I23 | Macro Paper Warehouse

Digital Distractions with Peer Influence

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

This paper estimates the causal effects of mobile app usage on college students’ academic performance, physical health, and labor market outcomes, while separately identifying behavioral (endogenous) and contextual (exogenous) peer effects in app usage — the first study to do so within a unified empirical framework. The analysis draws on administrative data for three freshman cohorts (2018–2020) at a mid-tier Chinese university, linked to individual-level mobile phone usage records from a major telecommunications carrier covering 6,430 students over four years (excluding COVID semester). High-frequency GPS data, hourly app usage records for the 2020 cohort, and two waves of university surveys supplement the main dataset.

The identification strategy addresses three challenges: endogeneity of own app usage, endogeneity of peer group formation, and the reflection problem in peer effects. For own usage, two instrumental variables are used: (1) a shift-share instrument interacting the September 2020 launch of the blockbuster game Yuanshen with students’ pre-college app usage intensity; and (2) China’s October 2019 minors’ game restriction policy (prohibiting under-18s from playing online games 10 p.m.–8 a.m. and capping weekday gaming at 90 minutes/day) interacted with the evolving number of underage pre-college friends. For peer effects, the university’s random dormitory assignment within gender-class units provides exogenous peer variation; behavioral peer effects are further isolated using the minors’ restriction policy interacted with roommates’ pre-college underage friend networks, an instrument that affects roommates but not the focal student. Contextual peer effects are recovered by subtracting the estimated behavioral component from reduced-form estimates.

The main findings are as follows. First, app usage is contagious: a one standard deviation (s.d.) increase in roommates’ in-college total app usage raises a student’s own usage by 5.8% (IV). Behavioral peer effects dominate: contextual peer effects are small and statistically insignificant. Second, own app usage severely harms academic performance: a one s.d. increase in total app usage reduces GPA for required courses by 36.2% of a within-cohort-major s.d. (IV), and a one s.d. increase in game app usage alone reduces GPA by 56.6% of a within-cohort-major s.d. The direct disruption effect of roommates’ app usage reduces GPA by a further 20.6% of a within-cohort-major s.d.; combining the indirect channel (behavioral contagion), the total roommate effect reaches 22.7% of a within-cohort-major s.d., more than 60% of the own-usage effect. Third, the effect on physical education scores is roughly four times larger than on required-course GPA: a one s.d. increase in own app usage reduces PE scores by 2.74 points, while roommates’ app usage has no direct effect on PE. Fourth, a one s.d. increase in own in-college app usage reduces initial wages upon graduation by 2.3% (12.1% of within-cohort-major wage s.d.); a one s.d. increase in roommates’ usage reduces wages by 0.9% directly, with a total effect (including the contagion channel) of approximately 1.0% (5.3% of within-cohort-major s.d.). Controlling for cumulative GPA reduces the gaming-to-wage coefficient by roughly one-third, indicating that academic performance is an important but partial mediator.

A back-of-the-envelope policy simulation extending the minors’ gaming cap (3 hours/week) to college students — binding for 34.3% of student-month observations — projects an average wage increase of 0.9% at graduation, approximately half the wage premium from one additional year of work experience in developing countries.

Mechanism evidence from GPS data shows that Yuanshen’s launch caused students to arrive at study halls 18.2 minutes later and leave 23.4 minutes earlier per day. High-frequency sleep data show that a one s.d. increase in nighttime app usage reduces sleep duration by approximately 30 minutes and raises the probability of sleeping late by 34 percentage points. Survey evidence indicates that heavy app users recognize the addictive nature of gaming, pointing to self-control problems rather than lack of awareness.

The scope conditions are: single mid-tier Chinese university; 2018–2020 cohorts; outcomes through initial job placement only; peer group restricted to dormitory roommates; findings rely on IV exclusion restrictions conditional on student and time fixed effects.

Q: What is the core research question? A: The paper asks how individual and peer mobile app usage affect college students’ academic performance, physical health, and early labor market outcomes, and it separately identifies the behavioral (endogenous) versus contextual (exogenous) components of peer influence in app usage. This is claimed as the first study to disentangle these two types of peer effects within a unified empirical framework.

