on both sides and defining a time difference ( _△_ ) yields an expression commonly used to study changes in wage inequality: In this equation, changes in relative wages depend on two components. The first is technical changes in the relative productivity of the two labor inputs. Skill-biased technical change, or _△_<sup>_A_</sup> _<u>t</u>_<sup>_g_The second is changes in relative supply, adjusted</sup> ln( _A_<sup>_h_</sup> _t_<sup>)</sup><sup>_>_0, increases the college premium.</sup> by the elasticity of substitution. An increase in the supply of college graduates lowers the college premium by an amount inversely related to _ω_ . Over time, the evolution of the college premium depends on the relative strength of these two opposite forces.

To investigate the extent to which the increased supply of college graduates might depress the college premium, we focus on universal free college, which increases supply the most and provides an upper bound to the potential college premium decline. We examine short- and longrun effects. For the latter, we assume that universal free college becomes a permanent policy beginning with our 2006 cohort, and simulate the evolution of the share of college graduates (relative to all workers in the economy) and the college premium. We assume no skill-biased technical change and therefore estimate an upper bound to the college premium decline.

The critical parameter for this exercise is _ω_ , which we estimate as 3.2 for Colombia.<sup>29</sup> Using this estimate, the left and right panel of Figure 16 show the evolution of the share of college educated workers and the college premium, respectively. The former rises over time as young, more educated cohorts replace older, less educated ones. The replacement is complete around the year 2045, when the economy reaches steady state.

**Figure 16: Free College and and the College Premium**

<!-- Start of picture text --> 45 3<br>40 2.5<br>35 2<br>30 1.5 ω = 3.2<br>ω = 2.5<br>25 1 ω = 1.4<br>20 .5 ω = 1.2<br>2015 2020 2025 2030 2035 2040 2045 2050 2015 2020 2025 2030 2035 2040 2045 2050<br>Year Year<br>a. Share College in Labor Force b.College Premium<br>Percent<br>College premium<br><!-- End of picture text --> _Source_ : Own calculations based on estimates.

_Notes_ : Panel a shows predicted share of college graduates in the labor force, calculated as the share of workers (of all ages) with a college degree relative to all workers (all ages and educational attainment) in the economy. Panel b shows predicted college premium, calculated as the ratio between wage for college graduates and wage for high school graduates.

> 29There is a large number of estimates for this parameter in the literature. For example, Katz and Murphy (1992) estimate it to be 1.4 for the U.S. for the period 1963-1987, but the low range of estimates also include 0.5. Card and Lemieux (2001) estimate it for the United States (1959 to 1996) and the United Kingdom (1974-1996) and find estimates between 2 and 2.5. Following Card and Lemieux (2001), we estimate the production function parameters using Colombia’s household surveys (SEDLAC) for 2001-12. Due to data limitations, college graduates include those from 2- and 4-year programs.

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