Marginal Returns to Public Universities: Mountjoy (2026)

What this is. The paper’s core results, the identification design with its key equations, and the intensive/extensive margin bounding method: enough to know what it found and how without reading all 69 pages. To replicate or extend it, read the full source at https://doi.org/10.1093/qje/qjaf055.

TL;DR

Barrow and Malamud (2015) documented the scarcity of credible causal evidence on the returns to college, and Carneiro, Heckman, and Vytlacil (2011) showed that marginal returns to education may be heterogeneous across individuals. This paper addresses both gaps. It assembles a large collection of decentralized SAT/ACT admission score cutoffs at all 35 Texas public universities and links them to administrative records on high school preparation, college trajectories, and long-run quarterly earnings. A fuzzy regression discontinuity (RD) design compares barely admitted versus barely rejected applicants at each cutoff. Marginally admitted students gain roughly one additional year of four-year college credits, become 12 percentage points more likely to ever earn a bachelor’s degree, and earn 8.6% more than their marginally rejected counterparts eight to twelve years out. Grant aid nearly fully offsets the additional tuition cost, so marginally admitted students pay essentially no additional net tuition. A formal cost-benefit analysis finds internal rates of return of 26% for students, 16% for society, and 7% for the government. Earnings gains are similar across institutions of widely varying selectivity, while students from low-income families reap smaller earnings gains. Lower degree completion, more time enrolled, and less lucrative majors are potential explanations for this gap. A bounding method reveals that the pooled gains are driven primarily by students who would not have enrolled in any four-year college if rejected (the extensive margin), with a smaller contribution from students who would have attended a less selective four-year institution (the intensive margin).

