Thinking about U: Theorizing and testing U - and inverted U-shaped relationships in strategy research

U- and inverted U-shaped relationships are increasingly explored in strategy research, with 11 percent of all articles published in Strategic Management Journal (SMJ) in 2008–2012 investigating such quadratic relationships. Moreover, a movement towards introducing moderation to quadratic relationships has emerged. By reviewing 110 articles published in SMJ from 1980 to 2012, we identify several critical issues in theorizing and testing of these relationships for which current practice falls short. These include insufficient causal argumentation, incorrect testing, mixing up two different types of moderation, and not realizing that the curve can flip completely. For these and other issues, a guideline is provided which, when followed, may bring clarity to theoretical motivation and rigor to empirical testing.