Multivariate distributional stochastic frontier models

Abstract

The primary objective of Stochastic Frontier (SF) Analysis is the deconvolution of the estimated composed error terms into noise and inefficiency. Thus, getting unbiased estimates of the composed error terms should be of uttermost importance. Assuming a parametric production function (e.g. Cobb-Douglas, Translog, etc.), homoscedastic noise and (in)efficiency are restrictions, which can counteract this objective. In order to overcome these three restrictions, the SF model can be cast into the framework of distributional regression models. Within this model class, all parameters of the output (or cost) distribution can be modelled as functions of covariates via smoothers. Consequently, non-linear, random and spatial effects can be included with ease. The Distributional Stochastic Frontier Model (DSFM) is introduced. Furthermore, the model is extended to allow for the production of several outputs, which may be dependent. The multivariate distribution of the outputs (or costs) is modeled utilizing copulas. The serviceability of the approach is demonstrated via a Monte Carlo simulation. Additionally, the applicability of the proposed method is showcased by estimating the production of palm oil and rubber in Indonesia.