A Research Read · Financial Aid & Yield

The Price of a Yes

Every spring, families read the same acceptance letters and reach different verdicts. The deciding factor, more often than not, is money — but not in the way most people think. A grant of $1,000 moves enrollment by 11 points; a $1,000 tuition cut barely registers at 2. What follows is six decades of research, charted.

+11pp Avery & Hoxby's grant effect at selective colleges
7.66M Students across 86 studies in the 2024 meta-analysis
56.3% Average tuition discount at private colleges, 2024-25
88-95% Estimated HYPSM yield among Pell-eligible admits
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Chapter I

What Actually Drives a Yes

Before the aid offers arrive, the decision is already half-built. Six factors do most of the work: the school's prestige, how well it fits a student's archetype, legacy ties, the noise of personal preference, the financial picture, and whether the campus is in-state.

In a calibrated yield model, prestige carries 35% of the weight and archetype fit carries 25%. Financial aid — the lever everyone obsesses over — accounts for just 10%. That headline understates the real story: money does not show up as one factor, it shows up correlated with everything else.

10% Aid's nominal weight in the enrollment-decision function. The same number applies whether the family earns $30K or $300K — a known weakness of generic models.

Move past the weights and the asymmetries get strange. A dollar of aid does not equal a dollar of tuition cut.

Chapter II

A Dollar Is Not a Dollar

The seminal study on aid and college choice came from Christopher Avery and Caroline Hoxby in 2003, working with the 1999-2000 cohort of high-aptitude applicants. What they found has been replicated, qualified, and never fully overturned.

Per $1,000 of aid: grants moved enrollment 11 percentage points, loans moved it 7, work-study 7. A $1,000 tuition increase only knocked enrollment down 2 points. Room and board hit hardest of all — students seemed to treat dorm bills as more "real" than tuition, perhaps because they pay them every month.

Two takeaways. Gains are bigger than losses: an extra $1K of aid boosts yield more than a $1K tuition cut. And the form of money matters more than the amount: a grant punches roughly 1.6× the weight of a loan dollar-for-dollar.

+11 vs −2 Asymmetry between a $1,000 grant gain and a $1,000 tuition increase. Loss aversion, but with a twist — students react more to the form of an offer than its bottom-line cost.

Behind the percentage points is a quieter parameter: how price-elastic each student really is.

Chapter III

The Elasticity Ladder

Across nearly six decades of work, economists have estimated the price elasticity of college enrollment — the percent change in attendance for a 1% change in net price. The estimates cluster between −0.4 and −1.2, but where a study lands depends almost entirely on which students it observed.

Buss, Parker, and Rivenburg's 2004 study at selective liberal arts colleges found aid recipients were 55% more price-elastic than full-pay families: −1.18 versus −0.76. A $1K change for a financial-aid family hit nearly twice as hard.

Income elasticity tells the inverse story. At private institutions, Hight's 1970 estimates put it at +1.70 — wealthier families don't just attend more; they upgrade more. Public-university income elasticity is closer to 1.0.

−1.18 Price elasticity for aid recipients at selective LACs. Compare to −0.76 for full-pay families at the same schools. The aid-receiving cohort is almost twice as sensitive.

Avery and Hoxby's 11pp number is a ceiling. The consensus across policy experiments is far lower — and arguably more useful.

Chapter IV

The 3-to-4 Point Consensus

Susan Dynarski's 2003 study of Georgia's HOPE Scholarship is the most-replicated finding in the literature. Each $1,000 in aid lifted college attendance by 3.7 to 4.2 percentage points. Not 11. Closer to a third of that.

The 2022 follow-up by Dynarski, Page, and Scott-Clayton reviewed 50 years of federal and state aid experiments and concluded: "Typical financial aid programs have impacts in a range of about 3 to 4 percentage points per $1,000 increase in aid eligibility."

Why the gap with Avery & Hoxby? Their 11pp came from cross-admits at selective colleges — students choosing between elite options where every alternative is high-quality. The 3-4pp consensus describes the broader population, where many alternatives are "don't go" or "go to community college."

Typical financial aid programs have impacts in a range of about 3 to 4 percentage points per $1,000 increase in aid eligibility. — Dynarski, Page & Scott-Clayton, NBER WP #30275 (2022)

A 2024 meta-analysis, the largest in the field, set the bar even lower.

Chapter V

The Meta-Analysis Verdict

LaSota and colleagues, writing in Review of Educational Research in 2024, produced the most comprehensive synthesis to date: 709 effect sizes from 86 studies covering 7.66 million students.

The translated estimate: grants increased enrollment by 2.8 percentage points on average, with smaller boosts to persistence (+2.0pp) and completion (+0.4pp). Effects on academic achievement and post-college labor outcomes were not statistically distinguishable from zero.

Notably, effects did not vary significantly by eligibility criteria, program type, early-commitment requirements, or award amount — though grants had larger effects at two-year institutions than four-year ones, consistent with community-college students being closer to the enrollment margin.

+2.8 pp Average enrollment lift per $1,000 grant in the LaSota meta-analysis. The number is small, but the population is enormous and the effect is robust across study designs.

The averages hide an income gradient that matters far more than any policy lever.

Chapter VI

The Yield Gradient

At full-need elite colleges, the same admit letter lands very differently depending on family income. Pell-eligible students yield at an estimated 88-95% — almost no one walks away from a near-free Harvard. Full-pay families yield at 65-75%; they have alternatives, and those alternatives compete on prestige, not price.

The pattern inverts at Near-Ivy and Selective schools that don't meet full need. Low-income yield can be lower than at HYPSM because the unmet-need gap forces a financial reckoning that the admit letter doesn't acknowledge.

