Abstract
Economic theory provides researchers little guidance when selecting the appropriate estimating functional form model, given the data. The flexible Box and Cox [J. Roy. Stat. Soc., 1964] power transformation model is one relatively simple device for minimizing functional approximation errors in single-equation, least-squares models. However, the Box-Cox may induce heteroscedastic residuals [Sarkar, Comm. Stats.Theory and Methods, 1985] and is only operational for strictly positive data values. Dynamic econometric models often involve variables calibrated in differences--not levels. Difference data containing negative values incapacitate Box-Cox transformations. Therefore, John and Draper [Appl. Stats., 1980] proposed the modulus alternative power family of transformations. Currently, implementation of the Modulus for econometric modelling does not exist in the literature. The purpose of this note is to increase the awareness of the Modulus and point out its usefulness when the Box-Cox is incapacitated. Consider the general linear model:
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