Core results

Magnitudes are as reported; all estimates use the main fuzzy RD specification of Section II.D. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Marginal admission increases cumulative four-year credits by 28.4 (roughly 1 full year of four-year education)	Table II, p. 463; Figure VI, p. 456	LATE = 28.4 credits (se = 3.0); untreated complier mean = 64.7 credits; net gain in two-year credits = -15.5 (se = 1.9)
R2	Marginal admission raises the probability of ever earning a BA by 12 pp	Table II, p. 463; Figure VI, p. 456	LATE = 0.119 (se = 0.026); untreated complier mean = 0.406; effect is entirely in non-STEM fields (Figure VII, p. 458)
R3	Log earnings gain of 8.6% (pooled 8-12 years after application)	Table II, p. 463; Figure VIII, p. 460	LATE = 0.086 (se = 0.032); crossover from negative to positive earnings effects at year 6
R4	Annual dollar earnings premium of $3,339 (8-12 years out)	Table II, p. 463; Figure VIII, p. 460	LATE = $3,339 (se = 1,288); untreated mean = $40,829; 8.2% of baseline mean
R5	Earnings rank gain of 4.1 percentile points in statewide distribution	Table II, p. 463; Figure VIII, p. 460	LATE = 4.1 pp (se = 1.4); untreated mean = 52.4; from about the 50th to the 54th percentile
R6	Zero additional net tuition; private IRR of 26%, social IRR of 16%, taxpayer IRR of 7%	Online Appendix Figure A.13; Figure X, p. 469	Net tuition LATE ≈ $0 (grant aid offsets $4,600 gross tuition increase); NPV at 3%: $70,000 student, $80,000 social; society payoff horizon: 11 years, taxpayer: 19 years
R7	No systematic earnings difference across institution selectivity	Figure XII, p. 477	Log-earnings slope per 100 SAT points of selectivity = -0.000 (se = 0.019); dollar-earnings slope weakly positive but not significant; selectivity predicts peer earnings gain (~$3,000 per 100 SAT) but not complier own-earnings gain (~$900 per 100 SAT, insignificant)
R8	Low-income (FRPL-eligible) compliers experience near-zero earnings gains 8-12 years out	Figure XIII, p. 480	Point estimate for FRPL group indistinguishable from zero; non-FRPL gains are positive and significant; lower degree completion, more time enrolled, and less lucrative majors are potential explanations for the gap
R9	Extensive-margin BA completion effect is 20-25 pp; intensive-margin effect is only 4-7 pp	Figure XIV, p. 486; Figure XV, p. 489	A₀=0 group (93% extensive-margin) LATE bounds: [20, 25] pp; A₀=1 group (71% intensive-margin) LATE bounds: [4, 7] pp; extensive margin drives the majority of the pooled 12 pp effect
R10	Complier fallback enrollment is split across another four-year college, a two-year college, and no Texas college covered by THECB records	Figure V, p. 453; text p. 454	If rejected from the target: 47% attend another Texas four-year college, 43% attend a Texas two-year college, and 9% do not enroll in a Texas public or nonprofit private college covered by THECB records
R11	Marginal admission displaces some two-year credits and certificate or associate degree completion	Table II, p. 463	Two-year credits: LATE = -15.5 (se = 1.9); certificate or AA: LATE = -0.069 (se = 0.020)
R12	Admission has no detectable effect on whether compliers have positive earnings	Table II, p. 463; Figure VIII, p. 460	LATE = 0.016 (se = 0.021); the estimate is statistically indistinguishable from zero
R13	BA completion gains are smaller for low-income students, while the subgroup difference is imprecise	Figure XIII, p. 480	FRPL compliers: +9.7 pp; non-FRPL compliers: +13.5 pp; estimates are not statistically distinguishable
R14	Admission and enrollment discontinuities support the fuzzy RD first stage	Figure III, p. 446	Admission rises 27 pp; target-university enrollment rises 15 pp (se = 0.3 pp; F = 2,024)
R15	Density and covariate-predicted outcomes show no discontinuity at the cutoff	Figure IV, p. 447	Log density RD = 0.005 (se = 0.011); predicted BA RD = -0.0013 (se = 0.0012); predicted earnings RD = 19 (se = 63)
R16	The extensive-margin group has larger bounds for gains in college peer quality	Figure XV, p. 489	Peer-score bounds: A₀=0 [0.51, 0.56] SD, A₀=1 [0.40, 0.45] SD; peer-earnings bounds: A₀=0 [$7,716, $9,233], A₀=1 [$5,224, $6,110]
R17	Four-year credit gains are concentrated among the extensive-margin group	Figure XV, p. 489	Credit LATE bounds: A₀=0 [52.2, 58.5]; A₀=1 [1.8, 14.5]
R18	Earnings gains are positive in both margin groups and larger for the extensive-margin group	Figure XV, p. 489	Dollar earnings bounds: A₀=0 [$2,947, $4,087], A₀=1 [$2,903, $3,569]; log-earnings bounds: A₀=0 [0.100, 0.129], A₀=1 [0.060, 0.077]
R19	Earnings-rank bounds are larger for the extensive-margin group	Figure XV, p. 489	A₀=0 [5.3, 6.9] percentile points; A₀=1 [2.5, 3.4] percentile points
R20	Cutoff crossing reduces the share with another Texas public university admission offer	Text p. 484 (Online Appendix Figure A.24 discussed)	Reduced-form effect = -4.7 pp; this makes the observable stratifier endogenous to cutoff crossing
R21	Gender and race subgroup returns are not statistically different, despite large baseline demographic gaps	Figure XIII, pp. 480-481; text p. 482	Gender earnings and BA effects are not statistically distinguishable; white/Asian and Black/Hispanic complier gains are similar despite baseline gaps exceeding 10 pp in BA and $10,000 in earnings

Overall (paper’s conclusion). Marginal admission to U.S. public universities generates positive returns for students, society, and taxpayers, even after accounting for the costs of additional education and the delay before earnings gains materialize. The returns are associated with increases in four-year credits and degree completion; grant aid offsets added tuition. Lower degree completion, more time enrolled, and less lucrative majors are potential explanations for smaller earnings gains among low-income students. The returns are broadly similar across institutions of varying selectivity, but smaller for students from low-income families. The predominance of extensive-margin gains suggests that the returns are primarily from expanding access to any four-year institution rather than from upgrading to a more selective one.

Theory / model

The paper has no structural economic model. The key parameter of interest is the local average treatment effect (LATE) of enrolling at a target public university for marginal applicants who enroll if and only if they barely cross the admission cutoff.

