In this paper, we estimate a collective model of household consumption and test the restrictions of collective rationality using z-conditional demands in the context of a large Conditional Cash Transfer programme in rural Mexico. We show that the model is able to explain the impacts the programme has on the structure of food consumption. We use two plausible and novel distribution factors, that is variables that describe the mechanism by which decisions are reached within the household: the random allocation of a cash transfer to women, and the relative size and wealth of the husband and wife's family networks. We find that the structure we propose does better at predicting the effect of exogenous increases in household income than an alternative, unitary, structure. We cannot reject efficiency of household decisions.