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With or Without U? - The appropriate test for a U shaped relationship.
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Abstract
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.U shape; hypothesis test; Kuznets curve; Fieller interval