Statistical Approaches for Nonparametric Frontier Models: A Guided Tour
(2015) International Statistical Review — Vol. 83, n° 1, p. 77-110 (2015)
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- Abstract
- A rich theory of production and analysis of productive efficiency has developed since pioneering work by Koopmans (1951) and Debreu (1951). Farrell (1957) is the earliest published empirical study, and appeared in a statistical journal (JRSS), even though Farrell provided no statistical theory. The literature in econometrics, management sciences, operations research and mathematical statistics has since been enriched by hundreds of papers trying to develop or implement new tools for analyzing productivity and efficiency of firms. Both parametric and nonparametric approaches have been proposed. The mathematical challenge is to derive estimators of production, cost, revenue, or profit frontiers which represent, in the case of production frontiers, the optimal loci of combinations of inputs (like labor, energy, capital, etc.) and outputs (the products or services produced by the firms). Optimality is defined in terms of various economic considerations. Then the efficiency of a particular unit is measured by its distance to the estimated frontier. The statistical problem can be viewed as the problem of estimating the support of a multivariate random variable, subject to some shape constraints, in multiple dimensions. These techniques are applied in thousands of papers in the economic and business literature. This “Guided Tour" reviews the development of various nonparametric approaches since the early work of Farrell. Remaining challenges and open issues in this challenging arena are also described.
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Simar, L., & Wilson, P. (2015). Statistical Approaches for Nonparametric Frontier Models: A Guided Tour. International Statistical Review, 83(1), 77-110. https://doi.org/10.1111/insr.12056 (Original work published 2015)