Nonparametric Estimation of Production Functions Available to Purchase

While the primary use of data envelopment analysis is the estimation of production frontiers and the subsequent measurement of efficiency, a more recent literature has been concerned with the estimation of production functions that allow observed points beyond the frontier. This could arise with noisy data for example. Banker and Maindiratta (1992) provided a foundation by extending DEA to estimate efficiency in the presence of statistical noise. The programming model estimates the frontier via maximum likelihood while constraining the production set to be convex by imposing the celebrated Afriat conditions. Since then, there have been several alternative models that have been developed. In this paper we apply several competing methodologies to estimate production functions using data from the English Premier League from 2009 to 2010.