Stochastic data envelopment analysis: A quantile regression approach to estimate the production frontier

Data Envelopment Analysis was developed as a deterministic model that assumed that deviations from the production frontier were one sided representing technical inefficiency. The model provides biased estimates of production and inefficiency if deviations from the frontier arise not only from inefficiency but also from statistical noise. Banker (1988, “Stochastic Data Envelopment Analysis,” Working Paper, Carnegie Mellon University) extended Data Envelopment Analysis with a stochastic model to allow not only inefficiency but also statistical noise. Banker's model can be considered a nonparametric quantile regression. Using the celebrated Afriat constraints, the model estimates a piecewise linear production function through the middle of the data. In this paper, we extend Banker's Stochastic DEA model by considering a semi-parametric model that identifies the most likely quantile based on assumptions of the composed error terms. We focus on the most common stochastic frontier model with an error structured constrained to a convolution of the normal and half-normal distributions. Using simulated data, we compare the model to the econometric stochastic frontier model under different distributional assumptions.