On estimation of monotone and concave frontier functions
A way for measuring the efficiency of enterprises is via the estimation of the so-called production frontier, which is the upper boundary of the support of the population density in the input and output space. It is reasonable to assume that the production frontier is a concave monotone function. Then, a famous estimator is the data envelopment analysis (DEA) estimator, which is the lowest concave monotone increasing function covering all sample points. This estimator is biased downwards since it never exceeds the true production frontier. In this paper we derive the asymptotic distribution of the DEA estimator, which enables us to assess the asymptotic bias and hence to propose an improved bias corrected estimator. This bias corrected estimator involves consistent estimation of the density function as well as of the second derivative of the production frontier. We also discuss briefly the construction of asymptotic confidence intervals. The finite sample performance of the bias corrected estimator is investigated via a simulation study and the procedure is illustrated for a real data example.
|Date of creation:||01 Apr 1997|
|Date of revision:|
|Contact details of provider:|| Postal: Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium)|
Fax: +32 10474304
Web page: http://www.uclouvain.be/core
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
- Berndt, Ernst R. & Christensen, Laurits R., 1973. "The translog function and the substitution of equipment, structures, and labor in U.S. manufacturing 1929-68," Journal of Econometrics, Elsevier, vol. 1(1), pages 81-113, March.
- Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-76, August.
- Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
- Hardle, W. & Park, B. U. & Tsybakov, A. B., 1995. "Estimation of Non-sharp Support Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 205-218, November.
- Greene, William H., 1980. "Maximum likelihood estimation of econometric frontier functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 27-56, May.
When requesting a correction, please mention this item's handle: RePEc:cor:louvco:1997031. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alain GILLIS)
If references are entirely missing, you can add them using this form.