Abstract
This work examines the effects of early skill advantages on parental beliefs, investments, and children’s long-run outcomes measured up to age 27. We exploit exogenous variation in skills due to school entry rules, combining 20 years of Chilean administrative records with a regression discontinuity design. Our results show that these rules shift parental beliefs and increase their material investments. Children benefited from the early skill advantage have higher in-school performance and college entrance scores and sizable effects on college attendance and enrollment at selective institutions. These long-run effects are more pronounced for low-income families and likely mediated by parental beliefs and material investments.
I. Introduction
Several studies show that early life disparities affect children’s development (Bharadwaj et al. 2013), with lasting effects on adult outcomes (Almond, Currie, and Duque 2018). Parental investments can mediate these long-term consequences; therefore, there is growing interest in better understanding how parents respond to their children’s (dis)advantages (Boneva and Rauh 2018; Carneiro et al. 2019; Dizon-Ross 2019).1
We examine how parental beliefs, investments, and children’s long-run outcomes respond to (perceived signals of) early skills. We study this question exploiting exogenous variation in skills due to school entry rules, combining 20 years of Chilean administrative micro-data with a regression discontinuity (RD) design. We supplement the administrative records with survey data containing information on parental investments and beliefs reported by parents and students.
We first start documenting effects on in-school measures of performance, replicating results from the existing literature that uses age-at-entry rules as exogenous variation on early skills.2 Second, we contribute with novel evidence to this literature by showing how parental beliefs and investments respond to the initial skill disparities produced by the entry rule and how these responses vary by type of investment. Third, we follow children over 20 years to estimate long-run effects. Finally, we place our findings within a human capital accumulation framework that connects parental responses with their children’s long-run outcomes.
Our research design mimics a local experiment where children are exogenously allocated to start school at different ages due to birth date cutoff rules. These age differences translate into large disparities in multiples skills measured just before school entry, as we show in Section II.B.3 Consistently with the related literature, we find that children who start school with higher skills perform better on several in-school outcomes like GPA and test scores (0.20 standard deviations) measured from the first through the fourth grade.
We uncover new evidence showing that parents causally react with changed beliefs and material investments. By the end of fourth grade, parents of children with the age skill advantage are more likely to believe that they will complete post-secondary degrees, such as graduate school, college, and technical careers (effect sizes of 13 percent, 4 percent, and 2 percent, respectively). Parents do not invest time differentially but reinforce initial skill gaps by investing an additional 0.11 standard deviation of financial resources in children with higher skills at entry.
We find sizable effects in the long run. Following the same students over time, we find that early skill gaps lead to higher take-up (6 percent) and scores (0.08 standard deviations) in the national college entrance exam and a higher probability of college enrollment, both overall (15 percent) and at selective programs (20 percent). The magnitude of the estimates on college enrollment are sizable and within those found by the early childhood interventions literature (Elango et al. 2015), suggesting that policy shocks on early skills can be as important as programs that are especially designed to bolster children’s capacities. Leveraging large sample sizes, we are also able to estimate precisely how our results vary by socioeconomic background. All our effects on financial investments and college enrollment are more pronounced for low-income children.
Our work contributes to two related strands of the literature. First, it complements recent research connecting parental investments and beliefs (for example, Attanasio, Boneva, and Rauh 2022; Biroli et al. 2022; Boneva and Rauh 2018; Dizon-Ross 2019). Our findings on beliefs suggest that parents interpret the results on in-school performance as signals of their child ability and adjust their investments according to their perceived return. Our findings on the neutrality of parental time investments are consistent with the results of Bharadwaj, Løken, and Neilson (2013) for Norway and Chile, in the context of an early health intervention. We add to these results by showing that financial investments respond differently to early skills gaps. These results are consistent with parents of high-performing children perceiving that the returns to monetary investments are higher than time investments.
Second, this work also adds to the literature documenting long-term effects of early life disparities.4 We track students for 20 years with repeated measures across time. Few studies can observe outcomes in the middle years of life (the “missing middle” in Almond, Currie, and Duque 2018), which are important to fully understand effects. For instance, Heckman, Stixrud, and Urzua (2006); Elango et al. (2015); and Beuermann and Jackson (2022) highlight that the effects of early life disparities might fade out in the medium term but emerge in the long run. We measure relevant outcomes at ages six (GPA), ten (test scores), 14 (primary school completion), 18–20 (high school completion and college entrance exams), and up to 27 (college completion).
Overall, our empirical findings suggest that parents respond to perceived signals of children’s ability in different ways depending on the type of investment. Those responses may reinforce early gaps with consequences for long-term educational outcomes. We argue that signals could disappear if adjusted by age, but parents and children themselves observe and react based on the unadjusted in-school differences. The natural policy implication of these findings is to provide parents both raw and age-adjusted measures of performance. Schools could also train teachers to communicate results to parents so that they take age into account when assessing children’ skills, particularly during the early school years when age-performance gaps are larger.
In the following, Section II introduces a simple model of human capital accumulation and outline our empirical strategy. In Section III we describe the data. Section IV presents the results and connects our main findings to the conceptual framework. Section V concludes.
II. Methods
We outline a simple model of human capital accumulation that serves to help us understand how different types of parental investment might respond to early shocks. Then we describe the empirical strategy we use to estimate the causal effect of early disparities on children’s outcomes and parental investments.
