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Intergenerational Impacts of Secondary Education: Experimental Evidence from Ghana

Mon, 01 Jan 0001 00:00:00 +0000

This paper provides experimental evidence on the intergenerational impacts of secondary education subsidies in a low-income context, leveraging a randomized controlled trial (RCT) conducted in rural Ghana with a 15-year longitudinal follow-up. The study exploits a 2008 scholarship lottery in which 682 students — drawn from 2,064 rural youth who had been admitted to public senior high school but had not enrolled due to financial constraints — were randomly selected to receive four-year secondary school scholarships covering full tuition and fees. Scholarship receipt increased senior high school completion by 27–28 percentage points for both men and women (from 39.8% to 67.2% for women; from 49.7% to 77.9% for men), and raised average years of education by 1.33 years.

The central research question is whether secondary education subsidies generate intergenerational benefits — specifically, whether children of scholarship recipients have better survival and cognitive development outcomes — and what mechanisms drive any such effects.

For female scholarship recipients, the scholarship significantly altered fertility timing and partnership. By 2013, female recipients were 6.9 percentage points less likely to have ever been pregnant (on a control-group base of 48.3%), with the decline driven almost entirely by a 7 percentage point (17%) reduction in unwanted pregnancies. Though total fertility eventually caught up by 2022, recipients were still less likely to be married or cohabiting as of 2019 and were significantly more likely to have a partner with tertiary education.

Children of female scholarship recipients experienced substantially lower mortality. Among control-group female respondents, 3.5% of children died before age one and 4.0% before age three. These rates fell to 1.7% (p=0.028) and 2.2% (p=0.065) respectively among children of female recipients — a roughly 45–51% reduction in under-one and under-three mortality.

Child cognitive development gains emerge only once children reach school age. Children of female recipients show no significant cognitive score differences at 18 months, 2.5 years, or 3.5 years, but score 0.238 standard deviations higher at age five (p=0.005) and 0.252 standard deviations higher at age seven (p=0.035). Effects span language, math and numeracy, spatial reasoning, and executive function, but not socio-cognitive development. These effect sizes fall between the 75th and 80th percentile of RCT-based educational intervention effect sizes in low- and middle-income countries.

The primary mechanism is not higher income or greater monetary investment in children. The study finds no significant treatment effect on household SES index (0.107 SDs, p=0.103), no impact on formal schooling inputs, and no difference in parental aspirations or knowledge of child stimulation’s importance. Instead, more-educated mothers seek more prenatal care, engage in more preventive health behaviors, and — critically — spend more time interacting with their children in stimulating ways. Day-long LENA (Language Environment Analysis) recordings at 18 months confirm 20% more adult-child conversational turns per minute (effect size 0.068, p=0.005) and 17% more child vocalizations per minute (effect size 0.32, p=0.014) for children of female recipients.

For male scholarship recipients, no analogous intergenerational benefits appear. Their partners are not more educated (in fact slightly less educated on tertiary rates), their children show no mortality improvement, and cognitive scores are if anything negative at age five (point estimate -0.22, p=0.069). The absence of effects is attributed to male scholarship recipients having caregivers — overwhelmingly mothers — with no more education than in the control group, and to children of male recipients being 8.7 percentage points less likely to live with their father.

A cost-benefit analysis finds internal rates of return (IRR) of 27%–76% for a female-only means-tested scholarship program and 20%–51% for a mixed-gender program. The cost per under-three death averted ($15,184 for female-only) places the scholarship program within the range of the 10th-percentile most cost-effective WHO-recommended child health interventions.

Scope conditions: the study estimates effects for students who qualified for senior high school but faced binding financial constraints in rural Ghana in 2008 — a population that is well-prepared academically but economically disadvantaged. Results may not generalize to students who would not have qualified for secondary school or to contexts where financial barriers are not binding.

Q: What was the experimental design and who was in the study sample? A: In 2008, 2,064 rural Ghanaian students who had been admitted to senior high school (SHS) but had not enrolled — typically due to inability to pay fees — were sampled. After a baseline survey, 682 were randomly selected (approximately one-third) by lottery to receive a four-year scholarship covering full tuition and fees for a day (non-boarding) student, stratified by district, school, gender, and exam-year cohort. The two-thirds comparison group received no scholarship. Students were on average 17 years old at baseline and just over 31 at the last follow-up in Spring 2023.

