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 worldi¯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.