Is there a relationship between inequality and terrorism? Evidence from a semi-parametric approach

ABSTRACT Understanding links between income inequality and terrorism is crucially important for social scientists. The current empirical literature suggests that this relationship is positive but inconclusive. In this paper we use a semi-parametric approach to model the relationship between inequality and terrorism, in order to identify nonlinearities in the relationship. We use top income percentile shares as our measure of inequality in response to the inequality measurement literature identifying problems with the Gini. We find that after controlling for explanations of terrorism other than inequality, the positive relationship between inequality and terrorism discussed in the existing empirical literature is very weakly evident. We also find that the semi-parametric model crucially exposes the nonlinear nature of the relationship between inequality and terrorism. The results are different for developed and developing countries. We find that the relationship between inequality and terrorism is nonlinear and at most weakly positive for developed countries, with a slightly stronger positive relationship for developing and middle-income countries.


I. Introduction
In this paper we investigate the relationship between income inequality and terrorism using several inequality measures. Current empirical evidence of the effects of income inequality on terrorism is inconclusive, albeit mostly positive (Enders, Hoover, and Sandler 2016;Gaibulloev and Sandler 2019;Piazza 2011). To uncover this relationship, we employ inequality measures defined by distributional patterns at the top end of the income distribution, following the inequality measurement literature (Atkinson and Brandolini 2010;Bandyopadhyay 2018). We also employ semiparametric methods (Robinson 1988) to identify possible nonlinearities in the relationship.
With a sample of 139 countries, including 104 developing and middle-income group countries, we use top income percentile shares to provide robust evidence that inequality is weakly positively associated with terrorism. In addition, we observe that inequality has different nonlinear associations with terrorism for developed, middle-income and developing countries. This finding accords with evidence from Enders, Hoover, and Sandler (2016).

II. Current empirical literature on inequality and terrorism
The empirical evidence on the relationship between income inequality and terrorism has been difficult to pin down, though the literature suggests that the relationship exists in different ways (Enders, Hoover, and Sandler 2016). There is more empirical evidence suggesting associations of income inequality with domestic terrorism than with transnational terrorism (Piazza 2011;Krieger and Meierrieks 2019), even if in specific periods of international instability (prior to 1993(prior to , Enders et al. 2011. Empirical studies that control for inequality provide very little evidence that income inequality systematically matters to terrorism (e.g. Abadie 2006). However, using survey responses on income inequality and preferences for domestic revolt, MacCulloch (2005) finds a negative association of preferences for revolt in the face of inequality-reducing policies. The evidence thus far has given us reason to believe income inequality should be significantly associated with dissent, possible revolt and also terrorism, but has eluded full empirical validation. The possible lack of conclusive evidence could be due to the need for novel modelling techniques or due to the specific inequality measures used for the analyses.
Thus, in our analysis we undertake a thorough investigation using distribution-specific inequality measures, and adopt a semi-parametric approach which allows for nonlinearities in the relationship.