Q: How large was the scholarship’s effect on educational attainment? A: Scholarship receipt raised SHS completion from 39.8% to 67.2% among women (a 69% increase) and from 49.7% to 77.9% among men (a 57% increase). Overall, the scholarship led to an average of 1.33 more years of education. For women only, it also significantly raised tertiary education: by 2023, scholarship receipt increased tertiary completion by 10.8 percentage points for women, but had no significant tertiary effect for men.

Q: What were the effects on fertility and family formation for female scholarship recipients? A: By 2013, female recipients were 6.9 percentage points less likely to have ever been pregnant (base: 48.3% in control), driven almost entirely by a 7 percentage point (17%) reduction in unwanted pregnancies. By 2019, recipients were still 6 percentage points less likely to have started childbearing and had 0.152 fewer children on average (p=0.065). Total fertility eventually caught up by 2022. By 2016, female recipients were 12.1 percentage points (24% of control mean) less likely to have ever lived with a partner, and by 2019 were 6.2 percentage points less likely to be married or cohabiting. Conditional on having a partner, they were significantly more likely to have a partner who completed tertiary education (p=0.071).

Q: What were the effects on fertility and family formation for male scholarship recipients? A: Male recipients showed few changes in fertility or marriage behavior. They were 7.8 percentage points (30% of control mean) more likely to still be living with their parents as of 2019. Their partners were not more educated; in the cognitive games subsample, treatment actually reduced the share of partners with tertiary education by 3.6 percentage points from a control base of 4.3%.

Q: What were the child mortality results for children of female scholarship recipients? A: Among children of female control respondents, 3.5% died before age one and 4.0% before age three. These fell to 1.7% (p=0.028) and 2.2% (p=0.065), respectively, among children of female recipients — approximately a halving of under-one and under-three mortality. These point estimates are robust to varying the covariates (linear vs. fixed effects for birth year, dropping or adding controls). After multiple-hypothesis testing adjustment using the Romano-Wolf step-down procedure, the p-value for survived-to-one rises from 0.028 to 0.119.

Q: What were the child mortality results for children of male scholarship recipients? A: The estimated effects for children of male recipients were smaller and statistically insignificant: a 1.4 percentage point increase in survived-to-one (p=0.161) and 0.9 percentage points in survived-to-three (p=0.549). These estimates are not significantly different from those for female recipients. Results were sensitive to sample perturbations given the smaller sample: only 26 of 1,016 children of male respondents died before age one.

Q: What child cognitive development gains did children of female scholarship recipients show, and at what ages? A: No significant differences emerged at 18 months (-0.066 SDs, p=0.489), 2.5 years (-0.024 SDs, p=0.850), or 3.5 years (0.026 SDs, p=0.736). Significant gains appeared at age five (0.238 SDs, p=0.005) and age seven (0.252 SDs, p=0.035). Effects span language (0.15 SDs at five; 0.27 SDs at seven), math and numeracy (0.15 SDs; 0.26 SDs), spatial reasoning (0.20 SDs; 0.12 SDs), and executive function (0.25 SDs; 0.20 SDs), but not socio-cognitive development. These effect sizes fall between the 75th and 80th percentile of educational RCT effect sizes in low- and middle-income countries.

Q: What cognitive development effects did children of male scholarship recipients show? A: No significant positive effects emerged at any age. Point estimates were negative at all ages except 18 months, and marginally significantly negative at age five (-0.22 SDs, p=0.069). The difference in treatment effects between children of male and female recipients is statistically significant at age five (p=0.005).

Q: Why do cognitive gains appear only at age five and not earlier? A: The authors offer three interpretations: first, that the cognitive tests for younger children are noisier instruments (cross-sectional and longitudinal correlations within domains are much lower for 1.5-year tests than 5-year tests); second, that impacts on cognitive development may take time to materialize; third, that marginal survivors in the treatment group may start with a cognitive deficit (e.g., surviving a cerebral malaria episode), and maternal education effects require time to overcome this initial handicap. Gains concentrate on skills underlying literacy and numeracy, consistent with more educated mothers bridging home and school environments.

