Economic growth and political extremism

Abstract

We argue that the growth rate, but not the level of aggregate income, affects the support for extreme political parties. In our model, extreme parties offer short-run benefits to part of the population at the expense of a minority. Growth effects on the support for such parties arise when uncertainty exists over whether the same subset of individuals will receive the same benefits in the future. More people are willing to take political risks if economic growth is slow. Based on a panel of 16 European countries, our empirical analysis shows that slower growth rates are associated with a significant increase in right-wing extremism. We find no significant effect of economic growth on the support for extreme left-wing parties.

Appendix

In the main text, the positive relationship between economic growth and the support for the moderate regime has been established for the case when $s_{1}=s_{2}$. If it is the case that $s_{1}\ne s_{2}$, no closed form solution exists for $\hat{y}$. The following analysis addresses that issue.

Table 12 List of extreme right-wing and extreme left-wing parties

Proposition 1

Let $\tau \ge 0$. For any given $p\in \left[ 0,1\right]$the following holds. Consider given values of $s_{1}$and q. If p is sufficiently large and if the critical income value $\hat{y}$satisfies $\hat{y}<\bar{y}_{1}$then $d\hat{y}/dg<0$.

Proof

First note that $s_{1},$p, and q determine $s_{2}=s_{1}q+\left( 1-s_{1}\right) p$. Define

$$\begin{aligned} F\left( \delta ,g,p,q,\hat{y},s_{1}\right) := \hat{y}^{\alpha }+\delta g^{\alpha }\hat{y}^{\alpha } \end{aligned}$$

(14)

$$\begin{aligned}&-\left( \left( 1-\tau \right) \hat{y}+\left( \tau +\frac{s_{1}}{1-s_{1}}\right) \bar{y}\right) ^{\alpha } \end{aligned}$$

(15)

$$\begin{aligned}&-\delta \left( 1-p\right) \end{aligned}$$

(16)

$$\begin{aligned}&\cdot \left( g\left( \left( 1-\tau \right) \hat{y}+\left( \tau +\frac{s_{1}q+\left( 1-s_{1}\right) p}{1-s_{1}q-\left( 1-s_{1}\right) p}\right) \bar{y}\right) \right) ^{\alpha }. \end{aligned}$$

(17)

When $F\left( \delta ,g,p,q,\hat{y},s_{1}\right) =0$, non-stigmatized voters with income $\hat{y}$ are indifferent between the two regimes, i.e., $U^{M}=U^{E}$. We have

$$\begin{aligned} F_{g}= & {} \alpha \delta \hat{y}^{\alpha }g^{\alpha -1} \end{aligned}$$

(18)

$$\begin{aligned}&-\delta \left( 1-p\right) \alpha \left( \left( 1-\tau \right) \hat{y}+\left( \tau +\frac{s_{2}}{1-s_{2}}\right) \bar{y}\right) \end{aligned}$$

(19)

$$\begin{aligned}&\cdot \left( g\left( \left( 1-\tau \right) \hat{y}+\left( \tau +\frac{s_{2}}{1-s_{2}}\right) \bar{y}\right) \right) ^{\alpha -1}, \end{aligned}$$

(20)

and

$$\begin{aligned} F_{\hat{y}}= & {} \alpha \hat{y}^{\alpha -1}+\delta \alpha g^{\alpha }\hat{y}^{\alpha -1} \end{aligned}$$

(21)

$$\begin{aligned}&-\alpha \left( 1-\tau \right) \left( \left( 1-\tau \right) \hat{y}+\left( \tau +\frac{s_{1}}{1-s_{1}}\right) \bar{y}\right) ^{\alpha -1} \end{aligned}$$

(22)

$$\begin{aligned}&-\delta \alpha \left( 1-p\right) g\left( 1-\tau \right) \end{aligned}$$

