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Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers

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  • Ferreira, Jose T.A.S.
  • Steel, Mark F.J.

Abstract

We consider classes of multivariate distributions which can model skewness and are closed under orthogonal transformations. We review two classes of such distributions proposed in the literature and focus our attention on a particular, yet quite flexible, subclass of one of these classes. Members of this subclass are defined by affine transformations of univariate (skewed) distributions that ensure the existence of a set of coordinate axes along which there is independence and the marginals are known analytically. The choice of an appropriate m-dimensional skewed distribution is then restricted to the simpler problem of choosing m univariate skewed distributions. We introduce a Bayesian model comparison setup for selection of these univariate skewed distributions. The analysis does not rely on the existence of moments (allowing for any tail behaviour) and uses equivalent priors on the common characteristics of the different models. Finally, we apply this framework to multi-output stochastic frontiers using data from Dutch dairy farms.
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Suggested Citation

  • Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
  • Handle: RePEc:eee:econom:v:137:y:2007:i:2:p:641-673
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    References listed on IDEAS

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    1. Fernandez C. & Koop G. & Steel M.F.J., 2002. "Multiple-Output Production With Undesirable Outputs: An Application to Nitrogen Surplus in Agriculture," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 432-442, June.
    2. Fernandez, Carmen & Koop, Gary & Steel, Mark, 2000. "A Bayesian analysis of multiple-output production frontiers," Journal of Econometrics, Elsevier, vol. 98(1), pages 47-79, September.
    3. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    4. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    5. Barry Arnold & Robert Beaver & A. Azzalini & N. Balakrishnan & A. Bhaumik & D. Dey & C. Cuadras & J. Sarabia & Barry Arnold & Robert Beaver, 2002. "Skewed multivariate models related to hidden truncation and/or selective reporting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 7-54, June.
    6. Fernandez, Carmen & Koop, Gary & Steel, Mark F.J., 2005. "Alternative efficiency measures for multiple-output production," Journal of Econometrics, Elsevier, vol. 126(2), pages 411-444, June.
    7. C. J. Hoggart & S. G. Walker & A. F. M. Smith, 2003. "Bivariate kurtotic distributions of garment fibre data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(3), pages 323-335.
    8. Gupta, Arjun K. & González-Farías, Graciela & Domínguez-Molina, J. Armando, 2004. "A multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 181-190, April.
    9. Stijn Reinhard & C.A. Knox Lovell & Geert Thijssen, 1999. "Econometric Estimation of Technical and Environmental Efficiency: An Application to Dutch Dairy Farms," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(1), pages 44-60.
    10. 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.
    11. 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.
    12. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
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    Cited by:

    1. Maximiano Pinheiro & Paulo Esteves, 2012. "On the uncertainty and risks of macroeconomic forecasts: combining judgements with sample and model information," Empirical Economics, Springer, vol. 42(3), pages 639-665, June.
    2. Carta, Alessandro & Steel, Mark F.J., 2012. "Modelling multi-output stochastic frontiers using copulas," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3757-3773.
    3. Jorge Galán & Helena Veiga & Michael Wiper, 2014. "Bayesian estimation of inefficiency heterogeneity in stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 42(1), pages 85-101, August.
    4. Henningsen, Arne & Bělín, Matěj & Henningsen, Géraldine, 2017. "New insights into the stochastic ray production frontier," Economics Letters, Elsevier, vol. 156(C), pages 18-21.
    5. Galán, Jorge E. & Pollitt, Michael G., 2014. "Inefficiency persistence and heterogeneity in Colombian electricity utilities," Energy Economics, Elsevier, vol. 46(C), pages 31-44.
    6. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    7. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    8. Panagiotelis, Anastasios & Smith, Michael, 2010. "Bayesian skew selection for multivariate models," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1824-1839, July.
    9. De la Cruz, Rolando, 2008. "Bayesian non-linear regression models with skew-elliptical errors: Applications to the classification of longitudinal profiles," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 436-449, December.
    10. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.
    11. Sarmiento, Miguel & Galán, Jorge E., 2014. "Heterogeneous effects of risk-taking on bank efficiency : a stochastic frontier model with random coefficients," DES - Working Papers. Statistics and Econometrics. WS ws142013, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. J. T. A. S. Ferreira & M. F. J. Steel, 2004. "On Describing Multivariate Skewness: A Directional Approach," Econometrics 0409010, EconWPA.
    13. Galán, Jorge E. & Veiga, Helena & Wiper, Michael P., 2015. "Dynamic effects in inefficiency: Evidence from the Colombian banking sector," European Journal of Operational Research, Elsevier, vol. 240(2), pages 562-571.
    14. Maximiano Pinheiro, 2010. "Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables," Working Papers w201013, Banco de Portugal, Economics and Research Department.
    15. Galán, Jorge & Ramos, Sofía B. & Veiga, Helena, 2015. "An analysis of the dynamics of efficiency of mutual funds," DES - Working Papers. Statistics and Econometrics. WS ws1517, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Wraith, Darren & Forbes, Florence, 2015. "Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 61-73.
    17. Jorge E. Galán & Michael G. Pollitt, 2014. "Inefficiency persistence and heterogeneity in Colombian electricity distribution utilities," Cambridge Working Papers in Economics 1423, Faculty of Economics, University of Cambridge.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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