Q: What is the primary mechanism driving intergenerational effects? A: The primary mechanism is changes in parenting behaviors, not income. Female recipients do not invest more money in children (no significant difference in SES index or child investment index). Instead, they seek more prenatal care, engage in significantly more preventive health behaviors, and interact more with their children in cognitively stimulating ways. Day-long LENA recordings at 18 months show 20% more conversational turns per minute (effect size 0.068, p=0.005) and 17% more child vocalizations per minute (effect size 0.32, p=0.014). Caregiver reports confirm more playing, singing, and doing simple mathematics with children.

Q: Does the income effect of scholarship receipt explain the child outcomes? A: No. Duflo et al. (2024) find no significant earnings impacts until 2019 or later, meaning children tested at ages five and seven by 2023 largely grew up before their mothers’ earnings improved. The household SES index shows only a 0.107 SD gain (p=0.103), indistinguishable from the effect for children of male recipients. There is also no evidence of a quality-quantity trade-off: caregivers of scholarship recipients do not have fewer children to care for.

Q: Does the increase in maternal age at birth explain the child mortality reduction? A: It is not the primary driver. Maternal age at birth increases by only 0.349 years on average (p=0.142) for children of female recipients, and 0.64 years for first-born children (p=0.040). Point estimates on mortality for first-born children are somewhat smaller than for the full sample, suggesting maternal age is not the main channel. Moreover, maternal age at birth falls for children of male recipients yet their survival point estimates are positive, which further argues against maternal age as the primary mechanism.

Q: How does the education of the primary caregiver mediate the results? A: For 84% of children in the sample, the primary caregiver is the child’s mother. Children of female scholarship recipients have caregivers who are 25 percentage points more likely to have completed secondary school and 5 percentage points more likely to have completed tertiary education. Children of male scholarship recipients have caregivers with no more education than the control group, because the recipients’ partners — the typical caregivers — are not more educated. Treatment effects for female recipients are not altered when father’s education is added as a control, confirming maternal education as the main driver.

Q: What threat to validity arises from co-residence of the father? A: Children of male scholarship recipients are 8.7 percentage points less likely to live with their father (p=0.024), compared to no such effect for children of female recipients (92% of whom live with their scholarship-recipient mother). LENA recordings show negative treatment effects for children of male recipients — fewer adult words and conversational turns — consistent with father absence mechanically reducing auditory engagement and possibly leaving single mothers less time to verbally interact with each child.

Q: How are multiple-hypothesis testing concerns addressed? A: The pre-analysis plan pre-specified child survival and child cognitive development as primary outcomes. The authors apply the Romano-Wolf step-down procedure for multiple hypothesis testing adjustment. After adjustment, the p-value for survived-to-one for children of female recipients rises from 0.028 to 0.119; the cognitive development effects at age five and seven remain significant.

Q: How does the study address potential sample selection bias in the child outcomes sample? A: The authors use entropy balancing (Hainmueller, 2012) to reweight observations so that baseline (2008) characteristics are balanced between treatment and control within the subsample of recipients who had children. Results are qualitatively unchanged for both female and male recipients. The authors also note that children of female recipients are younger on average (4.71 months, p=0.067), which is why the study collects data at fixed age windows (14-22 months, 2.5 years, 3.5 years, 5 years, 7 years) rather than in a single cross-sectional wave.

Q: What is the cost-effectiveness and cost-benefit result for secondary school scholarships? A: Social costs are estimated at $585 per recipient for a mixed-gender program and $505 for a female-only program (combining school fees, materials, and foregone wages). The cost per under-three death averted is $23,582 for mixed-gender and $15,184 for female-only — placing the female-only program within the range of the 10th-percentile most cost-effective WHO-recommended child health interventions. The IRR is 27%–76% for a female-only means-tested scholarship program and 20%–51% for a mixed-gender program. These are likely conservative, as they exclude welfare gains from avoiding unwanted pregnancies, greater female agency, and recipient health benefits.

