The Estimation of Meta-Frontiers by Constrained Maximum Likelihood

Existing approaches to the meta-frontier estimation are largely based on the linear programming technique, which does not hinge on any statistical underpinnings. We suggest estimating meta-frontiers by constrained maximum likelihood subject to the constraints that specify the way in which the estimated meta-frontier overarches the individual group frontiers. We present a methodology that allows one to either estimate meta-frontiers using the conventional set of constraints that guarantees overarching at the observed combinations of production inputs, or to specify a range of inputs within which such overarching will hold. In either case the estimated meta-frontier coefficients allow for the statistical inference that is not straightforward in case of the linear programming estimation. We apply our methodology to the world's FAO agricultural data and find similar estimates of the meta-frontier parameters in case of the same set of constraints. On the contrary, the parameter estimates differ a lot between different sets of constraints.