Potential outcomes setup (Section II.D, p. 449). Let D indicate whether applicant i enrolls at the target university. Define $Y_1$ as the potential outcome if enrolled and $Y_0$ if not. The applicant’s concorded test score serves as the running variable R, with c the admission cutoff for a given application cell. The marginal applicants are those with $R = c$; among them, $D_1(c) = 1$ (would enroll if admitted) and $D_0(c) = 0$ (would not enroll if rejected) defines the complier population. The parameter of interest is:

$$\text{LATE} = \mathbb{E}[Y_1 - Y_0 \mid R = c,\; D_1(c) = 1,\; D_0(c) = 0]$$

This is identified by the fuzzy RD estimand (equation 1, p. 449):

$$\text{LATE} = \frac{\lim_{r \downarrow c} \mathbb{E}[Y \mid R=r] - \lim_{r \uparrow c} \mathbb{E}[Y \mid R=r]}{\lim_{r \downarrow c} \mathbb{E}[D \mid R=r] - \lim_{r \uparrow c} \mathbb{E}[D \mid R=r]} \tag{1}$$

Four standard assumptions justify this (Hahn, Todd, and Van der Klaauw (2001); Dong (2018)): (i) first-stage relevance (Figure III bottom panel, p. 446: first-stage LATE = 0.150, F = 2,024); (ii) continuity of conditional expectations of unobservables through the cutoff; (iii) monotonicity (cutoff-crossing weakly increases enrollment); and (iv) the exclusion restriction (cutoff-crossing affects outcomes only through initial enrollment at the target university). The smooth density of applicants and their pre-college characteristics through the cutoffs supports assumption (ii) (Figure IV, p. 447).

The pooled estimand identified by pooling all application cells is a weighted average of cell-specific LATEs, with more weight on cells where applicants at the cutoff are more numerous and more likely to be compliers (Cattaneo et al. (2016), p. 450).

Identified hypotheses. The paper tests three conceptually distinct questions: (1) Does marginal admission increase four-year educational attainment? (2) Does it generate long-run earnings gains that exceed the costs of additional education? (3) Are the effects driven by the extensive margin (first access to four-year college) or the intensive margin (upgrading selectivity)? These are tested sequentially across Sections III, IV, and VII respectively.

Method

Cutoff inference (Section II.B-C, pp. 441-443). Because publicly posted admissions criteria may differ from operative criteria and invite strategic manipulation, cutoffs are inferred from the data. For each of roughly 700 application cells (university × year × high-school GPA quartile × test type), local linear regressions are estimated at each distinct test-score value and the cutoff is defined as the value producing the largest discontinuity in admission and enrollment. The search evaluates local linear discontinuities at each distinct test score; about 20% of initially inferred cutoffs with significant density or covariate discontinuities are excluded from the main analysis. Porter and Yu (2015) show this yields a superconsistent estimator of the true cutoff, leaving the asymptotic distribution of the second-stage RD estimator unaffected. The procedure identifies cutoffs distributed across the full SAT/ACT score range (Figure I, p. 444).

Intensive/extensive margin bounding method (Section VII, p. 484-489). This builds on partial-identification-bounds from Manski and Pepper (2000) and the complier-describing logic of Abadie (2002). Let $A \in \{0, 1\}$ indicate whether a given applicant has any other Texas public university admission offer. The pooled LATE decomposes as (equation 2, p. 485):

$$\mathbb{E}[Y_1 - Y_0 \mid D_0=0, D_1=1] = \omega\, \mathbb{E}[Y_1-Y_0 \mid D_0=0, D_1=1, A_0=1] + (1-\omega)\,\mathbb{E}[Y_1-Y_0 \mid D_0=0, D_1=1, A_0=0] \tag{2}$$

where $\omega$ is the share of cutoff compliers with $A_0 = 1$ (another four-year option available) and $(1-\omega)$ is the share with $A_0 = 0$ (no other four-year option). Since $A_0$ is a latent type (endogenous to cutoff-crossing), the paper imposes a rank assumption: A-always-takers have weakly better treated potential outcomes than A-compliers, who have weakly better outcomes than A-never-takers. This assumption is supported by observed covariate patterns (Figure XIV top right panel, p. 486) and yields sharp bounds on the separate intensive- and extensive-margin LATEs (Figure XV, p. 489).

