Youth bulges, insurrections and labor-market restrictions

Abstract

This paper analyzes the link between large youth cohorts and violent conflicts when labor-market restrictions are present. Such restrictions are expected to limit the youth cohort’s access to income opportunities in the formal economy, and thus lower the youth-specific opportunity cost of insurrection activities. We develop a theoretical model of insurrection markets and integrate the youth cohort’s relative size. In equilibrium, a binding labor-market constraint interacts with the youth bulge in determining the level of insurrection activities within the society. We test the implications of our model on a sample of 135 non-OECD countries in the post-Cold War period and find the effect of the youth cohort’s relative size on conflict onsets to be moderated by changes in the labor-market conditions as measured by unemployment rates. Generally, the results provide evidence that the underlying institutional setting shapes the conflict potential inherent in a given demographic structure.

Appendix

1.1 The revolutionary elite’s maximization problem

Considering Eq. (4) in combination with Eq. (2), the maximization problem of the revolutionary elite is:

$$\begin{aligned} {\mathfrak {I}}=t^{R} \beta I- \rho \ w_{I}I+\lambda (\tau ^{R}Y-t^{R}). \end{aligned}$$

The Kuhn–Tucker conditions are then:

$$\begin{aligned} {\mathfrak {I}}_{I}= &\;t^{R}\beta - \rho \ w_{I}\leqslant 0; \end{aligned}$$

(A.1)

$$\begin{aligned} {\mathfrak {I}}_{t^{R}}= &\;\beta I-\lambda \leqslant 0; \end{aligned}$$

(A.2)

$$\begin{aligned} {\mathfrak {I}}_{\lambda }= &\;\tau ^{R}Y-t^{R}\geqslant 0; \end{aligned}$$

(A.3)

$$\begin{aligned} I,t^{R},\lambda\geqslant & 0; \end{aligned}$$

(A.4)

$$\begin{aligned} I{\mathfrak {I}}_{I}= &\;I(t^{R}\beta - \rho \ w_{I})=0; \end{aligned}$$

(A.5)

$$\begin{aligned} t^{R}{\mathfrak {I}}_{t^{R}}= &\;t^{R}(\beta I-\lambda )=0; \end{aligned}$$

(A.6)

$$\begin{aligned} \lambda {\mathfrak {I}}_{\lambda }= &\;\lambda (\tau ^{R}Y-t^{R})=0. \end{aligned}$$

(A.7)

1.2 The citizens’ maximization problem

The citizens maximize (6) subject to their time restriction $l+i\le 1$ and subject to the labor-market restriction $l\le \varepsilon$. The Lagrangian is as follows:

$$\begin{aligned} {\mathfrak {I}}=(1-t^{G}A^{G})w_{L}l+\rho ((1+w_{I})^{r\mu }-1)i+\lambda _{1}(1-l-i)+\lambda _{2}(\varepsilon -l). \end{aligned}$$

(A.8)

The Kuhn–Tucker conditions of the citizens’ maximization problem are:

$$\begin{aligned} {\mathfrak {I}}_{l}= &\;(1-t^{G}A^{G})w_{L} - \lambda _{1} - \lambda _{2}\leqslant 0; \end{aligned}$$

(A.9)

$$\begin{aligned} {\mathfrak {I}}_{i}= &\;\rho ((1+w_{I})^{r\mu }-1)-\lambda _{1}\leqslant 0; \end{aligned}$$

(A.10)

$$\begin{aligned} {\mathfrak {I}}_{\lambda _{1}}= &\;1-l-i\geqslant 0; \end{aligned}$$

(A.11)

$$\begin{aligned} {\mathfrak {I}}_{\lambda _{2}}= &\;\varepsilon - l\geqslant 0; \end{aligned}$$

(A.12)

$$\begin{aligned} l> & 0;\quad i,\lambda _{1},\lambda _{2}\geqslant 0; \end{aligned}$$

(A.13)

$$\begin{aligned} l{\mathfrak {I}}_{l}= &\;l((1-t^{G}A^{G})w_{L} - \lambda _{1} - \lambda _{2})=0; \end{aligned}$$

(A.14)

$$\begin{aligned} i{\mathfrak {I}}_{i}= &\;i (\rho ((1+w_{I})^{r\mu }-1)-\lambda _{1})=0; \end{aligned}$$

(A.15)

$$\begin{aligned} \lambda _{1}{\mathfrak {I}}_{\lambda _{1}}= &\;\lambda _{1}(1-l-i)=0; \end{aligned}$$

