Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models

TLDR

Efficiency scores of production units are measured relative to an estimated production frontier, and the bootstrap offers a straightforward method to assess how sampling variations affect these scores. The study aims to validate the bootstrap by defining a realistic data‑generating process and proposing a general bootstrapping methodology for nonparametric frontier models. The authors illustrate adapted bootstrapping methods by analyzing bootstrap sampling variations of input efficiency measures in electricity plants. Nonparametric estimators such as DEA and FDH rely on a finite sample of observed production units.

Abstract

Efficiency scores of production units are generally measured relative to an estimated production frontier. Nonparametric estimators (DEA, FDH, ⋯) are based on a finite sample of observed production units. The bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier. The main point in order to validate the bootstrap is to define a reasonable data-generating process in this complex framework and to propose a reasonable estimator of it. This paper provides a general methodology of bootstrapping in nonparametric frontier models. Some adapted methods are illustrated in analyzing the bootstrap sampling variations of input efficiency measures of electricity plants.