Risk sharing and the household collective model

When the joint assumption of optimal risk sharing and coincidence of beliefs is added to the collective model of Browning and Chiappori (1998) income pooling and symmetry of the pseudo-Hicksian matrix are shown to be restored. Because these are also the features of the unitary model usually rejected in empirical studies one may argue that these assumptions are at odds with evidence. We argue that this needs not be the case. The use of cross-section data to generate price and income variation is based Oil a definition of income pooling or symmetry suitable for testing the unitary model, but not the collective model with risk sharing. AIso, by relaxing assumptions on beliefs, we show that symmetry and income pooling is lost. However, with usual assumptions on existence of assignable goods, we show that beliefs are identifiable. More importantly, if di:fferences in beliefs are not too extreme, the risk sharing hypothesis is still testable.