Q: What is the scope of the experiment and to what population do findings generalize? A: The study estimates ITT effects for students in rural Ghana who qualified for SHS on exam performance but faced binding financial constraints in 2008 — a population that is academically prepared but economically disadvantaged. Results do not directly apply to students who would not have qualified, to contexts without binding financial barriers, or to settings where secondary school quality or the marriage market differs substantially. The study also cannot yet observe complete fertility, since scholarship-lottery participants were only 31 years old on average at last follow-up.

LENA (Language Environment Analysis): A day-long recording device worn by a child that uses speech recognition software to generate count-based metrics — adult word count, adult-child conversational turns, and child vocalizations per minute — providing an objective measure of the child’s auditory environment and caregiver engagement quality without reliance on self-report.

IRT Score (Item Response Theory Score): A latent-trait measure of child cognitive ability estimated from a one-parameter logistic model applied to binary correct/incorrect responses across cognitive game questions, assigned a difficulty level to each question and a latent ability to each child, then standardized. Used as the primary cognitive development outcome across age windows.

Incarceration Effect: The hypothesis that education delays fertility mechanically only while students are in school (analogous to incarceration preventing activity), with no persistent effect once they exit. The authors rule this out by showing that the fertility gap between female treatment and control groups persists well after the majority of scholarship recipients have graduated.

Quality-Quantity Trade-off (Becker 1991): The economic framework predicting that more educated parents, facing higher opportunity costs of children and lower costs of investing in child quality, will have fewer but better-invested-in children. The authors find delayed and reduced fertility but do not find that recipients have fewer children to care for in the cognitive assessment sample, suggesting the child quality gains operate primarily through parenting practices rather than resource concentration.

Intent-to-Treat (ITT) Effect: The treatment effect estimated by comparing all lottery winners to all losers regardless of whether winners actually enrolled, which captures the effect of the scholarship offer (including compliance costs). The cost-benefit analysis uses ITT estimates, so the cost of subsidizing inframarginal students who would have attended anyway is incorporated.

Entropy Balancing: A reweighting procedure (Hainmueller, 2012) that assigns weights to observations in the control group so that the weighted distribution of baseline covariates matches that of the treatment group, used to assess whether imbalances in the subsample of participants who had children drive the results. The authors apply this as a robustness check for both mortality and cognitive development outcomes.

Unwanted Pregnancy: A pregnancy reported by the respondent as unplanned at the time of conception, which the authors use to distinguish fertility reduction from a change in desired fertility versus a reduction in unintended out-of-wedlock pregnancies. The scholarship’s early fertility impact is almost entirely a reduction in unwanted pregnancies (7 percentage point decline, 17% reduction).

Marginal Returns to Public Universities

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks whether enrolling in an American public university generates positive net returns for marginal students — those who barely qualify for admission — and whether those returns justify public expenditures. The question is policy-relevant because marginal students have weak academic preparation, face high dropout risk, and the net returns to expanding admission margins are theoretically ambiguous.

The author assembles administrative records spanning all 35 public universities in Texas, covering the universe of Texas public high school graduates from 2004–2014 (approximately 2.7 million students). Texas public universities collectively enroll over 10 percent of all American public university students. The data link high school records (test scores, demographics, coursework, attendance, disciplinary infractions) to college application and admission records, postsecondary enrollment and degree completion records, financial aid packages, institutional expenditure data from IPEDS, and quarterly earnings records from the Texas Workforce Commission unemployment insurance system.

The identification strategy exploits hundreds of decentralized SAT/ACT score cutoffs in university admissions — varying across schools and application years — that generate sharp discontinuities in admission probability. A fuzzy regression discontinuity design compares applicants just above versus just below each cutoff. On average, crossing a cutoff raises the probability of admission by 27 percentage points and the probability of enrolling at the target university by 15 percentage points. Density tests and pre-college covariate balance validate the smoothness assumptions. The typical cutoff complier is more disadvantaged than the average college applicant but comparable to the average Texas high school graduate.

