Box-Cox Transformations and Error Term Specification in Demand Models

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 func-tional form while the equation error term is postulated to be both heteroskedastic and autore-gressive. 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 intro-duced by Box and Cox has become a pop-ular tool for both discriminating among alternative functional forms and provid-ing added flexibility in model specifica-tion. 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 im-portant as functional form when the trans-formation is applied to the dependent variable. Savin and White have shown that estimating BCT models without specify-ing an autocorrelated error structure can yield both inefficient estimators and er-roneous results of hypothesis tests. Zar-embka has shown that if the true under-lying 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 ho-moskedastic. This can result in inconsis-tent estimators for all model parameters