boys and girls with well-educated parents, the difference is insignificant and very close to zero.13 There are several reasons why the effect varies with parental education. To begin with, education is closely related to wealth and wealthier parents can afford additional support for their children (e.g., by hiring private tutors), and this may compensate for any disadvantage.14 Table 6 confirms that similar results are found if we split the sample by household income. That is, the effect on both boys and girls is stronger and significant if they come from poor households, but it is very close to zero if they come from households that receive more than five minimum wages per month.15 Moreover, wealthier parents can send their children to better schools, which may give special attention to the youngest pupils. Table 7 confirms that the birthday effect is significant for candidates from public high schools but insignificant for candidates from private institutions. If parents assumed that private schools are better for disadvantaged students, candidates’ birthday might be correlated with private school enrollment. We observe in the first graph of Fig. 8 that there is no significant relationship between birthday and attendance at a private institution at early ages. However, candidates born on or after January 1 are more likely to come from private high schools (second graph at the top). The difference between the two graphs at the top of Fig. 8 suggests that children are not initially sorted into primary schools on the basis of their birthday. But after then, advantaged students who were born in January are more likely to be in private high schools. The graphs in the bottom row reveal that this difference is not due to the movement of disadvantaged students from private to public schools but rather to the movement of advantaged students from public to private institutions. That is, parents of older (and better) students in public schools are more willing to pay the cost of a private high school. This result has two potential implications. First, the movement of better students from public primary/middle schools to private high schools may lower the average above the cutoff point in both public and private high schools. As a result, the effects presented in Table 7 would be underestimated—i.e., they represent lower bounds. Second, this movement also represents a self-tracking mechanism that keeps disadvantaged students in public schools and moves advantaged students to private schools. Although Brazil does not have a formal tracking system, sorting of this kind may explain why early disadvantages have persistent effects. According to Hsieh and Urquiola (2006) and Muralidharan and Sundararaman (2015), however, private schools do not necessarily improve students’ test scores in developing countries. A back-of-the-envelope calculation using estimates from Figs. 7 and 8 and Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 16 of 25 Table 5 RD estimates of test scores by parental education Less-educated parents Well-educated parents Polyn. CCT procedure IW procedure CCT procedure IW procedure degree τz-stat Bandwidth τz-stat Bandwidth τz-stat Bandwidth τz-stat Bandwidth Male 0 0.177** 2.447 23.28 0.159*** 2.639 33.51 0.046 1.482 44.83 0.035 1.322 60.86 1 0.205** 2.149 48.14 0.217*** 2.845 76.23 0.149** 2.374 37.33 0.060 1.429 88.54 2 0.209** 1.962 83.50 0.213** 2.085 91.51 0.190** 2.518 56.81 0.102* 1.853 105.42 Female 0 0.09** 2.220 45.63 0.082*** 2.604 76.65 −0.004 −0.160 40.91 0.001 0.055 61.08 1 0.107* 1.825 80.29 0.110** 2.059 96.40 −0.014 −0.354 78.42 −0.011 −0.392 134.77 2 0.030 0.282 60.86 0.106 1.511 125.08 −0.083 −1.207 55.88 −0.028 −0.571 105.52 This table shows the RD estimates of test scores using different local-polynomial degrees (per row) and different bandwidth selection procedures (per column). The first panel on the left has the results for candidates whose parents have no college degree and at least one has no high school education. The second panel on the right has the results for candidates whose either both parents have a high school diploma or at least one has a college degree. The CCT procedure is proposed by Calonico et al. (2014). The IW procedure is proposed by Imbens and Kalyanaraman (2012). All functions are estimated using a triangular kernel. Data come from applications for undergraduate programs at UFPE from 2002 to 2005. The sample is restricted to those who graduated from high school in the same year and were under 18.5 years old. τis the robust RD estimate ***, **, * represent statistical significance at the 1, 5, and 10 % levels, respectively Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 17 of 25 Table 6 RD estimates of test scores by household income <5 MWs 5–10 MWs >10 MWs Polyn. CCT procedure IW procedure CCT procedure IW procedure CCT procedure IW procedure degree τz-stat τz-stat τz-stat τz-stat τz-stat τz-stat Male 0 0.220*** 2.808 0.040 1.188 0.075 1.430 0.074 1.626 0.033 0.668 