We propose a new nonlinear model of social interactions. The model allows point identification of peer effects as a function of group means, even with group level fixed effects. The model is robust to measurement problems resulting from only observing a small number of members of each group, and therefore can be estimated using standard survey datasets. We apply our method to a national consumer expenditure survey dataset from India. We find that each additional rupee spent by one’s peer group increases one’s own perceived needs by roughly 0.5 rupees. This implies that if I and my peers each increase spending by 1 rupee, that has the same effect on my utility as if I alone increased spending by only 0.5 rupees. Our estimates have important policy implications, e.g., we show potentially considerable welfare gains from replacing government transfers of private goods with the provision of public goods.