Stochastic Frontier Analysis: Foundations and Advances II

This chapter reviews some of the most important developments in the econometric estimation of productivity and efficiency surrounding the stochastic frontier model. We highlight endogeneity issues, recent advances in generalized panel data stochastic frontier models, nonparametric estimation of the frontier, quantile estimation and distribution free methods. An emphasis is placed on highlighting recent research and providing broad coverage, while details are left for further reading in the abundant (although not limited to) list of references provided.

[1]  Robin C. Sickles,et al.  The Skewness Issue in Stochastic Frontiers Models: Fact or Fiction? , 2011 .

[2]  B. Greenwald,et al.  Externalities in Economies with Imperfect Information and Incomplete Markets , 1986 .

[3]  Subal C. Kumbhakar,et al.  The specification of technical and allocative inefficiency in stochastic production and profit frontiers , 1987 .

[4]  G. Battese,et al.  ESTIMATION OF A PRODUCTION FRONTIER MODEL: WITH APPLICATION TO THE PASTORAL ZONE OF EASTERN AUSTRALIA , 1977 .

[5]  P. Robinson.  ROOT-N-CONSISTENT SEMIPARAMETRIC REGRESSION , 1988 .

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

[7]  Toru Hattori,et al.  Relative Performance of U.S. and Japanese Electricity Distribution: An Application of Stochastic Frontier Analysis , 2003 .

[8]  J. Richmond.  Estimating the Efficiency of Production , 1974 .

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

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

[11]  Efthymios G. Tsionas,et al.  Maximum likelihood estimation of stochastic frontier models by the Fourier transform , 2012 .

[12]  Lung-fei Lee,et al.  The measurement and sources of technical inefficiency in the Indonesian weaving industry , 1981 .

[13]  Peter Schmidt,et al.  A Monte Carlo study of estimators of stochastic frontier production functions , 1980 .

[14]  Byeong-Ho Gong.  A Study on the Estimation of Technical Efficiency , 1990 .

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

[16]  S. Kumbhakar,et al.  Estimation of technical and allocative inefficiency: A primal system approach , 2006 .

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

[18]  Timo Kuosmanen,et al.  Neoclassical Versus Frontier Production Models? Testing for the Skewness of Regression Residuals , 2009 .

[19]  Subal C. Kumbhakar,et al.  Relative performance of public and private ownership under yardstick competition: electricity retail distribution , 1998 .

[20]  T. Coelli.  Estimators and hypothesis tests for a stochastic frontier function: A Monte Carlo analysis , 1995 .

[21]  Subal C. Kumbhakar,et al.  A Practitioner's Guide to Stochastic Frontier Analysis Using Stata , 2015 .

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

[23]  S. Caudill,et al.  Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity , 1995 .

[24]  Q. Lib,et al.  Nonparametric estimation of regression functions with both categorical and continuous data , 2004 .

[25]  G. González-Farías,et al.  SKEW-NORMALITY IN STOCHASTIC FRONTIER ANALYSIS , 2003 .

[26]  Andreas Behr,et al.  Quantile regression for robust bank efficiency score estimation , 2010, Eur. J. Oper. Res..

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

[28]  Kien C. Tran,et al.  GMM estimation of stochastic frontier model with endogenous regressors , 2013 .

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

[30]  G. Battese,et al.  A Metafrontier Production Function for Estimation of Technical Efficiencies and Technology Gaps for Firms Operating Under Different Technologies , 2004 .

[31]  George E. Battese,et al.  Technology Gap, Efficiency, and a Stochastic Metafrontier Function , 2002 .

[32]  Léopold Simar,et al.  Nonparametric least squares methods for stochastic frontier models , 2017 .

[33]  Peter Schmidt,et al.  Endogeneity in Stochastic Frontier Models , 2016 .

[34]  A. O'Hagan,et al.  Bayes estimation subject to uncertainty about parameter constraints , 1976 .

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

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

[37]  L. Simar,et al.  Robust nonparametric estimators of monotone boundaries , 2005 .

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

[39]  Léopold Simar,et al.  Stochastic frontiers incorporating exogenous influences on efficiency , 1994 .

