Scandinavian Working Papers in Economics

Memorandum,
Oslo University, Department of Economics

No 21/2007: With or Without U? The appropriate test for a U shaped relationship

Jo Thori Lind () and Halvor Mehlum ()
Additional contact information
Jo Thori Lind: Dept. of Economics, University of Oslo, Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Halvor Mehlum: Dept. of Economics, University of Oslo, Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway

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.

Keywords: U shape; hypothesis test; Kuznets curve; Fieller interval

JEL-codes: C12; C20

14 pages, September 1, 2007

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