Invariance axioms and functional form restrictions in structural models

The dominant practice in economics is to choose the mathematical specification of model relations on the basis of convenience, without much theoretical support. This paper discusses how quantitative model specifications can, in some cases, be given a more formal scientific underpinning in the sense of being based on a priori theory. I use an example from discrete choice theory to illustrate that it is sometimes possible to obtain a complete characterization of the choice model derived from a set of plausible axioms. Furthermore, I discuss how axioms can be tested non-parametrically, given that suitable Stated Preference data are available.