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Using Copulas to Model Time Dependence in Stochastic Frontier Models

Author

Listed:
  • Christine Amsler

    (Michigan State University)

  • Artem Prokhorov

    (Concordia University and CIREQ)

  • Peter Schmidt

    (Michigan State University and Yonsei University)

Abstract

We consider stochastic frontier models in a panel data setting where there is dependence over time. Current methods of modelling time dependence in this setting are either unduly restrictive or computationally infeasible. Some impose restrictive assumptions on the nature of dependence such as the "scaling" property. Others involve T-dimensional integration, where T is the number of cross-sections, which may be large. Moreover, no known multivariate distribution has the property of having commonly used, convenient marginals such as normal/half-normal. We show how to use copulas to resolve these issues. The range of dependence we allow for is unrestricted and the computational task involved is easy compared to the alternatives. Also, the resulting estimators are more efficient than those that assume independence over time. We propose two alternative specifications. One applies a copula function to the distribution of the composed error term. This permits the use of MLE and GMM. The other applies a copula to the distribution of the one-sided error term. This allows for a simulated MLE and improved estimation of inefficiencies. An application demonstrates the usefulness of our approach.

Suggested Citation

  • Christine Amsler & Artem Prokhorov & Peter Schmidt, 2011. "Using Copulas to Model Time Dependence in Stochastic Frontier Models," Working Papers 11002, Concordia University, Department of Economics.
  • Handle: RePEc:crd:wpaper:11002
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    File URL: http://alcor.concordia.ca/~aprokhor/papers/frontier.pdf
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    References listed on IDEAS

    as
    1. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    2. Wei Wang & Christine Amsler & Peter Schmidt, 2011. "Goodness of fit tests in stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 95-118, April.
    3. Pitt, Mark M. & Lee, Lung-Fei, 1981. "The measurement and sources of technical inefficiency in the Indonesian weaving industry," Journal of Development Economics, Elsevier, vol. 9(1), pages 43-64, August.
    4. Prokhorov, Artem & Schmidt, Peter, 2009. "Likelihood-based estimation in a panel setting: Robustness, redundancy and validity of copulas," Journal of Econometrics, Elsevier, vol. 153(1), pages 93-104, November.
    5. 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.
    6. 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.
    7. Caudill, Steven B & Ford, Jon M & Gropper, Daniel M, 1995. "Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 105-111, January.
    8. William C. Horrace & Peter Schmidt, 2002. "Confidence Statements for Efficiency Estimates from Stochastic Frontier Models," Econometrics 0206006, EconWPA.
    9. Kumbhakar, Subal C., 1990. "Production frontiers, panel data, and time-varying technical inefficiency," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 201-211.
    10. Wang, Hung-Jen, 2006. "Stochastic frontier models," MPRA Paper 31079, University Library of Munich, Germany.
    11. Wen-Jen Tsay & Cliff J. Huang & Tsu-Tan Fu & I-Lin Ho, 2009. "Maximum Likelihood Estimation of Censored Stochastic Frontier Models: An Application to the Three-Stage DEA Method," IEAS Working Paper : academic research 09-A003, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    12. 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.
    13. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
    14. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
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    Citations

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    Cited by:

    1. Graziella Bonanno & Domenico De Giovanni & Filippo Domma, 2017. "The ‘wrong skewness’ problem: a re-specification of stochastic frontiers," Journal of Productivity Analysis, Springer, vol. 47(1), pages 49-64, February.
    2. Orea, Luis & Zofío, José L., 2017. "A primer on the theory and practice of efficiency and productivity analysis," Efficiency Series Papers 2017/05, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    3. Wen-Jen Tsay & Cliff Huang & Tsu-Tan Fu & I.-Lin Ho, 2013. "A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 39(3), pages 259-269, June.
    4. Hung-pin Lai & Cliff Huang, 2013. "Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions," Journal of Productivity Analysis, Springer, vol. 40(1), pages 1-14, August.
    5. Seunghwa Rho & Peter Schmidt, 2015. "Are all firms inefficient?," Journal of Productivity Analysis, Springer, vol. 43(3), pages 327-349, June.
    6. repec:eee:indorg:v:56:y:2018:i:c:p:107-144 is not listed on IDEAS
    7. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2016. "Endogeneity in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 190(2), pages 280-288.
    8. Tran, Kien C. & Tsionas, Mike G., 2016. "On the estimation of zero-inefficiency stochastic frontier models with endogenous regressors," Economics Letters, Elsevier, vol. 147(C), pages 19-22.
    9. repec:eee:quaeco:v:65:y:2017:i:c:p:212-226 is not listed on IDEAS
    10. Huang, Tai-Hsin & Lin, Chung-I & Chen, Kuan-Chen, 2017. "Evaluating efficiencies of Chinese commercial banks in the context of stochastic multistage technologies," Pacific-Basin Finance Journal, Elsevier, vol. 41(C), pages 93-110.
    11. Aivazian, Sergei & Afanasiev, Mikhail & Rudenko, Victoria, 2014. "Analysis of dependence between the random components of a stochastic production function for the purpose of technical efficiency estimation," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 34(2), pages 3-18.

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