[40]  W. Greene,et al.  Investigating the impact of endogeneity on inefficiency estimates in the application of stochastic frontier analysis to nursing homes , 2013 .

[41]  Robin C. Sickles,et al.  Measurement of Productivity and Efficiency , 2019 .

[42]  Robert A. Moffitt,et al.  A COMPUTATIONALLY EFFICIENT QUADRATURE PROCEDURE FOR THE ONE-FACTOR MULTINOMIAL PROBIT MODEL , 1982 .

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

[44]  P. W. Wilson,et al.  Two-stage DEA: caveat emptor , 2011 .

[45]  A.A.R. Madhavi,et al.  Efficiency Estimation of Production Functions , 2013 .

[46]  Christopher F. Parmeter,et al.  Estimation of hedonic price functions with incomplete information , 2010 .

[47]  Hung-Jen Wang,et al.  Estimating fixed-effect panel stochastic frontier models by model transformation , 2010 .

[48]  L. Simar,et al.  The “wrong skewness” problem in stochastic frontier models: A new approach , 2018 .

[49]  Yair Mundlak,et al.  Empirical Production Function Free of Management Bias , 1961 .

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

[51]  William H. Greene,et al.  Simulated Likelihood Estimation of the Normal-Gamma Stochastic Frontier Function , 2000 .

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

[53]  Abdelaati Daouia,et al.  On Projection‐type Estimators of Multivariate Isotonic Functions , 2013 .

[54]  S. Caudill,et al.  Biases in frontier estimation due to heteroscedasticity , 1993 .

[55]  Kien C. Tran,et al.  Estimation of nonparametric inefficiency effects stochastic frontier models with an application to British manufacturing , 2009 .

[56]  Valentin Zelenyuk,et al.  Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis , 2019, Oper. Res..

[57]  Léopold Simar,et al.  Statistical Approaches for Non‐parametric Frontier Models: A Guided Tour , 2015 .

[58]  E. Tsionas.  Efficiency Measurement with the Weibull Stochastic Frontier , 2007 .

[59]  Donald M. Waldman,et al.  A stationary point for the stochastic frontier likelihood , 1982 .

[60]  G. Battese,et al.  Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data , 1988 .

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

[62]  Mike G. Tsionas,et al.  Directional distance functions: Optimal endogenous directions , 2016 .

[63]  P. Schmidt,et al.  Endogenous Environmental Variables In Stochastic Frontier Models , 2017 .

[64]  G. Chamberlain.  Asymptotic efficiency in estimation with conditional moment restrictions , 1987 .

[65]  CL Huang,et al.  Estimation of a non-neutral stochastic frontier production function , 1994 .

[66]  Lung-fei Lee.  A Test for Distributional Assumptions for the Stochastic Frontier Functions , 1983 .

[67]  Subal C. Kumbhakar,et al.  Joint estimation of technology choice and technical efficiency: an application to organic and conventional dairy farming , 2009 .

[68]  Subal C. Kumbhakar,et al.  Estimation of production technology when the objective is to maximize return to the outlay , 2011, Eur. J. Oper. Res..

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

[70]  D. Reifschneider,et al.  SYSTEMATIC DEPARTURES FROM THE FRONTIER: A FRAMEWORK FOR THE ANALYSIS OF FIRM INEFFICIENCY* , 1991 .

[71]  The half-normal specification for the two-tier stochastic frontier model , 2015 .

[72]  Peter Schmidt,et al.  Goodness of fit tests in stochastic frontier models , 2011 .

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

[74]  Domenico De Giovanni,et al.  The ‘wrong skewness’ problem: a re-specification of stochastic frontiers , 2017 .

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

[76]  P. Schmidt.  On the Statistical Estimation of Parametric Frontier Production Functions , 1976 .

[77]  An Alternative Specification for Technical Efficiency Effects in a Stochastic Frontier Production Function , 2017 .

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

[79]  R. Banker,et al.  Maximum likelihood estimation of monotone and concave production frontiers , 1992 .

