2021
DOI: 10.1177/10944281211058466
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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 t… Show more

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Cited by 15 publications
(14 citation statements)
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References 103 publications
(120 reference statements)
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“…The identification of switch points is also important, and we will test our data for their possible existence. According to Arin et al (2022), inflection points, kinks, and jumps allow us to identify places where the relationship between dependent and independent variables switches in some important way. The identification of endogenous switch points may lead to significantly different conclusions from those obtained when switch points are ignored or their existence is conjectured arbitrarily (Arin et al 2022, 1).…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…The identification of switch points is also important, and we will test our data for their possible existence. According to Arin et al (2022), inflection points, kinks, and jumps allow us to identify places where the relationship between dependent and independent variables switches in some important way. The identification of endogenous switch points may lead to significantly different conclusions from those obtained when switch points are ignored or their existence is conjectured arbitrarily (Arin et al 2022, 1).…”
Section: Methodsmentioning
confidence: 99%
“…The identification of endogenous switch points may lead to significantly different conclusions from those obtained when switch points are ignored or their existence is conjectured arbitrarily (Arin et al 2022, 1). We will apply the methodology developed by Arin et al (2022) to all variables used and analyze the results obtained.…”
Section: Methodsmentioning
confidence: 99%
“…We also ensured that the observed functional form is indeed quadratic and, in turn, that alternative and more complex specifications can be ruled out, such as a cubic (S-shaped) functional form. We follow prior suggestions (e.g., Arin, Minniti, Murtinu, & Spagnolo, 2022) and leverage semiparametric techniques to inspect and explore alternative specifications of curvilinear functional forms.…”
Section: Alternative Functional Formsmentioning
confidence: 99%
“…With regard to H3, being that it is tested by means of an interaction term between a continuously bounded variable Political Relations and SWF Politicization, there is no theoretical motivation for using a threshold regression. However, following Arin et al (2022) discontinuities at different values of Political Relations * SWF Politicization. As an example, in Figure 1 we show this graphical test at the value zero, where we display two smoothed fifthorder polynomial approximations fitting the relationship between the dependent variable and Political Relations * SWF Politicization, before and after the value zero.…”
Section: Additional Evidencementioning
confidence: 99%
“…Following the procedure recently proposed by Arin et al (2022), in Table 7 we estimate an endogenous threshold regression. Namely, we re‐estimate our main model in Table 5 (column (1)), as many times as there are possible switch points in the distribution of SWF Politicization .…”
Section: Additional Evidencementioning
confidence: 99%