Robust Nonparametric Stochastic Frontier Analysis

Abstract: Benchmarking tools, including stochastic frontier analysis (SFA), data envelopment analysis (DEA), and its stochastic extension (StoNED) are core tools in economics used to estimate an efficiency envelope and production inefficiencies from data. The problem appears in a wide range of fields -- for example, in global health the frontier can quantify efficiency of interventions and funding of health initiatives. Despite their wide use, classic benchmarking approaches have key limitations that preclude even wider applicability. Here we propose a robust non-parametric stochastic frontier meta-analysis (SFMA) approach that fills these gaps. First, we use flexible basis splines and shape constraints to model the frontier function, so specifying a functional form of the frontier as in classic SFA is no longer necessary. Second, the user can specify relative errors on input datapoints, enabling population-level analyses. Third, we develop a likelihood-based trimming strategy to robustify the approach to outliers, which otherwise break available benchmarking methods. We provide a custom optimization algorithm for fast and reliable performance. We implement the approach and algorithm in an open source Python package `sfma'. Synthetic and real examples show the new capabilities of the method, and are used to compare SFMA to state of the art benchmarking packages that implement DEA, SFA, and StoNED.