Tie Turning Box-Cox including Quadratic Forms in Regression

Marc Gaudry, Ulrich Blum (ulrich.blum@wiwi.uni-halle.de) and Tran Liem

Working Papers of BETA from Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg

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.

Keywords: Box-Cox Transformation; Quadratic Form; Asymmetric U-shaped Forms; Regression. Classification-JEL : (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (16)

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Persistent link: https://EconPapers.repec.org/RePEc:ulp:sbbeta:2000-13

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