Ruling elites’ rotation and asset ownership: implications for property rights

Abstract

We provide a theory and empirical evidence indicating that the rotation of ruling elites in conjunction with elites’ asset ownership could improve property rights protection in non-democracies. The mechanism that upholds property rights is based on elites’ concern about the security of their own asset ownership in the event they lose power. Such incentives provide a solution to the credible commitment problem in maintaining secure property rights when institutional restrictions on expropriation are weak or absent.

Appendix A Proofs of Propositions

Proof of Proposition 1

Assume that group i holds power at time t, and consider for a small $\epsilon > 0$ and ${b^0} \in [0,1]$ the following “spike variation” $\widetilde{b}_i (s)$ of the strategy $b_i^{*}$: (i) $\widetilde{b}_i (s) = b^0$ for $s \in [t,t + \epsilon ]$, unless group i loses power before $s = t + \epsilon$, in which case ${b^0}$ is played until the first power shift, and both groups play their initial strategies afterwards; and (ii) group i reverts to its original strategy $b_i^{*}$ for $s > t + \epsilon$. The strategy $b_j^{*}$ of group j remains unchanged. One can verify that the change $\Delta {U_i}$ of group i’s expected utility from time t onwards allows the following representation:

$$\begin{aligned} \Delta U_i &= \bigg \{ \Big [ \pi U(b^{0}) + (1 - \pi )U(1 - (1 - b^{0})(1 - w_i)) \Big ] \\ &\quad - \Big [ \pi U(b_i^{*} w_i) + (1 - \pi )U(1 - (1 - b_i^{*})(1 - w_i)) \Big ] \bigg \} \\&\quad \times \exp {(-2 \lambda \epsilon )} \int _{\tau }^{\tau + \epsilon } \exp {(-\delta t)} \,d t + D(b^{0}, \epsilon ), \end{aligned}$$

where $\lim _{\epsilon \rightarrow 0} \dfrac{D(b^{0},\epsilon )}{\epsilon } = 0$ uniformly by ${b^{0}}$. (The expression $\exp {(-2 \lambda \epsilon )}$ is the probability that the incumbent group at time t will stay in power at least until $t + \epsilon$, and that the incumbent group at time $t + \tau$ will stay in power at least until $t + \tau + \epsilon$; given the nature of the Poisson process, these are independent events).

One has $\Delta U_i \le 0$, and therefore

$$\begin{aligned} 0 \ge \lim _{\epsilon \rightarrow 0} \dfrac{\Delta U_i}{\epsilon } &= \bigg \{ \Big [ \pi U(b^{0} w_i) + (1 - \pi )U(1 - (1 - b^{0})(1 - w_i)) \Big ] \\&\quad - \Big [ \pi U(b_i^{*} w_i) + (1 - \pi )U(1 - (1 - b_i^{*})(1 - w_i)) \Big ] \bigg \} \exp {(- \delta \tau )}, \end{aligned}$$

for any ${b^{0}}$, which entails Proposition 1. $\square$

Proof of Proposition 2

Since ${b^{*}} w + 1 - {b^{*}} \ge {b^{*}} w$, the left-hand side of the first-order condition (2) is less than or equal to one. On the other hand inequality (3) holds if and only if the right-hand side of (2) is greater than or equal to one, and therefore whenever $\pi + w \ge 1$, the corner solution ${b^{*}} = 1$ obtains. $\square$

Proof of Proposition 3

One can easily check that the left-hand side of the Eq. (2) is a monotonically increasing function of $b \in [0,1]$ and also takes values from $0$ to $1$. According to (2), it means that indeed $b$ increases from $0$ to $1$ in the range $\pi \in [0,1 - w]$. For $\pi > 1 - w$, the corner solution ${b^{*}} = 1$ obtains. $\square$

Proof of Proposition 4

When $w = 0,\; b^{*} = 0$—with no production assets elites are oblivious to property rights after losing power, and hence prefer full expropriation. When $w > 1 - \pi$, as stated earlier, property rights are fully secured (${b^{*}} = 1$). In the $(0,1 - \pi )$ range the problem (1) has an interim solutions, and differentiating the first-order condition (2) by $w$ yields

$$\dfrac{\partial {b^{*}}}{\partial w} \Big [ {w^2} R ({b^{*}} w) + w(1 - w)R({b^{*}} w + 1 - {b^{*}}) \Big ] = \dfrac{1}{1 - w} + {b^{*}} w \Big [ R({b^{*}} w + 1 - {b^{*}}) - R({b^{*}} w) \Big ].$$

Since ${b^{*}} w + 1 - {b^{*}} \ge {b^{*}} w$, the required result immediately follows from condition (i). Alternately observe that ${b^{*}} w R ({b^{*}} w) = r ({b^{*}} w) \le 1 < 1/(1 - w)$, and the same result follows from (ii). $\square$