“…[75] and [45] as well as the relationship between fees and level of enrolment by Ref. [76]; MK is the market share measured as the ratio between the number of enrolments at university i and the total number of enrolments in the universities located in the same region, included for capturing the potential effects due to the presence of more concentration or competition between universities; indeed, the market structure of the HEIs could play an important role in calculating the efficiency, as an increase in competition in the higher education sector could lead to greater efficiency (see Refs. [45,77,78] for a discussion); YEAR FOND is the year of foundation of the university as a proxy for the level of tradition of a given HEIs as, according to [19]; it is often perceived that HEIs with a longer tradition have a better reputation, but it could also be the case that younger HEIs have more flexible and modern structures, assuring a more efficient performance; WOMEN is the number of females among students in order to test the relation between the gender composition of the students and universities' efficiency scores; GDP is the gross domestic product corresponding to the total production of economic goods and services, with the aim of controlling for the growth of the economic system, as the university location can be an important determinant of its performance (the idea that rich and poor areas offer different surroundings has been already explored, with alternate results, by Ref.…”