IDEAS home Printed from https://ideas.repec.org/p/hal/psewpa/halshs-01261980.html
   My bibliography  Save this paper

Box-Cox transformations of terms nesting the Trans-Log: the example of rail infrastructure maintenance cost

Author

Listed:
  • Marc Gaudry

    (AJD - Agora Jules Dupuit - UdeM - Université de Montréal)

  • Emile Quinet

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

Abstract

We explore how the Trans-Log (TL) can be nested in Box-Cox transformed terms and show that a particular specification previously defined, but not fully tested, within the European CATRIN consortium (Gaudry & Quinet, 2010), the Unrestricted Generalized Box-Cox (U-GBC), constitutes a proper incarnation of the Generalized Flexible Quadratic class (Blackorby et al. (1977) and nests a number of more or less known intermediate Box-Cox-inspired partial generalizations of the TL, as well as the target TL itself. After a brief rail cost litterature review, our detailed references to such intermediate model specifications making partial use of Box-Cox transformations are focused on examples developed since 2002 using cross-sectional data, shown to differ profoundly from their ancestor aggregate time-series firm-wide explanations of total or of current maintenance rail cost published before 2002. Notably, the TL, devoid of prices, has since 2002 become a rail engineering degradation cost model under an unchanged econometric terminological form garb on which we dwell. We estimate three main rail maintenance cost model specifications strictly nesting the TL from real 1999 France-wide segment network data and compare their improved log likelihood values under different engineering hypotheses concerning physical interactions among four rail Traffic types and four track Quality characteristics. We find the Trans-Log to be an inadequate model of railway damage because physical interactions among track Quality indicators and train Traffic types are not of log-log form but of other forms better handled by common flexible Box-Cox Transformations, twelve of which are estimated in our most general U-GBC specification, all but one actually differing from the logarithmic case. And, of course, not all physical interactions turn out to matter in the explanation of degradation cost: track Quality-Quality interactions, for instance, are of nugatory importance.

