Inflection Points, Kinks, and Jumps: A Statistical Approach to Detecting Nonlinearities

Abstract

Inflection points, kinks, and jumps identify places where the relationship between dependent and independent variables switches in some important way. Although these switch points are often mentioned in management research, their presence in the data is either ignored, or postulated ad hoc by testing arbitrarily specified functional forms (e.g., U or inverted U-shaped relationships). This is problematic if we want accurate tests for our theories. To address this issue, we provide an integrative framework for the identification of nonlinearities. Our approach constitutes a precursor step that researchers will want to conduct before deciding which estimation model may be most appropriate. We also provide instructions on how our approach can be implemented, and a replicable illustration of the procedure. Our illustrative example shows how the identification of endogenous switch points may lead to significantly different conclusions compared to those obtained when switch points are ignored or their existence is conjectured arbitrarily. This supports our claim that capturing empirically the presence of nonlinearity is important and should be included in our empirical investigations.