Operational Conditions in Regulatory Benchmarking Models: A Monte Carlo Analysis

Benchmarking methods are widely used in the regulation of firms in network industries working under heterogeneous exogenous environments. In this paper we compare three recently developed estimators, namely conditional DEA (Daraio and Simar, 2005, 2007b), latent class SFA (Orea and Kumbhakar, 2004; Greene, 2005), and the StoNEZD approach (Johnson and Kuosmanen, 2011) by means of Monte Carlo simulation focusing on their ability to identify production frontiers in the presence of environmental factors. Data generation replicates regulatory data from the energy sector in terms of sample size, sample dispersion and distribution, and correlations of variables. Although results show strengths of each of the three estimators in particular settings, latent class SFA perform best in nearly all simulations. Further, results indicate that the accuracy of the estimators is less sensitive against different distributions of environmental factors, their correlations with inputs, and their impact on the production process, but performance of all approaches deteriorates with increasing noise. For regulators this study provides orientation to adopt new benchmarking methods given industry characteristics.

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

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

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

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

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

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

[7]  A. Shleifer,et al.  A Theory of Yardstick Competition , 1985 .

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

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

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

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

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

[13]  A. Cullmann.  Benchmarking and firm heterogeneity: a latent class analysis for German electricity distribution companies , 2012 .

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

[15]  W. Greene.  The Econometric Approach to Efficiency Analysis , 2008 .

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

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

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

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

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

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

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

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

[26]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

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

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

[29]  A. Cullmann,et al.  Finding the Right Yardstick: Regulation Under Heterogeneous Environments , 2016 .

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

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

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

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

[34]  M. Pollitt,et al.  Benchmarking and regulation: international electricity experience , 2000 .

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

[36]  Timo Kuosmanen,et al.  Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints , 2012 .

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

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

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

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

[41]  M. Armstrong,et al.  Recent developments in the theory of regulation , 2007 .

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

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

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

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

[46]  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 .

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