Transforming the Dependent Variable in Regression Models

A scale-invariant family of transformations is proposed which, unlike the Box-Cox transformation, can be applied to variables that are equal to zero or of either sign. Two Lagrange Multiplier tests are derived for testing the null hypothesis of no dependent variable transformation against the alternative of a transformation from this family. These tests do not require explicit specification of the transformation and are related to the RESET test. We discuss a model that uses a particular case of this transformation, based on sinh-1, in some detail. Monte Carlo results are given, and an empirical example is provided.

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