Non-linear relationships are common in economic theory, and such relationships are also frequently tested empirically. We argue that the usual test of non-linear relationships is flawed, and derive the appropriate test for a U shaped relationship.Our test gives the exact necessary and sufficient conditions for the test of a U shape in both finite samples and for a large class of models. JEL: C12, C20

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I study the effect of voters with a group-based social conscience. Voters care more about the well-being of those belonging to their own group than the rest of the population. Within a model of political tax determination, both fractionalization and group antagonism reduce the support for redistribution. Whereas within group inequality increases support for redistribution, inequality between groups has the opposite effect. All these results hold even if a poor group forms a majority. Using a panel data set constructed from US micro data, I find support for the hypothesis that within race inequality increases redistribution while between race inequality decreases redistribution.

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