# **8.4.2 Graduation**

To compare graduation rates in the baseline and counterfactuals we focus on existing students, whose graduation rate changes are entirely driven by the incentives created by free college.<sup>21</sup> Following the same logic as with enrollment, Table 12 shows baseline graduation rates (panel a), as well as the graduation rate changes relative to baseline under universal and performancebased free college (panels b and c, respectively.)

**Table 12: Free College Counterfactuals: Graduation Rate Effects for Existing Students.**

||a.|Baseli|ne|b|. Unive|rsal|c. Per|forman|ce-Based|
|---|---|---|---|---|---|---|---|---|---|
||Grad|uation|Rate|Free C|ollege: <br>Abil|Change<br>ity|Free|College:|Change|
|Income|High|Mid|Low|High|Mid|Low|High|Mid|Low|
|High|59.3|44.4|26.3|-1.8|-1.9|3.9|4.4|3.2|5.5|
|Mid|55.6|39.9|29.9|-1.9|3.5|1.7|4.9|6.6|6.5|
|Low|53.3|42.5|32.1|-1.3|4.4|-1.5|8.1|8.8|2.6|

_Source_ : Model’s predictions for baseline and counterfactuals. _Notes_ : For existing students of each type, panel a shows predicted graduation rate (%) in the baseline; panel b shows graduation rate difference (pp) between universal free college and baseline; and panel c shows graduation rate difference (pp) between performance-based free college and baseline.

**Universal free college.** Although it raises graduation rates for some groups, it lowers them for others. The reason is that the prevailing effort effect—loss of urgency, substitution, or risk— varies among student groups. Loss of urgency is generally stronger among higher-income students, whose high baseline consumption only gets higher with free college. The substitution effect is stronger among lower-ability students, for whom effort is more costly and have greater need of compensation for additional effort. The risk effect is stronger for students with fewer cumulative classes completed, particularly when loss of urgency has slowed down their progress, exposing them to risk for a longer time.

As panel b shows, graduation rates fall in the upper triangle (students of high ability or high income) and generally rise in the lower triangle (students of low ability or low income). In the upper triangle, baseline effort is already high because effort cost is low and consumption high. Given the little room for additional effort, the substitution effect is weak. A strong loss-of-urgency effect prevails given the already high consumption, and leads to lower effort, greater risk, and lower graduation rates.

The story is reversed in the lower triangle. Baseline effort there is low because effort cost is high and consumption low, which gives room for a strong substitution effect. Since consumption remains low even with free college, the loss-of-urgency effect is weak and the substitution effect prevails, leading to higher effort, lower risk, and higher graduation rates.<sup>22</sup>

> 21Free college generates incentives both for existing and new students. We focus on existing students because they allow us to compare behavioral changes between the baseline and counterfactuals. New students do not allow for this comparison because they do not enroll in teh baseline.

> 22The exception in the lower triangle is the students with the lowest income and ability, for whom graduation rates fall. The combination of lowest ability (which renders effort very costly) and lowest income (which makes consumption as a college dropout higher than as a college student, even with free college) leads these students to exert lower effort and drop out at higher rates than in the baseline.

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