A. Conceptual Framework
We present a conceptual framework that describes the mapping of early childhood shocks and parental investments into a child’s future human capital, building on multiple studies from the related literature (for example, Almond, Currie, and Duque 2018; Boneva and Rauh 2018; Cunha, Heckman, and Schennach 2010; Francesconi and Heckman 2016).
We consider a simple model with two periods, where the first period is childhood and the second is child i’s young adulthood. Child i’s human capital in the second period is determined by the following production technology,5
where θ0i represents endowed skills, 
are monetary investments made by parents of child i (such as school related expenditures) in Period 1, 
is child i’s parent time investment (such as mentoring activities) in Period 1, and ζ1i is a shock during childhood (for example, a skill advantage in the first grade). We assume that h(·) is differentiable, monotone, weakly increasing, and concave in 
Parents have an expectation about the level of human capital that their child will achieve in adulthood, which depends on their beliefs about child i’s skill endowment. We introduce these beliefs to point out that parents decide to invest considering their child’s expected human capital in adulthood, which may differ from the human capital that they finally acquire (h2i). Importantly, it may be the case that the shock ζ1i does not change the skill endowment of child i, θ0i, but does change parents’ beliefs about it.
Parents choose optimal monetary and time investments 
in their child during the childhood period (for example, spending additional time on educational activities or investing additional money on school related items), to maximize their own utility subject to the production technology, and their own budget, and time constraints.6
Given these optimal investment decisions, the effect of an early shock on human capital in the next period can be decomposed as,
The total effect, A, equals a direct effect of an early shock, B, which can be mitigated or reinforced through behavioral effects of different investment decisions, C and D. We assume that human capital is weakly increasing in investments, so the sign of C and D is determined by how parental investments respond to the shock. An investment decision is reinforcing when it increases investment in response to a positive shock, while a compensating strategy consists in parents increasing investment as a response to a negative shock.
Parents might respond to shocks differently by type of investment. We hypothesize that the response would differ by the productivity of each investment given the shock and socioeconomic background of the family. Our rich data and research strategy allow us to test these hypotheses in our empirical analysis. We outline our empirical strategy below.
B. Empirical Strategy
Our research design resembles a local experiment where children born days apart due to chance start primary school at different ages and thus with very different sets of skills at school entry. In Figure 1 we show that there are large differences between older and younger children in a host of tests, measured just before starting school. The age differences translate into skill gaps, measured in standard deviation units (σ) that range from 0.52σ to 0.86σ on a battery of tests commonly used in the early childhood literature (for example, Rubio-Codina et al. 2016).
Baseline Differences in Skills
Notes: Figure 1 plots mean differences (with 95 percent confidence intervals) on a host of tests for July- and June-born children, measured just before they start their respective first grade. Due to the birth date cutoff rule, July-born children are about a year older than June-born children at school entry. The y-axis shows the measure of different tests and subjects measured. The TADI test is the Test de Aprendizaje y Desarrollo Infantil, a test developed by Chilean research centers that specialize in early life development measures. The HTKS test is the Head, Toes, Knees, and Shoulders exam; the PPVT test is the Peabody Picture Vocabulary Test, and the Battelle test corresponds to the Battelle Developmental Inventory for Young Children. The data come from the Encuesta Longitudinal de Primera Infancia (ELPI), a nationally representative longitudinal survey that follows cohorts of children since birth until early youth.
Our empirical strategy takes advantage of the birth date cutoff rules in Chile, which states that prospective students who are not six years old by June 30 of the academic year should start in the next one.7 We employ a regression discontinuity (RD) design using exact birth dates for children born in June and July to compare outcomes between children born days apart but with very different skill levels at school entrance.
Our identifying assumptions are standard for RD designs. Essentially, we assume that there are no other changes occurring at the threshold that could confound our analysis. In Online Appendix A, we run a series of robustness tests showing that there are no differences in a host of different covariates at the cutoff and no evidence of manipulation of birth dates around the threshold, and our estimates are stable to using different bandwidths and specifications.
Our main estimating equation is
1The variable Zi is equal to one if child i is born in July and is equal to zero if child i is born in June of the same year. f(Bi) is a function of birth date (Bi) interacted with Zi to allow for different slopes on each side of the cutoff. We cluster standard errors within birth date. We also include a set of predetermined variables as controls in Xi, such as child gender, measures of household socioeconomic status, class size, school rurality, and type of school. All these control variables behave smoothly near the cutoff (Online Appendix A.2) and serve mainly to improve precision of our RD estimates. We also add year of birth indicators to control for secular trends common to all children.
Our parameter of interest is α1, which is the intention-to-treat effect of starting school older—with a skill advantage—on the outcome Yi. We restrict ourselves to these reduced-form effects and do not “scale up” our estimates instrumenting starting age with the threshold because in that case we would need the LATE additional assumptions to hold.8
We still consider carefully whether there could be a potential violation of the monotonicity assumption in our setup, as described in Barua and Lang (2016) and eloquently addressed in Dhuey et al. (2019). While monotonicity is not directly testable, we make three points aiming to moderate this concern.
First, we include a time trend at the daily level. Dates of birth are often only available aggregated at some level, say at a monthly, quarterly, or annual frequency level. In RD designs for these cases, outcomes in very narrow bins just to the right and left of the cutoff point cannot be compared (Lee and Lemieux 2010), suffering a higher risk of monotonicity violations. In our setup, we feed our regression discontinuity design with exact birth dates, available at the daily level. Aided by having many observations per day, we include a time trend at the daily level, which substantially reduces the potential of monotonicity violation because the estimated effect is computed at (an infinitely small approximation of) the threshold.