[80]  Jeffrey M. Wooldridge,et al.  Solutions Manual and Supplementary Materials for Econometric Analysis of Cross Section and Panel Data , 2003 .

[81]  P. Schmidt.  One-step and two-step estimation in SFA models , 2011 .

[82]  W. Greene.  On the estimation of a flexible frontier production model , 1980 .

[83]  Kaliappa Kalirajan,et al.  On Measuring Economic Efficiency , 1990 .

[84]  Valentin Zelenyuk,et al.  Generalized nonparametric smoothing with mixed discrete and continuous data , 2016, Comput. Stat. Data Anal..

[85]  R. Koenker,et al.  Regression Quantiles , 2007 .

[86]  Jean Tirole,et al.  Mindful Economics: The Production, Consumption, and Value of Beliefs , 2016 .

[87]  A. Heshmati,et al.  Efficiency Measurement in Swedish Dairy Farms: An Application of Rotating Panel Data, 1976–88 , 1995 .

[88]  A. Azzalini.  A class of distributions which includes the normal ones , 1985 .

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

[90]  W. Greene.  A stochastic frontier model with correction for sample selection , 2010 .

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

[92]  Subal C. Kumbhakar,et al.  THE MEASUREMENT AND DECOMPOSITION OF COST-INEFFICIENCY: THE TRANSLOG COST SYSTEM* , 1991 .

[93]  Jeffrey S. Racine,et al.  Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints , 2012 .

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

[95]  A. Heshmati,et al.  DEA, DFA and SFA: A comparison , 1996 .

[96]  Lung-fei Lee,et al.  The stochastic frontier production function and average efficiency: An empirical analysis☆ , 1978 .

[97]  Christopher F. Parmeter,et al.  A zero inefficiency stochastic frontier model , 2013 .

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

[99]  Laure Latruffe,et al.  Subsidies and Technical Efficiency in Agriculture: Evidence from European Dairy Farms , 2017 .

[100]  Rolf Färe,et al.  On functional form representation of multi-output production technologies , 2010 .

[101]  Subal C. Kumbhakar,et al.  Stochastic frontier analysis , 2000 .

[102]  Levent Kutlu.  Battese-coelli estimator with endogenous regressors , 2010 .

[103]  Takeshi Amemiya,et al.  The nonlinear two-stage least-squares estimator , 1974 .

[104]  R. Koenker.  Quantile Regression: Name Index , 2005 .

[105]  E. Blankmeyer,et al.  Technical efficiency in texas nursing facilities: A stochastic production frontier approach , 2007 .

[106]  S. Kumbhakar,et al.  Accounting for risk in productivity analysis: an application to Norwegian dairy farming , 2017 .

[107]  Martin Carree,et al.  Technological inefficiency and the skewness of the error component in stochastic frontier analysis , 2002 .

[108]  R. Solow.  TECHNICAL CHANGE AND THE AGGREGATE PRODUCTION FUNCTION , 1957 .

[109]  Christopher F. Parmeter,et al.  The effects of match uncertainty and bargaining on labor market outcomes: evidence from firm and worker specific estimates , 2009 .

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

[111]  J. V. Reenen,et al.  International Data on Measuring Management Practices , 2016 .

[112]  Christopher F. Parmeter,et al.  A Laplace stochastic frontier model , 2018 .

[113]  Jeffrey S. Racine,et al.  Nonparametric estimation of regression functions with both categorical and continuous data , 2004 .

[114]  W. Greene,et al.  Understanding prediction intervals for firm specific inefficiency scores from parametric stochastic frontier models , 2014 .

[115]  Solomon W. Polachek,et al.  A Two-tiered Earnings Frontier Estimation of Employer and Employee Information in the Labor Market , 1987 .

[116]  Poomthan Rangkakulnuwat,et al.  A Practitioner’s Guide to Stochastic Frontier Analysis Using STATA , 2017 .

[117]  Valid tests of whether technical inefficiency depends on firm characteristics , 2008 .

[118]  Oleg Badunenko,et al.  Economies of scale, technical change and persistent and time-varying cost efficiency in Indian banking: Do ownership, regulation and heterogeneity matter? , 2017, Eur. J. Oper. Res..

