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ROBUSTIFIED EXPECTED MAXIMUM PRODUCTION FRONTIERS

Published online by Cambridge University Press:  27 March 2020

Abdelaati Daouia ,
Jean-Pierre Florens  and
Léopold Simar
Abdelaati Daouia
Affiliation:
University of Toulouse Capitole
Jean-Pierre Florens
Affiliation:
University of Toulouse Capitole
Léopold Simar*
Affiliation:
Université Catholique de Louvain
*
Address correspondence to Léopold Simar, Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Belgium; e-mail: [email protected].
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Abstract

The aim of this paper is to construct a robust nonparametric estimator for the production frontier. We study this problem under a regression model with one-sided errors, where the regression function defines the achievable maximum output, for a given level of inputs-usage, and the regression error defines the inefficiency term. The main tool is a concept of partial regression boundary defined as a special probability-weighted moment. This concept motivates a robustified unconditional alternative to the pioneering class of nonparametric conditional expected maximum production functions. We prove that both the resulting benchmark partial frontier and its estimator share the desirable monotonicity of the true full frontier. We derive the asymptotic properties of the partial and full frontier estimators, and unravel their behavior from a robustness theory point of view. We provide numerical illustrations and Monte Carlo evidence that the presented concept of unconditional expected maximum production functions is more efficient and reliable in filtering out noise than the original conditional version. The methodology is very easy and fast to implement. Its usefulness is discussed through two concrete datasets from the sector of Delivery Services, where outliers are likely to affect the traditional conditional approach.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 2 , April 2021 , pp. 346 - 387
Copyright
© Cambridge University Press 2020

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Footnotes

The authors would like to thank two referees and the Co-Editor for their valuable suggestions, which have significantly improved the paper. They acknowledge funding from the French National Research Agency (ANR) under the Investments for the Future (Investissements d'Avenir) program, grant ANR-17-EURE-0010. This research was also supported by the French National Research Agency under the grant ANR-19-CE40-0013-01/ExtremReg project. Support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy) is also gratefully acknowledged.

References

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