Latent separability: grouping goods without weak separability

This paper develops a new separability concept - latent separability. This is shown to provide a useful empirical and theoretical framework for investigating the grouping of goods and prices. It is a generalisation of weak separability in which groups are identified by specific exclusive goods but where other goods are allowed to enter more than one group. It is shown to be equivalent to weak separability in latent rather than purchased goods and provides a relationship between separability and household production theory. For the popular class of Linear, Almost Ideal and Translog demand models and their generalisations, the number of groups is shown to relate directly to an empirical rank condition. A detailed method for exploring the presence of latent separability is presented and applied to a long time series of household level consumption data for the UK.