Stochastic Nonparametric Envelopment of Data: Combining Virtues of Sfa and DEA in a Unified Framework

The literature of productive efficiency analysis is divided into two main branches: the parametric Stochastic Frontier Analysis (SFA) and nonparametric Data Envelopment Analysis (DEA). This paper attempts to combine the virtues of both approaches in a unified framework. We follow the SFA literature and introduce a stochastic component decomposed into idiosyncratic error and technical inefficiency components imposing the standard SFA assumptions. In contrast to the SFA, we do not make any prior assumptions about the functional form of the deterministic production function. In this respect, we follow the nonparametric route of DEA that only imposes free disposability, convexity, and some specification of returns to scale. From the postulated class of production functions, the proposed method identifies the production function with the best empirical fit to the data. The resulting function will always take a piece-wise linear form analogous to the DEA frontiers. We discuss the practical implementation of the method and illustrate its potential by means empirical examples.

[1]  P. W. Wilson,et al.  Estimation and inference in two-stage, semi-parametric models of production processes , 2007 .

[2]  C. Timmer.  Using a Probabilistic Frontier Production Function to Measure Technical Efficiency , 1971, Journal of Political Economy.

[3]  A. Worthington.  AN EMPIRICAL SURVEY OF FRONTIER EFFICIENCY MEASUREMENT TECHNIQUES IN HEALTHCARE SERVICES , 1999 .

[4]  Léopold Simar,et al.  Efficient Semiparametric Estimation in a Stochastic Frontier Model , 1994 .

[5]  C. Lovell,et al.  Stochastic Frontier Analysis: Frontmatter , 2000 .

[6]  John Ruggiero,et al.  Efficiency measurement in the stochastic frontier model , 2001, Eur. J. Oper. Res..

[7]  Konkurrencestyrelsen,et al.  Nordic food markets : a taste for competition. , 2005 .

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

[9]  W. Greene.  Frontier Production Functions , 1993 .

[10]  Stefanka Chukova,et al.  On the relationship between regression analysis and mathematical programming , 2004, Adv. Decis. Sci..

[11]  Timo Kuosmanen,et al.  Duality Theory of Non-convex Technologies , 2003 .

[12]  Efthymios G. Tsionas,et al.  Stochastic Frontier Models with Random Coefficients , 2002 .

[13]  C. Thomas-Agnan,et al.  NONPARAMETRIC FRONTIER ESTIMATION: A CONDITIONAL QUANTILE-BASED APPROACH , 2005, Econometric Theory.

[14]  Yanqin Fan,et al.  Semiparametric Estimation of Stochastic Production Frontier Models , 1996 .

[15]  P. Schmidt,et al.  Production frontiers with cross-sectional and time-series variation in efficiency levels , 1990 .

[16]  R. Färe,et al.  Benefit and Distance Functions , 1996 .

[17]  Luis R. Murillo-Zamorano.  Economic Efficiency and Frontier Techniques , 2004 .

[18]  P. Bauer.  Recent developments in the econometric estimation of frontiers , 1990 .

[19]  Léopold Simar,et al.  A fully nonparametric stochastic frontier model for panel data , 2005 .

[20]  William H. Greene,et al.  Reconsidering heterogeneity in panel data estimators of the stochastic frontier model , 2005 .

[21]  Léopold Simar,et al.  Stochastic panel frontiers: A semiparametric approach☆ , 1998 .

[22]  Cheng Hsiao,et al.  Panel Data Models , 2007 .

[23]  J. Florens,et al.  Nonparametric frontier estimation: a robust approach , 2002 .

[24]  R. Färe,et al.  Profit, Directional Distance Functions, and Nerlovian Efficiency , 1998 .

[25]  Hal R. Varian,et al.  Non-parametric analysis of optimizing behavior with measurement error , 1985 .

[26]  Lawrence M. Seiford,et al.  Recent developments in dea : the mathematical programming approach to frontier analysis , 1990 .

[27]  C. Lovell,et al.  On the estimation of technical inefficiency in the stochastic frontier production function model , 1982 .

[28]  Thierry Post,et al.  Erim Report Series Research in Management Methodological Advances in Dea: a Survey and an Application for the Dutch Electricity Sector Bibliographic Data and Classifications , 2022 .

[29]  John Ruggiero,et al.  Data envelopment analysis with stochastic data , 2004, J. Oper. Res. Soc..

[30]  P. Schmidt,et al.  Confidence statements for efficiency estimates from stochastic frontier models , 1996 .

[31]  A. U.S.,et al.  FORMULATION AND ESTIMATION OF STOCHASTIC FRONTIER PRODUCTION FUNCTION MODELS , 2001 .

[32]  W. Meeusen,et al.  Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error , 1977 .

[33]  C. Hildreth.  Point Estimates of Ordinates of Concave Functions , 1954 .

[34]  Léopold Simar,et al.  Nonparametric stochastic frontiers: A local maximum likelihood approach , 2007 .

[35]  Mette Asmild,et al.  Combining DEA Window Analysis with the Malmquist Index Approach in a Study of the Canadian Banking Industry , 2004 .

[36]  Peter Schmidt,et al.  One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels , 2002 .

[37]  R. Färe,et al.  Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries , 1994 .

[38]  Léopold Simar,et al.  Semiparametric efficient estimation of AR(1) panel data models. , 2003 .

[39]  A. Worthington.  An Empirical Survey of Frontier Efficiency Measurement Techniques in Education , 2001 .

[40]  W. Greene.  Maximum likelihood estimation of econometric frontier functions , 1980 .

[41]  Timo Kuosmanen,et al.  The law of one price in data envelopment analysis: Restricting weight flexibility across firms , 2003, Eur. J. Oper. Res..

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

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