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

Abstract

Efficiency scores of production units are generally measured relative to an estimated production frontier. Nonparametric estimators (DEA, FDH, \cdots ) 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.Data Envelopment Analysis, Bootstrap, Resampling Methods, Frontier Efficiency Models

Economic Efficiency and Frontier Techniques

“…To avoid this inconsistency, Simar and Wilson (1998) provide an alternative approach by analysing the bootstrap sampling variations of input efficiency measures of a set of electricity plants. In doing so, Simar and Wilson (1998) show how in order to validate the bootstrap it is necessary to define a reasonable data-generating process and to propose a reasonable estimator of it.…”

“…In doing so, Simar and Wilson (1998) show how in order to validate the bootstrap it is necessary to define a reasonable data-generating process and to propose a reasonable estimator of it. As Simar and Wilson (2000a) establish, the procedure described in Simar and Wilson (1998) for constructing confidence intervals depends on using bootstrap estimates of bias to correct for the bias of the DEA estimators.…”

“…Simar and Wilson (1999c) overcome this modus operandi's weakness by implementing an improved procedure which automatically corrects for bias without explicit use of a noisy bias estimator. Moreover, the initial methodology proposed in Simar and Wilson (1998) is also extended to a less restrictive framework by allowing heterogeneity in the structure of efficiency in Simar and Wilson (2000b).…”

Universities in Mexico: a measure of its efficiency through data envelopment analysis with bootstrap

“…Posteriormente, Simar (1992) proporcionó la primera aplicación que, en un contexto de frontera, se sirvió del bootstrap al incorporarlo a la estimación semiparamétrica de modelos de datos de panel. Sin embargo, la adaptación consistente del bootstrap a estimaciones del DEA fue formulada por primera vez por Simar & Wilson (1998).…”

Finding the Right Yardstick: Regulation Under Heterogeneous Environments

“…by construction they are upward-biased Simar and Wilson (1998). We correct for the bias inθ andθ c by applying the m-bootstrap first proposed by Kneip et al (2008), and extended by Simar and Wilson (2011).…”