Second, our estimations include controls that resemble endowments. As Dhuey et al. (2019) highlight, potential monotonicity problems might also arise due to essential heterogeneity (Heckman, Urzua, and Vytlacil 2006). Therefore, we control for proxies of endowments that might help address that essential heterogeneity, like proxies of socioeconomic status and measures of paternal and maternal schooling.
Third, we implemented a sibling fixed-effects strategy. Even after controlling for socioeconomic status and parental schooling, there might be some other unobservable factors playing a role. To address this concern, we gathered the necessary additional administrative records and implemented a sibling fixed-effects design to address this potential issue, as proposed by Dhuey et al. (2019).
As a final methodological point, we estimate Equation 1 on many outcomes and therefore simultaneously test multiple hypothesis. To account for the probability of incorrectly rejecting one or more null hypotheses belonging to a family of hypotheses, we follow Anderson (2008) and adjust our standard errors controlling for the family-wise error rate. In the next section, we describe the rich administrative records that we use to implement our empirical strategy.
III. Data
We use administrative data provided by the Ministry of Education (MINEDUC) for the population of students in Chile supplemented with test scores, parental surveys, and student surveys. We link students across their entire school life using an encrypted national identification number and follow them as they complete high school, take the college entrance exam, enroll in higher education, and graduate from college. We describe our data below.
A. Sources
Our primary data source comes from administrative data sets with yearly information on the population of students in primary school (first to eighth grade) and high school (ninth to 12th grade) since year 2002 and up to 2019. Each data set provides individual data on exact birth date, gender, school characteristics, and in-school outcomes like GPA and passing rates.
We supplement these data with standardized test scores from the SIMCE (Sistema de Medicion de Calidad Escolar) exam, accompanied by parent and student surveys administered in the fourth grade. We use the surveys to measure parental investments, which we describe in detail in the next subsection. We further combine these data with three additional sources of information to measure long-term outcomes. The first comes from the national college entrance exam (Prueba de Selección Universitaria, PSU) for years 2004–2018. The exam is taken at the end of the high school senior year and is required for admission to most universities in the country.9 The second and third sources are further administrative data sets on higher education enrollment and graduation, respectively. The data is available for years 2007–2019. Each year, the MINEDUC collects information from all higher education institutions in the country and produces individual-level lists of all students and graduates with information on major, area of study, and institution.
B. Measures of Parental Investments and Beliefs
We use two surveys to measure parental investment. In one survey, parents provide information on investment in school related items. For example, if they have a computer or internet at home, the number of books they own, and the money they spend every month on their child’s education. We define binary indicators for these last two variables because they are reported in brackets. We label these variables “ten or more books” and “higher spending,” each of which equals one for half of respondents and zero otherwise. About half of parents report to spend more than CLP10,000, which is the threshold we use as a proxy for “higher” spending.10 Our results are robust to other ways of grouping items of investments, as we show in Online Appendix B.4.
In a separate survey, students are asked about the time spent with their parents on educational activities. Children report on a 1–4 Likert scale whether their parents help them study or with their homework, help them understand difficult subjects, whether parents know their grades, and whether parents demand improving grades. Available answers for each item are on the scale of “Never,” “Sometimes,” “Most of the time,” and “Always.” We generate variables that equal one if the child answered that their parent does each activity “Always” and zero otherwise. As with financial investments, our analyses are robust to how we group answers.
Figure 2 shows descriptive nonparametric plots of the raw data relating financial and time investment variables to test scores (in standard deviation units). Figure 2A shows that parental financial investments are positively correlated with test scores. Figure 2B also shows a positive correlation between test scores and measures of whether parents always know and congratulate children for their grades. The figure shows a flatter, slightly U-shaped correlation between test scores and measures of whether parents demand good grades, help with homework, and help them study.
Parental Investments, Beliefs, and Test Scores
Notes: The graphs in Figure 2 plot measures of parental investments and beliefs within equal sized bins of fourth grade test scores (math–language average, in standard deviation units). The y-axis variables are all binary in Figure 2A, Figure 2B, and Figure 2C. The variables in Figure 2A are our measures of parental financial investments (having a computer, internet connection, more than ten books at home, and spending above the median on educational items). The variables in Figure 2B are our measures of parental time investments, each of which takes a value of one if the child answered that their parent does each activity “always” and zero otherwise. The variables in Figure 2C are our measures of parental expectations, where parents report their beliefs about child’s expected educational attainment.
We also generated two summary variables for each type of parental investment. The first is a simple average of all investments within type, which is plotted as “Average Index” in Figure 2A and Figure 2B, respectively. The second is a “Factor Index” computed using principal components, which reduces the dimensionality of the investment measures to one composite score. We provide details of the composite score computation in Online Appendix B.3.
Parents also report their beliefs on their child’s educational attainment in the future. We plot their answers against test scores in Figure 2C. Each answer takes the value one when the parent reports that the child will attain at least the respective level of education. The data show a positive correlation between higher expected educational attainment and test scores. The lower correlation comes from parents who expect their child to complete at least technical high school diploma because a high fraction (more than 90 percent) think children will reach that educational level.
