effects from the SC expansion but rather heterogeneous gains and losses–as we indeed find.

We exploit the local supply of higher education programs in Colombia as a source of exogenous variation for instruments. We use estimated propensity scores of enrollment choices to estimate the share of expansion and diversion compliers under a behavioral assumption (partial monotonicity, as in Mountjoy (2022) and Mogstad et al. (2021)) that allows us to isolate the effect of changes in the local supply of HEIs specialized in offering SC programs while holding the supply of other HEIs constant. To improve over standard two-stage least squares (TSLS) methods and identify the parameters of interest, we posit a multinomial model of enrollment choices, multiple IVs, and essential heterogeneity.<sup>2</sup> We use administrative information for the universe of Colombia’s high school graduates in 2005. We observe their high school exit exam ( _Saber 11_ ) scores, higher education enrollment choices, labor market outcomes between 2008 and 2013 (employment status and wages), and socioeconomic information. We link this data to municipality-level information on higher education supply, and focus on whether there is at least one HEI specialized in SC programs within the 10-kilometer radius of the student’s high school municipality. Hence, we compare the enrollment choices of high school students in municipalities with and without access to at least one specialized institution offering SC programs. Moreover, we examine whether the existence of such HEIs has different effects depending on the local supply of HEIs offering bachelor’s programs.

Our findings show that the presence of SC-specialized HEIs raises SC enrollment by 3 _._ 7 _−_ 4 _._ 5 percentage points (pp). This is a sizable increase, representing 40-50% of the sample enrollment rate in SC programs.<sup>3</sup> At least 70% of this increase is due to students who would have otherwise attended a bachelor’s program (the diversion margin), while the remaining students react along the expansion margin. The diversion share is higher among men than women (75 _−_ 83% versus 70 _−_ 74%, respectively). In addition, most of

> 2Models with essential heterogeneity are characterized by heterogeneous responses to treatments and self-selection into treatments with partial knowledge of idiosyncratic responses. In these models, Heckman and Urzúa (2010) show that if an instrument affects only one margin of choice (in our case, enrolling in a SC program vs. not doing so), IVs estimate the effect of one option vs. the next-best (in our case, the effect of enrolling in a SC program relative to a mixture of not enrolling in higher education and enrolling in a bachelor’s program). Also, Mountjoy (2022) shows that multivariate TSLS (multiple margins of choice and multiple IVs) estimate effects that are a combination of many margins of choice and do not necessarily identify well-defined effects. In our case, where there are three margins of choice (not enrolling in higher education vs. enrolling in SC programs, not enrolling in higher education vs. enrolling in bachelor’s programs, and enrolling in bachelor’s programs vs. enrolling in SC programs), multivariate TSLS would estimate a combination of effects for the three margins. Our empirical strategy takes into account these complexities.

> 3Our estimated effects are in the range of others in the literature, obtained for the U.S. with other sources of variation. For Texas, Mountjoy (2022) finds that a 10-mile increase in the distance between the student’s high school and the nearest two-year college decreases enrollment in two-year colleges by 4.3 percentage points. Acton (2020) finds that a $1000-tuition reduction in local community colleges increases their enrollment by 3.5 percentage points.

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