BOX-COX TRANSFORMATIONS AND ERROR TERM SPECIFICATION IN DEMAND MODELS

Abstract

This paper analyzes the influence of error-term specification and functional form on a quarterly demand model for beef. The Box-Cox transformation is used to generalize the functional form while the equation error term is postulated to be both heteroskedastic and autoregressive. Results indicated that both functional form and error-term specification can play a major role in elasticity estimation, elasticity behavior, and hypothesis testing. The monotonic transformation introduced by Box and Cox has become a popular tool for both discriminating among alternative functional forms and providing added flexibility in model specification. Most empirical analyses employing the Box-Cox transformation (BCT) have assumed that the model error term is homoskedastic and nonautoregressive. However, more recent evidence suggests that error specification is at least as important as functional form when the transformation is applied to the dependent variable. Savin and White have shown that estimating BCT models without specifying an autocorrelated error structure can yield both inefficient estimators and erroneous results of hypothesis tests. Zarembka has shown that if the true underlying error term is heteroskedastic, then the maximum likelihood estimator of the dependent variable's BCT parameter is biased in the direction which tends to make the estimated error term more homoskedastic. This can result in inconsistent estimators for all model parameters.