[119]  Models for Which the MLE and the Conditional MLE Coincide , 1992 .

[120]  Subal C. Kumbhakar,et al.  Technical efficiency in competing panel data models: a study of Norwegian grain farming , 2014 .

[122]  J. Aitchison,et al.  Multivariate binary discrimination by the kernel method , 1976 .

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

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

[125]  Rajiv D. Banker,et al.  Evaluating Contextual Variables Affecting Productivity Using Data Envelopment Analysis , 2008, Oper. Res..

[126]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

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

[128]  Estimating a stochastic production frontier when the adjusted error is symmetric , 1996 .

[129]  William H. Greene,et al.  Persistent and transient productive inefficiency: a maximum simulated likelihood approach , 2014 .

[130]  P. Schmidt,et al.  Production Frontiers and Panel Data , 1984 .

[131]  John Ruggiero,et al.  Efficiency estimation and error decomposition in the stochastic frontier model: A Monte Carlo analysis , 1999, Eur. J. Oper. Res..

[132]  Christopher R. Knittel.  Alternative Regulatory Methods and Firm Efficiency: Stochastic Frontier Evidence from the U.S. Electricity Industry , 2002, Review of Economics and Statistics.

[133]  D. McFadden.  A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration , 1989 .

[134]  Peter Schmidt,et al.  Consistent estimation of the fixed effects stochastic frontier model , 2014 .

[135]  R. Tibshirani,et al.  Local Likelihood Estimation , 1987 .

[136]  Levent Kutlu,et al.  Handling Endogeneity in Stochastic Frontier Analysis , 2015 .

[137]  Léopold Simar,et al.  Frontier estimation in the presence of measurement error with unknown variance , 2015 .

[138]  Liang Peng,et al.  Conditional variance estimation in heteroscedastic regression models , 2009 .

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

[140]  Hung-Jen Wang,et al.  Heteroscedasticity and Non-Monotonic Efficiency Effects of a Stochastic Frontier Model , 2002 .

[141]  Carlos Martins-Filho,et al.  Semiparametric Stochastic Frontier Estimation via Profile Likelihood , 2015 .

[142]  S. Kumbhakar.  Specification and estimation of multiple output technologies: A primal approach , 2013, Eur. J. Oper. Res..

[143]  Gianmaria Martini,et al.  A Stochastic Frontier Model with short-run and long-run inefficiency random effects , 2011 .

[144]  P. Hall,et al.  NONPARAMETRIC KERNEL REGRESSION SUBJECT TO MONOTONICITY CONSTRAINTS , 2001 .

[145]  L. Simar,et al.  Stochastic FDH/DEA estimators for frontier analysis , 2008 .

[146]  Christopher F. Parmeter,et al.  A Zero Inefficiency Stochastic Frontier Estimator , 2013 .

[147]  Yushi Shinada.  Influence of the Gap of Educational Investment on Economic Growth : Relevance of the Education and Growth in Postwar Japan(ESSAYS IN COMMEMORATION OF THE SEVENTIETH BIRTHDAY OF PROFESSOR SADAYOSHI KANEKO) , 2006 .

[148]  Rafael A. Cuesta.  A Production Model With Firm-Specific Temporal Variation in Technical Inefficiency: With Application to Spanish Dairy Farms , 2000 .

[149]  Marzia Freo,et al.  Quantile estimation of frontier production function , 2004 .

[150]  Subal C. Kumbhakar,et al.  Nonparametric estimation of the determinants of inefficiency , 2017 .

[151]  Hohsuk Noh.  Frontier estimation using kernel smoothing estimators with data transformation , 2014 .

[152]  Christopher F. Parmeter,et al.  Efficiency Analysis: A Primer on Recent Advances , 2014 .

[153]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[154]  QU Feng,et al.  Wrong Skewness and Finite Sample Correction in Parametric Stochastic Frontier Models , 2013 .

[155]  I. Ahmad,et al.  Testing symmetry of an unknown density function by kernel method , 1997 .

