Formal models of the political resource curse

Abstract

By surveying formal models, I demonstrate that the political resource curse is the misallocation of revenues from natural resources and other windfall gains by political agents. I show that the curse always exists if political agents are rent-seeking, since mechanisms of government accountability, e.g. electoral competition, the presence of political challengers, and even the threat of violent conflict, are inherently imperfect. However, the scope for rent-seeking becomes more limited as the competition over political power that threatens the incumbent government becomes more intense.

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Notes

  1. 1.

    This is not to say that the model is devoid of any political activity. On the contrary, as is subsequently shown, groups from the private sector erode property rights by fighting over rents. What makes the model an economic resource curse model is that such activities are undertaken by private actors who, unlike political agents whose principals are citizens/political constituents, cannot be made accountable by the latter through mechanisms of political turnover, e.g. elections, political coalitions, violent conflict.

  2. 2.

    Differentiating \(c^*\) with respect to \(\Omega \) gives \(\frac{\partial c^*}{\partial \Omega }=\frac{2(k-1)^2(a+1)\Omega -2[aX(k-1)]+aX[1-(k-1)(a+1)]}{aXk}\), which is positive if \(\Omega >\frac{(k-1)[2aX+aX(a+1)]-aX}{2(k-1)^2(a+1)}\).

  3. 3.

    More general forms of the contest function have been studied. See, for instance, Skaperdas (1996) and Hirshleifer (1989). In the political science literature, the contest function is typically used to describe investments in conflict and the relative coercive/military power of groups, whether in the domestic arena (see Sects. 4.2, 4.3) or interstate wars (see, e.g., Kydd 2015 for a summary.)

  4. 4.

    To my knowledge, there are no resource-curse models that incorporate any social costs of bribery.

  5. 5.

    This revolution option is only in Smith, and not included in Bueno de Mesquita et al.

  6. 6.

    Thus, a revolution, if successful, effectively changes institutions to a more democratic one in that the new leader now needs the support of half of the population. Although political institutions can change in this manner, I treat them as stable environments in that the institutional change does not explicitly involve violent conflict.

  7. 7.

    Recall that for L to be deposed, at least one of L’s coalition members has to defect to C. Thus, C has to nominate a coalition that includes a member of L’s, even though C has little affinity for that individual. She can then subsequently drop that individual from her coalition in the next period.

  8. 8.

    The success of revolution depends on the ease with which citizens can organize, which is assumed to increase with the amount of public goods.

  9. 9.

    To simplify, I restrict the analysis to the case where the costs of rebelling and of a failed revolution are too high such that (17) is always true so that the presence of a revolutionary activist poses no binding constraint. Smith also considers the case when the LHS of (17) is negative, and shows that there exists a region \((g_{1},g_{2})\), \(g_{2}>g_{1}\), for which the revolution constraint binds with equality. The incumbent then chooses either \(g_{1}\) or \(g_{2}\), depending on which yields relatively higher discretionary resources.

  10. 10.

    I simplify the exposition by abstracting from choices on taxation and transfers. Robinson et al. explicitly include such choices but show that since politicians value their own income more than others’, they will choose tax rate \(\delta \) that maximizes tax revenue, which they set to \(\delta =0\). By the same reasoning, promises of transfers are not credible, and voters realize this. Thus, both taxes and transfers are zero.

  11. 11.

    In Brollo et al., resources \(\tau \) are revenues that come from the federal government and, hence, are windfall gains from the point of view of the local government.

  12. 12.

    As the authors note, these are satisfied by the Tullock–Skaperdas type of contest function, \(\frac{\xi L^O}{\xi L^O+L^I},\xi \ge 1\), as well as the logistic form \(\frac{\exp [\xi _O L^O]}{\exp [\xi _O L^O]+\exp [\xi _I L^I]}\) in Hirschleifer and the semi-linear form \(\gamma _O+\xi _1[h(L^O)-\xi _2 h(L^I)]\).

  13. 13.

    Besley and Persson actually specify an infinitely repeated version, but where each generation dies at the end of the period after consuming all income and public goods, and a new generation replaces it in the next period. (Incumbency is inherited from the previous generation). However, there are no state variables - at each time period, new values of R and w are realized. To simplify, I thus present the game played by one generation.

  14. 14.

    This is \(g^*=(\tau -\alpha )y-\alpha R_2\) in Abdih et al., as they do not consider \(R_1\).

  15. 15.

    This is \(\frac{r^*}{y}=\alpha \Big (1+\frac{R_2}{y}\Big )\) in Abdih et al.

