How Financial Aid Affects Whether You'll Actually Enroll

financial_aid_yield.md · 2,513 words · 10 min read

How Financial Aid Affects Whether You'll Actually Enroll

Getting in is only half the story. Once the acceptance letters land, families have to choose — and money quietly drives more of that choice than most students realize. The same admit pile looks very different to a household weighing $5,000 a year against $40,000.

This piece pulls together what the research actually shows about how aid offers, sticker price, and the way money is presented shape enrollment decisions. The headline finding from Avery and Hoxby's foundational work: every $1,000 in grant aid lifts a student's likelihood of attending by about 11 percentage points, while $1,000 in loans moves the needle only about 7. The form of the offer matters as much as the number on it.

What follows walks through the elasticities by income, the behavioral quirks that make a "named scholarship" punch above its dollar weight, and why front-loaded freshman-year aid pulls harder than the same money spread evenly across four years. If you're trying to figure out which acceptance to take — or which schools are worth the application in the first place — this is the math behind the choice.

1. How the Enrollment Decision Gets Weighed

The Six Factors That Drive a Yes

When a student decides where to enroll, six considerations tend to dominate:

Additionally, a hard override forces HYPSM preference when a student has multiple HYPSM acceptances (lines 2607–2630).

Data Structures Supporting the Yield Model

CHETTY_YIELD_BY_INCOME (line 2124): Relative yield by income bracket (1=<$20K through 5=$80K+) for 30 colleges. Values represent rel_att_cond_app from Opportunity Insights (classes 2010–2015). Key patterns: - HYPSM bracket 5 ($80K+) values range 1.66–3.06 -- wealthy students disproportionately attend - Low-income brackets (1–2) at most non-Harvard schools are below 1.0 -- underrepresented relative to national average - Exception: Harvard bracket 1 = 1.78 (strong low-income yield, likely due to aggressive financial aid)

COLLEGE_AID_QUALITY (line 2110): 1–5 scale (5=meets 100% need, no-loan). Currently a fallback; Chetty table is the primary signal. HYPSM all rated 5; Tier 4–5 schools rated 2–3.

netCostByIncome in research_colleges.json: Real College Scorecard data (5 income brackets) for all 55 colleges. Example -- Harvard: $3,829 for <$30K vs. $42,072 for $110K+. This data exists but is NOT currently used in the yield decision function.

Identified Weaknesses

1. Aid score has low weight (10%): Financial considerations affect the decision less than prestige (35%) or fit (25%), which may underweight cost sensitivity for low-income students.
2. Chetty data conflates cause and effect: rel_att_cond_app captures observed attendance patterns (which include income-correlated application behavior, not just yield response to aid).
3. No net cost comparison: The model does not compare actual dollar costs between competing offers. A student choosing between a $5K net cost school and a $40K net cost school gets no direct price signal.
4. No income-differentiated price sensitivity: A $80K+ family and a <$20K family respond to aid with the same weight (0.10).
5. Named scholarship / merit framing effects absent: Research shows named scholarships boost yield beyond their dollar value.

2. Literature Review: Financial Aid Yield Elasticity

2.1 Foundational Research

Avery & Hoxby (2003/2004), NBER WP #9482 The most-cited study on aid and college choice among high-aptitude students.

Additional behavioral findings: - "Named scholarships" generate stronger enrollment response than equivalent dollar grants (price illusion / prestige signaling) - Front-loaded grants (more money freshman year) have significantly stronger effects than flat grants - ~30% of high-aptitude students respond irrationally -- reducing lifetime NPV of their choice - Students respond to gross tuition, not just net price (tuition + equal aid increase still lowers demand)

Limitation: Data from 1999–2000 cohort of high-aptitude students. The 11pp figure is for students choosing among multiple selective options, not for the general population.

2.2 Price Elasticity Estimates Across Studies

Key insight: Aid-receiving students are 55% more price-elastic than full-pay students at selective institutions (-1.18 vs -0.76).

Grant elasticity at selective LACs: +0.31 (grants boost enrollment). Loan elasticity: +0.12.