Empirical specifications

All specifications follow Section II.D (pp. 449-450) and use the regression-discontinuity-design approach. The running variable for each applicant is her concorded test score minus the admission cutoff of her target application cell, with SAT scores divided by 40 to convert to ACT units for pooled estimation.

Main RD specification (all results, R1-R8). For outcome Y measured at a given year:

$$Y_{iac} = \alpha_{ac} + \gamma_{ac}^{-} R_{iac} \cdot \mathbf{1}[R_{iac} < 0] + \beta_{\text{RF}} \cdot \mathbf{1}[R_{iac} \geq 0] + \gamma_{ac}^{+} R_{iac} \cdot \mathbf{1}[R_{iac} \geq 0] + \varepsilon_{iac}$$

where $\alpha_{ac}$ are application-cell fixed effects, $\gamma_{ac}^{-}$ and $\gamma_{ac}^{+}$ are cell-specific running-variable slopes on each side of the cutoff, and $\beta_{\text{RF}}$ is the reduced-form discontinuity. The bandwidth is 3 concorded ACT points (approximately 120 SAT points) with a triangular kernel. Standard errors are clustered at the applicant level (Kolesár and Rothe (2018)). The first-stage regression substitutes D (enrollment at the target university) for Y:

$$D_{iac} = \alpha_{ac}^D + \gamma_{ac}^{D-} R_{iac} \cdot \mathbf{1}[R_{iac} < 0] + \pi \cdot \mathbf{1}[R_{iac} \geq 0] + \gamma_{ac}^{D+} R_{iac} \cdot \mathbf{1}[R_{iac} \geq 0] + u_{iac}$$

with $\hat\pi = 0.150$ (se = 0.003; F = 2,024, Figure III, p. 446). The LATE is $\widehat{\text{LATE}} = \hat\beta_{\text{RF}} / \hat\pi$. No additional control variables are required; the estimates are very similar when adding the full suite of pre-college covariates.

Pooling across application cells. The running variable is normalized to zero at each cutoff, and application-cell fixed effects $\alpha_{ac}$ absorb all between-cell variation. The pooled estimand is a precision-weighted average of cell-specific LATEs (Cattaneo et al. (2016)); cells with a more numerous and more complier-dense pool at the cutoff receive more weight.

Local-linear estimation of the reduced form and first stage (Section II.D, pp. 449-451). The paper estimates the outcome and enrollment discontinuities separately, with application-cell fixed effects and cell-specific slopes on both sides of the cutoff. The exact local-linear structure corresponds to the displayed equations above; the reported treatment effect divides the reduced-form jump by the enrollment jump. The baseline uses a 3-point concorded-ACT bandwidth, a triangular kernel, no additional controls, and applicant-clustered standard errors. The estimation sample contains 234,271 applicants for education outcomes and 200,456 for earnings outcomes (Table II, p. 463).

Earnings stacked panel. For the pooled years 8-12 estimates, year-specific cell intercepts, running-variable slopes, and cutoff effects are estimated in the stacked individual-year panel:

$\text{Y}_{iacy} = \alpha_{acy} + \beta_y \text{Z}_{iac} + \gamma_{acy}^{-} R_{iac}\mathbf{1}[R_{iac}<0] + \gamma_{acy}^{+} R_{iac}\mathbf{1}[R_{iac}\geq 0] + \varepsilon_{iacy}$

Here $y \in \{8,9,10,11,12\}$ indexes years since application and $\text{Z}_{iac}=\mathbf{1}[R_{iac}\geq 0]$. The cutoff coefficients are scaled by the first-stage jump; year-specific cell intercepts/slopes absorb each year’s running-variable pattern. Standard errors cluster by individual. This specification is described in footnote 17, p. 461.

Balance and density checks. The McCrary specification uses local quadratic functions on either side of the cutoff with a four-point bandwidth; predicted BA and earnings are built from the predetermined-covariate models described in Figure IV’s notes (p. 447). Estimates are 0.005 (se = 0.011), -0.0013 (se = 0.0012), and 19 (se = 63), respectively (Figure IV, p. 447). The earnings-availability check is the outcome “has positive earnings,” whose RD estimate is 0.016 (se = 0.021; Table II, p. 463).

