**Performance-based free college.** In contrast to universal free college, performancebased free college raises graduation rates for _all_ student groups because it eliminates the lossof-urgency effect. Substitution effect leads to greater effort and therefore less risk. In the aggregate, performance-based free college raises the graduation rate of existing students from 45 to 51.3 percent (see Table 10), which is the greatest graduation rate increase for existing students among all programs considered here. Even new students attain a higher graduation rate under performance-based than universal free college (42.7 v. 40.9 percent).

Back to the policymaker’s goal of raising the fraction of high school graduates who complete college, Table 13 shows this fraction in the baseline (panel a) as well as the differences with respect to it under universal and performance-based free college (panels b and c, respectively.) Relative to the baseline, both programs raise this fraction for every student group. Performancebased free college is at least as effective as universal free college for every student group except low-income students of middle or low ability, for whom the difficulty of meeting performance requirements acts as an enrollment deterrent. In other words, a combination of unconditional free college for those students and performance-based free college for others could meet the policymaker’s goal not only in the aggregate but also by student group.

**Table 13: Free College Counterfactuals: Percent of High School Graduates That Complete College.**

||a. <br>Perc<br>Schoo|Baseli<br>ent of <br>l Grad|ne<br>High<br>uates|b<br>Free C|. Unive<br>ollege:|rsal<br> Change|c. Per<br>Free|forman<br>College:|ce-Based<br> Change|
|---|---|---|---|---|---|---|---|---|---|
||||||Abil|ity||||
|Income|High|Mid|Low|High|Mid|Low|High|Mid|Low|
|High|49.7|29.1|10.3|2.9|3.1|5.1|7.1|5.9|5.3|
|Mid|40.7|18.9|8.2|6.7|10.1|6.4|10.7|10.1|6.4|
|Low|27.4|11.0|4.4|16.7|17.5|8.5|19.1|15.5|7.0|

_Source_ : Model’s predictions for baseline and counterfactuals. _Notes_ : For existing students of each type, panel a shows the percent of high school graduates that graduate from college; panel b shows difference (pp) in this variable between universal free college and baseline; and panel c shows difference (pp) in this variable between performance-based free college and baseline.

# **8.5 Discussion**

We can now return to the cross-country evidence depicted in Figure 1, which shows that, in Latin America, government funding for college has a large, positive relationship with enrollment rates but a weak (actually negative) relationship with graduation rates. The evidence is consistent with our counterfactuals, as these predict a greater impact of free college on enrollment than graduation rates. The graduation rate evidence is also consistent with the financial aid regimes prevailing in those countries, where universal or need-based aid is most common, ability-based aid is rare, and performance-based aid is almost non-existing (Ferreyra et al 2017). Indeed, for the most common regimes in Latin America our counterfactuals predict a (slight) decline in graduation rate (see Table 12), consistent with Figure 1.

Our findings are also consistent with the literature on U.S. higher education financial aid, 38