Suggested Citation

  • Marc Gaudry & Emile Quinet, 2016. "Box-Cox transformations of terms nesting the Trans-Log: the example of rail infrastructure maintenance cost," PSE Working Papers halshs-01261980, HAL.
  • Handle: RePEc:hal:psewpa:halshs-01261980
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01261980
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-01261980/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Caves, Douglas W & Christensen, Laurits R & Tretheway, Michael W, 1980. "Flexible Cost Functions for Multiproduct Firms," The Review of Economics and Statistics, MIT Press, vol. 62(3), pages 477-481, August.
    2. Marc Gaudry & Bernard Lapeyre & Emile Quinet, 2015. "Infrastructure maintenance, regeneration and service quality economics: A rail example," Working Papers halshs-00559637, HAL.
    3. Douglas W. Caves & Laurits R. Christensen & Joseph A. Swanson, 1980. "Productivity in U.S. Railroads, 1951-1974," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 166-181, Spring.
    4. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    5. Burgess, David F, 1974. "A Cost Minimization Approach to Import Demand Equations," The Review of Economics and Statistics, MIT Press, vol. 56(2), pages 225-234, May.
    6. Diewert, W E, 1974. "Functional Forms for Revenue and Factor Requirements Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 119-130, February.
    7. Johansson, Per & Nilsson, Jan-Eric, 2004. "An economic analysis of track maintenance costs," Transport Policy, Elsevier, vol. 11(3), pages 277-286, July.
    8. Marc Gaudry & Emile Quinet, 2009. "Track wear-and-tear cost by traffic class: Functional form, zero output levels and marginal cost pricing recovery on the French rail network," PSE Working Papers halshs-00574977, HAL.
    9. Marc Gaudry & Bernard Lapeyre & Emile Quinet, 2015. "Infrastructure maintenance, regeneration and service quality economics: A rail example," PSE Working Papers halshs-00559637, HAL.
    10. Gaudry, Marc & Laferriere, Richard, 1989. "The box-cox transformation : Power invariance and a new interpretation," Economics Letters, Elsevier, vol. 30(1), pages 27-29.
    11. Russell Davidson & James G. MacKinnon, 1985. "Testing Linear and Loglinear Regressions against Box-Cox Alternatives," Canadian Journal of Economics, Canadian Economics Association, vol. 18(3), pages 499-517, August.
    12. Marc Gaudry & Emile Quinet, 2009. "Track wear-and-tear cost by traffic class: Functional form, zero output levels and marginal cost pricing recovery on the French rail network," Working Papers halshs-00574977, HAL.
    13. Blackorby, Charles & Primont, Daniel & Russell, R. Robert, 1977. "On testing separability restrictions with flexible functional forms," Journal of Econometrics, Elsevier, vol. 5(2), pages 195-209, March.
    14. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
    15. Berndt, Ernst R & Khaled, Mohammed S, 1979. "Parametric Productivity Measurement and Choice among Flexible Functional Forms," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1220-1245, December.
    16. Denny, Michael & Fuss, Melvyn A, 1977. "The Use of Approximation Analysis to Test for Separability and the Existence of Consistent Aggregates," American Economic Review, American Economic Association, vol. 67(3), pages 404-418, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gaudry, Marc, 2018. "The utility of journeys, from Dupuit's constant-time bridge crossing hops to commutes of chosen duration and reliability in the Paris region," Transport Policy, Elsevier, vol. 70(C), pages 53-68.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marc Gaudry & Emile Quinet, 2016. "Box-Cox transformations of terms nesting the Trans-Log: the example of rail infrastructure maintenance cost," Working Papers halshs-01261980, HAL.
    2. Marc Gaudry & Emile Quinet, 2009. "Track wear-and-tear cost by traffic class: Functional form, zero output levels and marginal cost pricing recovery on the French rail network," Working Papers halshs-00574977, HAL.
    3. Marc Gaudry & Emile Quinet, 2015. "Correlation within SNCF administrative regions among track segment maintenance cost equation residuals of a country-wide model," Working Papers halshs-01112249, HAL.
    4. Marc Gaudry & Emile Quinet, 2015. "Correlation within SNCF administrative regions among track segment maintenance cost equation residuals of a country-wide model," PSE Working Papers halshs-01112249, HAL.
    5. Dale W. Jorgenson, 1991. "Productivity and Economic Growth," NBER Chapters, in: Fifty Years of Economic Measurement: The Jubilee of the Conference on Research in Income and Wealth, pages 19-118, National Bureau of Economic Research, Inc.
    6. Kesavan, Thulasiram, 1988. "Monte Carlo experiments of market demand theory," ISU General Staff Papers 198801010800009854, Iowa State University, Department of Economics.
    7. Marc Gaudry & Bernard Lapeyre & Emile Quinet, 2015. "Infrastructure maintenance, regeneration and service quality economics: A rail example," PSE Working Papers halshs-00559637, HAL.
    8. Alfons Oude Lansink & Geert Thijssen, 1998. "Testing among functional forms: an extension of the Generalized Box-Cox formulation," Applied Economics, Taylor & Francis Journals, vol. 30(8), pages 1001-1010.
    9. Diewert, W. E. & Wales, T. J., 1995. "Flexible functional forms and tests of homogeneous separability," Journal of Econometrics, Elsevier, vol. 67(2), pages 259-302, June.
    10. Woo, C.K. & Liu, Y. & Zarnikau, J. & Shiu, A. & Luo, X. & Kahrl, F., 2018. "Price elasticities of retail energy demands in the United States: New evidence from a panel of monthly data for 2001–2016," Applied Energy, Elsevier, vol. 222(C), pages 460-474.
    11. W. Erwin Diewert, 2022. "Duality in Production," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 3, pages 57-168, Springer.
    12. GianCarlo Moschini, 2001. "A Flexible Multistage Demand System Based on Indirect Separability," Southern Economic Journal, John Wiley & Sons, vol. 68(1), pages 22-41, July.
    13. Link, Heike & Nilsson, Jan-Eric, 2005. "Infrastructure," Research in Transportation Economics, Elsevier, vol. 14(1), pages 49-83, January.
    14. William A. Barnett & Ikuyasu Usui, 2007. "The Theoretical Regularity Properties of the Normalized Quadratic Consumer Demand Model," International Symposia in Economic Theory and Econometrics, in: Functional Structure Inference, pages 107-127, Emerald Group Publishing Limited.
    15. Kamerschen, David R. & Klein, Peter G. & Porter, David V., 2005. "Market structure in the US electricity industry: A long-term perspective," Energy Economics, Elsevier, vol. 27(5), pages 731-751, September.
    16. Hamermesh, Daniel S., 1987. "The demand for labor in the long run," Handbook of Labor Economics, in: O. Ashenfelter & R. Layard (ed.), Handbook of Labor Economics, edition 1, volume 1, chapter 8, pages 429-471, Elsevier.
    17. Adelaja, Adesoji O. & Hoque, Anwarul, 1986. "A Multi-Product Analysis Of Energy Demand In Agricultural Subsectors," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 18(2), pages 1-13, December.
    18. Odolinski , Kristofer, 2016. "The impact of cumulative tons on rail infrastructure maintenance costs," Working papers in Transport Economics 2016:28, CTS - Centre for Transport Studies Stockholm (KTH and VTI).
    19. Link, Heike, 2006. "An econometric analysis of motorway renewal costs in Germany," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(1), pages 19-34, January.
    20. repec:eee:labchp:v:1:y:1986:i:c:p:429-471 is not listed on IDEAS
    21. Dumont, Michel, 2004. "The Impact of International Trade with Newly Industrialised Countries on the Wages and Employment of Low-Skilled and High-Skilled Workers in the European Union," Thesis Commons bmxag, Center for Open Science.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:psewpa:halshs-01261980. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.