Ray-homotheticity is proposed as a fruitful way of modelling scale economies. It permits scale economies to vary with the rate of output and the input mix, thus allowing ideal output to be input mix-dependent. Our empirical results illustrate the value of ray-homotheticity as a generalization of both homotheticity and ray-homogeneity. They also shed some light on the use of Wald and likelihood ratio tests for hypothesis testing in nested nonlinear models. We find instances of conflict between the two tests, and of reversal of the ordering that holds in linear models.