Efficiency and Technological Heterogeneity in Spanish Universities: A Stochastic Metafrontier Approach

This study analyses the technical efficiency of 72 Spanish universities (48 public and 24 private) over the 2011--2018 period using a stochastic frontier and metafrontier approach, distinguishing between public and private institutions. In a first stage, the estimation of group-specific frontiers reveals substantial differences in their production technologies: while public universities operate under a more balanced and stable structure, private universities rely more heavily on enrolment expansion and exhibit a more flexible technology. The inclusion of temporal dynamics shows that technological change is biased in the public sector, reflecting adjustments in the input mix, whereas in the private sector it is largely neutral but non-linear, associated with changes in the level of performance. In a second stage, the metafrontier estimation identifies a common technology shaped by human resources, institutional structure, and the scale of demand, while confirming the existence of trade-offs between teaching and research activities. The inefficiency equation indicates that scientific impact and regional R\&D intensity reduce the technology gap, whereas greater academic diversification and higher regional university density tend to widen it. The decomposition of efficiency reveals a clear segmentation of the system: public universities exhibit higher efficiency levels and lower dispersion, while private universities display greater heterogeneity. Quantitatively, public universities exhibit an average meta-technical efficiency of 0.836 and a technology gap ratio of 0.950, whereas private universities reach only 0.547 and 0.815, respectively. Overall, the results show that the differences between both groups are not limited to efficiency levels, but also reflect distinct production technologies, dynamic adjustment processes, and institutional environments. These findings have important implications for the design of higher education policies.