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WHEN BIAS KILLS THE VARIANCE: CENTRAL LIMIT THEOREMS FOR DEA AND FDH EFFICIENCY SCORES

Published online by Cambridge University Press:  08 September 2014

Alois Kneip ,
Léopold Simar  and
Paul W. Wilson
Alois Kneip*
Affiliation:
Universität Bonn
Léopold Simar
Affiliation:
Université Catholique de Louvain-la-Neuve
Paul W. Wilson
Affiliation:
Clemson University
*
*Address correspondence to Alois Kneip, Institute für Gessellschafts- und Wirtschaftswissennschafen, Statistische Abteilung, Universität Bonn, Bonn, Germany; e-mail: [email protected] or to Léopold Simar, Institut de Statistique, Biostatistique, et Sciences Actuarielles, Université Catholique de Louvain-la-Neuve, Louvain-la-Neuve, Belgium; e-mail: [email protected] or to Paul W. Wilson, Department of Economics and School of Computing, Clemson University, Clemson, South Carolina, USA; e-mail: [email protected].
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Abstract

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiencies of production units. In applications, both efficiency scores for individual units as well as average efficiency scores are typically reported. While several bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods have existed for making inference about mean efficiency levels. This paper shows that standard central limit theorems do not apply in the case of means of DEA or FDH efficiency scores due to the bias of the individual scores, which is of larger order than either the variance or covariances among individual scores. The main difficulty comes from the fact that such statistics depend on efficiency estimators evaluated at random points. Here, new central limit theorems are developed for means of DEA and FDH scores, and their efficacy for inference about mean efficiency levels is examined via Monte Carlo experiments.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 2: Haavelmo Memorial Issue: Part Two , April 2015 , pp. 394 - 422
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

Afriat, S. (1972) Efficiency estimation of production functions. International Economic Review 13, 568–598.Google Scholar
Banker, R.D., Charnes, A., & Cooper, W.W. (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 30, 1078–1092.Google Scholar
Banker, R.D. & Natarajan, R. (2008) Evaluating contextual variables affecting productivity using data envelopment analysis. Operations Research 56, 48–58.CrossRefGoogle Scholar
Chambers, R.G., Chung, Y., & Färe, R. (1996) Benefit and distance functions. Journal of Economic Theory 70, 407–419.CrossRefGoogle Scholar
Charnes, A., Cooper, W.W., & Rhodes, E. (1978) Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444.Google Scholar
Daouia, A., Florens, J.P., & Simar, L. (2012) Regularization of non-parametric frontier estimators. Journal of Econometrics 168, 285–299.CrossRefGoogle Scholar
Deprins, D., Simar, L., & Tulkens, H. (1984) Measuring labor inefficiency in post offices. In Pestieau, M.M.P. & Tulkens, H. (eds.), The Performance of Public Enterprises: Concepts and Measurements, pp. 243–267. North-Holland.Google Scholar
Färe, R. (1988) Fundamentals of Production Theory. Springer-Verlag.Google Scholar
Färe, R., Grosskopf, S., & Lovell, C.A.K. (1985) The Measurement of Efficiency of Production. Kluwer-Nijhoff.Google Scholar
Farrell, M.J. (1957) The measurement of productive efficiency. Journal of the Royal Statistical Society A 120, 253–281.Google Scholar
Gray, H.L. & Schucany, R.R. (1972) The Generalized Jackknife Statistic. Marcel Decker, Inc.Google Scholar
Jeong, S.O. (2004) Asymptotic distribution of DEA efficiency scores. Journal of the Korean Statistical Society 33, 449–458.Google Scholar
Jeong, S.O. & Park, B.U. (2006) Large sample approximation of the distribution for convex-hull estimators of boundaries. Scandinavian Journal of Statistics 33, 139–151.Google Scholar
Jeong, S.O., Park, B.U., & Simar, L. (2010) Nonparametric conditional efficiency measures: Asymptotic properties. Annals of Operations Research 173, 105–122.Google Scholar
Khan, S. & Lewbel, A. (2007) Weighted and two-stage least squares estimation of semiparametric truncated regression models. Econometric Theory 23, 309–347.Google Scholar
Kneip, A., Park, B., & Simar, L. (1998) A note on the convergence of nonparametric DEA efficiency measures. Econometric Theory 14, 783–793.CrossRefGoogle Scholar
Kneip, A., Simar, L., & Wilson, P.W. (2008) Asymptotics and consistent bootstraps for DEA estimators in non-parametric frontier models. Econometric Theory 24, 1663–1697.Google Scholar
Kneip, A., Simar, L., & Wilson, P.W. (2011) A computationally efficient, consistent bootstrap for inference with non-parametric DEA estimators. Computational Economics 38, 483–515.CrossRefGoogle Scholar
Lewbel, A. & Linton, O. (2002) Nonparametric censored and truncated regression. Econometrica 70, 765–779.CrossRefGoogle Scholar
Marsaglia, G. (1972) Choosing a point from the surface of a sphere. Annals of Mathematical Statistics 43, 645–646.Google Scholar
Muller, M.E. (1959) A note on a method for generating points uniformly on n-dimensional spheres. Communications of the Association for Computing Machinery 2, 19–20.Google Scholar
Park, B.U., Jeong, S.-O., & Simar, L. (2010) Asymptotic distribution of conical-hull estimators of directional edges. Annals of Statistics 38, 1320–1340.Google Scholar
Park, B.U., Simar, L., & Weiner, C. (2000) FDH efficiency scores from a stochastic point of view. Econometric Theory 16, 855–877.Google Scholar
Park, B.U., Simar, L., & Zelenyuk, V. (2008) Local likelihood estimation of truncated regression and its partial derivative: Theory and application. Journal of Econometrics 146, 185–2008.Google Scholar
Shephard, R.W. (1970) Theory of Cost and Production Functions. Princeton University Press.Google Scholar
Simar, L. & Vanhems, A. (2012) Probabilistic characterization of directional distances and their robust versions. Journal of Econometrics 166, 342–354.CrossRefGoogle Scholar
Simar, L., Vanhems, A., & Wilson, P.W. (2012) Statistical inference for DEA estimators of directional distances. European Journal of Operational Research 220, 853–864.Google Scholar
Simar, L. & Wilson, P.W. (2000) Statistical inference in nonparametric frontier models: The state of the art. Journal of Productivity Analysis 13, 49–78.Google Scholar
Simar, L. & Wilson, P.W. (2007) Estimation and inference in two-stage, semi-parametric models of productive efficiency. Journal of Econometrics 136, 31–64.Google Scholar
Simar, L. & Wilson, P.W. (2011a) Inference by the m out of n bootstrap in nonparametric frontier models. Journal of Productivity Analysis 36, 33–53.Google Scholar
Simar, L. & Wilson, P.W. (2011b) Two-stage DEA: Caveat emptor. Journal of Productivity Analysis 36, 205–218.Google Scholar
Simar, L. & Wilson, P.W. (2013) Estimation and inference in nonparametric frontier models: Recent developments and perspectives. Foundations and Trends in Econometrics 5, 183–337.Google Scholar
Wilson, P.W. (2011) Asymptotic properties of some non-parametric hyperbolic efficiency estimators. In Van Keilegom, I. & Wilson, P.W. (eds.), Exploring Research Frontiers in Contemporary Statistics and Econometrics, pp. 115–150. Springer-Verlag.Google Scholar