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Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach

  • Guohua FengEmail author
  • Chuan WangEmail author
  • Xibin ZhangEmail author
Article
  • 34 Downloads

Abstract

We propose a kernel-based Bayesian framework for the analysis of stochastic frontiers and efficiency measurement. The primary feature of this framework is that the unknown distribution of inefficiency is approximated by a transformed Rosenblatt-Parzen kernel density estimator. To justify the kernel-based model, we conduct a Monte Carlo study and also apply the model to a panel of U.S. large banks. Simulation results show that the kernel-based model is capable of providing more precise estimation and prediction results than the commonly-used exponential stochastic frontier model. The Bayes factor also favors the kernel-based model over the exponential model in the empirical application.

Keywords

Kernel density estimation Efficiency measurement Stochastic distance frontier Markov Chain Monte Carlo 

JEL Classification

C11 D24 G21 

Notes

Acknowledgements

We would like to thank Professor Cheng Hsiao at the University of Southern California for helpful discussion. We would also like to thank the reviewers for their constructive comments that have led to substantial improvement of the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Aigner D, Lovell CAK, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. J Econ 6:21–37CrossRefGoogle Scholar
  2. Basu S, Chib S (2003) Marginal likelihood and Bayes factors for Dirichlet process mixture models. J Am Stat Assoc 98:224–235CrossRefGoogle Scholar
  3. Berger J (1985) Statistical decision theory and Bayesian analysis. Springer-Verlag, New YorkCrossRefGoogle Scholar
  4. Battese GE, Coelli TJ (1992) Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data. J Econ 38:387–399CrossRefGoogle Scholar
  5. Berger AN, Mester LJ (2003) Explaining the dramatic changes in the performance of U.S. banks: technological change, deregulation, and dynamic changes in competition. J Financ Inter 12:57–95Google Scholar
  6. Brewer MJ (2000) A Bayesian model for local smoothing in kernel density estimation. Stat Comput 10(4):299–309CrossRefGoogle Scholar
  7. Buch-Larsen T, Nielsen JP, Guillen M, Bolance C (2005) Kernel density estimation for heavy-tailed distributions using the Champernowne transformation. Statistics 39:503–518CrossRefGoogle Scholar
  8. Caves DW, Christensen LR, Diewert WE (1982) The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica 50:1393–1414CrossRefGoogle Scholar
  9. Chen SX (2000) Probability density function estimation using gamma kernels. Ann Inst Stat Math 52:471–480CrossRefGoogle Scholar
  10. Chib S (1995) Marginal likelihood from the Gibbs output. J Am Stat Assoc 90:1313–1321CrossRefGoogle Scholar
  11. Chib S, Jeliazkov I (2001) Marginal likelihood from the Metropolis–Hastings output. J Am Stat Assoc 96:270–281CrossRefGoogle Scholar
  12. Cornwell C, Schmidt P, Sickles RC (1990) Production frontiers with cross-sectional and time-series variation in efficiency levels. J Econ 46(1-2):185–200CrossRefGoogle Scholar
  13. de Lima MS, Atuncar GS (2011) A Bayesian method to estimate the optimal bandwidth for multivariate kernel estimator. J Nonparametr Stat 23(1):137–148CrossRefGoogle Scholar
  14. Färe R, Grosskopf S (1994) Cost and revenue constrained production. Springer, New YorkCrossRefGoogle Scholar
  15. Feng G, Serletis A (2010) Efficiency, technical change, and returns to scale in large US banks: panel data evidence from an output distance function satisfying theoretical regularity. J Bank Financ 34:127–138CrossRefGoogle Scholar
  16. Feng G, Zhang X (2012) Productivity and efficiency at large and community banks in the U.S.: aBayesian true random effects stochastic distance frontier analysis. J Bank Financ 36:1883–1895CrossRefGoogle Scholar
  17. Ferguson T (1973) A Bayesian analysis of some nonparametric problems. Ann Stat 1:209–230CrossRefGoogle Scholar
  18. Fernandez C, Osiewalski J, Steel MFJ (1997) On the use of panel data in stochastic frontier models with improper priors. J Econ 79:169–193CrossRefGoogle Scholar
  19. Gangopadhyay AK, Cheung K (2002) A Bayesian approach to the kernel density estimation. J Nonparametr Stat 14:655–664CrossRefGoogle Scholar
  20. Gelfand AE, Sahu S, Carlin B (1995) Efficient parametrization for normal linear mixed effects models. Biometrika 82:479–488CrossRefGoogle Scholar
  21. Geweke JF (2005) Contemporary Bayesian econometrics and statistics. John Wiley and Sons, CanadaCrossRefGoogle Scholar