Roughly half of cutoff compliers would fall back to another, typically less selective, four-year institution if rejected; 43 percent would fall back to a two-year community college; and only about 6 percent would forgo higher education entirely. The pooled estimates therefore blend intensive-margin effects (more selective versus less selective four-year college) with extensive-margin effects (four-year college versus community college or no college).

Main causal findings for enrollment compliers: the typical marginally admitted student completes approximately one additional year of credits in the four-year sector and becomes 12 percentage points more likely to ever earn a bachelor’s degree from any institution. About half of the additional four-year credits are offset by 15 fewer credits in the two-year sector, and associate degree or certificate completion falls by 7 percentage points. All bachelor’s degree gains are in non-STEM fields; STEM degree completion shows no detectable increase. Compliers become about 3 percentage points more likely to hold a graduate degree by 10 years out.

On earnings, admitted compliers earn less than rejected counterparts in the first five years due to continued enrollment. Year six is the crossover point; by years 8–12, compliers earn a stable 8.6 percent earnings premium in log terms (8.2 percent in dollar ratio terms, representing a LATE of $3,339 against an untreated complier mean of $40,829), with earnings ranks rising approximately 4 percentiles from a base near the 50th percentile.

Marginally admitted students pay no additional net tuition on average: $4,600 in additional gross tuition is nearly fully offset by grant aid, though they take on $5,300 more in student loans. Society incurs approximately $10,000 in additional educational expenditures per complier. Internal rates of return are 26 percent for students, 16 percent for society, and 7 percent for the government budget. At a 3 percent discount rate, the lifetime net present value of enrolling the typical marginal applicant is approximately $80,000 — $70,000 accruing to the student and $10,000 to taxpayers.

Earnings gains are similar across institutions of varying selectivity, but significantly smaller for low-income compliers, who spend more time enrolled, complete fewer degrees, and major in less lucrative fields. A bounding method shows that extensive-margin compliers (those who would otherwise not attend any four-year college) experience larger effects than intensive-margin compliers.

Q: What is the core research question and why is credible evidence scarce? A: The paper asks whether enrolling marginal students in American public universities generates positive net returns — private, social, and fiscal — and what drives heterogeneity in those returns. Credible evidence is scarce because most existing work is correlational and fails to account for selection bias: individuals with more college education may have had pre-existing advantages, confounding college’s causal effect with systematic sorting into it. Even if average returns are positive, the policy-relevant question is whether the marginal student — who has weak preparation and high dropout risk — represents a good investment.

Q: What is the regression discontinuity design, and what does the first stage look like? A: The author infers hundreds of decentralized SAT/ACT score cutoffs across approximately 700 application cells (combinations of university, year, GPA quartile, and test type) by searching for the score value with the largest discontinuity in admission and enrollment within each cell. This procedure delivers a superconsistent estimator of each cell’s true cutoff. Pooled across all cells, crossing a cutoff raises the probability of admission by 27 percentage points and the probability of enrollment at the target university by a precisely estimated 15 percentage points. The density of applicants and a rich set of pre-college characteristics run smoothly through the cutoffs, supporting the exclusion restriction.

Q: Who are the cutoff compliers, and are they representative of any broader population? A: Compliers — applicants who enroll in the target university if and only if they barely cross its cutoff — comprise approximately 15 percent of marginal applicants. In observable characteristics, compliers are roughly representative of the broader population of marginal applicants at the cutoff. They are significantly more disadvantaged than the average public university applicant, but broadly comparable to the average Texas public high school graduate in terms of academic preparation and family income.

Q: What are the next-best alternatives for marginal applicants who are rejected? A: Approximately 47 percent of compliers would fall back to another Texas four-year college (mostly public), 43 percent to a two-year community college, and approximately 9 percent would not enroll in any Texas institution. National Student Clearinghouse data for the 2008–2014 cohorts confirm that only 4 percent of untreated compliers attend a college outside the THECB universe, meaning approximately 6 percent of all compliers truly forgo higher education altogether if rejected. The empirically relevant extensive margin is therefore between the four-year sector and the two-year sector, not between college and no college.

