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

Technical inefficiency of production reflects a shortfall of output from the potential permitted by inputs. Allocative inefficiency reflects deviations from the optimal ratio of inputs. It is the absolute value of allocative inefficiency that is economically important. Adding allocative inefficiency to a model of production requires high-dimensional distributions and jointly modelling the two types of inefficiency calls for a special dependence structure. The pairwise nature of dependence between technical and allocative terms means that canonical vine copulas offer a natural way to model dependence in production systems with multiple inputs. We show how to construct a simulated likelihood based upon a C-vine decomposition of the joint density of the production function error terms. Our approach uses a recently proposed family of bivariate copulas that permit dependence between the magnitude (but not the sign) of allocative inefficiency and the magnitude of technical inefficiency. We discuss estimation of such models and argue that they better reflect dependencies that arise in practice. Monte Carlo simulations and a classic empirical application to electricity generation plants illustrates the utility of the proposed approach