Marginal Returns to Public universities

 The study overview provided by the sources examines the marginal returns to public universities by comparing long-term outcomes for students who were "barely admitted" versus those who were "barely rejected" based on standardized test score cutoffs,. This research is situated in a context where public faith in the value of a four-year degree is declining, and existing causal evidence—as opposed to mere correlational data—is surprisingly rare,,.

Methodological Approach

To address whether the "marginal American college student" is a good investment, the study utilizes a fuzzy regression discontinuity (RD) research design,.

• Data Scope: The research leverages administrative records from all 35 public universities in Texas, which collectively represent 10 percent of all American public university students,.
• Identification Strategy: The author identifies hundreds of decentralized SAT/ACT score cutoffs that generate abrupt shifts in admission and enrollment,.
• Comparison Group: By focusing on applicants right at these cutoffs, the study compares individuals with nearly identical academic backgrounds, effectively eliminating the "selection bias" typically found in correlational studies,.

The Marginal Student Context

The "marginal student" is a critical population for several reasons highlighted in the sources:

1. Policy Levers: These students represent the margin along which public universities either expand or contract their enrollment,.
2. Academic Risk: Marginal students often have weaker academic preparation, making their potential returns to education ex ante ambiguous due to a higher likelihood of dropping out,.
3. Literature Gap: Unlike prior studies that focused on isolated institutions, this study offers a broad look at the entire public sector of a major state,.

Key Findings on Marginal Returns

The study concludes that enrolling in a public university yields substantial positive returns for the marginal student, society, and the government budget:

• Educational Attainment: The typical marginally admitted student gains an additional year of education in the four-year sector and is 12 percentage points more likely to earn a bachelor's degree,.
• Labor Market Outcomes: Admission leads to an 8 percent earnings premium that begins to solidify approximately eight years after application,.
• Cost-Benefit Analysis: Marginally admitted students often pay no additional net tuition because increased grant aid offsets higher sticker prices,. The Internal Rate of Return (IRR) is estimated at 26 percent for the students, 16 percent for society, and 7 percent for the government,.

Intensive vs. Extensive Margins

A significant contribution of this study is its ability to distinguish between two economically distinct margins,. The "extensive margin" involves students who would have attended no four-year college (usually falling back to a two-year community college) if rejected, while the "intensive margin" involves students who would have attended a different, typically less selective, four-year institution,,. The results show that the overall gains are driven primarily by larger effects on the extensive margin—getting students into the four-year sector in the first place,.

The sources indicate that for the marginal student, enrolling in a public university leads to significant and long-term educational impacts, primarily characterized by a shift in the sector of education attended and a substantial increase in degree completion. These impacts are a core component of the "marginal returns" because they represent the primary mechanism through which later earnings gains are realized.

Degree Completion and Credit Accumulation

The typical student barely admitted to a public university experiences a decisive increase in their educational trajectory compared to those barely rejected:

• Bachelor’s Degree Completion: Admission causes a 12 percentage point increase in the likelihood of ever earning a bachelor's degree from any institution. Within the specific "target" university that admitted them, the probability of earning a degree jumps by 34 percentage points.
• Years of Education: On average, these students gain one additional year of education within the four-year sector, equivalent to roughly 28 credits.
• Timeline to Graduation: Completion rates among this population are generally lower and take longer than average; most degrees are earned well after the four-year mark, with treatment effects stabilizing around seven years after the initial application.

Sector Substitution and Major Choice

The sources highlight that these educational gains do not happen in a vacuum but often involve "cannibalizing" other forms of higher education:

• Four-Year vs. Two-Year Sector: About half of the additional credits gained in the four-year sector are offset by a reduction in two-year community college attendance. Marginal students are 7 percentage points less likely to earn an associate's degree or certificate because they have shifted into the four-year sector.
• Fields of Study: Interestingly, almost all the gains in degree completion occur in non-STEM fields. There is no detectable increase in STEM degrees among marginally admitted students.
• Graduate Education: There is a small but statistically significant downstream impact, with marginal students becoming roughly 3 percentage points more likely to eventually hold a graduate degree.

