The Estimation of Productive Efficiency Through Machine Learning Techniques: Efficiency Analysis Trees

The determination of technical efficiency through the previous estimation of a production frontier has been a relevant topic in the literature related to production theory and engineering. Many parametric and nonparametric approaches have been introduced in the last forty years for estimating production frontiers given a data sample. However, few of these methodologies are based on machine learning techniques, despite being a growing field of research. Recently, a bridge has been built between these two literatures; machine learning and production theory, through a new technique proposed in Esteve et al. (Exp Syst Appl 162:113783, 2020), called Efficiency Analysis Trees (EAT). The algorithm corresponding to EAT builds upon the Classification and Regression Trees (CART) technique by Breiman et al. (Classification and regression trees. Taylor & Francis, 1984) for estimating upper enveloping surfaces of data clouds and satisfying monotonicity. In this study, we revise the fundamentals of this new methodology and extend it to the context of measuring productive efficiency under convexification, using the directional distance function. Additionally, a dedicated EATpy package in Python is provided for executing the EAT algorithm, which could be useful for analyzing both small and big data sets in practice. Finally, the methodology is applied to two different-sized empirical datasets.