A Constrained Maximum Likelihood Approach to the Estimation of Meta-Frontiers

We demonstrate that the estimation of meta-frontier parameters by minimizing the sum of the absolute values or squares of the distances between the meta-frontier and the individual group frontiers, which is an established practice in the literature, is equivalent to maximizing a constrained likelihood function that corresponds to a meta-frontier model treating those distances as a non-negative random variable distributed either exponentially or half-normally. We confirm our claim by empirical results based on the world's agricultural production data. Our procedure of estimating the meta-frontier parameters by constrained maximum likelihood allows for both the statistical inference on the meta-frontier parameters and on the choice of the most preferred specification. Not only the constrained maximum likelihood estimation allows for the statistical inference that is not straightforward in case of the linear or quadratic programming approach, it also expands the variety of the possible meta-frontiers, each corresponding to a particular distributional assumption on the distances between meta- and the group frontiers