Impact of Peer Environments and Institutional Quality

Marginal admission propels students into environments with significantly different "quality" metrics:

• Peer Quality: These students join cohorts where peers have substantially higher academic preparation (0.5 standard deviation increase in math scores) and are 28 percentage points more likely to graduate.
• Institutional Resources: They attend schools that spend approximately $3,200 more per student annually on educational expenditures compared to their fallback options.

Heterogeneity in Educational Outcomes

The educational impact varies significantly based on student background and the type of institutional margin:

• The Income Gap: Students from low-income families experience a more "unfavorable" educational path. While they gain access to higher-quality institutions, they are less likely to persist to a degree than higher-income peers, despite actually spending more time enrolled in college.
• The Extensive Margin: The most dramatic educational impacts occur for students on the extensive margin—those who would not have attended a four-year college at all if rejected. These students see a 20-25 percentage point increase in BA completion, whereas those on the intensive margin (who would have attended a less selective four-year school anyway) only see a 4-7 percentage point gain.

The sources indicate that enrolling in a public university yields substantial and enduring economic returns for the marginal student, with significant positive implications for both the government budget and society at large,. These returns are primarily driven by an 8 percent earnings premium that begins to solidify approximately eight years after a student initially applies to a "target" university,.

Earnings Trajectories and Premia

The economic impact of admission follows a distinct temporal pattern:

• Initial Opportunity Cost: In the first five years after application, admitted students typically earn less than their rejected counterparts because they are more likely to be actively enrolled in school,. Admitted students earn only about 10 percent less than untreated peers during this time, as many continue to work at least part-time while studying.
• The Crossover Point: Year six marks the "crossover" age, where admitted students have generally finished their education and begin to outearn those who were rejected,.
• Long-Term Gains: By years 8–12, the typical marginally admitted student realizes a gross earnings gain of 8.6 percent. In terms of relative distribution, rejected applicants usually end up around the 50th percentile of their cohort’s earnings, while admission boosts that rank by 4 percentiles,.

Costs and Net Financial Impact

A critical finding in the sources is that the marginal student bears very little of the direct financial burden for this investment:

• Net Tuition: While admitted students face roughly $4,600 in additional gross tuition, this is almost entirely offset by a corresponding $4,600 increase in grant aid, resulting in nearly zero additional net tuition for the average marginal student,.
• Student Debt: Despite the lack of net tuition costs, admitted students take on approximately $5,300 in additional student loans, likely used to finance higher room and board charges and other consumption associated with four-year college life,.
• Social and Taxpayer Costs: From society’s perspective, educating a marginal student costs roughly $10,000 in additional resource expenditures,. However, the government budget eventually nets $10,000 in present value (at a 3% discount rate) through increased tax revenue,.

Internal Rates of Return (IRR)

The study calculates the rate at which these educational investments "pay off," revealing highly favorable returns:

• Students: Reap a 26 percent IRR, reflecting the combination of significant earnings gains and roughly zero net tuition costs,,.
• Society: Realizes a 16 percent IRR, accounting for the total resource costs of the education,,.
• Taxpayers: Experience a 7 percent IRR, meaning the public subsidy of marginal students eventually pays for itself through increased future tax revenue,. The investment "pays off" (undiscounted) for the student after 8 years, for society after 11 years, and for the taxpayer after 19 years,.

Heterogeneity and Selectivity

The sources emphasize that economic returns are not uniform across all demographics or institutional types:

• The Selectivity Myth: Surprisingly, the selectivity of an institution is not a strong predictor of the earnings gains reaped by its marginal students,. While more selective schools have peers with higher earnings, using those "peer means" to judge value-added overpredicts the actual earnings gains for marginal students by a factor of two,.
• The Income Gap: Students from low-income families (eligible for free/reduced-price lunch) experience significantly smaller earnings gains compared to higher-income peers,. This is attributed to low-income students being less likely to complete their degrees, taking longer to graduate, and majoring in less lucrative fields,.
• Extensive vs. Intensive Margin: The largest economic returns are driven by the "extensive margin"—those who would not have attended a four-year college at all if rejected,. Those on the "intensive margin" (who would have attended a less selective four-year school anyway) see much smaller economic gains,.