First-generation students show the highest price sensitivity at every tier. Their elasticity of −1.25 reflects what Marifian (2024) calls cost uncertainty: without parents who navigated aid before, the sticker price feels less negotiable than it actually is.

88-95% Estimated yield among Pell-eligible HYPSM admits. The same letter yields 65-75% from full-pay families with multiple competing options.

Yield isn't only about who pays the sticker. The discount itself has become an industry.

Chapter VII

The Sticker That Almost No One Pays

NACUBO's 2024-25 Tuition Discounting Study found the average private-college discount rate — institutional grant aid divided by gross tuition revenue — has climbed to 56.3% for first-time undergrads. Grants now cover 63% of tuition and fees for that cohort. Roughly 83.4% of all undergrads receive some institutional grant aid.

Net tuition revenue, after the discounting, grew just 1.4% in real terms. Sticker price climbs every year. Take rate climbs faster. The list price has become a fiction priced for negotiation.

For families, the implication is that sticker comparisons are nearly meaningless. For colleges, it's an arms race they cannot exit: once one peer raises the discount, holding firm costs you yield.

56.3% Average institutional discount at private colleges. Up from 36.8% in 2003. The rate has compounded for two decades and shows no signs of cresting.

Even the schools sitting on the largest endowments don't translate that wealth into broader access.

Chapter VIII

The Endowment Paradox

Bulman's 2022 NBER paper looked at what happens when a college's endowment grows. The intuitive answer — they admit more students, more low-income families, more aid recipients — turns out to be wrong.

Wealthier colleges, on the margin, did not increase the number of students served or the share receiving aid. They modestly upped aid generosity for existing recipients, then redirected the surplus into selectivity: higher rejection rates, more institutional spending, better rankings.

On race and income composition, the effect actually went the other way. Wealthier colleges enrolled fewer low-income students and students of color, on average. Endowment growth funded prestige, not access.

Wealthier colleges do not increase the number of students served or the fraction receiving aid. Instead, they offset higher yield rates by becoming more selective. — Bulman (2022), NBER WP #30404

If the dollars don't tell the whole story, what does? Often, the framing.

Chapter IX

Naming the Money

The behavioral literature has its own punchline. A "Presidential Scholar" award yields better than an institutional grant of identical net cost. Avery & Hoxby estimated +3 to +5 percentage points just from the naming. Front-loading the freshman-year award (with smaller upper-class amounts) added another 2-3pp.

A 2023 field experiment in Behavioural Public Policy went further: a simplified letter affirming belonging while making cost calculations salient boosted enrollment in the lowest-cost option by 10.4 percentage points — with no change to the dollar offer.

The full picture, then, is that yield responds to three layers: the dollars themselves (3-4pp per $1K, 11pp at the high end), the form of those dollars (grants > loans, named > unnamed, front-loaded > flat), and the framing of the offer (a clear letter beats a confusing one by 10pp on its own). Schools that get all three right yield substantially better than peers that out-spend them by half.

+10.4 pp Boost in lowest-cost-option enrollment from a simpler, belonging-affirming letter — with zero change to the dollars on offer. Framing pulls a comparable weight to a meaningful price cut.

For families, the practical version is that an aid letter is also a salesmanship document. For colleges, financial-aid policy is a behavioral product, not just a pricing one.

The Six Factors That Drive a Yes
Decision weights from a calibrated yield function
Source: financial_aid_yield.md, "Six Factors That Drive a Yes." Decision-function weights, score ranges in tooltips.
Per-$1,000 Effect on Enrollment Probability
Grants outweigh loans; gains outweigh equivalent losses
Source: Avery & Hoxby (2003), NBER WP #9482. High-aptitude cross-admit cohort, 1999-2000. Negative bars are tuition / room-and-board increases.
Price Elasticity of Enrollment, by Study
Aid-receiving students respond about 1.6× more sharply than full-pay
Sources: Campbell & Siegel (1967); Hight (1970); Hoenack (1967); Moore et al. (1991); Buss, Parker & Rivenburg (2004). All values are negative own-price elasticity of demand.
Per-$1,000 Grant Effect: Five Estimates
From the meta-analytic floor to Avery & Hoxby's selective-cohort ceiling
Sources: LaSota et al. (2024); Dynarski (2003); Dynarski, Page & Scott-Clayton (2022); Buss, Parker & Rivenburg (2004); Avery & Hoxby (2003).
LaSota et al. (2024) Meta-Analysis Outcomes
Average effect of grants on five outcome measures, percentage points
Source: LaSota, Polanin et al. (2024), Review of Educational Research. 709 effect sizes, 86 studies, 7.66M students. Achievement and labor effects not statistically distinguishable from zero.
Estimated Yield by Family Income, HYPSM vs Tier 3-4
Same admit letter, different verdicts depending on the unmet-need gap
Source: financial_aid_yield.md §3.1, synthesized from Chetty et al. (2023), Avery & Hoxby (2003), and reported HYPSM yield data. Ranges shown as midpoints with whiskers.
Tuition Discounting at Private Colleges
Three NACUBO 2024-25 headline numbers
Source: NACUBO Tuition Discounting Study 2024-25.
What Endowment Growth Does (and Doesn't) Do
Direction of effect when a college's endowment expands
Source: Bulman (2022), NBER WP #30404. Direction-of-effect summary; underlying paper estimates magnitudes per $10K of per-student endowment.
Five Behavioral Boosts on Top of Dollars
Yield gains independent of net price
Sources: Avery & Hoxby (2003); behavioral econ literature; Behavioural Public Policy (Cambridge, 2023) for the salience-letter result.