Q: What data does the paper use? A: Administrative records for 7,479 undergraduates across three freshman cohorts (2018–2020) at a medium-sized mid-tier Chinese university are linked to monthly mobile app usage records from a telecommunications provider covering 75% of the provincial population; 6,430 students are matched. The dataset also includes GPS location data at 5-minute intervals, hourly app usage for the 2020 cohort (used to infer sleep), and two waves of voluntary annual surveys with 1,798 respondents (24% response rate). Labor market outcomes — employment status, wages, post-graduate admissions — are available for the 2018 and 2019 cohorts.

Q: How does the paper address the endogeneity of own app usage? A: Two sets of instruments are used. The first interacts the September 2020 launch of Yuanshen (the most popular game in China, with over 13 million Chinese users by 2021, the majority under age 25) with students’ pre-college app usage, forming a shift-share instrument under the assumption that the game launch is orthogonal to unobserved GPA determinants conditional on student fixed effects. The second interacts China’s October 2019 minors’ game restriction policy with the evolving count of a student’s underage pre-college friends; event studies confirm no pre-trends and a sharp, transitory drop in app usage post-policy that dissipates as friends age out of the restricted group.

Q: How does the paper solve the reflection problem and separate behavioral from contextual peer effects? A: Three-step procedure: (1) random dormitory assignment within gender-class units yields reduced-form peer effect estimates using roommates’ pre-college app usage as the exogenous peer shifter; (2) behavioral peer effects are isolated via an IV using the minors’ restriction policy interacted with roommates’ (not the focal student’s) underage pre-college friend networks — an instrument that shifts roommates’ app usage but is orthogonal to the focal student’s outcomes; (3) contextual peer effects are recovered as the residual from subtracting the estimated behavioral effect from the reduced-form estimate.

Q: How large and significant are the behavioral versus contextual peer effects in app usage? A: A one s.d. increase in roommates’ in-college total app usage raises own usage by 5.8% (IV estimate, significant). For game apps alone the behavioral spillover is 10.7%, and for games plus video it is 6.5%. Contextual peer effects (identified from roommates’ pre-college characteristics) are much smaller and statistically insignificant, indicating that peer influence operates primarily through the direct imitation of peers’ actions rather than their background traits.

Q: What is the effect of own app usage on GPA? A: The IV estimate shows a one s.d. increase in total in-college app usage reduces GPA for required courses by 0.716 points, equivalent to 36.2% of a within-cohort-major GPA s.d. (significant at 1%). For game apps alone, a one s.d. increase reduces GPA by 1.119 points, or 56.6% of a within-cohort-major s.d. OLS estimates are biased toward zero, likely because negative health shocks reduce both GPA and app usage simultaneously.

Q: How large is the total peer effect of roommates’ app usage on a student’s GPA? A: Roommates’ app usage directly lowers GPA by 0.408 points (20.6% of within-cohort-major s.d.) through disruption of the dormitory study environment or crowding out of group study. The behavioral contagion channel (5.8% increase in own usage per s.d. of roommates’ usage) adds an additional 0.042 points, bringing the total effect to approximately 0.450 points, or 22.7% of a within-cohort-major s.d. — over 60% of the own-usage effect.

Q: What is the effect on physical education (PE) scores, and why do roommates’ app usage not matter there? A: A one s.d. increase in own total app usage reduces PE scores by 2.74 points (IV), approximately four times the magnitude of the effect on required-course GPA, consistent with health literature on excessive screen time. Roommates’ app usage has no statistically significant direct effect on PE, which the authors attribute to the irrelevance of dormitory noise and study disruptions for outdoor physical activity.

Q: What are the effects of app usage on wages at graduation? A: Doubling total app usage during college reduces initial wages by approximately 2% (IV). A one s.d. increase in own usage reduces wages by 2.3%, or 12.1% of a within-cohort-major wage s.d. A one s.d. increase in roommates’ usage directly reduces wages by 0.9% (4.8% of within-cohort-major s.d.); including the behavioral contagion channel, the total roommate effect is approximately 1.0% (5.3% of within-cohort-major s.d.). Controlling for cumulative GPA reduces the game-usage-to-wage coefficient by about one-third, implying GPA is a partial but not complete mediator.

Q: What does the policy simulation of the gaming cap say? A: Extending the minors’ game restriction (3 hours/week cap) to college students would bind for 34.3% of student-month observations, reducing average monthly gaming from 12.1 hours to 8 hours (a one-third decrease). Incorporating the behavioral peer multiplier for gaming (0.078), average gaming further converges to approximately 7.65 hours in steady state. The implied wage gain at graduation is 0.9%, approximately half the wage premium from one additional year of work experience in developing countries (Lagakos et al., 2019 estimate).

