As in our model, the 2006 entry cohort starts to graduate in 2010. In 2006, the initial share of college graduates in the workforce equals 27 percent.<sup>30</sup> Universal free college raises this share for a particular cohort by 12 pp, to a long-run value of 39 percent (panel a). In the short-run the college premium falls relatively little (panel b) because the increase in college graduates from the first few cohorts is small relative to the stock of college-educated workers, which includes individuals from 35 to 40 cohorts. Over time, the continuous inflow of a greater number of college graduates produces a larger college premium impact—but still small, given our estimated _ω_ , and unlikely to dissuade many high school graduates from college enrollment. As a robustness check, panel b depicts the implied college premium path for several _ω_ estimates for developed economies.<sup>31</sup> The college premium declines more for these values, yet even the greatest decline -down to 1.70- still leaves the economy with a substantial college premium, comparable to that in the U.S. Skill-biased technical change, of course, would lead to an even smaller decline for any value of _ω_ .

In sum, both the short- and long-run college premium decline induced by free college would likely be small in Colombia. As a result, abstracting away from the general equilibrium implications of free college is not likely to bias our predictions substantially. College, thus, would remain a worthy investment even if free college produced more college graduates.<sup>32</sup>

# **9 Conclusions**

In this paper we have developed and estimated a dynamic model of college enrollment, performance, and graduation. A central piece of the model, student effort, has a direct effect on the completion of classes and an indirect effect mitigating risks on class completion or college persistence. We have estimated the model using rich administrative data from Colombia. According to our estimates, effort has a much greater impact than ability on class completion. Failing to model effort as an input to class completion leads to overestimating the role of ability by two or three times, and to favoring policies that promote positive selection of new students instead of effort. We have used our parameter estimates to simulate multiple free college programs. According to our simulations, universal free college expands enrollment the most but has the highest per-graduate cost and does not raise graduation rates. Performance-based free college, in contrast, delivers a slightly lower enrollment expansion but has a greater graduation rate and a lower per-graduate cost. Performance-based free college faces students with greater risks than the current baseline or universal free college; precisely for this reason it elicits greater

> 30Notice that the initial share of 27 percent is higher than the initial fraction of high school graduates that finish college, equal to 14.5 in the baseline. The reason is that 27 percent includes graduates from all bachelor’s programs (rather than only five-year programs) as well as graduates from two-year programs. This is because the college premium is calculated for all higher education graduates, based on data that does not distinguish between graduates from bachelor’s and two-year programs.

> 31We use the point estimates of 1.4 from Katz and Murphy (1992) and Heckman et al (1998), 2.5 from Card and Lemieux (2001), and include lower value of 1.2. For each _ω_ value, the intercept has been adjusted to generate the same college premium for the year 2012.

> 32These results are consistent with Garriga and Keightley (2007), who conduct a similar analysis for the U.S. in a model that endogenizes the college premium, government budget constraint, after-tax earnings, and labor supply decisions. They show that tuition subsidies have small effects on the college premium even when accounting for taxes. Their results are partly due to the limited effects of the policy on graduation rates, and to the high elasticity of substitution between college and high school graduates.

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