Maximum likelihood estimation of monotone and concave production frontiers

In this paper we bring together the previously separate parametric and nonparametric approaches to production frontier estimation by developing composed error models for maximum likelihood estimation from nonparametrically specified classes of frontiers. This approach avoids the untestable restrictions of parametric functional forms and also provides a statistical foundation for nonparametric frontier estimation. We first examine the single output setting and then extend our formulation to the multiple output setting. The key step in developing the estimation problems is to identify operational constraint sets to ensure estimation from the desired class of frontiers. We also suggest algorithms for solving the resulting constrained likelihood function optimization problems.