Modeling joint production of multiple outputs in StoNED: Directional distance function approach

Estimation of joint production technologies involving multiple outputs has proved a vexing challenge. Existing methods are unsatisfactory as they either assume away stochastic noise or restrict to functional forms that have incorrect output curvature. The first contribution of this paper is to develop a new probabilistic data generating process that is compatible with the directional distance function. The directional distance function is a very general functional characterization of production technology that has proved useful for modeling joint production of multiple outputs. The second contribution of this paper is to develop a new estimator of the directional distance function that builds upon axiomatic properties and does not require any functional form assumptions. The proposed estimator is a natural extension of stochastic nonparametric envelopment of data (StoNED) framework to multiple output setting. We examine the practical aspects and usefulness of the proposed approach in the context of incentive regulation of the Finnish electricity distribution firms.