Measuring Operational Inefficiency in Urban Road Traffic Systems Using a By-Production Technology: A Machine Learning Approach Based on Convex and Nonconvex Efficiency Analysis Trees

This paper challenges a central but rarely tested assumption in the by-production framework for modelling technologies that jointly generate desirable and undesirable outputs: the convexity of its constituent sub-technologies. We argue that imposing convexity without empirical validation may lead to misspecified frontiers and biased efficiency assessments. To address this gap, we employ a data-driven methodology that integrates traditional nonparametric frontier estimators with machine-learning based Efficiency Analysis Trees (EAT) and its convexified extension (CEAT). This combination allows us to flexibly approximate the production frontier under alternative geometric assumptions and, for the first time in the by-production literature, to statistically test convexity for each sub-technology using the Kneip-Simar-Wilson (KSW) procedure. Applying the approach to a panel of 119 Chinese cities over the period 2014-2021 and distinguishing between desirable outputs and undesirable outputs, we find a notable asymmetry: convexity is systematically rejected for the desirable-output sub-technology, whereas for the undesirable-output sub-technology the evidence is mixed, with convexity rejected in some years but not in others. These results caution against the routine imposition of convexity in byproduction models and provide a statistical foundation for hybrid estimation strategies. Moreover, we show that incorrect convexity assumptions produce substantial divergences in efficiency distributions, underscoring the practical relevance of testing and method choice. The proposed framework offers a robust tool for operational efficiency analysis in urban road traffic systems and other settings where joint production of desirable and undesirable outputs is present.