Non-parametric tests of returns to scale

This paper discusses various statistics for testing hypotheses regarding returns to scale in the context of non-parametric models of technical efficiency. In addition, the paper presents bootstrap estimation procedures which yield appropriate critical values for the test statistics. Evidence on the true sizes and power of the various proposed tests is obtained from Monte-Carlo experiments. This paper is an extension of earlier work in [Manage. Sci. 44 (1998) 49 J. Appl. Statist. 27 (2000b) 779]. (C) 2002 Elsevier Science B.V. All rights reserved.

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

[2]  Paul W. Wilson,et al.  TECHNICAL EFFICIENCY IN THE DECENTRALIZED CARE OF THE DEVELOPMENTALLY DISABLED , 1994 .

[3]  R. Shepherd Theory of cost and production functions , 1970 .

[4]  S. Grosskopf,et al.  Efficiency and Ownership: Further Evidence , 1986 .

[5]  Magnus Tambour,et al.  Alternative Approaches to Estimate Returns to Scale in DEA- Models , 1996 .

[6]  B. Efron Bootstrap Methods: Another Look at the Jackknife , 1979 .

[7]  Selected Tables in Mathematical Statistics , 1971 .

[8]  Leâ Opold Simar,et al.  A general methodology for bootstrapping in non-parametric frontier models , 2000 .

[9]  P. W. Wilson,et al.  Some Problems with the Ferrier/Hirschberg Bootstrap Idea , 1997 .

[10]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[11]  William H. Press,et al.  Numerical recipes , 1990 .

[12]  A. Charnes,et al.  Data Envelopment Analysis Theory, Methodology and Applications , 1995 .

[13]  Rolf Färe,et al.  Fundamentals of production theory , 1988 .

[14]  R. Färe,et al.  The measurement of efficiency of production , 1985 .

[15]  R. Färe,et al.  Theory and Application of Directional Distance Functions , 2000 .

[16]  Harold O. Fried,et al.  The measurement of productive efficiency : techniques and applications , 1993 .

[17]  P. A. W. Lewis,et al.  A Pseudo-Random Number Generator for the System/360 , 1969, IBM Syst. J..

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

[19]  Gary D. Ferrier,et al.  Ownership Type, Property Rights, and Relative Efficiency , 1994 .

[20]  Magnus Tambour,et al.  Testing scale efficiency in DEA models: a bootstrapping approach , 1999 .

[21]  R. Färe,et al.  Nonparametric Cost Approach to Scale Efficiency , 1985 .

[22]  G. Debreu The Coefficient of Resource Utilization , 1951 .

[23]  Rajiv D. Banker,et al.  Hypothesis tests using data envelopment analysis , 1996 .

[24]  Léopold Simar,et al.  Of Course We Can Bootstrap DEA Scores! But Does It Mean Anything? Logic Trumps Wishful Thinking , 1999 .

[25]  Magnus Tambour,et al.  Scale Efficiency and Scale Elasticity in DEA-models - A Bootstrapping Approach , 1996 .

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

[27]  S. Afriat Efficiency Estimation of Production Function , 1972 .

[28]  Shawna Grosskopf,et al.  The Role of the Reference Technology in Measuring Productive Efficiency , 1986 .

[29]  P. W. Wilson,et al.  Statistical Inference in Nonparametric Frontier Models: The State of the Art , 1999 .

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

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

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

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

[34]  Lawrence M. Seiford,et al.  A bibliography for Data Envelopment Analysis (1978-1996) , 1997, Ann. Oper. Res..

[35]  S. Grosskopf,et al.  Measuring hospital performance. A non-parametric approach. , 1987, Journal of health economics.