graduates, yet performance-based free college does it at a lower per-graduate cost. This is because the incentives embedded in performance-based free college produce fewer dropouts and graduate students faster than universal free college. By adopting performance-based rather than universal free college, the policymaker would save no less than 40 percent of per capita GDP per graduate.

Nonetheless, the policymaker might be reluctant to adopt performance-based free college, perhaps for political considerations. Indeed, students throughout Latin America have been clamoring for unconditional, universal free college ( _gratuidad_ ). As Figure 15 shows, universal free college raises the number of graduates only slightly more than need-based free college yet costs an additional 50 percent of per capita GDP per graduate. The reason is that universal free college provides a transfer to medium- and high-income students who would attend college anyway. If choosing between unconditional programs, then need-based is preferable to universal free college.

One caveat is in order. College dropouts seem to acquire some human capital during college given their wage premium relative to high school graduates. This may motivate the policymaker to raise enrollment regardless of graduation. The question, then, is whether starting but not completing a bachelor’s program is the most efficient way of acquiring post-secondary human capital. A short-cycle program, lasting two or three years, might be more cost-effective.<sup>28</sup> Subsidizing these programs—in the spirit of subsidies to community college students in the U.S.—might therefore be preferable.

# **8.8 Long-run effects**

We have assumed that, despite the greater supply of college graduates due to free college, the college premium does not change. However, the college premium might actually fall, thereby reducing the incentives to attend college. In addition, free college might be funded with taxes, further depressing after-tax wages for college graduates. In other words, free college might unleash general equilibrium effects that could undermine some of the free college effects previously described (Heckman et al 1998).

To analyze the equilibrium relationship between college premium and number of college graduates, we postulate a production function following Katz and Murphy (1992), Heckman et al (1998), and Card and Lemieux (2001). Ignoring for the moment the connection between capital and technology, consider a CES production function, _F_ ( _Nt_<sup>_h, N_</sup> _t_<sup>_g_) =</sup> � _A_<sup>_h_</sup> _t_<sup>(</sup><sup>_N h_</sup> _t_<sup>)</sup><sup>_λ_+</sup><sup>_A_</sup> _t_<sup>_g_(</sup><sup>_N g_</sup> _t_<sup>)</sup><sup>_λ_�</sup> _λ_<sup><u>1</u></sup> , that combines high school and college graduates, whose amounts are _Nt_<sup>_h_and</sup><sup>_N g_</sup> _t_<sup>respectively,</sup> to produce aggregate output. In this function, _A_<sup>_h_</sup> _t_<sup>and</sup><sup>_Ag_</sup> _t_<sup>areefficiencyparameters,and</sup> _ω_ = 1 _/_ (1 _− λ_ ) is the elasticity of substitution between college and high school graduates. In a competitive labor market, the college premium is equal to where _wt_<sup>_g_and</sup><sup>_w_</sup> _t_<sup>_h_arethewagesofcollegeandhighschoolgraduates,respectively.Takinglogs</sup>

> 28Ferreyra et al (2021) shows that students in short-cycle programs graduate at higher rates than those in bachelor’s programs, and that their graduates obtain better labor market outcomes than dropouts from bachelor’s programs.

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