In the past year we have seen students in countries around the world protesting about the cost of higher education and lack of financial aid: Chilean students have been protesting for 7 months to change the overall educational financing system; Californians have occupied the UC Berkeley campus to protest fee hikes, and thousands of English students last year have taken part in protests against increases in tuition fees. Why is this happening all over the world? The message is that students perceive that college returns are high and they have high preferences for higher education, but they are not able to afford it, or they do not have access to a credit market that give them enough resources to invest in this form of human capital. This explains in part the college enrollment gap between high and low income students, an empirical regularity that has been very well documented.
Economists, nevertheless, do not agree on the nature of this gap. Some have argued that there is no credit constraint and the gap is a consequence of differences in background (higher income students receive better quality education, preferences, information, etc.) See for example Cameron and Heckman (2001) , Carneiro and Heckman (2002) , Nielsen et al (2010) , among others. However, others, sometimes using the same data, have presented evidence in favor of the existence of credit constraints (Kane (1994 , 1996 ), Dynarski, (2003) , Belley and Lochner (2007) , and Lochner and Monge-Naranjo (2011) .
Finding evidence on the importance of credit constraints is difficult for two reasons: credit constraint status is not observable, and enrollment also depends in un-observables that are correlated with credit access. Therefore indirect measures of access to credit markets have been used and, not surprisingly, the conclusions on the literature are often contradictory and controversial.
In my job market paper , I exploit the sharp eligibility rules of two student loan programs in Chile that give access to college tuition loans. To be eligible students need to
- Apply for the programs before taking the national college admission test (PSU test).
- Be classified by the tax authority in the poorest 4 income quintiles
- And score above 475 points (more or less the mean) on the PSU test.
For the group of students that score around the program cutoff, scoring barely above or below is quasi random (a simple mistake may change the score from above to below the cutoff) and therefore the loan eligibility depends on that natural randomization enabling a regression discontinuity design. Comparing just below with just above the cutoff addresses the problems of unobserved omitted variables and self-selection, allowing for an unbiased estimate of the causal effect of loan access (directly) on college enrollment.
One additional complexity to the estimation of the effects of loans on college enrollment is usually that there are several unobserved sources of variation in enrollment and in the availability of loans. On one hand, in many countries, college admission depends on the evaluation of subjective variables (i.e. letters of recommendation) that are unobserved by the econometrician. On the other hand, loans (and aid in general) are used as a mechanism to compete among universities trying to attract better students. A key feature of my analysis is the availability of a detailed student-level data set that presents several advantages. First, I observe the entire population of individuals who participate in the national college admission process, including full information on their enrollment, loan eligibility, loan take-up, scholarships, objectively-measured family income, and socio-economic characteristics. Second, I observe the two variables that completely determine college admission: the score on the national college admission test and high school GPA. Finally, the two loan programs of interest offer standardized loans to eligible students. The nature of the loan programs and the availability of these data allow evaluation of the causal effects of credit access on college enrollment and college persistence.
The following figure shows the main result of the analysis: access to the loan programs increases the college enrollment probability by 18 percentage points -- equivalent to a nearly 100% increase in the enrollment rate of the group with test scores just below the eligibility cutoff. Students from the lowest family income quintile benefit the most: for these students access to the loans causes a 140% increase in the probability of enrollment (on a baseline enrollment rate of 15% for students just below the test score cutoff).
More importantly, access to the loan program appears to effectively eliminate the relatively large income gradient in enrollment for students with scores just below the eligibility threshold. The following figure shows that for students who are barely ineligible for loans the enrollment is 15% while for students from the richest quintile the enrollment rate is 30%. Among students who are barely eligible, the gap is statistically zero, i.e. (34% for the poorest and 32 for the richest)
Access to loans not only increases enrollment, but also improves progress in college. Eligible students are 20 percentage points more likely to enroll for a second year and 21 percentage points more likely to enroll for a third year of college. Those numbers are equivalent to a 213% and 445% increase, respectively, when compared with the enrollment probability for the groups without access.
Students with access to loans are 6 percentage points less likely to drop out after their first year and 11 percentage points less likely to drop out after their second year, which are equivalent to a 31% and 38% decrease, respectively. These results contrast with previous findings using a direct question about the importance of credit constraints for the decision of dropping out in an almost tuition free college in the US (Stinebrickner and Stinebrickner (2008) ).
The main weakness is that regression discontinuity is highly consistent for the students around the discontinuity, but we cannot learn much about what happen to students in other part of the score distribution. To deal with this problem I present a second identification strategy that neutralizes family background: I show regressions using family fixed effects for a sample of twins. The results are statistically indistinguishable from the results using RD, which indicates that the effect of loan access on enrollment is similar in other parts of the test core distribution.
This evidence shows that loan access is very important in explaining college enrollment and the enrollment gap by family income. It also sheds light on the importance of policies that complete credit markets in countries with less financial development, to allow not only increasing human capital stock favoring economic growth, but also alleviating intergenerational income inequality.
Alex Solis  is a PhD student from The University of California at Berkeley currently on the job market.