Estimating Frontier Cost Models Using Extremiles
In the econometric literature on the estimation of production technologies, there has been considerable interest in estimating so called cost frontier models that relate closely to models for extreme non-standard conditional quantiles (Aragon et al. Econ Theor 21:358–389, 2005) and expected minimum input functions (Cazals et al. J Econometrics 106:1–25, 2002). In this paper, we introduce a class of extremile-based cost frontiers which includes the family of expected minimum input frontiers and parallels the class of quantile-type frontiers. The class is motivated via several angles, which reveals its specific merits and strengths. We discuss nonparametric estimation of the extremile-based costs frontiers and establish asymptotic normality and weak convergence of the associated process. Empirical illustrations are provided.
KeywordsCost Function Joint Density Tail Index Stochastic Frontier Model Free Disposal Hull
This research was supported by the French “Agence Nationale pour la Recherche” under grant ANR-08-BLAN-0106-01/EPI project (Abdelaati Daouia) and the Research Fund KULeuven (GOA/07/04-project) and by the IAP research network P6/03, Federal Science Policy, Belgium (Irène Gijbels).
- Daouia, A., & Gijbels, I. (2009). Extremiles, manuscript.Google Scholar
- Deprins, D., Simar, L., & Tulkens, H. (1984). Measuring labor inefficiency in post offices. In M. Marchand, P. Pestieau, & H. Tulkens (Eds.) The performance of public enterprises: concepts and measurements (pp. 243–267). Amsterdam: North-Holland.Google Scholar
- Koopmans, T. C. (1951). An analysis of production as an efficient combination of activities. In T.C. Koopmans (Ed.) Activitity analysis of production and allocation, Cowles Commission for Research in Economics, Monograph 13. New York: Wiley.Google Scholar
- Shephard, R. W. (1970). Theory of cost and production function. Princeton, New-Jersey: Princeton University Press.Google Scholar
- Simar, L., & Wilson, P. (2008). Statistical inference in nonparametric frontier models: recent developments and perspectives. In Harold O. Fried, C.A. Knox Lovell, & Shelton S. Schmidt (Eds.) The measurement of productive efficiency, 2nd edn. Oxford: Oxford University Press.Google Scholar