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Stochastic Frontier Analysis

  • Christopher J. O’DonnellEmail author
Chapter

Abstract

Distance, revenue, cost and profit functions can always be written in the form of regression models with unobserved error terms representing statistical noise and different types of inefficiency. In practice, the noise components are almost always assumed to be random variables (i.e., stochastic). The associated frontiers are known as stochastic frontiers. This chapter explains how to estimate and draw inferences concerning the unknown parameters in so-called stochastic frontier models (SFMs). It then explains how the estimated parameters can be used to predict levels of efficiency and analyse productivity change. The focus is on maximum likelihood estimators and predictors.

References

  1. Ackerberg D, Caves K, Frazer G (2015) Identification properties of recent production function estimators. Econometrica 83(6):2411–2451Google Scholar
  2. Aigner D, Lovell C, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. J Econ 6:21–37Google Scholar
  3. Ali M, Flinn J (1989) Profit efficiency among basmati rice producers in Pakistan Punjab. Am J Agric Econ 71(2):303–310Google Scholar
  4. Almanidis P, Qian J, Sickles R (2014) Stochastic frontier models with bounded inefficiency. In: Sickles R (ed) Festschrift in Honor of Peter Schmidt: econometric methods and applications. Springer, BerlinGoogle Scholar
  5. Amsler C, O’Donnell C, Schmidt P (2017) Stochastic metafrontiers. Econ Rev 36(6–9):1007–1020Google Scholar
  6. Assaf A, Gillen G, Tsionas E (2014) Understanding relative efficiency among airports: a general dynamic model for distinguishing technical and allocative efficiency. Transp Res Part B 70:18–34Google Scholar
  7. Asteriou D, Hall S (2015) Applied econometrics. Palgrave Macmillan, New YorkGoogle Scholar
  8. Bandyopadhyay D, Das A (2006) On measures of technical inefficiency and production uncertainty in stochastic frontier production model with correlated error components. J Prod Anal 26(2):165–180Google Scholar
  9. Battese G, Coelli T (1992) Frontier production functions, technical efficiency and panel data: with application to paddy farmers in India. J Prod Anal 3(1–2):153–169Google Scholar
  10. Battese G, Coelli T (1993) A stochastic frontier production function incorporating a model for technical inefficiency effects. Working Papers in Econometrics and Applied Statistics 69, University of New EnglandGoogle Scholar
  11. Battese G, Coelli T (1995) A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Econ 20:325–332Google Scholar
  12. Battese G, Corra G (1977) Estimation of a production frontier model: with application to the pastoral zone of Eastern Australia. Aust J Agric Econ 21(3):169–179Google Scholar
  13. Burns P, Weyman-Jones T (1996) Cost functions and cost efficiency in electricity distribution: a stochastic frontier approach. Bull Econ Res 48(1):44–64Google Scholar
  14. Byma J, Tauer L (2007) Exploring the role of managerial ability in determining firm efficiency. Selected paper prepared for presentation at the American Agricultural Economics Association Annual Meeting, Portland, Oregon, 30–31 JuneGoogle Scholar
  15. Carta A, Steel M (2012) Modelling multi-output stochastic frontiers using copulas. Comput Stat Data Anal 56(11):3757–3773Google Scholar
  16. Casella G, George E (1992) Explaining the Gibbs sampler. Am Stat 46(3):167–174Google Scholar
  17. Caudill S, Ford J (1993) Biases in frontier estimation due to heteroskedasticity. Econ Lett 41:17–20Google Scholar
  18. Coelli T (1995) Estimators and hypothesis tests for a stochastic frontier function: a Monte Carlo analysis. J Prod Anal 6:247–268Google Scholar
  19. Emvalomatis G (2012) Adjustment and unobserved heterogeneity in dynamic stochastic frontier models. J Prod Anal 37(1):7–16Google Scholar
  20. Fan Y, Li Q, Weersink A (1996) Semiparametric estimation of stochastic production frontier models. J Bus Econ Stat 14(4):460–468Google Scholar
