Stochastic frontier estimation through parametric modelling of quantile regression coefficients

Stochastic frontiers are a very popular tool used to compare production units in terms of efficiency. The parameters of this class of models are usually estimated through the use of the classic maximum likelihood method even, in the last years, some authors suggested to conceive and estimate the productive frontier within the quantile regression framework. The main advantages of the quantile approach lie in the weaker assumptions about data distribution and in the greater robustness to the presence of outliers respect to the maximum likelihood approach. However, empirical evidence and theoretical contributions have highlighted that the quantile regression applied to the tails of the conditional distribution, namely the frontiers, suffers from instability in estimates and needs specific tools and approaches. To avoid this limitation, we propose to model the parameters of the stochastic frontier as a function of the quantile in order to smooth its trend and, consequently, reduce its instability. The approach has been illustrated using real data and simulated experiments confirming the good robustness and efficiency properties of the proposed method.