(23)

$$\begin{aligned}&\cdot \left( g\left( \left( 1-\tau \right) \hat{y}+\left( \tau +\frac{s_{2}}{1-s_{2}}\right) \bar{y}\right) \right) ^{\alpha -1}. \end{aligned}$$

(24)

Now let $p=1$. In that case

$$\begin{aligned} F_{g}=\alpha \delta \hat{y}^{\alpha }g^{\alpha -1}>0, \end{aligned}$$

and

$$\begin{aligned} F_{\hat{y}}=\alpha \hat{y}^{\alpha -1}+\delta \alpha g^{\alpha }\hat{y}^{\alpha -1}-\alpha \left( 1-\tau \right) \left( \left( 1-\tau \right) \hat{y}+\left( \tau +\frac{s_{1}}{1-s_{1}}\right) \bar{y}\right) ^{\alpha -1}. \end{aligned}$$

(25)

Hence,

$$\begin{aligned} F_{\hat{y}}>0\Leftrightarrow \left( 1+\delta g^{\alpha }\right) \hat{y}^{\alpha -1}>\left( 1-\tau \right) \left( \left( 1-\tau \right) \hat{y}+\left( \tau +\frac{s_{1}}{1-s_{1}}\right) \bar{y}\right) ^{\alpha -1}. \end{aligned}$$

(26)

When $\hat{y}<\bar{y}$ we have

$$\begin{aligned} \left( 1-\tau \right) \left( \hat{y}+\frac{s_{1}}{1-s_{1}}\hat{y}\right) ^{\alpha -1}>\left( 1-\tau \right) \left( \left( 1-\tau \right) \hat{y}+\left( \tau +\frac{s_{1}}{1-s_{1}}\right) \bar{y}\right) ^{\alpha -1}. \end{aligned}$$

Hence,

$$\begin{aligned} F_{\hat{y}}> & {} 0\Leftarrow \left( 1+\delta g^{\alpha }\right) \hat{y}^{\alpha -1}>\left( 1-\tau \right) \left( \hat{y}+\frac{s_{1}}{1-s_{1}}\hat{y}\right) ^{\alpha -1} \end{aligned}$$

(27)

$$\begin{aligned}\Leftrightarrow & {} 1+\delta g^{\alpha }>\left( 1-\tau \right) \left( \frac{1}{1-s_{1}}\right) ^{\alpha -1} \end{aligned}$$

(28)

$$\begin{aligned}\Leftrightarrow & {} 1+\delta g^{\alpha }>\left( 1-\tau \right) \left( 1-s_{1}\right) ^{1-\alpha }. \end{aligned}$$

(29)

The foregoing holds obviously. Therefore, using the implicit function theorem we get $d\hat{y}/dg<0$. The proposition follows from the continuity of the functions $F,F_{g}$, and $F_{\hat{y}}$ in all of their arguments. $\square$

Proof of Results 2 and 4.

Result 2 Result 2 follows from

$$\begin{aligned} U^{M}= & {} U^{E}\Leftrightarrow \end{aligned}$$

(30)

$$\begin{aligned} \left( 1+\delta g^{\alpha }\right) \gamma _{i}^{\alpha }= & {} \left( \left( 1-\tau \right) \gamma _{i}+\left( \tau +\frac{s_{1}}{1-s_{1}}\right) \right) ^{\alpha } \end{aligned}$$

(31)

$$\begin{aligned}&+\,\delta \left( 1-p\right) \left( g\left( \left( 1-\tau \right) \gamma _{i}+\left( \tau +\frac{s_{2}}{1-s_{2}}\right) \right) \right) ^{\alpha }. \end{aligned}$$

(32)

Only relative income $\gamma _{i1}$ is an argument in that equation, not absolute income.

Result 4 Economic growth shifts the threshold income $\hat{y}$ to the left. The mass of individuals between the new and the old values of the threshold gives us the additional support for the extreme party. Result 4 follows from the fact that, with a uniform income distribution, more inequality is associated with fewer individuals being located in any given income bracket. $\square$