which has generally found positive enrollment and graduation effects.<sup>23</sup> In recent years, several states have implemented a variety of financial aid programs based on ability and/or need,<sup>24</sup> as well as “Promise” programs, which provide free tuition to eligible students for local community colleges or state four-year institutions.<sup>25</sup> Overall, these programs have had positive effects on enrollment and graduation. Also consistent with our counterfactuals, the literature has found greater effects of financial aid on enrollment than on graduation (the latter being in the modest range of 0 to 6 or 7 pp)<sup>26</sup> and greater effects for performance-based than unconditional aid (Dynarski and Scott-Clayton 2013).

Even though performance-based free college raises graduation rates the most in our simulations, it still delivers a relatively small graduation rate increase (approximately 10 percent of the baseline graduation rate). This begs the question of why free college (or financial aid, in general) fails to substantially raise graduation rates.

The answer emerging from our model is that free college fails to induce in many students a large, non-marginal effort increase. As Table 9 shows, students who need to catch up exert more effort. Particularly when the student has fallen far behind, catching up is difficult (Section 4), which limits the effectiveness of performance incentives. This suggests that additional supports for class completion—particularly in year 1—may be needed, including remedial education, advising, and tutoring.<sup>27</sup> Indeed, in their study of possible policies to raise graduation rates in the U.S., Avery et al (2019) conclude that need-based free college combined with institutional funding for these supports might be the most cost-effective policy. A cautionary tale, however, comes from Oreopoulos and Petronijevic (2019), who find that these supports help students realize the need for greater effort but have little effect on college continuity or graduation. The reason is that students respond not by raising effort but by expecting less of themselves.

Moreover, our counterfactuals have assumed some highly favorable—perhaps unrealistic— conditions, as discussed before. One of them is no capacity constraints in higher education. Free college, however, would likely run into capacity constraints and force institutions to ration access. Bucarey (2018) explores the potential effects of free college ( _gratuidad_ ) in Chile, where it was introduced in 2016 for the bottom 60 percent of the income distribution. Data prior to 2016 shows that when low-income students are given additional financial aid, institutions respond by becoming more selective, thereby leading to a _lower_ share of low-income students. Using his structural model, Bucarey (2018) predicts that capacity-constrained institutions would follow a similar strategy under free college. We have also implicitly assumed that college quality remains the same after college becomes free. This may not happen if the policymaker reimburses colleges for less than the per-student average cost. Indeed, Murphy et al (2019) provide evidence that

> 23See, for instance, Bettinger (2004), Dynarski (2003), Hoxby and Turner (2013) and the references therein, as well as the surveys by Avery et al (2019), Deming and Dynarski (2009), Dynarski and Scott-Clayton (2013), Long (2008), Page and Scott-Clayton (2016).

> 24See Bettinger et al (2019), Castleman and Long (2016), Cornwell et al (2006), Dynarski (2000, 2004, 2008), Scott-Clayton (2011), Scott-Clayton and Zafar (2016), and the references therein.

> 25These programs vary across states in terms of eligible institutions (community colleges v. four-year institutions) and students. See, for instance, Carruthers et al (2018), Dynarski et al (2018), Gurantz (2020).

> 26For recent, well-identified studies, see Bettinger et al (2019), Denning (2017), Mayer et al (2015), and ScottClayton (2011).

> 27In the context of our model, these policies would amount to changing parameters from the distribution of _z_ in order to reach higher _E_ ( _z_ ) and lower _V_ ( _z_ ) _._ Clotfelter et al (2018), Evans et al (2017), Scrivener et al (2015) and Sommo et al (2018) document positive effects of these supports on graduation rates.

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