Q: What does the GPS evidence show about time allocation? A: Following Yuanshen’s launch, the average student arrives at the study hall 18.2 minutes later and returns to the dormitory 23.4 minutes earlier per day. The minors’ restriction reverses this: students with the average number of minor friends arrive at study halls 17.4 minutes earlier and return to the dorm 19.8 minutes later. Both game shocks also shift tardiness and absence rates for major-required courses in the expected directions, and the effects intensify over time with Yuanshen’s growing popularity.

Q: What do the sleep data show? A: A one s.d. increase in nighttime app usage (9 p.m.–3 a.m.) is associated with roughly 30 minutes less sleep (7% of the mean), a 34 percentage point higher probability of sleeping late, and a 4.5 percentage point higher probability of waking up late. Daytime app usage (8 a.m.–9 p.m.) is also associated with 7.2 fewer minutes of sleep (1.8% of mean) and a 3.7 percentage point higher probability of late wake-up. These results are descriptive (from the 2020 cohort hourly data) rather than IV-based.

Q: What does the survey evidence show about mechanisms and self-awareness? A: Heavier app users report worse physical health and higher stress, are less likely to have obtained professional certifications by graduation, submit fewer job applications, and express lower satisfaction with job offers. Notably, heavier users are more likely to acknowledge the addictive nature of apps and games, suggesting a self-control problem rather than informational deficiency. They also report better relationships with roommates and greater likelihood of following roommates’ advice on post-graduation choices, a potential direct channel for peer labor market effects.

Q: How representative is the sample, and what are the key scope conditions? A: The university is a mid-tier institution in southern China with students predominantly from the 30th–80th CEE score percentile among provincial college-admitted applicants; it is less female (42% vs. 53% nationally) and more rural (40% vs. 27% nationally). Survey respondents oversample less advantaged backgrounds and are re-weighted. Findings pertain to dormitory roommates as the peer group; all labor market outcomes are initial wages upon graduation; the sample covers 2018–2021 with COVID semester excluded. The peer effects estimates rest on random dormitory assignment, which the authors verify by showing no within-dorm correlation in pre-college characteristics.

Behavioral (endogenous) peer effects: The mechanism by which a peer’s actual behavior — here, contemporaneous app usage — directly influences a focal individual’s own behavior. In this paper, identified via IV using the minors’ game restriction policy interacted with roommates’ underage pre-college friend networks, which shifts roommates’ usage but not the focal student’s characteristics.

Contextual (exogenous) peer effects: The influence of peers’ pre-determined background characteristics (e.g., pre-college app usage, reflecting motivation, study habits, attitudes toward academics) on a focal individual’s outcomes, independent of peers’ actual in-college behavior. Recovered as the residual after subtracting estimated behavioral peer effects from reduced-form estimates; found to be small and insignificant in this setting.

Shift-share instrument (Yuanshen): A quasi-experimental instrument constructed by interacting the mid-sample launch date of the blockbuster game Yuanshen (September 2020) with students’ pre-college app usage intensity, under the assumption that pre-college usage predicts differential susceptibility to the shock while the launch itself is orthogonal to the university’s academic environment.

Minors’ game restriction policy: China’s October 2019 policy prohibiting individuals under 18 from playing online games between 10 p.m. and 8 a.m. and capping weekday gaming at 90 minutes per day (tightened to 3 hours/week in September 2021). Used both as an instrument for own app usage (via underage pre-college friends) and as an instrument for roommates’ usage (via roommates’ underage friends) to isolate behavioral peer effects.

Reflection problem: The identification challenge first articulated by Manski (1993) arising because an individual’s behavior both affects and is affected by peers simultaneously, making it impossible to separately identify the direction of influence from observational data without exogenous variation in peer behavior.

Source text origin: The paper’s own data provenance category distinguishing whether summaries are based on full working paper text (pdf or oa-html) versus abstract only — a distinction the paper itself does not use but that is relevant to the review pipeline running this analysis.

Within-cohort-major GPA standard deviation: The unit used to scale all GPA effect sizes, defined as the standard deviation of GPA within students of the same graduation cohort and declared major. This normalization accounts for systematic differences in grading across fields and years, making effect magnitudes comparable across specifications.

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.