  16. 16.

    That \(\partial x/\partial \tau <0\) can be seen by getting \(\partial \frac{V_2^H}{V_2^L}/\partial \tau =\frac{\psi R}{(V_2^L)^2}(\alpha ^H-\alpha ^L)<0\).

  17. 17.

    A similar exercise can be done for case 2 by setting \(\tau _{y,t}^*=0\).

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Correspondence to Desiree A. Desierto.

Additional information

I thank Scott Gehlbach, Andrew Kydd, Robert Deacon, and seminar participants at the UP School of Economics for helpful comments.

Appendix

Appendix

Proof of Proposition 3.1

Solving (6) obtains reaction function

$$\begin{aligned} f_i^R(f_{-i})=\sqrt{\frac{k\Omega f_{-i}}{a}}-f_{-i}. \end{aligned}$$
(63)

Since this holds for each group, then

$$\begin{aligned} \sum _{j=1}^kf_j=\sqrt{\frac{k\Omega f_{-i}}{a}}. \end{aligned}$$
(64)

In equilibrium, \(f_i^*=f^*\), in which case \(f^*\) can replace \(f_i\) for all \(i=1,2,\ldots k\) in (64) to obtain each group’s equilibrium level of fighting,

$$\begin{aligned} f^*=\frac{(k-1)\Omega }{ka}, \end{aligned}$$
(65)

which can then be substituted into (5) to get the extent of property rights in equilibrium

$$\begin{aligned} p^*=1-(k-1)\frac{\Omega }{aX}, \end{aligned}$$
(66)

and which, with (2), (3) and (4), gives \(c^*=[1-\frac{(k-1)\Omega }{aX}][\frac{aX-(k-1)\Omega }{k}]+\frac{1}{k}[\frac{(k-1)^2\Omega ^2}{X}+\Omega (1-(k-1)(a+1))+aX]\).

Differentiating (65) and (66) with respect to windfall gains \(\Omega \) obtains the following comparative statics: \(\frac{\partial f^*}{\partial \Omega }=\frac{k-1}{ka}>0\); \(\frac{\partial p^*}{\partial \Omega }=-\frac{k-1}{aX}<0\). Note also how a larger value of parameter a implies a smaller effect of \(\Omega \) on \(f^*\) and \(p^*\). \(\square \)

Proof of Proposition 4.1

By (9) and (10), the optimal level of public-good substitutes that households provide themselves is

$$\begin{aligned} z^*=(1-\lambda )[(1-\tau )y+R_2]-\lambda g, \end{aligned}$$
(67)

which is clearly increasing in remittances \(R_2\). Plugging (67) into (10) gives \(c^*\) which, with \(z^*\), obtains \(U_h^*\). The government thus incorporates the latter into its problem ((7) and (8)), which yields equilibrium public good provisionFootnote 14

$$\begin{aligned} g^*=(\tau -\alpha )y+(1-\alpha )R_1-\alpha R_2. \end{aligned}$$
(68)

Substituting into (8), rearranging, and dividing by y give the share of income that the incumbent appropriates as rents:Footnote 15

$$\begin{aligned} \frac{r^*}{y}=\alpha \Big (1+\frac{R_1+R_2}{y}\Big ), \end{aligned}$$
(69)

which is increasing in the share of unearned income to total income. (By (8), larger rents imply lower public good provision.) Specifically, \(\frac{\partial \frac{r^*}{y}}{\partial \frac{R_1+R_2}{y}}=\alpha >0\). Note, then, that the rate of increase is lower when \(1-\alpha \) is high (since \(\alpha \) is small). \(\square \)

Proof of Proposition 4.2

I derive the comparative statics of g and r with respect to unearned income R by applying Cramer’s rule to (18), (19), and (14):

$$\begin{aligned} \frac{\partial g}{\partial R}= & {} -\frac{\det \left( \begin{array}{ccc} 0 &{} 0&{}v_g\\ 0&{}\lambda u_{rr}&{}u_r\\ -\frac{1}{W}-\frac{\partial g_C}{\partial R} &{} u_r &{} 0 \end{array} \right) }{\det \left( \begin{array}{ccc} \lambda v_{gg} &{} 0&{}v_g\\ 0&{}\lambda u_{rr}&{}u_r\\ v_g &{} u_r &{} 0 \end{array}\right) } \end{aligned}$$
(70)
$$\begin{aligned} \frac{\partial r}{\partial R}= & {} -\frac{\det \left( \begin{array}{ccc} \lambda v_{gg} &{} 0&{}v_g\\ 0&{}0 &{}u_r\\ v_g &{} -\frac{1}{W}-\frac{\partial g_C}{\partial R} &{} 0 \end{array} \right) }{\det \left( \begin{array}{ccc} \lambda v_{gg} &{} 0&{}v_g\\ 0&{}\lambda u_{rr}&{}u_r\\ v_g &{} u_r &{} 0 \end{array}\right) } \end{aligned}$$
(71)

