With or Without U? The Appropriate Test for a U-Shaped Relationship*

doi:10.1111/j.1468-0084.2009.00569.x

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Wiley InterScience

Oxford Bulletin of Economics and Statistics

Volume 72 Issue 1, Pages 109 - 118

Published Online: 31 Aug 2009

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With or Without U? The Appropriate Test for a U-Shaped Relationship*

Jo Thori Lind ¹ and Halvor Mehlum ¹

¹ Department of Economics, University of Oslo, PB 1095 Blindern, 0317 Oslo, Norway
(e-mail: j.t.lind@econ.uio.no; halvor.mehlum@econ.uio)

*While carrying out this research, the authors have been associated with the ESOP centre at the Department of Economics, University of Oslo. ESOP is supported by The Research Council of Norway. The authors are grateful for comments from two anonymous referees, Kalle Moene, and seminar participants at the University of Oslo and PRIO. They also thank Dustin Chambers for making his data available. A companion STATA module utest is available from: http://ideas.repec.org/c/boc/bocode/s456874.html

KEYWORDS

C12 • C20

ABSTRACT

Nonlinear relationships are common in economic theory, and such relationships are also frequently tested empirically. We argue that the usual test of nonlinear 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 finite samples in a large class of models.

Final Manuscript Received: June 2009

DIGITAL OBJECT IDENTIFIER (DOI)

10.1111/j.1468-0084.2009.00569.x About DOI