  21. Fernandez C, Osiewalski J, Steel M (1997) On the use of panel data in stochastic frontier models with improper priors. J Econ 79(1):169–93Google Scholar
  22. Gómez-Déniz E, Pérez-Rodríguez J (2015) Closed-form solution for a bivariate distribution in stochastic frontier models with dependent errors. J Prod Anal 43(2):215–223Google Scholar
  23. Gouriéroux C, Holly A, Monfort A (1982) Likelihood ratio test, Wald test, and Kuhn-Tucker test in linear models with inequality constraints on the regression parameters. Econometrica 50(1):63–80Google Scholar
  24. Greene W (1990) A Gamma-distributed stochastic frontier model. J Econ 46(1–2):141–163Google Scholar
  25. Greene W (2004) Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. J Econ 126(2005):269–303Google Scholar
  26. Greene W (2005) Fixed and random effects in stochastic frontier models. J Prod Anal 23(1):7–32Google Scholar
  27. Hajargasht G (2015) Stochastic frontiers with a Rayleigh distribution. J Prod Anal 44(2):199–208Google Scholar
  28. Henderson D, Simar L (2005) A fully nonparametric stochastic frontier model for panel data. Department of Economics Working Paper 0519, State University of New York at BinghamtonGoogle Scholar
  29. Henderson DJ, Parmeter CF (2015) A consistent bootstrap procedure for nonparametric symmetry tests. Econ Lett 131(C):78–82,  https://doi.org/10.1016/j.econlet.2015.03, https://ideas.repec.org/a/eee/ecolet/v131y2015icp78-82.html
  30. Herr A (2008) Cost and technical efficiency of German hospitals: Does ownership matter? Health Econ 17(9):1057–1071Google Scholar
  31. Hill R, Griffiths W, Lim G (2011) Principles of econometrics, 4th edn. Wiley, HobokenGoogle Scholar
  32. Horrace W, Parmeter C (2018) A laplace stochastic frontier model. Econ Rev 37(3):260–280Google Scholar
  33. Horrace W, Schmidt P (1996) Confidence statements for efficiency estimates from stochastic frontier models. J Prod Anal 7(2–3):257–282Google Scholar
  34. Huang YF, Luo S, Wang HJ (2018) Flexible panel stochastic frontier model with serially correlated error. Econ Lett 163:55–58Google Scholar
  35. Jondrow J, Lovell C, Materov I, Schmidt P (1982) On the estimation of technical inefficiency in the stochastic frontier production function model. J Econ 19(2–3):233–238Google Scholar
  36. Kneip A, Simar L (1996) A general framework for frontier estimation with panel data. J Prod Anal 7(2–3):187–212Google Scholar
  37. Kumbhakar S (1987) The specification of technical and allocative inefficiency in stochastic production and profit frontiers. J Econ 34(3):335–348Google Scholar
  38. Kumbhakar S (1991) Estimation of technical inefficiency in panel data models with firm- and time-specific effects. Econ Lett 36(1):43–48Google Scholar
  39. Kumbhakar S, Lovell C (2000) Stochastic frontier analysis. Cambridge University Press, CambridgeGoogle Scholar
  40. Kumbhakar S, Park B, Simar L, Tsionas E (2007) Nonparametric stochastic frontiers: a local maximum likelihood approach. J Econ 137(1):1–27Google Scholar
  41. Kumbhakar S, Wang HJ, Horncastle A (2015) A practitioner’s guide to stochastic frontier analysis using stata. Cambridge University Press, New YorkGoogle Scholar
  42. Kuosmanen T, Fosgerau M (2009) Neoclassical versus frontier production models? Testing for the skewness of regression residuals. Scand J Econ 111(2):351–367Google Scholar
  43. Kuosmanen T, Kortelainen M (2012) Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints. J Prod Anal 38(1):11–28Google Scholar
  44. Lai HP, Kumbhakar S (2018) Estimation of dynamic stochastic frontier model using likelihood-based approaches. MPRA Paper 87830, Munich Personal RePEc ArchiveGoogle Scholar
  45. Lee L, Tyler W (1978) The stochastic frontier production function and average efficiency. J Econ 7(1978):385–389Google Scholar
  46. Levinsohn J, Petrin A (2003) Estimating production functions using inputs to control for unobservables. Rev Econ Stud 70(2):317–341Google Scholar
  47. Li Q (1996) Estimating a stochastic production frontier when the adjusted error is symmetric. Econ Lett 52(3):221–228Google Scholar