0.025 0.717 1 0.257*** 2.826 0.216*** 2.877 0.067 0.870 0.096* 1.791 0.013 0.210 0.044 1.026 2 0.280*** 2.928 0.246*** 2.924 0.063 0.633 0.083 1.133 0.078 0.805 0.006 0.080 Female 0 0.094** 2.314 0.061** 2.568 0.050 1.222 0.055 1.517 −0.063 −1.356 −0.007 −0.285 1 0.108** 2.036 0.109** 2.277 −0.028 −0.370 0.067 1.328 −0.088 −1.458 −0.078 −1.558 2 0.100 1.197 0.123** 2.013 −0.057 −0.625 0.005 0.076 −0.119 −1.338 −0.103* −1.875 This table shows the RD estimates of test scores using different local-polynomial degrees (per row) and different bandwidth selection procedures (per column). The first panel on the left has the results for candidates from households that receive less than five minimum wages (<5 MWs) per month. The second panel in the center has the results for candidates from households that receive between five and ten minimum wages (5–10 MWs) per month. The third panel on the right has the results for candidates from households that receive more than ten minimum wages (>10 MWs) per month. The CCT procedure is proposed by Calonico et al. (2014). The IW procedure is proposed by Imbens and Kalyanaraman (2012). All functions are estimated using a triangular kernel. Data come from applications for undergraduate programs at UFPE from 2002 to 2005. The sample is restricted to those who graduated from high school in the same year and were under 18.5 years old. τis the robust RD estimate ***, **, * represent statistical significance at the 1, 5, and 10 % levels, respectively Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 18 of 25 Table 7 RD estimates of test scores by school choice Public high school Private high school Polyn. CCT procedure IW procedure CCT procedure IW procedure degree τz-stat Bandwidth τz-stat Bandwidth τz-stat Bandwidth τz-stat Bandwidth Male 0 0.184** 2.225 24.65 0.090* 1.787 64.52 0.036 1.166 45.04 0.031 1.073 53.11 1 0.211** 2.185 64.14 0.181** 2.095 79.54 0.081 1.513 52.60 0.044 1.120 99.72 2 0.296** 2.091 65.62 0.230** 2.061 102.88 0.089 1.404 78.92 0.048 1.095 171.98 Female 0 0.082 1.477 32.86 0.076** 2.002 76.17 −0.029 −0.904 29.33 0.001 0.057 60.36 1 0.041 0.429 42.69 0.089* 1.697 144.49 −0.038 −0.977 72.78 −0.020 −0.630 107.40 2 0.001 0.005 59.70 0.149** 1.983 143.90 −0.136** −1.981 53.75 −0.043 −1.012 130.34 This table shows the RD estimates of test scores using different local-polynomial degrees (per row) and different bandwidth selection procedures (per column). The first panel on the left has the results for candidates who graduated from a public high school. The second panel on the right has the results for candidates who graduated from a private high school. The CCT procedure is proposed by Calonico et al. (2014). The IW procedure is proposed by Imbens and Kalyanaraman (2012). All functions are estimated using a triangular kernel. Data come from applications for undergraduate programs at UFPE from 2002 to 2005. The sample is restricted to those who graduated from high school in the same year and were under 18.5 years old. τistherobustRDestimate ** and * represent statistical significance at the 5 and 10 % levels, respectively Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 19 of 25 = 0.022 (0.020) .6 .65 .7 .75 .8 Jan 1-100 -75 -50 -25 25 50 75 100 Birthday Studied in Private Primary/Middle School = 0.046** (0.022) .6 .65 .7 .75 .8 Jan 1-100 -75 -50 -25 25 50 75 100 Birthday Studied in Private High School = 0.016 (0.014) .8 .85 .9 .95 1 Jan 1-100 -75 -50 -25 25 50 75 100 Birthday Stayed in Private School = 0.102** (0.050) .15 .2 .25 .3 .35 Jan 1-100 -75 -50 -25 25 50 75 100 Birthday Moved to Private School Fig. 8 Probability of studying in a private school. This figure shows the relationships between birthday and studying in a private institution in primary and middle school (top left), between birthday and graduating from a private high school (top right), between birthday and having always studied in private institutions (bottom right), and between birthday and moving from a public middle school to a private high school (bottom left). The center of the graphs is zero, which represents January 1. Data come from applications for undergraduate programs at UFPE from 2002 to 2005. The sample is restricted to those who graduated from high school in the same year and were under 18.5 years old. Functions are estimated using a triangular kernel with the bandwidth selection procedure proposed by Calonico et al. (2014). τis the RD estimate, with robust standard errors in parentheses. ***, **, * represent statistical significance at the 1, 5, and 10 % levels, respectively Table 7 tells that attending private school is responsible for 9 % of the average effect on boys and 267 % on girls (not significant).16 4.5 The effect on early employment and earnings Since our sample is from college candidates who have recently entered the labor market, we cannot estimate the effect on lifetime earnings. Nonetheless, we can verify whether these candidates have gains/losses related to their birth date