This paper analyzes the relative importance of short-term financial constraints "vis-a-vis" skills and other background factors when explaining higher education access in Peru. We focus on the disparities in university enrollment between rich and poor households. We use a novel household survey that includes special tests to measure cognitive and socio-emotional skills of the urban population age 14-50. These are complemented with retrospective data on basic education and family socioeconomic conditions in a multinomial model. We find that the strong correlation between university enrollment and family income in urban Peru is not only explained by short-term credit constraints, but also by poor cognitive skills and by family and educational backgrounds affecting tastes and aptitudes for formal education. Family income explains, at most, half of the university access gap between poor and non-poor households. The other half is related to differences in parental education, educational backgrounds, and cognitive skills. Our results indicate that credit or scholarship schemes alone will not suffice to change the regressive nature of higher education enrollment in Peru, and that such programs will face strong equity-efficiency trade-offs.