Some Alternatives to the Box- Cox Regression Model

A nonlinear regression model is proposed as an alternative to the Box-Cox regression model for nonnegative variables. The functional form contains as special cases the linear, exponential, constant elasticity, and generalized CES specifications, as well as other functional forms used by applied econometricians . The model can be derived from but is more general than a particular modification of the Box-Cox model. Because the model is specified directly in terms of E(y|x), the parameters are easy to interpet and economic quantities are straightforward to compute. Unlike Box-Cox type approaches, the proposed weighted nonlinear least squares estimators of the conditional mean function are robust to conditional variance and other distributional misspecifications ; in some leading cases they are also asymptotically efficient. Computationally simple, robust lagrange multiplier statistics for various restricted versions of the model are derived. The explained variable can be continuous, discrete, or some combination of the two. A method for obtaining scaleinvariant t-statistics is also discussed, while the lagrange multiplier test for exclusion restrictions is shown to be scale invariant.