in the early stages of their career. Table 8 presents the estimated effect of birthday on employment, college graduation, and earnings at the age of 25 for UFPE candidates from poor households.17 For male candidates, being born on or after January 1 has no significant effect on the probability of graduating from college or being employed, but it increases earnings by 15–22 %. Namely, the difference in admission test scores found earlier does not imply that male candidates born in January will graduate and be in the market sooner than their Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 20 of 25 Table 8 RD estimates of employment and earnings at 25 years old Less-educated parents Less-educated parents HH income <5 MWs and HH income <10 MWs CCT procedure IW procedure CCT procedure IW procedure CCT procedure IW procedure τz-stat τz-stat τz-stat τz-stat τz-stat τz-stat Male Employed −0.024 −0.465 −0.025 −0.505 −0.012 −0.259 −0.017 −0.384 −0.010 −0.193 −0.013 −0.261 Employed and graduated 0.024 0.366 0.045 0.969 −0.020 −0.336 0.015 0.362 −0.002 −0.025 0.031 0.694 Log earnings 0.189* 1.949 0.162* 1.874 0.194* 1.873 0.150* 1.943 0.224** 2.222 0.210** 2.259 Female Employed −0.054 −1.216 −0.044 −1.416 −0.042 −0.982 −0.015 −0.569 −0.055 −1.268 −0.045 −1.430 Employed and graduated 0.136** 2.172 0.077* 1.692 0.053 1.100 0.043 1.400 0.136** 2.159 0.094* 1.859 Log earnings 0.125 1.445 0.050 0.801 0.051 0.854 0.033 0.657 0.138 1.566 0.057 0.904 This table shows the RD estimates of employment outcomes at the age of 25 (per row) and different bandwidth selection procedures (per column). The outcomes are as follows: being employed, having graduated from college and being employed, and log of earnings. The first panel on the left has the results for candidates whose parents have no college degree and at least one has no high school education. The second panel in the center has the results for candidates from households that receive less than five minimum wages (<5 MWs). The third panel on the right has the results for candidates from households that receive less than ten minimum wages (<10 MWs) and where parents have no college degree and at least one has no high school education. The CCT procedure is proposed by Calonico et al. (2014). The IW procedure is proposed by Imbens and Kalyanaraman (2012). All functions are estimated using a triangular kernel. Data come from applications for undergraduate programs at UFPE from 2002 to 2005. The sample is restricted to those who graduated from high school in the same year and were under 18.5 years old. τis the robust RD estimate ** and * represent statistical significance at the 5 and 10 % levels, respectively Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 21 of 25 counterparts born the previous December. However, the ability gap continues in the labor market and is reflected in earnings. For female candidates, the effect on earnings is not as strong and significant as it is for men. Yet the probability of graduating from college and being employed by the age of 25 is 4–14 % higher if they were born on or after January 1. Unlike men, women who are born in January do graduate sooner than women born in the previous December. This means that the potential return for a college degree emerges earlier in their life cycle, which probably increases their lifetime earnings. 5Conclusions Delaying primary school entry tends to affect students’ outcomes not merely in the early grades. We reach this conclusion by exploiting an exogenous variation in birthdays between late December and early January and the minimum-age rule enforced by primary schools in Brazil. In particular, we find that college applicants who were older than their classmates in the first grade are more likely to be admitted to a flagship university right after high school. On the one hand, the age difference created by the minimumage rule disappears over time because younger students are more likely to repeat grades. Once they have to repeat a grade, they become one of the oldest in their class. On the other hand, candidates born on January 1 still outperform those born on December 31, even though they are the same age when they apply for college. Thus, it is not necessarily the current maturity gap that affects their test scores but the difference in their learning abilities at school. The difference in aptitude test scores, as well as in the likelihood of college admission, created by the minimum-age rule is much greater for boys than for girls. This indicates that the maturity gap in primary school, which affects long-run outcomes, tends to close faster for girls, who usually mature earlier than boys. Moreover, this rule affects mainly college candidates whose parents are poorer and less educated. In this group, delaying primary school for a year increases by 0.73–0.86 sds the college admission test score of boys and by 0.14–0.57 sds the score of girls. As long as human capital accumulation before primary school is related to