Poor people are more generous than rich people when giving to charities. Their donations to churches are proportionally also higher. That seems rather puzzling, as the marginal utility of consumption is higher for a poor person, to she should be less willing to give something away. Of course, you could also argue that this person is poor because she is giving away too much. But there should be a better explanation.
Julio Rotemberg offers one. He bases his model on the fact that people like making donations to causes they can identify with: they are OK with making anonymous donations in such a case because it helps like-minded people, and they like it when others agree with them, and are thus willing to help them. The model yields multiple equilibria, some in which the rich give the bulk of donations, others where the poor do. This can help rationalize why the proportion donors varies so much from one country to another, and so independently from the size of the welfare state. Some parameter values lead to people donating in the hope it will encourage others to do so. These equilibria should be dismissed, according to results I recently discussed. The model also seems to build on the fact that there is little crowding out of private charity from public funds, which I doubt according to recent evidence I discussed here. But the model predicts nicely that there is a strong incentive for charities to differentiate themselves to capture donations, even if this not increase total donations.