# **2 Related Literature**

Our paper relates to a large literature estimating sequential schooling models under uncertainty, with seminal contributions by Keane and Wolpin (2001), Eckstein and Wolpin (1998), and Keane (2002). This literature models college enrollment, performance, and college outcomes, and uncovers structural parameters based on students’ observed choices during college. In one strand of this literature, researchers model students as acquiring information (learning) throughout college—regarding, for instance, their ability and preferences for college or specific majors, and their expected labor market performance. This literature includes Arcidiacono (2004), Arcidiacono et al (2016), Ozdagli and Trachter (2011), Stinebrickner and Stinebrickner (2014), and Trachter (2015). As in these papers, students in our model adjust their expected graduation probability based on classes completed and choose effort accordingly.

The idea that higher education is risky is not new (Levhari and Weiss 1974, Altonji 1993, Akyol and Athreya 2005), but the recent availability of college transcript data in the U.S. has helped estimate the role of risk in students’ performance. These data reveal substantial and persistent heterogeneity in students’ credit accumulation rates, which are strongly related to graduation probability. According to Hendricks and Leukhina (2017, 2018), based on their credit accumulation rates more than 50 percent of college entrants should be able to forecast whether they are at least 80 percent likely to graduate. According to Stange (2012), the large uncertainty faced by students makes them place a high value on the ability to drop out at any point rather than pre-commit to completing all graduation requirements. Our paper is similar to these in the use of administrative data to track students’ performance, but different in that the risk associated to class completion or college continuity is not fully exogenous as in these papers but depends on an endogenous variable—student effort.

While the literature has placed much attention on the role of ability in performance and college outcomes, a growing line of research highlights the role of effort. Zamarro, Hitt, and Mendez (2019) use data from the Program for International Student Assessment (PISA) to show that different effort measures explain about a third of observed cross-country test score variation. Stinebrickner and Stinebrickner (2004) rely on time use surveys to estimate the effects of study time on grades. Ariely et al (2009) show that using incentives can help the average student improve her test performance, though the effect is limited on high-ability students. Beneito et al (2018) provide evidence that the tuition increase implemented by Spanish colleges in 2012 boosted student effort. Ahn et al (2019) model effort in response to grading policies. We contribute to this line of research by explicitly modeling the role of effort and embedding it in a dynamic setting, where it affects class accumulation and risk mitigation.

In an efficient and equitable world, college enrollment would depend on student ability rather than parental resources (Cameron and Heckman 1998 and 1999, Carneiro and Heckman 2002). In Colombia, as in other countries, parental resources matter greatly to college enrollment even controlling for ability. This provides strong evidence for credit constraints limiting college access, as discussed in a large literature. Lochner and Monge-Naranjo (2011) develop a model that helps explain the rising importance of family income for college attendance in the U.S. even in the presence of credit. Solis (2017) finds that relaxing credit constraints in Chile had a positive impact on enrollment and college years completed, particularly for low-income students. Parental resources and background, however, may be of limited importance. Hai and Heckman (2017) show that equalizing initial ability has larger effects on college outcomes and 6