2.3 Dynarski's Work on State Aid Programs

Dynarski (2003), AER Georgia's HOPE Scholarship: each $1,000 in aid increased college attendance by 3.7–4.2 percentage points. This is the most-replicated finding in the literature and represents the "consensus estimate" for broad-based aid programs.

Dynarski, Page & Scott-Clayton (2022), NBER WP #30275 Review of 50 years of policy experimentation. Concludes: "Typical financial aid programs have impacts in a range of about 3 to 4 percentage points per $1,000 increase in aid eligibility." More targeted programs (like Pell) show smaller effects due to complexity and take-up issues.

2.4 LaSota et al. (2024/2025) Meta-Analysis

"Does Aid Matter?" -- Review of Educational Research Most comprehensive meta-analysis to date: 709 effect sizes from 86 studies representing 7.66 million students.

Key findings: - Grants produce small but meaningful positive effects on enrollment, credit accumulation, persistence, and completion - Translated estimate: grants increased enrollment by 2.8 percentage points on average - Grants increased persistence by 2.0pp and completion by 0.4pp - Effects did not vary significantly by: eligibility criteria, grant program type, early commitment requirements, award duration, average award amount, or cost coverage type - Grants had larger effects at 2-year institutions than 4-year institutions for credit accumulation - No significant effect on academic achievement or post-college labor market outcomes

2.5 Endowment and Institutional Wealth Effects

Bulman (2022), NBER WP #30404 Counter-intuitive finding: wealthier colleges do NOT increase the number of students served or the fraction receiving aid. Instead, they: - Only modestly increase aid generosity - Offset higher yield rates by becoming MORE selective - Enroll FEWER low-income students and students of color - Use resources to increase spending and institutional rankings

Implication for simulation: At wealthy schools (HYPSM), increased endowment leads to higher selectivity rather than broader access. The current COLLEGE_AID_QUALITY=5 for HYPSM is correct in that these schools meet full need, but the simulation should not assume this translates to higher low-income enrollment rates.

2.6 Merit Aid vs Need-Based Aid

Research on how merit and need-based aid affect yield differently:

Strategic equilibrium (Social Choice & Welfare, 2023): When one college ranks above another, the dominant strategy is for the higher-ranked college to offer need-based aid and the lower-ranked college to offer merit aid. This maps directly to observed behavior: - HYPSM/Ivy+: pure need-based aid, no merit scholarships - Tier 3–4 (Vanderbilt, WashU, Emory, etc.): heavy merit aid to compete for cross-admits - Tier 5–6 (state flagships): mix of merit and need-based

Price illusion / scholarship naming effect: Students are more likely to enroll when they receive a "named scholarship" vs. an equivalent dollar grant, even at identical net prices. A simplified letter affirming belonging while making cost calculations salient increased enrollment in the lowest-cost option by 10.4pp (Behavioural Public Policy, Cambridge).

NACUBO Tuition Discounting Study (2024–25): - Average discount rate at private colleges: 56.3% for first-time undergrads - 83.4% of all undergrads receive some institutional grant aid - Grants cover 63% of tuition and fees for first-time students - Net tuition revenue increased only 1.4% (inflation-adjusted) despite higher discount rates

2.7 Income-Differentiated Yield at Elite Colleges

Chetty et al. (2023), "Diversifying Society's Leaders?"

Children from the top 1% are 2x more likely to attend Ivy-Plus colleges than middle-class students with comparable test scores. Two-thirds of this gap comes from higher admission rates; the remaining third comes from differences in application and matriculation rates.

Observed yield patterns (Class of 2029): - Harvard yield: 84% overall - Princeton yield: 78% - Yale yield: 68% (70% in some sources) - Stanford yield: 82%

Low-income enrollment trends (2024–2025): - Yale, Duke, JHU, MIT all set records for Pell-eligible students - MIT: Pell-eligible students rose 43% over two years, now >25% of freshman class - MIT policy: free tuition for families earning <$200K/year - Princeton: ~25% of Class of 2029 is Pell-eligible

These trends suggest that at full-need schools, yield among low-income admitted students is extremely high (likely 85–95%), while wealthy students with multiple elite options yield at lower rates (65–80%).

