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NONPARAMETRIC FRONTIER ESTIMATION: A CONDITIONAL QUANTILE-BASED APPROACH

Published online by Cambridge University Press:  31 March 2005

Y. Aragon ,
A. Daouia  and
C. Thomas-Agnan
Y. Aragon
Affiliation:
Groupe de Recherche en Economie Mathématique et Quantitative et Laboratoire de Statistique et Probabilités, Université de Toulouse
A. Daouia
Affiliation:
Groupe de Recherche en Economie Mathématique et Quantitative et Laboratoire de Statistique et Probabilités, Université de Toulouse
C. Thomas-Agnan
Affiliation:
Groupe de Recherche en Economie Mathématique et Quantitative et Laboratoire de Statistique et Probabilités, Université de Toulouse
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Abstract

In frontier analysis, most of the nonparametric approaches (free disposal hull [FDH], data envelopment analysis [DEA]) are based on envelopment ideas, and their statistical theory is now mostly available. However, by construction, they are very sensitive to outliers. Recently, a robust nonparametric estimator has been suggested by Cazals, Florens, and Simar (2002, Journal of Econometrics 1, 1–25). In place of estimating the full frontier, they propose rather to estimate an expected frontier of order m. Similarly, we construct a new nonparametric estimator of the efficient frontier. It is based on conditional quantiles of an appropriate distribution associated with the production process. We show how these quantiles are interesting in efficiency analysis. We provide the statistical theory of the obtained estimators. We illustrate with some simulated examples and a frontier analysis of French post offices, showing the advantage of our estimators compared with the estimators of the expected maximal output frontiers of order m.We thank J.P. Florens for helpful discussions and C. Cazals for providing the post office data set. We also are very grateful to the referees for useful suggestions.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 2 , April 2005 , pp. 358 - 389
Copyright
© 2005 Cambridge University Press

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References

REFERENCES

Aigner, D.J., C.A.K. Lovell, & P. Schmidt (1977) Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 6, 21–37.Google Scholar
Battese, G.E. & T.J. Coelli (1988) Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data. Journal of Econometrics 3, 387–399.Google Scholar
Berlinet, A., B. Cadre, & A. Gannoun (2001) On the conditional L1-median and its estimation. Journal of Nonparametric Statistics 13, 631–645.Google Scholar
Caudill, S.B., J.M. Ford, & D.M. Groper (1995) Frontier estimation and firm-specific inefficiency measures in the presence of heteroscedasticity. Journal of Business & Economic Statistics 13, 105–111.Google Scholar
Cazals, C., J.P. Florens, & L. Simar (2002) Nonparametric frontier estimation: A robust approach. Journal of Econometrics 1, 1–25.Google Scholar
Charnes, A., W.W. Cooper, & E. Rhodes (1978) Measuring the efficiency of decision making units. European Journal of Operations Research 2, 429–444.Google Scholar
Debreu, G. (1951) The coefficient of resource utilization. Econometrica 19, 273–292.Google Scholar
Deprins, D., L. Simar, & H. Tulkens (1984) Measuring labor efficiency in post offices. In M. Marchand, P. Pestieau, & H. Tulkens (eds.), The Performance of Public Enterprises: Concepts and Measurements, pp. 243–267. North-Holland.
Ducharme, G.R., A. Gannoun, M.C. Guertin, & J.C. Jequier (1995) Reference values obtained by kernel-based estimation of quantile regression. Biometrics 51, 1105–1116.Google Scholar
Farrell, M.J. (1957) The measurement of productive efficiency. Journal of the Royal Statistical Society, Series A 120, 253–281.Google Scholar
Ghosh, J.K. (1971) A new proof of the Bahadur representation of quantiles and an application. Annals of Mathematical Statistics 42, 1957–1961.Google Scholar
Gijbels, I., E. Mammen, B.U. Park, & L. Simar (1999) On estimation of monotone and concave frontier functions. Journal of the American Statistical Association 94, 220–228.Google Scholar
Hendricks, W. & R. Koenker (1992) Hierarchical spline models for conditional quantiles and the demand for electricity. Journal of the American Statistical Association 87, 58–68.Google Scholar
Koopmans, T.C. (1951) An analysis of production as an efficient combination of activities. In T.C. Koopmans (ed.), Activity Analysis of Production and Allocation, Cowles Commission for Research in Economics, Monograph 13. Wiley.
Meeusen, W. & J. van den Broek (1977) Efficiency estimation from Cobb-Douglas production function with composed error. International Economic Review 8, 435–444.Google Scholar
Olsen, J.A., P. Schmidt, & D.M. Waldman (1980) A Monte Carlo study of estimators of stochastic frontier production functions. Journal of Econometrics 13, 67–82.Google Scholar
Park, B.U., L. Simar, & C. Weiner (2000) The FDH estimator for productivity efficiency scores. Econometric Theory 16, 855–877.Google Scholar
Schwartz, L. (1991) Analyse. I. Hermann, éditeurs des sciences et des arts.
Serfling, R.J. (1980) Approximation Theorems of Mathematical Statistics. Wiley Series in Probability and Mathematical Statistics. Wiley.
Serfling, R.J. (2002) Quantile functions for multivariate analysis: Approaches and applications. Statistica Neerlandica 56, 214–232.Google Scholar
Shephard, R.W. (1970) Theory of Cost and Production Function. Princeton University Press.
Shorack, G.R. & J.A. Wellner (1986) Empirical Processes with Applications to Statistics. Wiley.
Simar, L. (2003) Detecting Outliers in Frontier Models: A Simple Approach. Discussion paper 0146, UCL (http://www.stat.ucl.ac.be). Forthcoming in Journal of Productivity Analysis.Google Scholar
Simar, L. & P. Wilson (2000) Statistical inference in nonparametric frontier models: The state of the art. Journal of Productivity Analysis 13, 49–78.Google Scholar
Stevenson, R.E. (1980) Likelihood functions for generalised stochastic frontier estimation. Journal of Econometrics 13, 57–66.Google Scholar