(A.16)

$$\begin{aligned} \lambda _{2}{\mathfrak {I}}_{\lambda _{2}}= &\;\lambda _{2}(\varepsilon - l)=0;\,\,\, hence: \,\,\lambda _{2}{\mathfrak {I}}_{\lambda _{2}}=\lambda _{2}(\varepsilon N-N)=0. \end{aligned}$$

(A.17)

If both restrictions in (A.8) were non-binding, so that $\lambda _{1}=\lambda _{2}=0$, then this would imply by Eq. (A.14) that either $w_{L}=0$ or $l=0$ since both are non-negative. Note, however, that $l=0$ is ruled out by the Inada conditions for the production function, while $w_{L}=0$ is ruled out by both the Inada conditions and by $\delta r^{-1}>0$ in combination with the firm’s first-order maximization condition (7); this is at least true as long as the effective tax rate is not fully confiscatory, i.e., as long as $t^{G}A^{G}<1$. A non-binding time restriction of the citizens (i.e., $l+i<1$ and hence $\lambda _{1}=0$) is nevertheless possible, but that presupposes the labor-market imperfection to induce a binding constraint, so that $\lambda _{2}>0$. Both restrictions being non-binding, however, is not possible as long as $t^{G}A^{G}<1$.

Given $\lambda _{2}>0$, however, a non-binding time constraint of the citizens remains possible, but this would, by Eq. (A.15), be associated with either $i=0$, or with $\rho ((1+w_{I})^{r \mu }-1)=0$, or both. The implication is this: Should $\lambda _{2}>0$, so that the citizens are rationed in their labor-market supply, and should the marginal utility from insurrection activities $\rho ((1+w_{I})^{r \mu }-1)$ be zero, then the citizens are unable to fully employ their disposable time for income generation: On the market for insurrection, they have no incentive for being active because of $\rho ((1+w_{I})^{r \mu }-1)=0$; and on the labor market, they would want to be active to the full extent of their time devoted for income-generating activities, but they cannot do so because of the positive chance $\varepsilon >0$ of being unemployed.

Finally, combinations of $\lambda _{1}>0$ with $\lambda _{2}=0$ or with $\lambda _{2}>0$ are also possible. In the former case, the labor market clears, whereas in the latter case, all unemployed labor-market time will be supplied to the revolutionary elite.

1.3 Analyses of cases A and B

Case A: $\lambda _{1}=0;\;\lambda _{2}>0.$

From Eq. (A.14) and from $\lambda _{1}=0$, we have $l((1-t^{G} A^{G})w_{L}-\lambda _{2})=0$. Since the Inada conditions of the production function $F(\delta r^{-1}L,A)$ rule out $L=lN=0$, we have $(1-t^{G} A^{G})w_{L}=\lambda _{2}>0$. The non-negativity of $\rho ((1+w_{I})^{r\mu }-1)$ in combination with Eq. (A.10) implies $\rho ((1+w_{I})^{r\mu }-1)=0$ because of $\lambda _{1}=0$. Substituting the compensation rates $w_{L}$ and $w_{I}$ by the marginal productivities from (7) and (8), and considering the labor-market restriction in (A.17) as well as the assumption of case A that $\lambda _{2}>0$, the equilibrium in case A is:

$$\begin{aligned}&(1-t^{G} A^{G})\delta r^{-1}F'(L)-\lambda _{2}=\rho ((1+t^{R}\beta \rho ^{-1})^{r\mu }-1)=0; \nonumber \\&\quad {\text{and}} \,\, (1-t^{G} A^{G})\delta r^{-1}F'(L)=\lambda _{2}>0. \end{aligned}$$

(A.18)

Note that, because of $\lambda _{2}>0$, employment L in equilibrium is lower than N and the wage rate in equilibrium $w_{L}=\delta r^{-1}F'$ is higher than its market-clearing value. We define the latter as $w_{L}^{e}=w_{L}(L=N)$.

Case B: $\lambda _{1} >0; \;\lambda _{2} \geqslant 0.$

Case B is characterized by:

$$\begin{aligned} (1-t^{G}A^{G})\delta r^{-1}F'(L)-\lambda _{2}=\rho ((1+t^{R}\beta \rho ^{-1})^{r\mu }-1) \end{aligned}$$

(A.19)

which, according to (A.15), is associated with $i\ge 0$.

Fig. 5

Unemployment rates against youth bulges in MENA countries. Note Scatter plot for 135 non-OECD countries. MENA countries are labeled by triangle markers and their country names, while all other countries are indicated by circular markers. The y-axis plots the unemployment rate in the total labor force, averaged over 1992–2012. The x-axis plots the relative youth cohort size [measured as the ratio of the male youth cohort (aged 15–24 years) relative to the economically active population (ages 15–69)], averaged over 1992–2012. The vertical and horizontal lines indicate the median values of the x- and y-axis variables