[156]  Peter Schmidt,et al.  On the distribution of estimated technical efficiency in stochastic frontier models , 2009 .

[157]  Jianqing Fan,et al.  Efficient Estimation of Conditional Variance Functions in Stochastic Regression , 1998 .

[158]  P. Schmidt,et al.  Stochastic metafrontiers , 2017 .

[159]  G. Battese,et al.  Metafrontier frameworks for the study of firm-level efficiencies and technology ratios , 2008 .

[160]  R. Sickles,et al.  Stochastic Frontier Models with Bounded Inefficiency , 2014 .

[161]  K. Hadri.  Estimation of a Doubly Heteroscedastic Stochastic Frontier Cost Function , 1999 .

[162]  Anil K. Bera,et al.  Estimating Production Uncertainty in Stochastic Frontier Production Function Models , 1999 .

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

[164]  W. Greene,et al.  A stochastic frontier model with correction for sample selection , 2008 .

[165]  B. Casu,et al.  Regulatory Reform and Productivity Change in Indian Banking , 2009, Review of Economics and Statistics.

[166]  John Hicks,et al.  A Revision of Demand Theory. , 1957 .

[167]  James B. McDonald,et al.  Instrumental Variables Estimation With Flexible Distributions , 2007 .

[168]  P. Schmidt,et al.  Models for which the MLE and the conditional MLE coincide , 1992 .

[169]  W. Meeusen,et al.  Technical efficiency and dimension of the firm: Some results on the use of frontier production functions , 1977 .

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

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

[172]  Robert Henry Dugger.  An application of bounded nonparametric estimating functions to the analysis of bank cost and production functions , 1977 .

[173]  Ngoc Nguyen.  Estimation of Technical Efficiency in Stochastic Frontier Analysis , 2010 .

[174]  B. Hollingsworth.  The measurement of efficiency and productivity of health care delivery. , 2008, Health economics.

[175]  Christopher F. Parmeter,et al.  Semiparametric deconvolution with unknown error variance , 2008 .

[176]  W. Greene.  Distinguishing between Heterogeneity and Inefficiency: Stochastic Frontier Analysis of the World Health Organization S Panel Data on National Health Care Systems , 2003, Health economics.

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

[178]  W. Greene.  Fixed and Random Effects in Stochastic Frontier Models , 2002 .

[179]  Christopher F. Parmeter,et al.  Applied Nonparametric Econometrics , 2015 .

[180]  Mubarik Ali,et al.  Profit Efficiency Among Basmati Rice Producers in Pakistan Punjab , 1989 .

[181]  S. Kumbhakar.  Production frontiers, panel data, and time-varying technical inefficiency , 1990 .

[182]  A. Laporte,et al.  The quantile regression approach to efficiency measurement: insights from Monte Carlo simulations. , 2008, Health economics.

[183]  Léopold Simar,et al.  Categorical data in local maximum likelihood: theory and applications to productivity analysis , 2015 .

[184]  Peter Schmidt,et al.  Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics , 2006 .

[185]  Christopher F. Parmeter,et al.  A consistent bootstrap procedure for nonparametric symmetry tests , 2015 .

[186]  G. Battese,et al.  Frontier production functions, technical efficiency and panel data: With application to paddy farmers in India , 1992 .

[187]  S. Kumbhakar,et al.  A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms , 1991 .

[188]  Valentin Zelenyuk,et al.  A Bridge Too Far? The State of the Art in Combining the Virtues of Stochastic Frontier Analysis and Data Envelopement Analysis , 2016 .

[189]  Giorgio Vittadini,et al.  Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency , 2014 .

[190]  C. Hulten,et al.  New Developments in Productivity Analysis , 2001 .

[191]  Marc Ivaldi,et al.  Stochastic Frontiers and Asymmetric Information Models , 2002 .

[192]  Solomon W. Polachek,et al.  Panel estimates of a two‐tiered earnings frontier , 1996 .

[193]  Boris E. Bravo-Ureta,et al.  Dairy Farm Efficiency Measurement Using Stochastic Frontiers and Neoclassical Duality , 1991 .