Analytical Derivations of New Specifications for Stochastic Frontiers with Applications

Abstract

In this paper, we propose the analytical derivations of new specifications for the stochastic frontier (SF) approach. In order to avoid some limitations of the traditional SF method, we introduce dependence between the two error components through copula functions and the asymmetry of the random error assigning a generalized logistic distribution. We report the density functions of the overall error term, some important summary measures and the derivation of the efficiency scores for both cost and production frontiers. Finally, we propose two empirical applications in order to test our methodological approach: the first one refers to the estimation of production frontiers for the Italian airport system; the second one investigates the cost efficiency of the Italian banking sector.

Keywords

• stochastic frontier models
• skewness
• generalized logistic distribution
• dependence
• copula functions