Examining the extensive and intensive margins of financial aid

#JHR_Threads 2021a: Who and how does financial aid help?

Jeff Denning is an assistant professor in the economics department at Brigham Young. In addition to being an active researcher in the field of education, he is also an avid fisherman. I know this because he posts pictures of fish he’s caught from streams and rivers, and because of how grossed out I get by holding fish, I usually skip to pictures that don’t involve him holding the latest fish he has caught. All joking aside, Jeff is a productive young economist who graduated from the University of Texas and writes on a variety of topics covering education and labor economics. This week’s #JHR_Threads will discuss his solo authored paper in the Journal of Human Resources, “Born Under a Lucky Star”.

Financial aid in the United States cuts through a variety of subsidies and transfers from both federal grants as well as the tax system more generally. Students depend on these programs because the last several decades have seen a dramatic rise in college tuition costs that have far outpaced inflation adjusted rises in median incomes. While college tuition has risen, time to completion has also risen which given higher tuition costs suggests the total cost of college has itself risen along multiple margins. Earlier work by economists showed that an increase in the demand for educated labor has contributed to growing inequality in the US. Insofar as the college degree, as opposed to merely the human capital contained in it, is a strong signal of unobserved productivity, then the fact that college completion rates have also fallen is a bellwether of challenging life circumstances for many Americans given the college degree insulates many from unemployment and poverty. Given the ratio of earnings for college completion compared to high school only accreditation has itself risen over the last 50 years, many see an investment in college as a necessary condition for middle class levels of earnings, wealth and overall, a higher quality of life.

Denning’s paper is valuable against the backdrop of these larger macro labor conditions because it focuses intently on the financial aid loans that are given to students to complete their college educations. But the impact, if it does exist, can be expressed in two ways. First, financial aid may change the incentives of a potential student who stands at the margin of investing in college education, waiting to get in. If financial aid lowers the total cost of college, then the returns, net of total cost, rise and the marginal student exits the labor force to invest in college education. But the extensive margin is not the only way in which financial aid may affect students; it may also affect the intensive margin of incumbent students who decide to persevere towards completion as a result of financial aid lowering the marginal cost of their schooling. Disentangling these two may help us better understand the mechanisms relating financial aid to the college degree.

Denning’s project is able to crack this black box open to a larger degree than other studies because of the rich state-wide administrative dataset he analyzes using a classic type of regression discontinuity design. I say classic because it bears similarities with Angrist and Krueger’s classic study using quarter of birth as an instrument for schooling when evaluating school’s impact on earnings. The design used in Denning’s study is a regression discontinuity design wherein an arbitrary cutoff based on date of birth substantially increases the amount of financial aid a student can access. The reason that they are able to access more financial aid feeds into larger questions making the identification strategy more than merely a clever trick that can be used to leverage estimation of causal effects. Denning’s design allows us to better understand how older students, who have become a sizable share of all college students around the country, respond to financial aid itself, because the eligibility that he exploits is one which only applies to “financially independent” students, a group often referred to as “nontraditional students”.

Consider two students: Mike and Jon. Mike was born on December 31st, and Jon was born on January 1st. When Mike and Jon first entered college, their loan applications for financial aid required listing their parents’ assets and income, as well as their own. The higher their parents’ earning potential and savings, the less that Mike and Jon could borrow. But, the linking of financial aid to parental income disappears at age 24 because at that point, students seeking financial aid only use their own earnings and assets when seeking aid. Such students are considered “financially independent” and as such experience an exogenous rise in financial aid coming from having the excellent foresight to be born earlier than others. This is why Denning names his article “Born Under a Lucky Star”, for it is luck, not unobserved ability, which causes the financial aid opportunities to rise for older students. Mike, born somewhat earlier than Jon, becomes financially independent one day earlier than a cutoff thus allowing comparisons between the two to measure causal effects of exogenous spikes in financial aid on college enrollment, completion and education itself.

The age cutoff that Denning uses increases grants and loans by $1450. This in turn results in a 1.8 percentage point increase in the probability that college seniors graduate a year earlier. But this is not, it appears, caused by the extensive margin changes in enrollment by nontraditional students. Rather it reflects changes in the behavior of the inframarginal student who decides to persist in their studies as a result of the help from financial aid.

The data comes from the Texas Higher Education Coordinating Board which contains the universe of students enrolled in Texas’s public universities from 2002 to 2014. Such datasets have become common in the field of labor and education due to the digitization of student records and cooperation with schools to share these data with researchers. These data, which contain information on financial aid, demographics, students enrollment, credits attempted and graduation are then linked to quarterly earnings using the Texas Workforce Commission.1 Because the research design focuses on the financially independent students, he limits his sample to college seniors enrolled at Texas public universities in the year they turned 24. His regression equation is an RDD with age interacted with treatment so that slopes on age (his running variable) can differ on either side of the birthday cutoff itself:

The parameter of interest is theta, which under either a smoothness assumption or a design-based randomization assumption, will pick up the average treatment effect for compliers at the cutoff itself. These compliers, as I said earlier, can be either the extensive margin or inframarginal students, but Denning’s data shows that the estimated causal effect he recovers is only for the inframarginal students who persist as a result of receiving aid. As is often considered mandatory for designs like the one Denning uses, he checks for whether students are fraudulently misreporting their dates of birth — a difficult and impressive task indeed given birth dates are verified by Social Security records — so as to receive these higher levels of aid, and finds that students in his data do not do this. Denning suspect that in addition to the sheer heroic difficulties of achieving such levels of fraud, part of the reason that students do not manipulate where they are around the arbitrary birthday cutoff is because many do not know about these subtle matters.

