A copula‐based approach to the simultaneous estimation of group and meta‐frontiers by constrained maximum likelihood

Existing approaches to the meta‐frontier estimation consist of two stages where the estimates of the local frontier parameters obtained in the first step are used to estimate meta‐frontier parameters by means of a linear or quadratic minimisation procedure in the second. Since it was shown by Schmidt (Review of Economics and Statistics 58: 238) that the second step is equivalent to constrained maximisation of a likelihood function, we extend this idea and offer a copula‐based approach to the estimation of the parameters of both meta‐ and group frontiers in a one‐step setting. In this way, we ensure a single data‐generating mechanism for the estimated parameters, expand the set of potential meta‐frontiers and account for the fact that shocks to the individual production units may be correlated with shocks to the local technological environment as a whole. We apply our estimation methodology to a data set on the world agriculture and find that the deviations from the group frontiers are positively correlated with deviations from the meta‐frontier, which is a conclusion that is impossible to reach without accounting for stochastic dependence between the two deviation types represented by a copula.