III. Data and empirical estimations
Our dataset includes 139 countries for years 2001-2018, of which 104 are developing and middleincome countries ( Table A1 in Appendix). The dataset includes countries and years for which complete terrorism and inequality data is available. We use several definitions of terrorism for our analysis: Our principal dependent variable is the total number of terrorist incidents per country-year observation. We also present results with domestic terrorism, due to it being more frequently observed than transnational terrorism and being associated with income inequality (Piazza 2011). Summary statistics of the variables are available at the following link here. Finally, we separate our dataset into two samples -developed, and developing and middle-income countries. 2 We combine the latter two groups of countries into one and have labelled them as ' developing' for brevity in figures and tables below. We use several top income percentile shares as our principal inequality measure, obtained from the World Inequality Database, and present our results using the top 1% and top 10% income shares. We also use the Gini measure for robustness, obtained from the World Income Inequality Database (United Nations University 2019).
In order to observe the nature of the relationship between terrorism and inequality, and to include other explanatory factors of terrorism, we estimate a semi-parametric model. We assume a nonlinear relationship between inequality and terrorism, where inequality enters the equation nonlinearly according to a non-binding function f . It then includes the rest of the determinants of terrorism linearly. We use Robinson's (1988) double residual semi-parametric regression estimator, where the nonparametric estimator for f used is a Gaussian kernelweighted local polynomial fit. 3 Bootstrapped 95% confidence intervals are presented in the figures. The model estimated is: where Terr it is the incidence of terrorism for country i and time t, Z it is a vector of control variables, α i is a country fixed effect and e it is an error term assumed to have 0 mean and constant variance σ 2 e it : As other explanatory variables that explain terrorism, we include GDP per capita, foreign direct investment (FDI), corruption, military expenditure, unemployment, consumption expenditure, rural population, armed forces personnel and the Polity Index. Table 1 presents the parametric estimates of coefficients of the controls that enter the model linearly. We obtain signficant negative coefficients for rural population, which indicates that countries with large rural populations have a lower incidence of terrorism. This highlights the importance of developing and middle income countries in the sample being associated with low levels of terrorism. We also find consumption expenditure to be significant and negatively associated with all definitions of terrorism, again indicating that terrorism is characteristic of low income/consumption expenditure countries (rather than high income countries). The signs and magnitudes of the coefficients for most other variables broadly accord with those obtained in the literature, though they are not significant for many (i.e. positive and significant for FDI once, negative and significant for the Polity score once). Corruption and unemployment are not signifcantly associated with terrorism.
The following Figure 1-4 present the nonparametric component of the models estimated above using total and domestic terrorism. 4 The figures highlight two salient features. First, they highlight that after controlling for explanations of terrorism other than inequality, the positive relationship between inequality and terrorism discussed in the existing empirical literature is very weakly evident for both total and domestic terrorism. For Figure 1-3, which use the top 1% income percentile share inequality measures the relationship is barely positive.
For the sample of developing countries, the relationship observed in Figure 3 using both top 1% and top 10% shares reveals more promising evidence of a weak positive relationship, even if it is still not pronounced.
Second, the non-parametric components in Figure 1-3 crucially expose the nonlinear nature of the relationship between inequality and terrorism. When we use the Gini as the inequality measure (in Figure 4) we obtain a barely positive relationship for both ' all countries' and 'developing countries' samples. The recent literature on the time dependent properties of inequality measures (Atkinson and Brandolini 2010;Bandyopadhyay 2018), however, has highlighted that mean-dependent measures of inequality, such as the Gini (as ' relative' inequality measures), are less reliable representations of inequality over time. Thus, 'absolute' inequality measures, such as the top income percentile shares are more reliable compared with the Gini in Note: Standard errors in parentheses are clustered by country 4 A 'rule-of-thumb' bandwidth estimator is calculated by Stata for specifying the bandwidth for the non-parametric component. All non-parametric plots have been estimated by trimming the inequality measure, with the plot of the estimates within the 15th to 85th percentile of the inequality measure. This is because non-parametric functions can be outlier-driven near the edges of the sample domain. We thank a referee for this suggestion. Results using other terrorism indicators are available with authors.
identifying underlying relationships between inequality and terrorism. Our results in Figure 1-3 using the top income shares indicate that there is weak evidence of a nonlinear positive relationship between the two entities. Thus, the non-parametric components reveal weak evidence of a positive relationship between inequality (measured as top 1% and top 10% income shares), mainly for the developing and middle-income countries, and for domestic terrorism and is far from linear. While this result weakly accords with recent empirical research that the relationship is positive, the key finding is that the relationship is nonlinear and sensitive to the   sample in use. This indicates that the mechanisms discussed in the economics and political science literature may yield different effects for different levels of inequality and deserves further research.

IV. Conclusion
In this paper we have highlighted two new salient empirical features of the relationship between income inequality and terrorism. Using recently recommended measures of inequality, i.e., top percentile income shares, we fail to confirm previous evidence of a positive relationship between inequality and terrorism. It is, at best, weakly observed, in particular for developing and middleincome group countries. We also find that the relationship is nonlinear, suggesting no particular functional form, and thus deserves future research to identify the mechanisms which govern this relationship. This result of nonlinearity accords with evidence obtained in Enders, Hoover, and Sandler (2016).