C. Long-Run Outcomes
Our main long-run outcomes are take-up rates and scores of the national college entrance exam, college enrollment and college graduation. We construct take-up and scores of the entrance exam measuring them up to age 20 for first-graders. The college entrance exam is taken by the end of high school senior year, when students are approximately 17–18 years old. While every year some test-takers are older (the test-taker median age is 19 years old), a very small fraction of all test-takers (less than 5 percent) takes the test after turning 20 years old. Therefore, measuring take-up at age 20 is a good proxy of ever taking the entrance exam.
We measure college enrollment similarly for first-graders. We define college enrollment as the rate of students who enroll as freshmen in any college in the country. As for the entrance exam take-up, a very small fraction of freshmen are older than 20 years old. We also measure enrollment at selective institutions. The selective universities are nonprofit institutions, grouped in the Council of Rectors of the Universities of Chile (CRUCH), which receive students with highest scores in the country. Finally, we measure college graduation as the rate of students who graduated from any college in the country at age 27.
D. Working Sample
We study two sets of student cohorts. The first cohorts correspond to first-graders in years 2002–2005 (born 1996–1998), and the second cohorts consist of eighth-graders in the same years (born 1989–1991). The data permit measuring outcomes up to age 20 for first-graders because the youngest first-graders were born in 1998, and we have data up to year 2019. Analogously, the younger eighth-graders were born in 1991, and hence we can follow them until they are 27 years old in 2019.
We build our working samples for first-graders and eighth-graders as follows. After excluding the 7 percent of children enrolled in private schools who do not use the July 1 cutoff to enroll students, our administrative records contain approximately one million children in first grade (N = 987,264) and eighth grade (N = 1,048,983). The first sample is composed of first-graders born in June and July from years 1996–1998, and the second contains eighth-graders born in June and July, 1989–1991. Figure 3 shows our research design for first-graders. Those born in July just missed the cutoff date and therefore would start first grade in the next academic year. For example, those born in June 1996 would start the first grade in 2002, while those born in July of the same year start in 2003. We exploit the three discontinuities occurring between June and July from years 1996–1998 and pool our sample according to month of birth (June or July) in year T, and school starting date, in year T + 6 or year T + 7. We control for cohort fixed effects in our analyses.
Research Design for First-Graders
Notes: Figure 3 illustrates our research design for first-graders. About 19,000 children were born in either June or July in 1996–1998. According to the age-at-entry rule, those born in June from year T should start the first grade in year T + 6, while July-born children should start in year T + 7.
Ideally, we would like to have birth records to avoid attrition between birth and first grade enrollment. In addition, if that attrition was differential by month of birth, it would also affect the internal validity of our analysis. We believe that neither is an important problem in the Chilean context because first grade enrollment is mandatory, and compliance is very high nationwide. According to official vital statistics (MINSAL 1996), the number of births was close to 21,000 each month for the years we study. If we exclude 7 percent of the children (those enrolled in private schools), the total number of monthly births is very close to our sample of 19,000 per month. Further, the same source indicates that the number of births was evenly distributed by month of birth, as we also find in our data with first grade enrollment.
E. Summary Statistics
Table 1 presents mean characteristics for students in our working samples. Column 1 presents values for our working sample of first-graders, while Column 2 does the same for the total population of first-graders as a benchmark. Columns 3 and 4 describe eighth-graders analogously. Overall, Table 1 shows that our working samples and the student population are fairly similar in a host of individual and school baseline characteristics, suggesting that results using our working samples are not prone to external validity bias (Andrews and Oster 2019). Table 1 also suggests that births are uniformly distributed by month because half of the students in our working samples were born in June and half in July, and the fraction born each month is 8 percent of the respective benchmark population. This result is consistent with the fact that each month of a given year accounts for approximately 8.3 percent of the births.
Summary Statistics
The descriptive statistics situate the sample in a context of a middle-income country. For instance, average parental schooling is close to 11 years, which is less than the 12 years needed to get a high school diploma. Levels of schooling in Chile are higher today,11 but our data describe students and their parents about 15 years ago, when the country exhibited lower levels of development. The average class size for first-graders is about 30 students and 32 students for an average eighth grade class, which again are similar to rates in developing countries. For reference, at about the same time (in the mid-2000s), the class size in primary school was 21 in the United States and 27 in Türkiye (OECD 2019).
The data also show that about half of the sample are girls, and students attend schools with a vulnerability index close to 30, on average. This index ranges between zero and 100 and resembles the percentage of students receiving free or reduced-price lunch, like the index often used in the United States as a proxy for poverty. In Chile, this index is computed by the government agency responsible for school meal programs (National School Assistance and Scholarship Board, JUNAEB).12 Approximately 37 percent of the students attend schools within the Metropolitan Region, which includes the national capital, Santiago, and 14 percent of first-graders and 11 percent of eighth-graders attend schools in rural areas. Finally, 52 percent of first-graders and 57 percent of eighth-graders attend public schools, with the remaining fraction attending voucher schools.13
IV. Results
We start by briefly presenting results on in-school outcomes to focus then on the effects on parental investments and beliefs. Then we describe our estimates on long-run outcomes, and we finish the results section discussing our findings by socioeconomic status.