Earnings stacked panel (R3-R5, R7-R8). For earnings outcomes over years 8-12, a long panel is constructed with one observation per individual per year. Year indicators are interacted with cell fixed effects and slopes; the coefficient on $\mathbf{1}[R_{iac} \geq 0]$ in this pooled specification delivers a precision-weighted average of the year-specific LATEs (Section III.C, p. 461, footnote 17).

Intensive/extensive margin specification (R9). Two separate fuzzy RD regressions replace Y and D with interactions involving the stratifier $A$ (whether the applicant has any other Texas public university offer). A series of RD regressions on $Y$, $D$, and $A$ interactions identifies the observable mean potential outcomes; the rank assumption then bounds the unobservable components (Online Appendix C; Figure XIV, p. 486).

Covariate balance and density tests. Figure IV (p. 447) verifies: (i) no discontinuity in log application density (McCrary (2008) test: RD estimate = 0.005, se = 0.011); (ii) smooth covariate-predicted BA completion through the cutoff (estimate = -0.0013, se = 0.0012); (iii) smooth covariate-predicted earnings through the cutoff (estimate = 19, se = 63). Specification checks across 12 alternative bandwidth and polynomial choices confirm robustness (Online Appendix Figure A.11).

Datasets used

Dataset	Role in paper	Wiki page
Texas administrative education records via UT-Dallas Education Research Center (UT-Dallas ERC): Texas Education Agency (TEA) high school records and Texas Higher Education Coordinating Board (THECB) college application, admission, and enrollment records	Running variable (SAT/ACT scores), admission decisions, enrollment trajectories, credit accumulation, degree completion, financial aid - 35 TX public universities, cohorts 2004-2014	No page yet
Texas Workforce Commission (TWC) quarterly earnings records	Labor market earnings outcomes, 8-12+ years post-application; quarterly “sandwich” earnings measure	No page yet
IPEDS (Integrated Postsecondary Education Data System, NCES)	Institution-level per-student expenditures, tuition sticker prices, for cost-benefit analysis	No page yet
National Student Clearinghouse (NSC)	College enrollment records outside Texas for 2008-2014 cohorts (two-thirds of sample), to verify no college enrollment elsewhere	No page yet

Sample: Texas public high school graduates 2004-2014; RD bandwidth yields 234,271 applicants for education outcomes and 200,456 applicants for earnings outcomes. Earnings outcomes are available for a 12-year post-application window; cost outcomes lag by one year and are observed for 9-year balanced panels.

When to read the full paper

Read the original if you need: the full battery of specification checks across bandwidths, polynomial forms, and cutoff definitions (Online Appendix Figures A.10-A.12); the institution-by-institution and demographic-subgroup heterogeneity results with confidence intervals (Figures XI-XIII); the detailed cost-benefit accounting under alternative assumptions about room and board, earnings growth, and life-cycle extrapolation (Online Appendix Figures A.15-A.18); the formal exposition of the intensive/extensive margin bounding method and its proofs (Online Appendix C); or the comparison with prior estimates from Hoekstra (2009), Zimmerman (2014), Kozakowski (2023), Goodman, Hurwitz, and Smith (2017), Bleemer (2024), and Smith, Goodman, and Hurwitz (2025) reconciling this paper’s smaller effect sizes with their larger estimates via differences in treatment size and institution type (Section III.D, pp. 463-465). The locators in the Core results table above point to the exact tables and figures.

Attribution and rights

Source: peer-reviewed, The Quarterly Journal of Economics 141(1), 2026. This distillation was extracted by an LLM on 2026-06-28 and is not human-verified or independently reproduced. The CC BY 4.0 licence permits mirroring; the verbatim PDF is not hosted in this batch.

Attribution (CC BY 4.0). Mountjoy, Jack. “Marginal Returns to Public Universities.” The Quarterly Journal of Economics 141, no. 1 (2026): 429-497. DOI: 10.1093/qje/qjaf055. Copyright The Author(s) 2025. Published by Oxford University Press on behalf of President and Fellows of Harvard College. Licensed under CC BY 4.0. This page is an adaptation by the Institute for Automated Research: core results extracted and re-expressed; changes were made.