Stochastic FDH/DEA estimators for frontier analysis

In this paper we extend the work of Simar (J Product Ananl 28:183–201, 2007) introducing noise in nonparametric frontier models. We develop an approach that synthesizes the best features of the two main methods in the estimation of production efficiency. Specifically, our approach first allows for statistical noise, similar to Stochastic frontier analysis (even in a more flexible way), and second, it allows modelling multiple-inputs-multiple-outputs technologies without imposing parametric assumptions on production relationship, similar to what is done in non-parametric methods, like Data Envelopment Analysis (DEA), Free Disposal Hull (FDH), etc.... The methodology is based on the theory of local maximum likelihood estimation and extends recent works of Kumbhakar et al. (J Econom 137(1):1–27, 2007) and Park et al. (J Econom 146:185–198, 2008). Our method is suitable for modelling and estimation of the marginal effects onto inefficiency level jointly with estimation of marginal effects of input. The approach is robust to heteroskedastic cases and to various (unknown) distributions of statistical noise and inefficiency, despite assuming simple anchorage models. The method also improves DEA/FDH estimators, by allowing them to be quite robust to statistical noise and especially to outliers, which were the main problems of the original DEA/FDH estimators. The procedure shows great performance for various simulated cases and is also illustrated for some real data sets. Even in the single-output case, our simulated examples show that our stochastic DEA/FDH improves the Kumbhakar et al. (J Econom 137(1):1–27, 2007) method, by making the resulting frontier smoother, monotonic and, if we wish, concave.

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

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

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

[4]  D. Aigner,et al.  P. Schmidt, 1977,?Formulation and estimation of stochastic frontier production function models,? , 1977 .

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

[6]  R. Stevenson.  Likelihood functions for generalized stochastic frontier estimation , 1980 .

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

[8]  W. Greene.  A Gamma-distributed stochastic frontier model , 1990 .

[9]  Kenneth C. Land,et al.  Chance‐constrained data envelopment analysis , 1993 .

[10]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[11]  N. Petersen,et al.  Chance constrained efficiency evaluation , 1995 .

[12]  Léopold Simar,et al.  A general framework for frontier estimation with panel data , 1996 .

[13]  Léopold Simar,et al.  Pitfalls of Normal-Gamma Stochastic Frontier Models , 1997 .

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

[15]  Dieter Gstach,et al.  Another Approach to Data Envelopment Analysis in Noisy Environments: DEA+ , 1998 .

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

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

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

[19]  Scott E. Atkinson,et al.  Stochastic estimation of firm technology, inefficiency, and productivity growth using shadow cost and distance functions , 2002 .

[20]  P. Hall,et al.  Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error , 2002 .

[21]  A. U.S.,et al.  Measuring the efficiency of decision making units , 2003 .

[22]  Léopold Simar,et al.  Estimation and inference in cross-sectional, stochastic frontier models , 2005 .

[23]  Léopold Simar,et al.  Local likelihood estimation of truncated regression and its partial derivatives: theory and application , 2008 .

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

[25]  L. Simar,et al.  Nonparametric efficiency analysis: a multivariate conditional quantile approach , 2007 .

[26]  Léopold Simar,et al.  How to improve the performances of DEA/FDH estimators in the presence of noise? , 2007 .

[27]  Léopold Simar,et al.  Advanced Robust and Nonparametric Methods in Efficiency Analysis: Methodology and Applications , 2007 .

[28]  P. W. Wilson,et al.  ASYMPTOTICS AND CONSISTENT BOOTSTRAPS FOR DEA ESTIMATORS IN NONPARAMETRIC FRONTIER MODELS , 2008, Econometric Theory.

[29]  P. W. Wilson,et al.  Inferences from Cross-Sectional, Stochastic Frontier Models , 2009 .