A. In-School Effects
In Figure 4 and Table 2, we present effects on in-school outcomes for our sample of first-graders. July-born children start the first grade 0.48 years older than their June-born counterparts (see Figure 4A), so they are more likely to enjoy a skill advantage over those who start younger, as discussed previously and depicted in Figure 1. Figures 4B, 4C, and 4D show that a skill advantage in the first grade translates into higher GPAs (0.26σ) and higher passing rates (2.4 percentage points) in the first grade and higher test scores (0.21σ) in the fourth grade. These results on in-school outcomes are consistent in direction and magnitude with the related literature. In the next sections, we complement the findings on educational outcomes exploring how parents react to these perceived signals of children ability. We then supplement the short-run effects during school with estimates of long-run outcomes.
In-School Effects
Notes: The graphs in Figure 4 are graphical analogs to estimates in Table 2. Each graph plots the mean of the y-axis variable within day of birth and fits estimated lines using all the underlying data, allowing for different slopes on each side of the cutoff. Each day of birth contains about 2,000 observations.
In-School Effects
B. Effects on Parental Investments and Beliefs
1. Investments
Figure 5 summarizes our main findings on parental investments. Figure 5A shows that July-born children receive 3.4 percentage points (∼0.11σ) of additional financial investments, while Figure 5B shows no effects on time investments. Going back to our conceptual framework, these findings suggest that parents reinforce skill gaps using financial investments, but do not use time investments to respond to differences in school performance.
Effects on Parental Investments
Notes: The graphs in Figure 5 are graphical analogs to estimates in Column 1, Panels A and B, in Table 3. Each graph plots the mean of the y-axis variable within day of birth and fits estimated lines using all the underlying data, allowing for different slopes on each side of the cutoff. Each day of birth contains about 2,000 observations.
We present the corresponding point estimates in Table 3. In Online Appendix B (Sections B.1 and B.2), we provide details on sample sizes and robustness checks. Panel A in Table 3 shows the results for financial investments. Column 1 shows the effect on the average index, plotted in Figure 5A. Parents increase average financial investments by 3.4 percentage points, which represents an effect of 0.11σ. In Column 2, we show the effect on the factor index, which shows the same effect of 0.11σ. Next, Columns 3–6 show the effects for each investment variable separately. July-born children are 10 percent (4.3 percentage points over 40 percent) more likely to have a computer at home, 20 percent (3.2 percentage points over 16 percent) more likely to have an internet connection, and 8 percent (3.7 percentage points over 48 percent) more likely to have ten or more books at home. In addition to investing in more educational assets, parents are 5 percent (2.2 percentage points over 48 percent) more likely to spend above the median of monthly expenditures for school items in our sample.
Effects on Parental Investments
We examine parental responses in terms of time investments in Panel B of Table 3. Column 1 shows that the estimate on the average index, plotted in Figure 5B, is a precise zero (0.4 percentage points over a mean of 64 percent). The factor index effect is of 0.01σ and not different from zero, as shown in Column 2. These results are consistent with the much smaller if not zero correlation between the index of time investments and test scores in Figure 2B.
When revising effects for each variable, we also find precise zero effects on whether parents congratulate their child for good grades (mean of 81 percent) and whether they know their grades (75 percent). This is despite the strong positive correlation between these variables and test scores shown in Figure 2B. We also find precise zeros on whether parents demand good grades (mean of 53 percent for both groups) and whether they help with study (56 percent). Finally, we find a small positive effect on whether parents help with homework (two percentage points over a mean of 57 percent).14
2. Beliefs
Parents of July-born children also have higher expectations about their child’s educational future, driven by beliefs on children completing postsecondary degrees, as we show in Table 4 and Figure 6. Parents are more likely to believe that their child will complete college (4 percent, or 2.1 percentage points over 53 percent), graduate school (13 percent, or 1.2 percentage points over 8.7 percent), and a four-year degree at a technical institute (2 percent, or 1.3 percentage points over 67 percent). We found no effects on beliefs on high school completion or technical high school completion (Columns 5 and 6). We hypothesize that these expectations about high school graduation are harder to move because they are already set at a high level.
Effects on Parental Beliefs
Notes: The graphs in Figure 6 are graphical analogs to estimates in Columns 1 and 2 in Table 4. Each graph plots the mean of the y-axis variable within day of birth and fits estimated lines using all the underlying data, allowing for different slopes on each side of the cutoffs. Each day of birth contains about 2,000 observations.
Effects on Parental Beliefs
These empirical findings are consistent with beliefs responding positively to signals about the child’s ability, which parents have been receiving between first and fourth grade. As documented in Section IV.A, July-born children started by chance with a skill advantage over those who started younger, and we know that parents are aware. Survey data from SIMCE indicate that 75 percent of students report that their parents know their grades (Panel B, Column 4 in Table 3). The fact that parents of July-born children are mostly aware that they perform relatively well (and the opposite for parents of June-born children) seems to translate into higher expectations about their educational long-term outcomes.
C. Long-Run Outcomes
Figure 7 summarizes our main effects on long-run outcomes. Following up children until they are 20 years old, we find that the early skill gaps lead to higher college entrance exam take-up and scores, and higher college enrollment rates both overall and at selective programs.
Effects on Long-Run Outcomes
Notes: The graphs in Figure 7 are graphical analogs to estimates in Columns 3 to 6 in Table 5. Each graph plots the mean of the y-axis variable within day of birth and fits estimated lines using all the underlying data, allowing for different slopes on each side of the cutoff. Each day of birth contains about 2,000 observations.
We show our point estimates in Table 5. Column 3 presents the estimate corresponding to Figure 7A showing that July-born students are 6 percent (3.6 percentage points over a mean of 58 percent) more likely to take the national college entrance exam.
