Introducing environmental variables in nonparametric frontier models: A probabilistic approach

This paper proposes a general formulation of a nonparametric frontier model introducing external environmental factors that might influence the production process but are neither inputs nor outputs under the control of the producer. A representation is proposed in terms of a probabilistic model which defines the data generating process. Our approach extends the basic ideas from Cazals, Florens and Simar (2002) to the full multivariate case. We introduce the concepts of conditional efficiency measure and of conditional efficiency measure of order-m. Afterwards we suggest a practical way for computing the nonparametric estimators. Finally, a simple methodology to investigate the influence of these external factors on the production process is proposed. Numerical illustrations through some simulated examples and through a real data set on Mutual Funds show the usefulness of the approach.