3. Synthesis: Yield Elasticity by Student Type

Combining all research sources, here are calibrated elasticity estimates for the simulation:

3.1 Yield Elasticity Table

Notes: - "pp" = percentage points of yield change - Price elasticity is own-price elasticity of enrollment demand - First-gen students have higher price sensitivity due to greater cost uncertainty (SSRN #4816609) and lack of parental guidance on aid negotiation - Low-income yield at Tier 3–4 schools can be LOWER than at HYPSM because Tier 3–4 often don't meet full need, creating unmet cost gaps

3.2 Key Asymmetries

1. Grants > Loans > Work-study: Students weight grant aid roughly 1.6x more than loans in enrollment decisions (Avery & Hoxby)
2. Gains > Losses: An additional $1K in aid boosts yield more (+3–4pp) than a $1K tuition increase reduces it (-2pp). This asymmetry is robust across studies.
3. Need-based > Merit at top schools: At HYPSM, need-based aid signals belonging and eliminates cost barriers. At Tier 3–5, merit aid signals "we want you specifically" which boosts yield through prestige signaling.
4. Named > Unnamed: A $20K "Presidential Scholar" award yields better than a $20K "institutional grant" at the same net cost. Estimate: +3–5pp boost from naming alone.
5. Front-loaded > Flat: Grants with higher freshman-year value yield better than equivalent total grants spread evenly. Estimate: +2–3pp boost from front-loading.

3.3 The Chetty Data Paradox

The simulation's CHETTY_YIELD_BY_INCOME shows bracket 5 ($80K+) with values >1.0 at nearly every school (e.g., Stanford 3.06, Harvard 1.95). This seems to suggest wealthy students are MORE likely to attend. But this is not a yield rate -- it is rel_att_cond_app, relative attendance conditional on being in the applicant pool compared to the national average.

The high values for bracket 5 at elite schools reflect that: - Wealthy students apply to elite schools at much higher rates - Once admitted, their yield is actually LOWER than low-income admits (who have fewer alternatives) - But the sheer volume of wealthy applicants and their higher admission rates (via legacy/donor hooks) means they are overrepresented in the enrolled class

Simulation implication: Using rel_att_cond_app directly as a yield modifier (current approach) is reasonable as a first approximation, but it confounds application behavior with enrollment decisions. A better model would separate the two effects.

5. Summary of Key Numbers for Implementation

Consensus Estimates from Literature

HYPSM Yield by Income (Estimated from Multiple Sources)

Tier 3–4 Yield by Income (Estimated)

Sources

Academic Papers

• Avery & Hoxby (2003) - NBER WP #9482 -- foundational study on aid and college choice
• Dynarski (2003) - Does Aid Matter? -- Georgia HOPE scholarship natural experiment
• Dynarski, Page & Scott-Clayton (2022) - NBER WP #30275 -- 50-year review of aid policy experiments
• Bulman (2022) - NBER WP #30404 -- endowments, aid, and student composition
• LaSota, Polanin et al. (2024) - Review of Educational Research -- meta-analysis of 86 studies, 7.66M students
• Buss, Parker & Rivenburg (2004) -- price elasticity at selective LACs
• Chetty et al. (2023) - Diversifying Society's Leaders -- income, admissions, and attendance at elite colleges
• Financial Aid in College Admissions: Need-Based vs Merit-Based (2023) -- game-theoretic model of aid strategy
• Marifian (2024) - Cost Uncertainty and Enrollment Choices -- FGLI student cost uncertainty

Data Sources

• College Board - Trends in College Pricing 2025
• NACUBO Tuition Discounting Study 2024-25
• Opportunity Insights Data
• NBER Student Aid Packages Digest

Industry / Journalism

• Inside Higher Ed - Rise of Non-Need Merit Aid (2023)
• Fortune - Elite Colleges Record Low-Income Enrollment (2025)
• College Board - Trends in College Pricing Highlights
• NASFAA - Sticker vs Net Price 2024-25
• Ivy Coach - Ivy League Yield Rates

Some sections containing simulation-specific implementation details have been omitted from this public version. The research data and analysis above is based on publicly available sources.