Effects on Long-Run Outcomes
Conditional on taking the test, students with an early skill advantage score 0.08σ higher, as shown in Figure 7B and in Column 4 of Table 5. We interpret this effect as a lower bound because, among non-test-takers, those who start school with a skill advantage would arguably have performed better had they taken the test. In any case, if there are positive effects on the college entrance exam (taking the exam or scoring higher), these should translate into effects on college enrollment.
The next results indeed show effects on multiple measures of college enrollment, reported in Columns 5–8 in Table 5. We find a 15 percent increase (3.7 percentage points over a mean of 25 percent) in college enrollment (see Figure 7C) for July-born students, which is consistent with the positive effects on the likelihood of being a test-taker. Meanwhile, the increases on enrollment at more selective universities (20 percent, 2.8 percentage points over a mean of 14 percent, see Figure 7D) and STEM programs (14 percent, one percentage point over a mean of 7 percent) are consistent with higher scores on the college entrance exam.
Finally, we use our sample of eighth-graders to estimate effects on college graduation later. The last column of Table 5 shows a precisely estimated effect of 0.7 percentage points, which represents an effect size of 4 percent (0.7 percentage points over a mean of 16.5 percent). On average, a share of 16.5 percent of both June- and July-born students obtain a college degree by age 27. These rates are similar to back-of-the-envelope computations from official reports by MINEDUC on higher education completion rates (MINEDUC 2019).
D. Effects by Socioeconomic Background
Figure 8 and Table 6 summarize our main results on parental investments, beliefs, and children long-run outcomes by socioeconomic status (SES). The main takeaway is that effect sizes on financial investments and college related outcomes are larger for lower SES children, with a clear negative SES gradient in most outcomes.
Effect Sizes by Socioeconomic Status
Notes: Figure 8 plots effect sizes (with their standard errors) on parental investments, beliefs, and children’s long-run outcomes by quartiles of the school vulnerability index. Financial and time investments are each measured by the average index described in Section III.B. Parental beliefs are measured as college completion expectations. The long-run outcomes are the college entrance exam take-up and scores, college enrollment (overall and at selective institutions), and college graduation.
Effect Sizes by Socioeconomic Status
We divide the sample of students into quartiles of the school vulnerability index and label each quartile as low SES, medium-low SES, medium-high SES, and high SES, accordingly. In this section, we present our findings using effect sizes as they are informative of the relative importance of the effects for each SES group.
We show results for financial and time investments using the respective average index described in Section III.B and using college completion expectations for parental beliefs. In Online Appendix C, we include results for each individual measure of investment and beliefs, which behave similarly to the summary measures presented here. Long-run outcomes consist of the college entrance exam take-up and scores, college enrollment (overall and at selective institutions), and college graduation.
1. Parental Investments and Beliefs
The effects on parental financial investments display a steep, negative SES gradient. The effect sizes are three times as large for the low SES versus the high SES group (19 vs. 6 percent). Our estimates on time investments are close to zero, with no distinguishable differences across groups. This result suggests that the average null effect shown in Table 3 did not hide differential effects by socioeconomic status.
Effects on parental beliefs, measured as college expectations, are decreasing by socioeconomic status but measured noisily. There is a difference of 4.6 percentage points between the low and high SES groups that we cannot distinguish from zero.
2. Long-run outcomes
Our estimates on the college exam take-up show an effect of 9 percent for low SES students, about 6 percent for students in the medium-low and medium-high group, and 4 percent for high SES students. Test scores increase similarly by about 0.08σ for each group, but from a lower baseline score for the more disadvantaged SES groups (that is, –0.42σ for low SES vs. 0.37σ for high SES). Thus, we expect a relatively larger impact on college enrollment among lower SES students.
Consistently, for college enrollment, we find effect sizes of 27 percent for the low SES group, 15 percent for the medium-low and medium-high SES, and 11 percent for the high SES group. This pattern is also present in our measures of enrollment at selective programs, with effects of 37 percent for low SES and 13 percent for high SES students. Finally, the results also show that the null average effect on college graduation in Table 5 was masking large SES differences. Low SES students with a skill advantage are 23 percent more likely to graduate from college versus a noisily estimated 3 percent for the higher SES group.
E. Are Parental Investments and Beliefs Mediating Long-Run Results?
1. Conceptual Framework
Our empirical results show that the long-run effects of an early skill advantage are positive and large. For example, the probability of college enrollment increases by 15 percent overall. In our conceptual framework, we decompose the global effect (A) into a direct effect component (B) and two components related to monetary and time investments, C and D, respectively. Our findings show that monetary investments reinforce the shock (that is, C is positive) while time-intensive investments are neutral (that is, D is zero). This result suggests that the overall effect of a skill advantage at school entry, A, is explained by a direct effect and by reinforcing financial investments from parents, B + C.
In our model, optimal investments of parents are a function of beliefs about their child’s abilities. Our empirical finding shows that parents have higher beliefs about their child’s future human capital if they benefited—by chance—from an early skill advantage. This result is consistent with parents interpreting in-school performance as signals of their child’s ability and adjusting their investments according to their perceived productivity.
Such a mechanism is in line with Attanasio et al. (2020), who show that investments vary according to parental beliefs on heterogeneity of returns to such investments. In our context, parents may perceive that investing in books, a computer, or other school related materials can be productive to complement the skills of children with higher grades. Our null results on time-intensive investments suggests that parents perceive their productivity to be similar for children with different skills at school entry.
