Environmental factors in frontier estimation - A Monte Carlo analysis

We compare three recently developed frontier estimators, namely the conditional DEA (Daraio and Simar, 2005; 2007b), the latent class SFA (Greene, 2005; Orea and Kumbhakar, 2004), and the StoNEZD approach (Johnson and Kuosmanen, 2011) by means of Monte Carlo simulation. We focus on their ability to identify production frontiers and efficiency rankings in the presence of environmental factors. Our simulations match features of real life datasets and cover a wide range of scenarios with variations in sample size, distribution of noise and inefficiency, as well as in distributions, intensity, and number of environmental variables. Our results provide insight in the finite sample properties of the estimators, while also identifying estimator-specific characteristics. Overall, the latent class approach is found to perform best, although in many cases StoNEZD shows a similar performance. Performance of cDEA is most often inferior.

[1]  Léopold Simar,et al.  How to measure the impact of environmental factors in a nonparametric production model , 2012, Eur. J. Oper. Res..

[2]  S. Afriat.  THE CONSTRUCTION OF UTILITY FUNCTIONS FROM EXPENDITURE DATA , 1967 .

[3]  Léopold Simar,et al.  Optimal bandwidth selection for conditional efficiency measures: A data-driven approach , 2010, Eur. J. Oper. Res..

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

[5]  S. Kumbhakar,et al.  Efficiency measurement using a latent class stochastic frontier model , 2004 .

[6]  Karim L. Anaya,et al.  Using stochastic frontier analysis to measure the impact of weather on the efficiency of electricity distribution businesses in developing economies , 2017, Eur. J. Oper. Res..

[7]  C. J. Stone,et al.  Optimal Global Rates of Convergence for Nonparametric Regression , 1982 .

[8]  P. W. Wilson,et al.  Estimation and Inference in Nonparametric Frontier Models: Recent Developments and Perspectives , 2013 .

[9]  Chunyan Yu,et al.  The effects of exogenous variables in efficiency measurement - A monte carlo study , 1998, Eur. J. Oper. Res..

[10]  Léopold Simar,et al.  Unobserved heterogeneity and endogeneity in nonparametric frontier estimation , 2016 .

[11]  Jens J. Krüger,et al.  A Monte Carlo study of old and new frontier methods for efficiency measurement , 2012, Eur. J. Oper. Res..

[12]  Marcel Clermont,et al.  Stochastic non-smooth envelopment of data for multi-dimensional output , 2018, Journal of Productivity Analysis.

[13]  Eleftherios Aggelopoulos,et al.  Bank branch efficiency under environmental change: A bootstrap DEA on monthly profit and loss accounting statements of Greek retail branches , 2017, Eur. J. Oper. Res..

[14]  Timo Kuosmanen,et al.  One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient, root-n consistent StoNEZD method , 2011 .

[15]  W. Greene.  Alternative Panel Data Estimators for Stochastic Frontier Models , 2002 .

[16]  Michael G. Pollitt,et al.  Using the latent class approach to cluster firms in benchmarking: An application to the US electricity transmission industry , 2014 .

[17]  L. Simar,et al.  Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach , 2007 .

[18]  Andrew L. Johnson,et al.  Stochastic Nonparametric Approach to Efficiency Analysis: A Unified Framework , 2015 .

[19]  Daniel Santín,et al.  Monte‐Carlo Comparison of Conditional Nonparametric Methods and Traditional Approaches to Include Exogenous Variables , 2016 .

[20]  Jeffrey S. Racine,et al.  Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data , 2008 .

[21]  Carla Haelermans,et al.  The role of innovations in secondary school performance - Evidence from a conditional efficiency model , 2012, Eur. J. Oper. Res..

[22]  Mark A. Andor,et al.  The StoNED age: the departure into a new era of efficiency analysis? A monte carlo comparison of StoNED and the “oldies” (SFA and DEA) , 2013, Journal of Productivity Analysis.

[23]  H. O. Fried,et al.  Accounting for Environmental Effects and Statistical Noise in Data Envelopment Analysis , 2002 .

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

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

[26]  J. Laffont,et al.  A Theory of Incentives in Procurement and Regulation , 1993 .

[27]  Qi Li,et al.  Nonparametric Econometrics: Theory and Practice , 2006 .

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

[29]  T. Coelli,et al.  A Primer on Efficiency Measurement for Utilities and Transport Regulators , 2003 .

[30]  Carmela Di Mauro,et al.  The impact of managerial and organizational aspects on hospital wards' efficiency: Evidence from a case study , 2009, Eur. J. Oper. Res..

[31]  Michael G. Pollitt,et al.  Efficiency analysis of energy networks: An international survey of regulators , 2009 .

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

[33]  G. Battese,et al.  A model for technical inefficiency effects in a stochastic frontier production function for panel data , 1995 .

[34]  Léopold Simar,et al.  Nonparametric conditional efficiency measures: asymptotic properties , 2010, Ann. Oper. Res..

[35]  Jeffrey S. Racine,et al.  Cross-Validation and the Estimation of Conditional Probability Densities , 2004 .

[36]  Timo Kuosmanen,et al.  Stochastic semi-nonparametric frontier estimation of electricity distribution networks: Application of the StoNED method in the Finnish regulatory model , 2012 .

[37]  Per Joakim Agrell,et al.  Benchmarking and Regulation , 2013 .

[38]  Per Joakim Agrell,et al.  Capturing heterogeneity in electricity distribution operations: a critical review of latent class modelling , 2017 .

[39]  Daniel Santín,et al.  Alternative approaches to include exogenous variables in DEA measures: A comparison using Monte Carlo , 2009, Comput. Oper. Res..

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

[41]  Timo Kuosmanen,et al.  What is the best practice for benchmark regulation of electricity distribution? Comparison of DEA, SFA and StoNED methods , 2013 .

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

[43]  Kristof De Witte,et al.  Citizen coproduction and efficient public good provision: Theory and evidence from local public libraries , 2013, Eur. J. Oper. Res..

[44]  Subal C. Kumbhakar,et al.  Estimation of TFP growth: a semiparametric smooth coefficient approach , 2012 .

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

[46]  Léopold Simar,et al.  Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach , 2005 .

[47]  S. Kumbhakar,et al.  When, where and how to perform efficiency estimation , 2011, SSRN Electronic Journal.

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

[49]  Endre Bjørndal,et al.  Benchmarking in Regulation of Electricity Networks in Norway: An Overview , 2010 .

[50]  L. Trujillo,et al.  Infrastructure Reform in Developing Economies: Evidence from a survey of efficiency measures , 2006 .

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

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

[53]  Steven B. Caudill,et al.  Estimating a mixture of stochastic frontier regression models via the em algorithm: A multiproduct cost function application , 2003 .

[54]  C. J. Stone,et al.  Optimal Rates of Convergence for Nonparametric Estimators , 1980 .

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

[56]  Rajiv D. Banker,et al.  Efficiency Analysis for Exogenously Fixed Inputs and Outputs , 1986, Oper. Res..