With or Without U? The Appropriate Test for a U-Shaped Relationship*
指出常用的非线性关系检验存在缺陷，推导出U形关系的正确检验方法，给出了有限样本和一大类模型下检验U形的充要条件。
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.