Transconcave data envelopment analysis

Transconcave data envelopment analysis (TDEA) extends standard data envelopment analysis (DEA), in order to account for non-convex production technologies, such as those involving increasing returns-to-scale or diseconomies of scope. TDEA introduces non-convexities by transforming the range and the domain of the production frontier, thus replacing the standard assumption that the production frontier is concave with the more general assumption that the frontier is concave transformable. TDEA gives statistically consistent estimates for all monotonically increasing and concave transformable frontiers. In addition, Monte Carlo simulations suggest that TDEA can substantially improve inefficiency estimation in small samples compared to the standard Banker, Charnes and Cooper model and the full disposable hull model (FDH).

[1]  N. Petersen Data Envelopment Analysis on a Relaxed Set of Assumptions , 1990 .

[2]  M. Farrell The Measurement of Productive Efficiency , 1957 .

[3]  A. Charnes,et al.  A multiplicative model for efficiency analysis , 1982 .

[4]  R. Banker Maximum likelihood, consistency and data envelopment analysis: a statistical foundation , 1993 .

[5]  B. Park,et al.  A NOTE ON THE CONVERGENCE OF NONPARAMETRIC DEA ESTIMATORS FOR PRODUCTION EFFICIENCY SCORES , 1998, Econometric Theory.

[6]  Sverre A.C. Kittelsen,et al.  Monte Carlo simulations of DEA efficiency measures and hypothesis tests , 1999 .

[7]  Peter Bogetoft,et al.  DEA on relaxed convexity assumptions , 1996 .

[8]  A. Tsybakov,et al.  Efficient Estimation of Monotone Boundaries , 1995 .

[9]  Thierry Post,et al.  A quasi-concave DEA model with an application for bank branch performance evaluation , 2001, Eur. J. Oper. Res..

[10]  A. Charnes,et al.  Invariant multiplicative efficiency and piecewise cobb-douglas envelopments , 1983 .

[11]  Kristiaan Kerstens,et al.  Distinguishing technical and scale efficiency on non-convex and convex technologies: theoretical analysis and empirical illustrations , 1998 .

[12]  E. Mammen,et al.  On estimation of monotone and concave frontier functions , 1999 .

[13]  Thierry Post,et al.  Estimating non-convex production sets - imposing convex input sets and output sets in data envelopment analysis , 2001, Eur. J. Oper. Res..

[14]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[15]  Léopold Simar,et al.  FDH Efficiency Scores from a Stochastic Point of View , 1997 .

[16]  Allen N. Berger,et al.  Efficiency of Financial Institutions: International Survey and Directions for Future Research , 1997 .

[17]  P. W. Wilson,et al.  Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models , 1998 .

[18]  B. Park,et al.  THE FDH ESTIMATOR FOR PRODUCTIVITY EFFICIENCY SCORES , 2000, Econometric Theory.

[19]  A. Charnes,et al.  Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis , 1984 .

[20]  A. Ben-Tal On generalized means and generalized convex functions , 1977 .

[21]  Léopold Simar,et al.  On estimation of monotone and convex boundaries , 1995 .