With or Without U? - The appropriate test for a U shaped relationship

By J. Lind, Halvor Mehlum. 2007

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Age, culture, and self-employment motivation (2015, methodology): “First, we draw on the tests of Lind and Mehlum (2010) to further assess the validity of the curvilinear Table 1 Description of variables Variable Description Individual-level variables Perceived desirability ‘‘Personally, how desirable is for you to become self-employed within the next 5 years?’’”
Economic development, structural change, and women’s labor force participation: (2013, positive): “As a further robustness check, we also use an alternative test for a U-shaped relationship recently proposed by Lind and Mehlum (2010).”
Counting Chickens when they Hatch: Timing and the Effects of Aid on Growth* (2012, positive): “18 In interpreting the standard errors on these delta-method estimates of the extremum in a U-shaped relationship, Lind and Mehlum (2010) suggest using a one-sided test, thus the 10% level of significance.”
Intra- and extra-bank determinants of Latin American Banks' profitability (2016, methodology): “This non-monotonic relationship is statistically significant according to the Lind and Mehlum (2010) test in all the estimations.”