An Efficient Nonparametric Test of the Collective Household Model

Recently Cherchye et al. (2007a) provided a nonparametric characterization of a general collective model for household consumption which includes externalities and public consumption. This characterization involved different testable necessary and sufficient conditions. We discuss the special case of the household model for which their sufficient conditions are also necessary. We show that verification of this sufficient condition is NP Complete and discuss the relevance of this result for empirical testing. We observe that testing this condition is equivalent to solving the acyclic partitioning problem on a directed graph. We devise an efficient algorithm which approximately solves the minimum acyclic partitioning problem on directed graphs. Hence, we compute an approximate solution to the problem of finding the minimum number K, so that the observed data is consistent with K decision makers. We implement our algorithm on a randomly generated price consumption data set and report the results