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

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.

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