Objective: To evaluate the relationship between the ownership structure of hospitals and the possibility of their being positioned on the frontier of technical efficiency in the economic crisis period 2010–2012, adjusting for hospital variables and regional characteristics in the areas where the Spanish National Health System (SNHS) hospitals are located. Methods: 230 National Health System hospitals were studied over the two-year period 2010–2012 according to their ownership structure—public hospitals, private hospitals and public–private partnership (PPP)—data envelopment analysis orientated to inputs was used to measure the overall technical efficiency, pure efficiency and efficiency of scale. A generalised linear mixed model (GLMM) with binomial distribution and logit link function was used to analyse the hospital and regional variables associated with positioning on the frontier. Results: There are substantial differences between the average pure technical efficiency of public, private and PPP hospitals, as well as a greater number of PPP models being positioned on the efficiency frontier (91.67% in 2012). The odds of being positioned on the frontier are 41.7 times higher in PPP models than in public hospitals. The average annual household income per region is related to the greater odds of hospitals being positioned on the frontier of efficiency. Conclusions: During the most acute period of recession in the Spanish economy, PPP formulas favoured hospital efficiency, by increasing the odds of being positioned on the frontier of efficiency when compared to private and public hospitals. The position on the frontier of efficiency of a hospital is related to the wealth of its region.