parents’ education and wealth, this finding suggests that differences in aptitude test scores are mostly created at primary school. We also observe that students born in January tend to move from public to private schools some time after their advantage with respect to their classmates is revealed. Although Brazil has no tracking system, this sorting mechanism may be a reason why the effect of age at school entry persists among poor students. The persistence of this effect is reflected not only in the test scores but also in the early gains in the labor market. These gains happen either directly through earnings (for men) or indirectly by graduating and entering the market sooner (for women). Our findings reinforce the need for change in the inflexible age-grade system that puts children with disparate learning abilities in the same class. Since children are assessed at times dictated by a fixed school calendar, younger pupils have a natural disadvantage that may continue to their adulthood. Although grade retention tends to adjust the age difference in the early grades, this is not an effective way of narrowing the learning gap (e.g., Manacorda 2012). To assess students’ actual ability, the school system should apply age-normalized exams, which ensure that they are compared to peers at exactly the same age. Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 22 of 25 One important caveat in interpreting the results of our study is their external validity. In fact, we cannot claim that our findings result from the long-term effects of age at school entry on the entire population of first graders. Given our setting and the available data, we have instead focused on their interval validity by selecting a very specific sample. Namely, our inferences are for a population of high school graduates with little age-grade distortion, aiming to join an elite institution. In that sense, our study differs, for instance, from Crawford et al. (2010), who estimates the likelihood of a first grader going to college, despite the quality of the institution. However, we still believe that our study contributes to the debate about school-entry age by showing estimated effects on students who are probably at the top of the distribution of skills. Endnotes 1Effects on labor market outcomes in the USA are in part explained by the compulsory laws that specify a minimum school leaving age. 2See Brewer et al. (1999) and Dale and Krueger (2002) on the returns of attending an elite institution. 3According to PREAL (2009), almost 25 % of first-grade students repeat the year and more than 40 % of high school students have fallen two or more years behind. 4This difference between genders is in line with McEwan and Shapiro (2008), who find that the effect of delaying school entry on test scores at the fourth grade is one third higher for boys than for girls. 5According to the Ministry of Education, UFPE is the largest and most selective university in the North and Northeast regions of Brazil. It has 62 undergraduate programs and 108 graduate programs. In 2004, the university had 25,000 enrolled students (20,500 in undergraduate programs and 4500 in graduate programs) and 1647 faculty members. 6Since 2010, the admission score has been composed of the vestibular and the National High School Exam (similar to the American SAT test). 7In Brazil, universities require candidates to choose their major when they apply for an undergraduate program. 8A law approved in 2012 requires that all federal universities implement quotas by 2016 on the basis of attendance at a public high school, family income, or qualifying as indigenous or an afrodescendant. 9This law changed in 2010. The new law added one more grade to primary education and now requires children to turn six by March 31 in the year of the first grade. 10We have two additional remarks regarding our sample. The first relates to the possibility of students being grade advanced. The implication for our estimates would be severe, because the selection bias would be negative instead of positive. In Brazil, however, the percentage of pupils skipping at least one grade has been close to zero. According to the National Institute for Educational Studies and Research (INEP), this number was 682 (around 31 students in the state of Pernambuco) in 2000. This situation started to change in 2005, when the Government launched a program to identify gifted students. In 2010, for example, the number of kids that skipped a grade in the country reached 8851, which still represents a small percentage. Nevertheless, acceleration should not affect our results given our sample period. The second remark is with regard to excluding those Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 23 of 25 taking the exam for at least the second time. These candidates are either high school graduates not accepted in the previous years, adults seeking professional training, or college students aiming to switch majors and/or institutions. We consider that this pool of candidates is very heterogeneous and it is not necessarily comparable to high school graduates. 