Multi-output Support Vector Frontiers

Abstract

In this paper, we show that both Free Disposal Hull (FDH) and Data Envelopment Analysis (DEA), which are well-known modern techniques for efficiency measurement, can be seen as particular cases of a more general model based upon Support Vector Regression (SVR) within machine learning. Our approach is based on the adaptation of SVR in a multi-response framework for dealing with standard microeconomic assumptions, such as free disposability and convexity of the underlying technology. This adaptation allows us to introduce a more robust notion of technical efficiency, linked to the concept of ɛ-insensitivity in standard SVR. Due to computational reasons, we also introduce a simplified version of the initial approach, whose validity is checked through simulation. By resorting to a computational experience, we also show that the new approach, called multi-output Support Vector Frontiers, outperforms FDH and DEA with respect to mean squared error and bias, avoiding the overfitting problem associated with the assumption of the principle of minimal extrapolation in the case of FDH and DEA. We finally show how to implement some usual efficiency measures under the new approach and illustrate their performance through an empirical example.