2. Mediation Analysis
We further explore to what extent parental beliefs and investments might be mediating long-run effects, applying methods from the latest related literature (Fagereng, Mogstad, and Rønning 2021), building on Heckman, Pinto, and Savelyev (2013).
As described elsewhere (see, for example, Almond and Mazumder 2013), we readily acknowledge that identifying the interactions between shocks and investments would require an exogenous variation on investments. Examples of recent papers studying these types of interactions are Duque, Rosales-Rueda, and Sanchez (2019); Johnson and Jackson (2019); Malamud, Pop-Eleches, and Urquiola (2016); and Rossin-Slater and Wüst (2019).15
We follow Fagereng, Mogstad, and Rønning (2021) making explicit assumptions in a mediation model.16 We adapt their model of mediation to our setup and empirically compute the parameters associated to our mediators. While we see this exercise as mostly descriptive, it provides an approximation of how much different channels (investments, beliefs, and the skill gap itself) might be contributing to differences in outcomes.17 In Online Appendix D, we present our mediation model and describe the estimation results in detail.
We find that our mediator variables (parental investment and beliefs) explain nearly 34 percent of the causal effect on college enrollment, while 66 percent is explained by the direct effects of the early skill gap (Figure 9A). As a benchmark, Fagereng, Mogstad, and Rønning (2021) find that their mediators (mainly parental wealth transfers) explain about 37 percent of the causal effect of having wealthier parents on children’s accumulation of wealth.
Effect of Starting School Later—Direct and Indirect
Notes: Panel A decomposes the causal effect of starting school later into shares of direct effect and an indirect effect (mediated by investments and beliefs). Panel B shows how much of the indirect effect can be attributed to financial investments made by parents.
Parental investments account for almost two-thirds of the mediated effect (Figure 9B), indicating that they account for a sizable fraction of the effect on children’s long-run outcomes. The last section of Online Appendix D shows that these results are robust to imposing a range of different assumptions on the mediation model.
3. Children within Same Families
We also study whether our main results are driven by family characteristics. The logic is that even after controlling for socioeconomic status and parental schooling, there might be some other unobservable factors playing a role in our estimated effects on parental investments, beliefs, and long-run outcomes.
We gathered the necessary additional administrative records and implemented a sibling fixed-effects design to address this potential issue, analogous to Dhuey et al. (2019). In Online Appendix E, we describe in detail the data and the related empirical strategy and report the results. The estimates from this sibling fixed-effects strategy are essentially the same as in our main specification, suggesting that our main results are not driven by family characteristics.18
V. Conclusion
We study the effects of having an early skill advantage at school entry on different types of parental investments and beliefs and children’s long-term outcomes. We combine rich administrative records with a regression discontinuity design in a middle-income country and interpret our results within a human capital accumulation model.
Children who—by chance—start school older perform better on in-school assessments. Parents causally react with stronger beliefs about the future schooling attainments, apparently interpreting these results as signals of their child´s ability. While parents do not appear to invest time differentially, they do reinforce the initial performance gaps by investing additional material resources in children benefited from the early age skill advantage. These reinforcing investments are more pronounced for children from lower socioeconomic backgrounds.
We further document that the early skill advantage translates into higher rates of college enrollment, with larger effects for low socioeconomic status students as well. The magnitude of these effects is within those found by the early childhood interventions literature (see, for example, Elango et al. 2015), suggesting that policy rules affecting early skills can be as important as programs designed to bolster children’s capacities.19 Overall, these results add to the literature by emphasizing that early skill gaps can have sizable and heterogeneous consequences in adulthood.
Our results have direct policy implications. Age-at-entry rules may generate noisy signals of skill because high-ability young starters might signal low ability. Due to their age, they perform worse on tests early on in school and hence receive less investments than their older, high-ability equivalents. These noisy signals could disappear if adjusted by age, but parents and children themselves observe and react based on the unadjusted in-school differences. The most direct policy recommendation would be to make parents aware of the age differences, providing them with both raw and age-adjusted measures of children’s performance. Schools could implement this recommendation by training teachers to communicate and help parents interpret the assessments of their child’s skills, particularly during the early school years.
From a broader perspective, our findings suggest that if parents simply perceive that their children are of higher ability, then they will invest more. This behavior shows up in the school starting age setup but could also generalize to many other sources of signals. For example, having a teacher who is encouraging and positive versus another teacher who is more negative about the same child’s skills could improve parental investments.
Finally, our findings underscore the importance of advancing the research agenda connecting parental beliefs and types of investments with children’s long-run outcomes.
Acknowledgments
The authors thank Philip Oreopoulos, Christopher Neilson, Arnaud Maurel, Susan Mayer, Pietro Biroli, Maria Fernanda Rosales, Oscar Mitnik, Diego Vera, Josefa Aguirre, and seminar participants at the University of Chicago, Princeton University, the Inter-American Development Bank, and the APPAM and SREE annual meetings for helpful comments. This paper is dedicated to the memory of their professor Robert J. LaLonde. The authors also thank the Ministry of Education of the Government of Chile and the DEMRE at Universidad de Chile for access to the sources of information. Gallegos thanks the Inter-American Development Bank (SPD/SDV), the Center for Studies of Conflict and Social Cohesion (ANID/FONDAP/1523A0005), and support from ANID (FONDECYT/Iniciacion/11220263). Celhay acknowledges financial support from ANID (FONDECYT/Regular/1221461) and support from ANID (PIA/PUENTE AFB230002). All errors are those of the authors; the views expressed in this paper are those of the authors and should not be attributed to the Inter-American Development Bank or to any other institution. The data used in this article can be obtained from the respective websites at http://datosabiertos.mineduc.cl/ and http://investigador.demre.cl/.
