Advertisement

Model averaging estimators for the stochastic frontier model

  • Christopher F. ParmeterEmail author
  • Alan T. K. Wan
  • Xinyu Zhang
Article
  • 20 Downloads

Abstract

Model uncertainty is a prominent feature in many applied settings. This is certainty true in the efficiency analysis realm where concerns over the proper distributional specification of the error components of a stochastic frontier model is, generally, still open along with which variables influence inefficiency. Given the concern over the impact that model uncertainty is likely to have on the stochastic frontier model in practice, the present research proposes two distinct model averaging estimators, one which averages over nested classes of inefficiency distributions and another that has the ability to average over distinct distributions of inefficiency. Both of these estimators are shown to produce optimal weights when the aim is to uncover conditional inefficiency at the firm level. We study the finite-sample performance of the model average estimator via Monte Carlo experiments and compare with traditional model averaging estimators based on weights constructed from model selection criteria and present a short empirical application.

Keywords

Optimality J-fold cross-validation Efficiency Model selection 

Notes

Acknowledgements

We thank participants at the New York Camp Econometrics X, the 14th European Workshop on Efficiency and Productivity Analysis, LECCEWEPA 2015, the CEPA Workshop on Economic Measurement and the 2016 North American Productivity Workshop for valuable insight. Xinyu Zhang acknowledges the support from National Natural Science Foundation of China (Grant numbers 71522004, 11471324 and 71631008). The usual disclaimer applies.

Author contributions

All three authors contributed equally to this work and the order of authorship has nothing other than alphabetical significance.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Aigner DJ, Lovell CAK, Schmidt P (1977) Formulation and estimation of stochastic frontier production functions. J Econom 6(1):21–37CrossRefGoogle Scholar
  2. Alvarez A, Amsler C, Orea L, Schmidt P (2006) Interpreting and testing the scaling property in models where inefficiency depends on firm characteristics. J Prod Anal 25(2):201–212CrossRefGoogle Scholar
  3. Battese GE, Coelli TJ (1988) Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data. J Econom 38:387–399CrossRefGoogle Scholar
  4. Buckland ST, Burnham KP, Augustin NH (1997) Model selection: an integral part of inference. Biometrics 53(4):603–618CrossRefGoogle Scholar
  5. Coelli TJ, Rao DP, O’Donnell CJ, Battese GE (2005) An Introduction to Efficiency and Productivity Analysis. Springer, New YorkGoogle Scholar
  6. Hansen BE (2007) Least squares model averaging. Econometrica 75(4):1175–1189CrossRefGoogle Scholar
  7. Hansen BE, Racine JS (2012) Jackknife model averaging. J Econom 167(1):38–46CrossRefGoogle Scholar
  8. Huang CJ, Lai H-P (2012) Estimation of stochastic frontier models based on multimodel inference. J Prod Anal 38:273–284CrossRefGoogle Scholar
  9. Jondrow J, Lovell CAK, Materov IS, Schmidt P (1982) On the estimation of technical efficiency in the stochastic frontier production function model. J Econom 19(2/3):233–238CrossRefGoogle Scholar
  10. Kneip A, Simar L, Van Keilegom I (2015) Frontier estimation in the presence of measurement error with unknown variance. J Econom 184:379–393CrossRefGoogle Scholar
  11. Kumbhakar SC, Parmeter CF, Tsionas E (2013) A zero inefficiency stochastic frontier estimator. J Econom 172(1):66–76CrossRefGoogle Scholar
  12. Lai H-P, Huang CJ (2010) Likelihood ratio tests for model selection of stochastic frontier models. J Prod Anal 34(1):3–13CrossRefGoogle Scholar
  13. Mallows CL (1973) Some comments on cp. Tehcnometrics 15:661–675Google Scholar
  14. Meeusen W, van den Broeck J (1977) Efficiency estimation from Cobb-Douglas production functions with composed error. Int Econ Rev 18(2):435–444CrossRefGoogle Scholar
  15. Olesen OB, Ruggiero J (2018) An improved Afriat-Diewert-Parkan nonparametric production function estimator. Eur J Operat Res 264:1172–1188CrossRefGoogle Scholar
  16. Parmeter CF, Kumbhakar SC (2014) Efficiency analysis: a primer on recent advances. Found Trends Econom 7(3-4):191–385CrossRefGoogle Scholar
  17. Parmeter CF, Wang H-J, Kumbhakar SC (2017) Nonparametric estimation of the determinants of inefficiency. J Prod Anal 47(3):205–221CrossRefGoogle Scholar
  18. Rho S, Schmidt P (2015) Are all firms inefficient? J Prod Anal 43(3):327–349CrossRefGoogle Scholar
  19. Shang C (2015) Essays on the use of duality, robust empirical methods, panel treatments, and model averaging with applications to housing price index construction and world productivity growth, PhD thesis, Rice UniversityGoogle Scholar
  20. Sickles RC (2005) Panel estimators and the identification of firm-specific efficiency levels in parametric, semiparametric and nonparametric settings. J Econom 126(2):305–334CrossRefGoogle Scholar
  21. Sickles RC, Hao J, Shang C (2014) Panel data and productivity measurement: an analysis of Asian productivity trends. J Chin Econ Bus Stud 12(3):211–231CrossRefGoogle Scholar
  22. Sickles RC, Hao J, Shang C (2015) Panel data and productivity measurement. In: Baltagi B (ed) Ch 17, Oxford Handbook fo Panel Data. Oxford University Press, New York, pp 517–547Google Scholar
  23. Simar L, Lovell CAK, van den Eeckaut P (1994) Stochastic frontiers incorporating exogenous inuences on efficiency. Discussion Papers No. 9403, Institut de Statistique, Universite de LouvainGoogle Scholar
  24. Stone M (2002) How not to measure the efficiency of public services (and how one might). J R Stat Soc Ser A 165:405–434Google Scholar
  25. Tsionas EG (2017) “When, where and how” of efficiency estimation: Improved procedures for stochastic frontier modeling. J Am Stat Assoc 112:948–965CrossRefGoogle Scholar
  26. Wan ATK, Zhang X, Zou G (2010) Least squares model averaging by Mallows criterion. J Econom 156(4):277–283CrossRefGoogle Scholar
  27. Wang H-J, Schmidt P (2002) One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels. J Prod Anal 18:129–144CrossRefGoogle Scholar
  28. White H (1982) Maximum likelihood estimation of misspecified models. Econometrica 50(1):1–25CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of MiamiMiamiUSA
  2. 2.Department of Management SciencesCity University of Hong KongKowloonHong Kong
  3. 3.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

Personalised recommendations