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.