The origins and development of statistical approaches in non-parametric frontier models: a survey of the first two decades of scholarly literature (1998-2020)

This paper surveys the increasing use of statistical approaches in non-parametric efficiency studies. Data Envelopment Analysis (DEA) and Free Disposable Hull (FDH) are recognized as standard non-parametric methods developed in the field of operations research. Kneip et al. (Econom Theory, 14:783-793, 1998) and Park et al. (Econom Theory, 16:855-877, 2000) develop statistical properties of the variable returns-to-scale (VRS) version of DEA estimators and FDH estimators, respectively. Simar & Wilson (Manag Sci 44, 49-61, 1998) show that conventional bootstrap methods cannot provide valid inference in the context of DEA or FDH estimators and introduce a smoothed bootstrap for use with DEA or FDH efficiency estimators. By doing so, they address the main drawback of non-parametric models as being deterministic and without a statistical interpretation. Since then, many articles have applied this innovative approach to examine efficiency and productivity in various fields while providing confidence interval estimates to gauge uncertainty. Despite this increasing research attention and significant theoretical and methodological developments in its first two decades, a specific and comprehensive bibliometric analysis of bootstrap DEA/FDH literature and subsequent statistical approaches is still missing. This paper thus, aims to provide an extensive overview of the key articles and their impact in the field. Specifically, in addition to some summary statistics such as citations, the most influential academic journals and authorship network analysis, we review the methodological developments as well as the pertinent software applications.

Automated summary

This paper surveys the increasing use of statistical approaches, specifically in the field of non-parametric efficiency studies. It highlights the development of Data Envelopment Analysis (DEA) and Free Disposable Hull (FDH) as standard non-parametric methods and discusses the statistical properties of their estimators. The paper also addresses the limitations of conventional bootstrap methods and introduces a smoothed bootstrap for use with DEA or FDH efficiency estimators. Furthermore, the paper reviews the application of these statistical approaches in various fields, providing confidence interval estimates to assess uncertainty. However, a comprehensive bibliometric analysis of bootstrap DEA/FDH literature and subsequent statistical approaches is still lacking.