Computational Inefficiency Of Nonparametric Tests For Consistency Of Data With Household Consumption

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 necessary and sufficient conditions. We identify a special case of the household model for which their sufficiency conditions are also necessary. We show that verification of this sufficiency condition is NP Complete which provides justification for the parametric techniques used in the empirical literature.