11We also estimate the difference in terms of high school education and find a similar magnitude. This result is available upon request. 12Differently from the USA, the numbers of kids moving a grade ahead in Brazil has been historically close to zero. According to the National Institute for Educational Studies and Research (INEP), the number of kids that moved ahead a grade in Brazil in 2000 was 682 (around 31 students in the State of Pernambuco). This situation however started to change after 2005, when the Government launched a program to train professors in identifying gifted students. In 2010, for example, the number of kids that moved ahead a grade in the country reached 8,851, still small but 62 % larger than that observed in 2009 (5478 students). 13The estimated effect on first-grade enrollment by parents’ education is available upon request. 14Sampaio et al. (2011), using similar data, show that wealthier parents are more likely to pay for private tutoring classes for children graduating from high school in the state of Pernambuco. They also provide evidence that tutoring classes increase scores significantly. 15We report differences in RD estimates presented in Tables 5 and 6 in the Appendix (see, respectively, Appendix: Tables 9 and 10). 16The effect through private school by gender is obtained by {average effect −[p* (effect on public students) + (1−p) * (effect on private students)]}/(average effect), where pis the proportion of candidates attending public schools. 17For wealthier candidates, no effect is significant. Appendix Table 9 Differences in RD estimates of test scores by parental education Less-educated vs. well-educated parents Polyn. CCT procedure IW procedure degree Diff. z-stat Diff. z-stat Male 0 0.131* 1.664 0.124* 1.884 1 0.056 0.490 0.157* 1.803 2 0.019 0.146 0.111 0.957 Female 0 0.094** 1.974 0.081** 2.228 1 0.121* 1.711 0.121** 2.005 2 0.113 0.892 0.134 1.566 This table shows the differences in RD estimates of test scores between well-educated parents and less-educated parents using different local-polynomial degrees (per row) and different bandwidth selection procedures (per column). The CCT procedure is proposed by Calonico et al. (2014). The IW procedure is proposed by Imbens and Kalyanaraman (2012). All functions are estimated using a triangular kernel. Data come from applications for undergraduate programs at UFPE from 2002 to 2005. The sample is restricted to those who graduated from high school in the same year and were under 18.5 years old ** and * represent statistical significance at the 5 and 10 % levels, respectively Matta et al. IZA Journal of Labor Economics (2016) 5:9 Page 24 of 25 Table 10 Differences in RD estimates of test scores by household income (<5 MWs)–(5–10 MWs) (5–10 MWs)–(>10 MWs) (<5 MWs)–(>10 MWs) Polyn. CCT procedure IW procedure CCT procedure IW procedure CCT procedure IW procedure degree Diff. z-stat Diff. z-stat Diff. z-stat Diff. z-stat Diff. z-stat Diff. z-stat Male 0 0.145 1.538 −0.034 −0.601 0.042 0.583 0.049 0.855 0.187** 2.019 0.015 0.309 1 0.190 1.594 0.120 1.301 0.054 0.547 0.052 0.758 0.244** 2.218 0.172** 1.989 2 0.217 1.572 0.163 1.461 −0.015 −0.108 0.077 0.734 0.202 1.484 0.240** 2.129 Female 0 0.044 0.763 0.006 0.138 0.113* 1.825 0.062 1.416 0.157** 2.544 0.068** 1.990 1 0.136 1.472 0.042 0.604 0.060 0.620 0.145** 2.040 0.196** 2.439 0.187*** 2.700 2 0.157 1.269 0.118 1.314 0.062 0.487 0.108 1.260 0.219* 1.795 0.226*** 2.751 This table shows the differences in RD estimates of test scores between household income ranges using different local-polynomial degrees (per row) and different bandwidth selection procedures (per column). The first panel on the left shows differences in estimates between candidates from households that receive less than five minimum wages (<5 MWs) per month and candidates from households that receive between five and ten minimum wages (5–10 MWs) per month. The second panel in the center shows differences in estimates between candidates from households that receive between five and ten minimum wages (5–10 MWs) per month and candidates from households that receive more than ten minimum wages (>10 MWs) per month. The third panel on the right shows differences in estimates between candidates from households that receive less than five minimum wages (<5 MWs) per month and candidates from households that receive more than ten minimum wages (>10 MWs) per month. The CCT procedure is proposed by Calonico et al. (2014). The IW procedure is proposed by Imbens and Kalyanaraman (2012). All functions are estimated using a triangular kernel. Data come from applications for undergraduate programs at UFPE from 2002 to 2005. The sample is restricted to those who graduated from high school in the same year and were under 18.5 years old ***, **, * represent statistical significance at the 1, 5, and 10 % levels, respectively