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Model averaging estimators for the stochastic frontier model

Author

Listed:
  • Christopher F. Parmeter

    (University of Miami)

  • Alan T. K. Wan

    (City University of Hong Kong)

  • Xinyu Zhang

    (Chinese Academy of Sciences)

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.

Suggested Citation

  • Christopher F. Parmeter & Alan T. K. Wan & Xinyu Zhang, 2019. "Model averaging estimators for the stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 51(2), pages 91-103, June.
  • Handle: RePEc:kap:jproda:v:51:y:2019:i:2:d:10.1007_s11123-019-00547-8
    DOI: 10.1007/s11123-019-00547-8
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    1. Robin C. Sickles & Jiaqi Hao & Chenjun Shang, 2014. "Panel data and productivity measurement: an analysis of Asian productivity trends," Journal of Chinese Economic and Business Studies, Taylor & Francis Journals, vol. 12(3), pages 211-231, August.
    2. Yuan, Zheng & Yang, Yuhong, 2005. "Combining Linear Regression Models: When and How?," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1202-1214, December.
    3. Hung-pin Lai & Cliff Huang, 2010. "Likelihood ratio tests for model selection of stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 34(1), pages 3-13, August.
    4. Sickles, Robin C. & Hao, Jiaqi & Shang, Chenjun, 2015. "Panel Data and Productivity Measurement," Working Papers 15-018, Rice University, Department of Economics.
    5. Kneip, Alois & Simar, Léopold & Van Keilegom, Ingrid, 2015. "Frontier estimation in the presence of measurement error with unknown variance," Journal of Econometrics, Elsevier, vol. 184(2), pages 379-393.
    6. Seunghwa Rho & Peter Schmidt, 2015. "Are all firms inefficient?," Journal of Productivity Analysis, Springer, vol. 43(3), pages 327-349, June.
    7. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
    8. Wan, Alan T.K. & Zhang, Xinyu & Wang, Shouyang, 2014. "Frequentist model averaging for multinomial and ordered logit models," International Journal of Forecasting, Elsevier, vol. 30(1), pages 118-128.
    9. Li, Qi, 1996. "Estimating a stochastic production frontier when the adjusted error is symmetric," Economics Letters, Elsevier, vol. 52(3), pages 221-228, September.
    10. Hung-jen Wang & Peter Schmidt, 2002. "One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels," Journal of Productivity Analysis, Springer, vol. 18(2), pages 129-144, September.
    11. Rafik Baccouche & Mokhtar Kouki, 2003. "Stochastic Production Frontier and Technical Inefficiency: A Sensitivity Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 22(1), pages 79-91, February.
    12. Baltagi, Badi H., 2015. "The Oxford Handbook of Panel Data," OUP Catalogue, Oxford University Press, number 9780199940042.
    13. Kumbhakar, Subal C. & Parmeter, Christopher F. & Tsionas, Efthymios G., 2013. "A zero inefficiency stochastic frontier model," Journal of Econometrics, Elsevier, vol. 172(1), pages 66-76.
    14. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    15. M. Stone, 2002. "How not to measure the efficiency of public services (and how one might)," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(3), pages 405-434, October.
    16. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    17. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
    18. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
    19. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
    20. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
    21. Magnus, Jan R. & Wan, Alan T.K. & Zhang, Xinyu, 2011. "Weighted average least squares estimation with nonspherical disturbances and an application to the Hong Kong housing market," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1331-1341, March.
    22. Cliff Huang & Hung-pin Lai, 2012. "Estimation of stochastic frontier models based on multimodel inference," Journal of Productivity Analysis, Springer, vol. 38(3), pages 273-284, December.
    23. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    24. Antonio Alvarez & Christine Amsler & Luis Orea & Peter Schmidt, 2006. "Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics," Journal of Productivity Analysis, Springer, vol. 25(3), pages 201-212, June.
    25. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    26. Christopher F. Parmeter & Hung-Jen Wang & Subal C. Kumbhakar, 2017. "Nonparametric estimation of the determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 47(3), pages 205-221, June.
    27. Liang, Hua & Zou, Guohua & Wan, Alan T. K. & Zhang, Xinyu, 2011. "Optimal Weight Choice for Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1053-1066.
    28. Olesen, O.B. & Ruggiero, J., 2018. "An improved Afriat–Diewert–Parkan nonparametric production function estimator," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1172-1188.
    29. Mike G. Tsionas, 2017. "“When, Where, and How” of Efficiency Estimation: Improved Procedures for Stochastic Frontier Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 948-965, July.
    30. Xinyu Zhang & Alan Wan & Sherry Zhou, 2012. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142.
    31. Carree, Martin A., 2002. "Technological inefficiency and the skewness of the error component in stochastic frontier analysis," Economics Letters, Elsevier, vol. 77(1), pages 101-107, September.
    32. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    33. Sickles, Robin C., 2005. "Panel estimators and the identification of firm-specific efficiency levels in parametric, semiparametric and nonparametric settings," Journal of Econometrics, Elsevier, vol. 126(2), pages 305-334, June.
    34. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    35. Parmeter, Christopher F. & Kumbhakar, Subal C., 2014. "Efficiency Analysis: A Primer on Recent Advances," Foundations and Trends(R) in Econometrics, now publishers, vol. 7(3-4), pages 191-385, December.
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    Cited by:

    1. Tsionas, Mike G. & Assaf, A. George & Andrikopoulos, Athanasios, 2020. "Quantile stochastic frontier models with endogeneity," Economics Letters, Elsevier, vol. 188(C).
    2. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.
    3. Kamil Makieła & Błażej Mazur, 2022. "Model uncertainty and efficiency measurement in stochastic frontier analysis with generalized errors," Journal of Productivity Analysis, Springer, vol. 58(1), pages 35-54, August.
    4. Quang Nguyen & Sean Pascoe & Louisa Coglan & Son Nghiem, 2021. "The sensitivity of efficiency scores to input and other choices in stochastic frontier analysis: an empirical investigation," Journal of Productivity Analysis, Springer, vol. 55(1), pages 31-40, February.
    5. E. Fusco & R. Benedetti & F. Vidoli, 2023. "Stochastic frontier estimation through parametric modelling of quantile regression coefficients," Empirical Economics, Springer, vol. 64(2), pages 869-896, February.
    6. Zangin Zeebari & Kristofer Månsson & Pär Sjölander & Magnus Söderberg, 2023. "Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market," Journal of Productivity Analysis, Springer, vol. 59(1), pages 79-97, February.
    7. Xu Guo & Gao-Rong Li & Michael McAleer & Wing-Keung Wong, 2018. "Specification Testing of Production in a Stochastic Frontier Model," Sustainability, MDPI, vol. 10(9), pages 1-10, August.
    8. Ali M. Oumer & Amin Mugera & Michael Burton & Atakelty Hailu, 2022. "Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia," Journal of Productivity Analysis, Springer, vol. 57(2), pages 213-241, April.
    9. Kassoum Ayouba, 2023. "Spatial dependence in production frontier models," Journal of Productivity Analysis, Springer, vol. 60(1), pages 21-36, August.
    10. Cinzia Daraio, 2017. "A framework for the Assessment of Research and its impacts," DIAG Technical Reports 2017-04, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    11. Paul, Satya & Shankar, Sriram, 2018. "On estimating efficiency effects in a stochastic frontier model," European Journal of Operational Research, Elsevier, vol. 271(2), pages 769-774.

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    More about this item

    Keywords

    Optimality; J-fold cross-validation; Efficiency; Model selection;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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