Q: How does cutoff crossing change the institutional characteristics a complier experiences? A: Compliers are propelled into substantially better-resourced environments: the average math test score of college peers rises by half a standard deviation; peers are 12 percentage points less likely to have been low-income; gross tuition rises by $2,400 (a 42 percent increase over the untreated complier mean of $5,700); educational spending per student rises by $3,200 (43 percent over the untreated mean); peers’ 10-year BA completion rate rises by 28 percentage points; and peer mean earnings 8–12 years after college entry are $6,700 higher.

Q: What are the educational attainment effects? A: Cutoff crossing causes compliers to complete approximately 28 additional credits at any four-year institution (roughly one full year of a four-year program) and increases the probability of ever earning a bachelor’s degree by 12 percentage points, raising the completion rate from approximately 40 percent to just above 50 percent. About 15 fewer two-year sector credits are offset against the four-year gains, and associate degree or certificate completion falls by 7 percentage points. All bachelor’s degree gains are in non-STEM fields; there is no detectable increase in STEM degrees. Graduate degree completion rises by approximately 3 percentage points by 10 years out.

Q: What is the earnings trajectory, and when does the premium materialize? A: Admitted compliers earn less than rejected counterparts in the first five years after application because they remain enrolled longer. Year six is the crossover point. By years 8–12, the earnings premium stabilizes at approximately 8.6 percent in log terms and 8.2 percent in dollar ratio terms (a LATE of $3,339 against an untreated complier mean of $40,829). Earnings rank rises by approximately 4 percentiles from a base near the 50th percentile. These results are robust across sandwich earnings, all-quarters-with-earnings, and zero-imputed specifications.

Q: What does the cost-benefit analysis show? A: Marginally admitted students pay no additional net tuition on average: $4,600 in additional gross tuition is nearly fully offset by additional grant aid. They do borrow $5,300 more in student loans, likely financing higher room, board, and consumption costs at four-year colleges. From society’s perspective, compliers generate approximately $10,000 in additional educational expenditures. Cumulative undiscounted earnings benefits surpass costs after 8 years for students, 11 years for society, and 19 years for taxpayers. At a 3 percent discount rate, the lifetime net present value is approximately $80,000 total — $70,000 accruing to the student and $10,000 to taxpayers — with internal rates of return of 26 percent for students, 16 percent for society, and 7 percent for the government budget.

Q: Does selectivity of the admitting institution predict larger earnings returns? A: No. Compliers at more selective institutions experience substantially larger increases in peer quality than those at less selective institutions, but they are also less likely to be on the extensive margin of four-year enrollment and experience smaller BA attainment gains. These factors roughly offset, producing no systematic difference in earnings gains across institutions of varying selectivity. More selective institutions also impose no additional cumulative cost on society, while compliers actually pay slightly less in additional net tuition at more selective schools.

Q: How does the commonly used measure of college value-added (mean peer earnings) compare to actual complier returns? A: Mean peer earnings overpredicts actual value-added for marginal students by a factor of two: compliers attend an institution with $6,700 higher average peer earnings as a result of admission but gain only $3,300 themselves. The measure also overpredicts the earnings return to selectivity by a factor of three: a 100-SAT-point increase in target school selectivity predicts $3,000 higher peer earnings but only a statistically insignificant $900 higher gain in the complier’s own earnings.

Q: How do earnings returns differ by family income? A: Compliers from low-income families experience significantly smaller earnings gains compared to higher-income compliers. The gap is not explained by differential changes in college quality induced by admission. Instead, low-income compliers gain fewer degrees despite spending more time in college and major in less lucrative fields, consistent with related findings in the literature on family income gaps in degree completion and major choice.

Q: How do earnings returns differ by gender and by race? A: Female and male compliers eventually earn similar log earnings and earnings rank gains, but women reach their gains more quickly — likely because men take longer to finish college. White and Asian compliers experience similar earnings gains and BA completion improvements as Black and Hispanic compliers, despite white and Asian students experiencing larger increases in college selectivity and spending per student as a result of admission.

