This paper studies how heterogeneity in income dynamics affects the POUM hypothesis (the idea that poor people do not support high level of redistribution because they hope to be rich in the future). We consider a setting where individuals evaluate their expected future income using both their current income and observable characteristics such as education, race or gender. We find that the POUM effect could increase or decrease the support for redistribution depending on the parameters of the model. Moreover we find that the POUM effect is independent of a particular shape (the concavity) of the resulting aggregate income transition function. Finally, using data from Italy, we test the model and perform a first empirical estimation of the POUM effect in Italy.