A study like this is meaningless if Denning can’t first establish that the cutoff does indeed increase the intensity of treatment itself, and Denning shows this using both classic RDD figures with the running variable (age) re-centered by subtracting the cutoff date of birth from students’ actual dates of birth. Total grants, total loans and borrowing all increase as a result of hitting age 24 one day earlier than others.

The nuanced impact that financial aid has on the inframarginal student is fascinating. For one, he finds that small increases on the order of what occurs at age 24 cause students to attempt more credit hours, thus representing more time spent away from leisure and work. This increase in credit hours has three opportunity costs. First, it reduces income from foregone work. Second, it causes total spending on college decline insofar as it allows the student to exit college earlier, ceteris paribus. Third, it increases the toll on student time and energy as they take on more coursework than they would’ve in counterfactual. Many of these can be evaluated using these data though. Denning finds no change in student GPA suggesting that whatever higher toll it has on students, it does not negatively impact their grades overall. It also represents, as said earlier, nearly a 2pp increase in graduation.

The good news of this study is it appears that financial aid causes students to complete college sooner than they would’ve counterfactual. We see this in the “reenroll 4 years” second column of the second row of the above table. Future reenrollment declines because graduate in the year of treatment rises. Earnings falls, as well, suggesting that the loans themselves are crowding out student labor supply at the intensive margin, thus freeing up more time.2 This may explain why there is no impact on GPA — student time has increased and in response, students take on more credit hours by enrolling in more classes.

Careful analysis is needed to better understand the degree to which financial aid is an investment in the nation’s savings rate by increasing the stock of workers with higher levels of human capital versus merely a transfer to wealthier families. The former would represent positive returns to financial aid because it implies that college completion is higher relative to a counterfactual as a result of the access of resources that financial aid opens up. But it would be the treatment effect of financial aid was small, or even zero, for students who collect financial aid and complete their degree. A zero treatment effect in this context would imply that an inframarginal student receiving financial aid would have completed their college degree under any scenario regardless of whether they obtained financial aid. Investments increase the productivity of workers thus driving up real wages, but the latter has no effect on productivity because it is nothing more than a transfer to a group already intent on finishing their degrees.

The neediest students are those who plausibly would not have finished college were it not for the aid itself. But these students cannot be directly observed as obviously there is no flag for students with counterfactual drop out probabilities. But, while Denning cannot observe them directly, he can infer them from choices made prior to turning 24. Denning examines this transfer versus investment question by exploiting facts about the students’ lives up to the point of turning 24, such as whether they had received family contributions or Pell grants before. This analysis is summarized in Table 4.

Denning notes that students who had not received a Pell grant when they were 23 years old generally come from families who are wealthier. Excluding their family’s income causes large changes in need-based financial aid, but despite a much larger change in grant aid, the impact that this has on completion time is smaller and is not statistically significant. The impact on those students who had received a Pell grant when there were 23 is meaningfully large. The additional aid caused 2.85 percent of students to graduate one year earlier suggesting that these students face more liquidity constraints than the sample as a whole. This analysis by such background factors causes Denning to conclude that while financial aid pushes students through the college pipeline faster, it is not well targeted. He writes:

“Taken together, the results on heterogeneity by previous Pell receipt suggest that financial independence gives more resources to relatively wealthier students. Despite this, the reduced time to graduation seems to be larger for needier students. In fact, aid is likely to be efficient when given to students who qualified for the Pell Grant in the year they turned 23 because the benefits to the students are less than or equal to the costs. These results on heterogeneity highlight the educational attainment benefits of targeting financial aid to the neediest students.”

Jeff Denning, a junior faculty in the profession focusing on education and labor economics questions, helped peel back the causal effects of financial aid on college enrollment, completion and increases in the stock of citizens with a college degree. All of these questions are relevant for thinking through optimal financial aid, but also optimal human capital investment, as these questions ultimately shape the distribution of earnings and resources around the country. Denning has found that financial aid has complex impacts on the inframarginal student population — time to degree increases, but not always causally insofar as some of the aid went to students who would’ve graduated anyway such as those from wealthier families. A takeaway of this study suggests that targeted financial aid programs aimed at the least well off may have larger returns than simply using the vanishing of family income as a mechanism of aid itself, for the vanishing of family income selects on both the needy and the wealthy. I applaud the author, editor, and referees for crafting such an important study.


The Texas Workforce Commission has never returned my phone calls or emails, so I am even more impressed in Denning’s study!


I emphasize the “intensive margin” of work because Denning finds no evidence that financial aid causes students to stop working. The coefficient on whether students have any non-zero earnings does not change as a result of financial aid. What does change is the amount of positive earnings. Earnings falls by $500 as a result of access to financial aid which suggests that under this regime, students work — they just work less.