Latent Separability: Grouping Goods without Weak Separability

This paper develops a new concept of separability with overlapping groups—latent separability. This is shown to provide a useful empirical and theoretical framework for investigating the grouping of goods and prices. It is a generalization of weak separability in which goods are allowed to enter more than one group and where the composition of groups is identified by the choice of group specific exclusive goods. Latent separability 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 generalizations, we provide a method for choosing the number of homothetic separable groups. A detailed method for exploring the composition of the separable groups is also presented. These methods are applied to a long time series of British individual household data on the consumption of twenty two nondurable and service goods.