The sources provide a detailed cost-benefit analysis (CBA) of the returns to public universities, evaluating the investment from three distinct perspectives: the marginal students, society, and the government (taxpayers). This analysis is significant because it accounts for both the up-front costs and the long-term earnings gains realized by those on the margin of admission.

The Cost Side of the Ledger

The initial investment required to educate a marginal student differs based on the perspective:

• Private Cost (Student): Remarkably, marginally admitted students pay nearly zero additional net tuition. While they face approximately $4,600 more in gross tuition, this is almost entirely offset by a $4,600 increase in grant aid. However, they do accumulate roughly $5,300 in additional student loans, likely to cover non-tuition expenses like room and board.
• Social Resource Cost: From society’s perspective, the investment is not free. It costs approximately $10,000 in additional educational expenditures (instruction, academic support, and student services) to educate the marginal student compared to their fallback option.
• Taxpayer Cost: Because students pay almost no net tuition, the government/taxpayers subsidize nearly the entire $10,000 resource cost.

Time Horizons for Payoff

The study calculates how long it takes for undiscounted cumulative earnings benefits to surpass the cumulative costs. The investment "pays off" at different intervals:

• Students: 8 years after application.
• Society: 11 years after application.
• Taxpayers: 19 years after application.

Net Present Value (NPV) and Internal Rate of Return (IRR)

Using a lifecycle horizon (up to age 65) and a 3 percent discount rate, the sources provide the following financial valuations:

Perspective	Net Present Value (NPV)	Internal Rate of Return (IRR)
Marginal Student	~$70,000	26%
Society	~$80,000	16%
Taxpayers/Gov	~$10,000	7%

(Source:)

Key Insights from the Analysis

• The "Infinite" Return for Taxpayers: A 7 percent IRR for the government implies that for any discount rate below 7 percent, the marginal value of public funds is infinite. In other words, subsidizing the education of marginal students eventually pays for itself through increased future tax revenues.
• High Private Returns: The student’s 26 percent IRR is exceptionally high because their up-front costs (net tuition) are near zero and their opportunity cost is low; treated compliers only earn about 10 percent less than untreated peers during their college years.
• Robustness to Consumption Costs: If the analysis includes the $7,600 in additional room and board charges (which may be viewed as consumption rather than investment), the student IRR drops to a still-substantial 15 percent, and the social IRR declines to 12 percent.
• Selectivity vs. Value: While more selective schools cost more to attend in "sticker price," students often pay less in net tuition due to more generous aid, even though the social resource costs remain similar across institutions.

The sources indicate that while the overall returns to public universities are high, they are not uniform. Heterogeneity—the variation in these returns—manifests across three primary dimensions: the type of institution admitting the student, the demographic background of the student, and the specific educational margin involved.

1. Institutional Heterogeneity: Selectivity vs. Spending

The impact of a university depends less on its selectivity and more on its resource levels:

• The Selectivity Paradox: Surprisingly, a university's selectivity (average SAT scores) is not a strong predictor of the earnings gains for its marginal students. While more selective schools offer higher "peer quality," marginal students at these institutions are less likely to be on the "extensive margin" and see smaller gains in degree attainment compared to those at less selective schools.
• Peer Quality Overestimation: Using an institution’s mean peer earnings as a proxy for "value-added" overpredicts actual earnings gains by a factor of two. A 100-point increase in a school's average SAT predicts a $3,000 gain in peer earnings but only a statistically insignificant $900 gain in the student's own earnings.
• Institutional Spending: There is suggestive evidence that "resourced" institutions—those with higher per-student educational expenditures—yield larger earnings gains for marginal students than schools with lower spending.
• Net Tuition Costs: Students admitted to more selective or better-resourced institutions actually tend to pay lower net tuition than those at less selective schools due to more generous grant aid.