Q: What is the method for separating intensive- and extensive-margin effects? A: The two complier types are not directly distinguishable in the data. The author first uses an endogenous but strong stratification variable — having at least one other Texas public university admission offer — to identify some mean potential outcomes for each type. He then imposes an empirically-informed rank assumption to bound the remaining unknown mean potential outcomes, delivering tightly informative upper and lower bounds on each margin’s effects without requiring full nonparametric identification. The results show that pooled effects are driven by larger returns for extensive-margin compliers who would not have attended any four-year college, with smaller contributions from intensive-margin compliers shifting between four-year institutions.

Q: How do this paper’s earnings estimates compare to prior studies, and what explains the differences? A: This paper’s 8 percent earnings gain is smaller than the 17–26 percent reported in prior studies (Zimmerman 2014: 22%; Kozakowski 2023: 26%; Smith, Goodman, and Hurwitz 2025: 17%; Bleemer 2024: 21%; Hoekstra 2009: 20%). The differences are likely explained by the much larger educational attainment and institutional quality gains induced by those studies’ natural experiments: in Zimmerman (2014), enrollment compliers gain roughly three additional years of four-year education versus one year in this paper; in Bleemer (2024), compliers experience roughly $30,000 more in institutional spending per student versus approximately $3,000 in this paper.

Q: What are the scope conditions for these results? A: The results pertain to marginal applicants to Texas public universities (excluding UT-Austin, which uses holistic admission with no detectable SAT/ACT cutoffs) from the 2004–2014 high school graduation cohorts. The identified effects are local average treatment effects for compliers — applicants who would enroll in the target university if and only if they barely crossed its admission cutoff — and do not represent effects for always-takers or infra-marginal students. Earnings are measured only for Texas-based workers covered by the state unemployment insurance system, which captures an estimated 90 percent of the civilian labor force.

Cutoff complier: An applicant who enrolls in their target university if and only if their SAT/ACT score barely exceeds that university’s admission cutoff. Compliers are the population whose behavior — and thus whose treatment effects — are identified by the fuzzy RD design. They comprise approximately 15 percent of marginal applicants and are more disadvantaged than the average public university applicant but broadly comparable to the average high school graduate.

Extensive versus intensive margin: The extensive margin refers to the contrast between attending any four-year college versus falling back to a two-year community college or no college. The intensive margin refers to the contrast between attending a more selective versus a less selective four-year institution. Approximately half of cutoff compliers are on each margin; the paper treats them as economically distinct parameters requiring separate identification.

Fuzzy regression discontinuity (RD) design: An identification strategy that uses the discontinuous jump in admission probability at a test score cutoff as an instrument for enrollment, recovering the LATE for compliers via the ratio of the reduced-form discontinuity in outcomes to the first-stage discontinuity in enrollment. “Fuzzy” refers to the fact that crossing the cutoff changes admission and enrollment probabilities with a discrete jump rather than with certainty.

Internal rate of return (IRR): The discount rate at which the net present value of an investment equals zero — here, the discount rate equating the discounted stream of earnings benefits to the discounted stream of costs. The paper estimates IRRs separately for students (26 percent), society (16 percent), and the government budget (7 percent), reflecting different cost and benefit definitions from each perspective.

Rank assumption (bounding method): An empirically-informed assumption about the ordering of mean potential outcomes across latent complier types (extensive vs. intensive margin) that, combined with partial identification from a strong endogenous stratification variable, yields tight upper and lower bounds on each margin’s causal effects without requiring full nonparametric identification.

Net tuition: Gross tuition charges minus grant aid. For the typical marginal complier, gross tuition rises by $4,600 but is nearly fully offset by additional grant aid, yielding approximately zero additional net tuition cost — meaning the private financial cost of attending a public university for marginal students is effectively zero on net, though they take on $5,300 more in student loans to finance room, board, and consumption.

Sandwich earnings measure: A procedure applied to quarterly state earnings data that retains only quarters with positive earnings sandwiched between other quarters with positive earnings, discarding high-variance transition quarters between employment spells. Annualized by multiplying the quarterly average by four; used to reduce noise from entry and exit transitions in administrative earnings records.