  22. Geweke JF (2009) Complete and incomplete econometric models. Princeton University Press, New JerseyGoogle Scholar
  23. Greene W (1990) A gamma-distributed stochastic frontier model. J Econ 46:141–163CrossRefGoogle Scholar
  24. Greene W (2004) Distinguishing between heterogeneity and inefficiency: stochastic frontier analysis of the world health organization’s panel data on national health care systems. Health Econ 13:959–980CrossRefGoogle Scholar
  25. Greene W (2008) The econometric approach to efficiency analysis. In: Fried HO, Knox Lovell CA, Schmidt P (eds) The Measurement of Productive Efficiency. Oxford University Press, New YorkGoogle Scholar
  26. Griffin J, Steel MFJ (2004) Semiparametric Bayesian inference for stochastic frontier models. J Econ 123:121–152CrossRefGoogle Scholar
  27. Griffin J, Steel MFJ (2008) Flexible mixture modeling of stochastic frontiers. J Product Anal 21:157–178Google Scholar
  28. Härdle W, Hall P, Ichimura H (1993) Optimal smoothing in single-index models. Ann Stat 21(1):157–178CrossRefGoogle Scholar
  29. Jaki T, West RW (2008) Maximum kernel likelihood estimation. J Comput Graph Stat 17:976–993CrossRefGoogle Scholar
  30. Johnson N, Kotz S (1972) Distributions in statistics: Continuous multivariate distributions. Wiley, New YorkGoogle Scholar
  31. Kass RE, Raftery AE (1995) Bayes factors. J Am Stat Assoc 90:773–795CrossRefGoogle Scholar
  32. Kim S, Shephard N, Chib S (1998) Stochastic volatility: likelihood inference and comparison with ARCH models. Rev Econ Stud 65:361–393CrossRefGoogle Scholar
  33. Koop G (2003) Bayesian econometrics. Wiley, ChichesterGoogle Scholar
  34. Koop G, Osiewalski J, Steel M (1997) Bayesian efficiency analysis through individual effects: hospital cost frontiers. J Econ 76:77–105CrossRefGoogle Scholar
  35. Lovell CA, Pastor JT, Turner JA (1994) Measuring macroeconomic performance in the OECD: a comparison of European and Non-European countries. Eur J Oper Res 87:507–518CrossRefGoogle Scholar
  36. Malikov, E., Kumbhakar, S., Tsionas, E. (2015) A cost system approach to the stochastic directional technology distance function with undesirable outputs: The case of US banks in 2001-2010. J Appl Econ.  https://doi.org/10.1002/jae.2491
  37. Meeusen W, Van Den Broeck J (1977) Efficiency estimation from Cobb-Douglas production functions with composed error. Int Econ Rev 18:435–444CrossRefGoogle Scholar
  38. O’Donnell CJ, Coelli TJ (2005) A Bayesian approach to imposing curvature on distance functions. J Econ 126:493–523CrossRefGoogle Scholar
  39. Ritter C, Simar L (1997) Pitfalls of normal-gamma stochastic frontier models. J Product Anal 8(2):167–182CrossRefGoogle Scholar
  40. Rothe C (2009) Semiparametric estimation of binary response models with endogenous regressors. J Econ 153(1):51–64CrossRefGoogle Scholar
  41. Sealey CW, Lindley JT (1977) Inputs, outputs, and a theory of production and cost at depository financial institutions. J Financ 34:1251–1266CrossRefGoogle Scholar
  42. Serletis A, Feng G (2015) Imposing theoretical regularity on flexible functional forms. Econom Rev 34:127–138CrossRefGoogle Scholar
  43. Schmidt P, Sickles RC (1984) Production frontiers and panel data. J Bus Econ Stat 2(4):367–374Google Scholar
  44. Stevenson R (1980) Likelihood functions for generalized stochastic frontier estimation. J Econ 13:57–66CrossRefGoogle Scholar
  45. Tierney L (1994) Markov Chains for exploring posterior distributions. Ann Stat 22:1701–1728CrossRefGoogle Scholar
  46. Terrell GR, Scott DW (1992) Variable kernel density estimation. Ann Stat 20:1236–1265CrossRefGoogle Scholar
  47. Wand MP, Marron JS, Ruppert D (1991) Transformations in density estimation. J Am Stat Assoc 86:343–353CrossRefGoogle Scholar
  48. Yuan A, de Gooijer JG (2007) Semiparametric regression with kernel error model. Scand J Stat 34(4):841–869Google Scholar
  49. Zhang X, Brooks R, King ML (2009) A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation. J Econ 153(1):21–32CrossRefGoogle Scholar
  50. Zhang X, King ML, Hyndman R (2006) A Bayesian approach to bandwidth selection for multivariate kernel density estimation. Comput Stat Data Anal 50(11):3009–3031CrossRefGoogle Scholar
  51. Zhang X, King ML, Shang HL (2014) A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density. Comput Stat Data Anal 78:218–234CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of North TexasDentonUSA
  2. 2.Wenlan School of BusinessZhongnan University of Economics and LawWuhanChina
  3. 3.Department of Econometrics and Business StatisticsMonash UniversityCaulfield EastAustralia

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