The matrix approach to evaluating demand equations

This study explores a new data set that contains information both on inputs and outputs for a sample of Portuguese secondary schools. An FDH reference technology is used to determine radial technical efficiency scores and slacks. Although it is known that there is no reason to assume convexity in the study of education efficiency frontiers, this is the first study ever to use FDH at the school level, effectively relaxing the convexity assumption. A two–stage approach is used, whereby the significant environmental variables that explain FDH efficiency scores and slacks are identified. For the purpose of statistical inference, the first application of the bootstrapping algorithms suggested by Simar and Wilson (2003 Simar, L and Wilson, PW. 2000. A general methodology for bootstrapping in nonparametric frontier models. Journal of Applied Statistics, 27: 779–802.  ) is conducted. The study concludes that the unemployment rate, access to health care services, adult education and living infrastructures are determinants of school efficiency. The differences between the coast and the interior of Portugal seem to be more relevant, as far as school efficiency is concerned, than whether or not the school belongs to one of the major coast metropolitan areas.