Copula-based Stochastic Cost Frontier with Correlated Technical and Allocative Inefficiency

This paper considers the duality between stochastic frontier production and cost functions, under the assumption of cost minimization (technical and allocative inefficiency) and dependence structure for both measures of technical and allocative inefficiency as assumed by (Schmidt and Lovell, Journal of Econometrics 13:83-100, 1980). However, the assumed dependence structure comprise of positive dependence for higher technical inefficiency and higher (positive) allocative inefficiency; and negative dependence for higher technical inefficiency and higher (negative) allocative inefficiency through a mixture of copula model. The dependence structure is presented by a multivariate Farlie-Gumbel-Morgenstern (FGM) copula as there will be choice of probability distributions for both technical and allocative inefficiency. The proposed model is estimated using simulated maximum likelihood (SML) method. An application of the illustrated model to the US electricity utility data (Greene, Journal of Econometrics 46:141-164, 1990) shows a significant dependence between technical and allocative inefficiency.