A Note on the Box-Cox Transformation Under Heteroskedasticity

The Box-Cox transformation (BCT) has been frequently used as both a flexible functional form and as a decision device to distinguish among alternative model specifications. Most researchers have failed to recognize that the BCT when applied to the dependent variable can compensate for heteroskedasticity. This paper investigates a new procedure which estimates both the BCT parameters and the analytic form of heteroskedasticity. Results from the new procedure are compared to estimates obtained from the traditional method of estimating BCT models. Comparisons indicate that proper specification of the error variance can influence the magnitude of BCT parameters and alter the results of hypothesis testing. The monotonic transformation introduced by Box and Cox has been employed in a number of econometric applications, includ-ing those in monetary economics [Zarembka, 1968], production theory [Appelbaum], and demand analysis [Chang, Kulshreshtha], for added flexibility in model specification. For example, application of the Box-Cox transfor-mation (BCT) to both the dependent and independent variables of a regression model defines a general class of functional forms which includes the linear and double-logarithmic functions as special cases. This feature of the BCT model allows the data added flexibility in determining the degree of nonlinearity in a relationship and provides a unified structure for statistically distin-guishing among alternative functional specifi-cations. However, Box and Cox have als