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Tie Turning Box-Cox including Quadratic Forms in Regression

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Listed:
  • Marc Gaudry
  • Ulrich Blum
  • Tran Liem

Abstract

In a regression model where a Box-Cox transformation is used on a positive independent variable X which appears only once in the equation, the effect of X on the dependent variable Y is either strictly increasing or decreasing over the whole range of X , since the transformation is a monotonic function of X , increasing or decreasing depending on the Box-Cox parameter ë. This paper considers the case where the variable X appears twice in the regression with two different Box-Cox parameters 1 ë and 2 ë , to allow a turning point in Y which can be a maximum or minimum. First and second-order conditions for the critical point are derived. This general specification includes as a special case the quadratic form in X where 1 ë and 2 ë are set equal to 1 and 2, respectively. If, instead of using the Box-Cox transformations, one uses simple powers of X , this form is equivalent to the Box-Cox form except that neither 1 ë nor 2 ë can be equal to zero, since in this case 1 ë X or 2 ë X reduces to a constant of value 1.

Suggested Citation

  • Marc Gaudry & Ulrich Blum & Tran Liem, 2000. "Tie Turning Box-Cox including Quadratic Forms in Regression," Working Papers of BETA 2000-13, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  • Handle: RePEc:ulp:sbbeta:2000-13
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    File URL: http://www.beta-umr7522.fr/productions/publications/2000/2000-13.pdf
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    References listed on IDEAS

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    1. Gaudry, Marc & Laferriere, Richard, 1989. "The box-cox transformation : Power invariance and a new interpretation," Economics Letters, Elsevier, vol. 30(1), pages 27-29.
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    Cited by:

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    2. Jeppe Rich & Stefan L. Mabit, 2016. "Cost damping and functional form in transport models," Transportation, Springer, vol. 43(5), pages 889-912, September.
    3. Estelle Dhont-Peltrault & Etienne Pfister, 2007. "R&D cooperation versus R&D subcontracting: empirical evidence from French survey data," Working Papers of BETA 2007-17, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    4. Gisèle Umbhauer, 2007. "De l’amiante au chrysotile, un glissement stratégique dans la désinformation," Working Papers of BETA 2007-15, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    5. 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.
    6. Jalal EL OUARDIGHI & Rabija SOMUN-KAPETANOVIC, 2006. "Convergence des contributions aux inégalités de richesse dans le développement des pays européens," Working Papers of BETA 2006-19, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    7. Meixing DAI, 2007. "A two-pillar strategy to keep inflation expectations at bay: A basic theoretical framework," Working Papers of BETA 2007-20, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    8. Meixing DAI & Moïse SIDIROPOULOS & Eleftherios SPYROMITROS, 2007. "La transparence de la politique monétaire et la dynamique des marchés financiers," Working Papers of BETA 2007-19, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    9. 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.
    10. Giovanni Dosi & Patrick Llerena & Mauro Sylos Labini, 2005. "Science-Technology-Industry Links and the ”European Paradox”: Some Notes on the Dynamics of Scientific and Technological Research in Europe," LEM Papers Series 2005/02, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    11. Stéphane Betrand & Kene Boun My & Alban Verchère, 2005. "Faire émerger la coopération internationale : une approche expérimentale comparée du bilatéralisme et du multilatéralisme," Working Papers of BETA 2005-13, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    12. Nicolas Carayol & Pascale Roux, 2006. "A strategic model of complex networks formation," Working Papers of BETA 2006-02, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    13. Tapas K. Mishra, 2006. "A Further Look into the Demography-based GDP Forecasting Method," Working Papers of BETA 2006-17, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    14. Li Qin & Eleftherios Spyromitros & Moïse Sidiropoulos, 2007. "Monetary Policy with Uncertain Central Bank Preferences for Robustness," Working Papers of BETA 2007-23, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    15. 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.
    16. Marc Gaudry & Bernard Lapeyre & Emile Quinet, 2015. "Infrastructure maintenance, regeneration and service quality economics: A rail example," PSE Working Papers halshs-00559637, HAL.
    17. Rachel Levy & Paul Muller, 2006. "Do academic laboratories correspond to scientific communities? Evidence from a large European university," Working Papers of BETA 2006-15, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    18. Sofia Pessoa e Costa & Stéphane Robin, 2007. "The Impact Of Training Programmes On Wages In France: An Evaluation Of The “Qualifying Contract” Using Propensity Scores," Working Papers of BETA 2007-18, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.

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    Keywords

    Box-Cox Transformation; Quadratic Form; Asymmetric U-shaped Forms; Regression. Classification-JEL :;

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