2. Student Demographic Heterogeneity

Returns vary significantly based on the student's personal background:

• The Family Income Gap: This is the most substantial area of heterogeneity. Students from low-income families (eligible for free/reduced-price lunch) experience significantly smaller earnings gains than higher-income students.
  • Mechanisms: Although they gain access to high-quality schools, low-income students are less likely to complete degrees, spend more time enrolled without finishing, and often major in less lucrative fields.
• Gender: Male and female students see similar proportional earnings gains. However, women realize these gains faster because men tend to remain in college longer before entering the workforce full-time.
• Race: White and Asian students see similar gains in earnings and degrees compared to Black and Hispanic students. While these expansions improve outcomes for all, the sources note that they neither shrink nor exacerbate existing racial disparities in the workforce.

3. Extensive vs. Intensive Margins

The sources distinguish between two economically different "margins" of enrollment:

• Extensive Margin (Attending any 4-year college): This involves students who would have attended a 2-year community college or no college if rejected. This group drives the majority of the study's positive findings, showing a 20–25 percentage point increase in bachelor's degree completion.
• Intensive Margin (Attending a more selective 4-year college): This involves students who would have attended a different, less selective 4-year school if rejected. These students see much smaller gains in degree completion (4–7 percentage points) and relative earnings.

The sources define admission margins as the specific boundaries—primarily decentralized SAT and ACT score cutoffs—that determine whether an applicant is "barely admitted" or "barely rejected" from a public university. These margins are critical for understanding the value of higher education because they allow researchers to isolate the causal impact of college enrollment by comparing nearly identical individuals who fall on either side of these cutoffs, thereby eliminating the selection bias found in traditional correlational studies.

The Two Primary Admission Margins

The research distinguishes between two economically different types of admission margins that characterize the "marginal student":

• The Extensive Margin: This involves students who, if rejected from their "target" university, would have fallen out of the four-year sector entirely. Approximately 52 percent of the study's subjects fall into this category, with most choosing a two-year community college as their fallback option.
• The Intensive Margin: This involves students who would have attended a different, typically less selective four-year institution if rejected from their target school. About 47 percent of the subjects are on this margin.

Which Margin Drives the Returns?

A central finding in the sources is that the substantial returns to public universities are primarily driven by the extensive margin.

• Degree Completion: Students on the extensive margin see a massive 20–25 percentage point increase in the probability of earning a bachelor's degree. In contrast, those on the intensive margin—who are merely upgrading to a more selective four-year school—see a much smaller gain of only 4–7 percentage points.
• Educational Attainment: Extensive margin compliers gain nearly two additional years of four-year education, whereas intensive margin effects on total credits are significantly smaller.
• Earnings: While both margins see benefits, the relative gains in log earnings and earnings rank are substantively larger for those induced to enter the four-year sector from outside of it (extensive) than for those simply switching between four-year schools (intensive).

Policy and Institutional Context

The sources highlight that these admission margins serve as the primary policy levers for state governments and university administrators.

• Enrollment Strategy: Decisions to expand or contract the "size" of a public university system happen at these exact margins. The research suggests that marginally expanding admission slots would likely yield positive net returns for society and the government budget.
• Profile of the Marginal Student: These students typically have weaker academic preparation than their peers at the same institution—often scoring 100–200 SAT points lower than the university average. Despite this, their outcomes are "significant improvements" over the trajectories they would have faced if rejected.
• Selectivity vs. Marginal Value: Interestingly, the selectivity of an institution is not a strong predictor of the earnings gains for its marginal students. While more selective schools have higher-earning peers, the actual "value-added" for a student right at the admission cutoff remains relatively consistent across different types of public universities.

Financial Implications at the Margin

For the student, the admission margin is financially "frictionless" in terms of tuition. While attending a four-year target university has a higher sticker price than a two-year fallback, increased grant aid almost entirely offsets the higher gross tuition. Consequently, the marginal student pays nearly zero additional net tuition, though they do take on roughly $5,300 more in student loans to cover the increased consumption costs (such as room and board) associated with four-year campus life.