Technical and Allocative Inefficiency in Production Systems: A Vine Copula Approach

Abstract

Modelling the error terms in stochastic frontier models of production systems requires multivariate distributions with certain characteristics. We argue that canonical vine copulas offer a
natural way to model the pairwise dependence between the two main error types that arise in
production systems with multiple inputs. We introduce a vine copula construction that permits
dependence between the magnitude (but not the sign) of the errors. Using a recently proposed
family of copulas we show how to construct a simulated likelihood based on C-vines. We discuss
issues that arise in estimation of such models and outline why such models better reflect the
dependencies that arise in practice. Monte Carlo simulations and a classic empirical application
to electricity generation plants illustrate the utility of the proposed approach.

Keywords: Vine copulas, Allocative inefficiency, Technical inefficiency, Production Functions

JEL Classification: C13