Footnotes
↵1. Parental investments in children have been a topic of study for a long time (for example, Becker and Tomes 1976 and Behrman, Pollak, and Taubman 1982), but interest has risen sharply in more recent years. See, for example, Francesconi and Heckman (2016), Doepke and Zilibotti (2017), and Attanasio, Meghir, and Nix (2020). The recent literature on parental investments has studied beliefs about their returns (for example, Carneiro et al. 2019; Boneva and Rauh 2018; Cunha, Elo, and Culhane 2013), information frictions (Dizon-Ross 2019), time and budget constraints (for example, Bono et al. 2016; Dahl and Lochner 2012), preferences (for example, Beuermann and Jackson 2020; Bharadwaj, Eberhard, and Neilson 2018), and the use of behavioral tools to promote investment in children’s human capital (Mayer et al. 2019; Kalil, Mayer, and Gallegos 2021).
↵2. Our paper complements the article by McEwan and Shapiro (2008), who studied in-school effects for first and fourth grades in Chile. While we replicate their results for those early outcomes, our contribution focuses on effects on different parental investments, long-run outcomes up to age 27, and a human capital accumulation model relating both. More examples of the wide literature studying in-school outcomes with age-at-entry rules are Attar and Cohen-Zada (2018), Bedard and Dhuey (2006), Calsamiglia and Loviglio (2020), Datar (2006), Elder and Lubotsky (2009), Fletcher and Kim (2016), Foureaux Koppensteiner (2018), Nam (2014), Peña (2017), and Smith (2010).
↵3. Among other factors, previous research has shown that older children have been exposed to more parenting time and are more mature than their younger peers, so they can perform higher in cognitive test scores and can better develop different skills (for example, Black, Devereux, and Salvanes 2011; Deming 2009; Dhuey et al. 2019; Lubotsky and Kaestner 2016).
↵4. We like to highlight that our work contributes with evidence that is still scarcer for developing countries, where endowments are lower and family background effects tend to be comparatively longer-lasting (Celhay and Gallegos 2015, 2022). Most of the related evidence studying age-at-entry effects on long-run outcomes comes from developed countries, like Norway, Sweden, or the United States. See, for example, Black, Devereux, and Salvanes (2011); Cascio and Schanzenbach (2016); Dobkin and Ferreira (2010); Fredriksson and Öckert (2013); and Kawaguchi (2011).
↵5. Since the choice of the production function might govern the response to early childhood shocks (Almond, Currie, and Duque 2018), we do not presuppose a particular functional form for preferences or technology relating human capital to later outcomes. This allows different investments to vary in magnitude and sign as a response to early shocks.
↵6. We explicate the complete model, with the constraints and objective functions in Online Appendix F.
↵7. The National Law #1718 explicitly states that the rule is equally enforced in all schools (voucher and regular public schools) because both receive funding from the government. We expand on this topic in Online Appendix C.1.
↵8. For instance, we would need to defend that the exclusion restriction holds in this setup. See Jones (2015) and Dhuey et al. (2019) for a discussion on this topic.
↵9. We signed an agreement with the agency in charge of developing and administering the exam (DEMRE), which provided us the data with the same encrypted identification number contained in the MINEDUC data.
↵10. The median of educational spending is CLP10,000. It amounts for about one-third of the per student funding provided by the government.
↵11. Chile has reached almost universal levels of educational coverage in primary (99 percent) and secondary school (92 percent), well above most Latin American countries (OECD 2019).
↵12. For details, see JUNAEB’s webpage at http://junaebabierta.junaeb.cl/catalogo-de-datos/indicadores-de-vulnerabilidad/ (accessed August 28, 2024).
↵13. Public schools are both publicly funded and administered. Voucher schools receive public funding but are privately managed, like charter schools in the United States.
↵14. It is possible that more refined information (for example, a more concise time use survey) would help us in confirming that parents do not change their time investments at the intensive margin.
↵15. In the absence of an additional instrument to correct for endogenous parental behavior, other papers jointly model parental behavior and interventions or shocks in structural models used to isolate parameters of parental behavior from the human capital production function. One examples of a recent paper in this area is Attanasio et al. (2020).
↵16. We thank the authors for sharing their programs and code.
↵17. We thank the referees for this suggestion.
↵18. These results also suggest that potential monotonicity violations are not playing an important role in our setup. The findings are consistent with Dhuey et al. (2019, p. 13), who write that “…it is clear that controlling for family characteristics and behavior does not substantially affect the estimated relationship between school starting age and test scores.”
↵19. Elango et al. (2015) provide an excellent review of these programs. For Head Start, Currie, Thomas, and Garces (2002) show that there is a marginally significant increase of 9 percent in the probability of attending college when they compare Head Starters to non-Head Starters. Likewise, Ludwig and Miller (2007) find that Head Start increases the likelihood of attending college by 5 percent. Deming (2009) shows that the same program increases the probability of attending college by approximately 10 percent. Anderson (2008) shows that participants of the Perry Preschool Program are 21 percent more likely to attend any college.
- Received September 2020.
- Accepted May 2022.
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