Modelling commodity demands and labour supply with m-demands

In the empirical modelling of demands and labour supply we often lack data on a full set of goods. The usual response is to invoke separability assumptions. Here we present an alternative based on modelling demands as a function of prices and the quantity of a reference good rather than total expenditure. We term such demands m-demands. The advantage of this approach is that we make maximum use of the data to hand without invoking implausible separability assumptions. In the theory section quasi-Slutsky conditions are derived and some structural and separability conditions are presented. We also derive functional forms for empirical work. Finally an empirical illustration on Canadian expenditure data is given. This illustrates both the implementation of the ideas presented in the theory section and the empirical costs of not having a full set of data.