  48. Martins-Filho C, Yao F, Torero M (2015) Higher-order conditional quantile estimation based on nonparametric models of regression. Econ Rev 34(6–10):907–958Google Scholar
  49. Meesters A (2013) A non-linear stochastic frontier model. Technical report, available at SSRN https://ssrn.com/abstract=2199540 or  https://doi.org/10.2139/ssrn.2199540
  50. Meeusen W, van den Broeck J (1977) Efficiency estimation from Cobb-Douglas production functions with composed error. Int Econ Rev 18(2):435–444Google Scholar
  51. O’Donnell C (2016) Using information about technologies, markets and firm behaviour to decompose a proper productivity index. J Econ 190(2):328–340Google Scholar
  52. O’Donnell C, Nguyen K (2013) An econometric approach to estimating support prices and measures of productivity change in public hospitals. J Prod Anal 40(3):323–335Google Scholar
  53. Olley G, Pakes A (1996) The dynamics of productivity in the telecommunications equipment industry. Econometrica 64(6):1263–1297Google Scholar
  54. Olson J, Schmidt P, Waldman D (1980) A Monte Carlo study of estimators of stochastic frontier production functions. J Econ 13(1):67–82Google Scholar
  55. Ondrich J, Ruggiero J (2001) Efficiency measurement in the stochastic frontier model. Eur Jo Oper Res 129(2):434–442Google Scholar
  56. Pal M, Sengupta A (1999) A model of FPF with correlated error componenets: an application to Indian agriculture. Sankhya: Indian J Stat Series B 61(2):337–350Google Scholar
  57. Park B, Simar L (1994) Efficient semiparametric estimation in a stochastic frontier model. J Am Stat Assoc 89(427):929–936Google Scholar
  58. Park B, Sickles R, Simar L (1998) Stochastic panel frontiers: a semiparametric approach. J Econ 84(2):273–301Google Scholar
  59. Parmeter CF, Wang HJ, Kumbhakar SC (2017) Nonparametric estimation of the determinants of inefficiency. J Prod Anal 47(3):205–221Google Scholar
  60. Pitt M, Lee LF (1981) The measurement and sources of technical inefficiency in the Indonesian weaving industry. J Dev Econ 9(1):43–64Google Scholar
  61. Reifschneider D, Stevenson R (1991) Systematic departures from the frontier: a framework for the analysis of firm inefficiency. Int Econ Rev 32(3):715–723Google Scholar
  62. Robert C, Casella G (2004) Monte Carlo statistical methods, 2nd edn. Springer texts in statistics, Springer, New YorkGoogle Scholar
  63. Salas-Velasco M (2018) Production efficiency measurement and its determinants across OECD countries: the role of business sophistication and innovation. Econ Anal Policy 57:60–73Google Scholar
  64. Schmidt P, Lin TF (1984) Simple tests of alternative specifications in stochastic frontier models. J Econ 24:349–361Google Scholar
  65. Schmidt P, Lovell C (1979) Estimating technical and allocative inefficiency relative to stochastic production and cost frontiers. J Econ 9(3):343–366Google Scholar
  66. Simar L, Zelenyuk V (2011) Stochastic FDH/DEA estimators for frontier analysis. J Prod Anal 36(1):1–20Google Scholar
  67. Simar L, van Keilegom I, Zelenyuk V (2017) Nonparametric least squares methods for stochastic frontier models. J Prod Anal 47(3):189–204Google Scholar
  68. Smith M (2008) Stochastic frontier models with dependent error components. Econ J 11(1):172–192Google Scholar
  69. Stevenson R (1980) Likelihood functions for generalized stochastic frontier estimation. J Econ 13(1):57–66Google Scholar
  70. Tierney L (1994) Markov chains for exploring posterior distributions. Ann Stat 22(4):1701–1728Google Scholar
  71. Tsionas E (2006) Inference in dynamic stochastic frontier models. J Appl Econ 21(5):669–676Google Scholar
  72. Tsionas E (2007) Efficiency measurement with the Weibull stochastic frontier. Oxford Bull Econ Stat 69(5):693–706Google Scholar
  73. van den Broeck J, Koop G, Osiewalski J, Steel M (1994) Stochastic frontier models: a Bayesian perspective. J Econ 61:273–303Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.University of QueenslandBrisbaneAustralia

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