On revolt and endogenous economic policy in autocratic regimes

Abstract

Numerous empirical studies have investigated the direction of causality between democracy and economic growth (as well as the level of income per capita), but this empirical work has been paralleled by relatively few theoretical models that endogenize the institutional structure of the regime. Moreover, the different types of autocratic regimes have received relatively little attention. This paper develops a game-theoretic model of endogenous economic policy in autocratic regimes facing a revolt or an insurgency. In this model, there are three players: the regime, the rebels, and the masses. There are three stages in the game. In the first stage, the regime determines the level of infrastructure and the tax rate. In the second stage, the masses allocate their time between production and helping the rebels. In the third stage, the regime and the rebels simultaneously choose their fighting effort levels in a contest, in which the probability of survival of the regime is determined. It is found that autocratic regimes facing a revolt endogenously sort themselves into “tinpot” regimes that maximize their consumption at the cost of their survival, and (weak and strong) “totalitarian” regimes that maximize their probability of survival at the expense of their consumption. Empirical implications of the model are derived, and the relevance of the model to public policy is discussed.

Appendix

Proof of Proposition 1

First, note that the second order condition is always satisfied for the opposition at the point where the first order conditions (10) and (12) hold. This can be seen by differentiating the left hand side of (12) w.r.t. e _o , noting that $\beta e_{r}^{\ast }- he_{o}^{\ast }=x$, to obtain:

$$\frac{\partial^{2}U_{o}}{\partial e_{o}^{2}}=-\frac{h^{2}\exp (x)(Y-e_{o})^{2}+[1+\exp (x)]^{2}}{(Y-e_{o})^{2}[1+\exp (x)]^{2}}<0. $$

The second order condition for the regime, in contrast, holds only when x>0. To see this, differentiate the left hand side of (10) w.r.t. e _r to obtain

$$\frac{\partial^{2}\ln U_{r}}{\partial e_{r}^{2}}=-\frac{\beta^{2}\exp (x)(z-e_{r})^{2}-[1+\exp (x)]^{2}}{\{[1+\exp (x)](z-e_{r})\}^{2}}. $$

While the denominator of this expression clearly is positive, the numerator is positive (and thus the entire expression will be negative) at the point where the first-order condition (10) holds, if and only if

$$\exp (x)>1, $$

since (11) implies that

$$\beta^{2}(z-e_{r})^{2}=\bigl[1+\exp (\beta e_{r}-he_{o})\bigr]^{2}=\bigl[1+\exp (x) \bigr]^{2}. $$

Consequently, the second order condition for the regime holds if and only if x>0. □

Proof of Proposition 2

If ∂x/∂g<0, the regime can either be a tinpot or a weak totalitarian. The regime will be a weak totalitarian if $\hat{x}>0$. Using the definition of x, together with (37) and (38), we get

By inspection of this equation, we find that

and (provided that $\overline{\tau }>0$, as assumed in the text)

as claimed. □

Proof of Proposition 3

If ∂x/∂g>0, the regime will be a totalitarian. We wish to show that, before the regime has invested in infrastructure, i.e., when g=0, ∂x/∂g is more likely to be positive, ceteris paribus, when α is relatively large and r is relatively small. The regime will not invest in infrastructure unless ∂x/∂g>0. If this condition holds, it will invest in infrastructure up to the point at which h ^∗=0, so that we need only check the effects of α and r on ∂z/∂g. From (27), it is clear that

$$ \frac{\partial }{\partial \alpha }\frac{\partial z}{\partial g}>0 $$

(A.1)

and

$$ \frac{\partial }{\partial r}\frac{\partial z}{\partial g}<0. $$

(A.2)

However, we want to show that these effects hold before the regime has invested to the point at which h ^∗=0.

Recall that x≡βz−hY. Moreover, from (20), we have²⁰

$$ \frac{\partial }{\partial \alpha }\frac{\partial h^{\ast }}{\partial g}=-\frac{\alpha^{\frac{\phi }{1-\phi }} \bigl[ \frac{\phi (1-\tau )}{(1-\beta \theta )} \bigr]^{\frac{1}{1-\phi }}}{1-\phi }<0, $$

(A.3)

while

$$ \frac{\partial }{\partial r}\frac{\partial h^{\ast }}{\partial g}=0. $$

(A.4)

Combining (A.1), (A.2), (A.3), (A.4) with the definition of x, we find that

$$\frac{\partial }{\partial \alpha }\frac{\partial x}{\partial g}>0 $$

and

$$\frac{\partial }{\partial r}\frac{\partial x}{\partial g}<0, $$

so that it is more likely that ∂x/∂g>0 when α is relatively large and r is relatively small, as claimed. □