where recall that \(u_{rr},v_{gg}<0\). Evaluating and simplifying gives:

$$\begin{aligned} \frac{\partial g}{\partial R}= & {} \frac{-v_g\left[ -\lambda u_{rr}\left( -\frac{1}{W}-\frac{\partial g_C}{\partial R}\right) \right] }{-\lambda v_{gg}u_r^2-\lambda v_g^2 u_{rr}} \end{aligned}$$
(72)
$$\begin{aligned} \frac{\partial r}{\partial R}= & {} \frac{u_{rr}\lambda v_{gg}\left( -\frac{1}{W}-\frac{\partial g_C}{\partial R}\right) }{-\lambda v_{gg}u_r^2-\lambda v_g^2 u_{rr}} \end{aligned}$$
(73)

Note that (13) implies that R increases \(g_C\), i.e. \(\frac{\partial g_C}{\partial R}>0\). It follows then that \(\frac{\partial g}{\partial R}<0\), while \(\frac{\partial r}{\partial R}>0\). From (72) and (73) the effects are smaller in absolute value the larger W is. The result is thus similar to Ahmed and Abdih et al. \(\square \)

Proof of Proposition 4.3

Robinson et al. derive the effect of price booms, i.e. changes in \(p_1\) and \(p_2\), on resource extraction, public sector employment, and total income. To be analogous to Ahmed, Abdih et al., BDM and Smith, I focus on the resource curse as it applies to public sector employment \(G_1\). Since the public sector is inefficient, employment therein is simply a particular form of patronage that politicians distribute to its supporters. Robinson et al. write (29) and (30) in differential form:

$$\begin{aligned} \phi _1de+\phi _2dG_1= & {} \phi _3dp_1+\phi _4dp_2 \end{aligned}$$
(74)
$$\begin{aligned} \psi _1de+\psi _2dG_1= & {} \psi _3dp_1+\psi _4dp_2, \end{aligned}$$
(75)

where \(\phi _1=\Pi p_2R_{ee}<0\), \(\phi _2=\Pi _{G_1}p_2R_e<0\), \(\phi _4=\Pi R_e<0\), \(\psi _1=p_2\Pi _{G_1}R_e<0\), \(\psi _2=-2[H-(1-\alpha )F]\Pi _{G_1}<0\), \(\psi _3=0\), and \(\psi _4=-R\Pi _{G_1}<0\), and show that: (i) when \(dp_1/p_1=dp_2/p_2=dp/p\), then \(\frac{dG_1}{dp/p}=-\frac{\Pi \Pi _{G_1}RR_{ee}}{D}>0\), (ii) when \(dp_1>0,dp_2\), then \(\frac{dG_1}{dp_1}=\frac{\Pi _{G_1}R_e}{D}<0\), and (iii) when \(dp_1=0,dp_2>0\), then \(\frac{dG_1}{dp_2}=\frac{\Pi \Pi _{G_1}[R_e^2-RR_{ee}]}{D}>0\), where \(D\equiv -2[H-(1-\alpha )F]\Pi \Pi _{G_1}R_{ee}-p_2\Pi _{G_1}^2R_e^2>0\).

To show the extent to which the political (electoral) competition mitigates the curse of patronage, I differentiate (i) and (iii) with respect to \(\Pi \). Since the latter is the incumbent’s probability of reelection, a high value of \(\Pi \) captures relatively weak competition. In turn, note from (25) that this is more likely the higher the cost F of firing a public employee and the lower the productivity H in the private sector. In such a case the efficiency loss (from allocating employment to the public rather than private sector) is small, which eases the electoral pressure on the incumbent, enabling her to favor her own group more easily.

Differentiating \(\frac{dG_1}{dp/p}\) with respect to \(\Pi \) gives \(\frac{-D\Pi _{G_1}RR_{ee}-(-\Pi \Pi _{G_1}RR_{ee})[-2(H-(1-\alpha )F)\Pi _{G_1}R_{ee}]}{D^2},\) which is positive (such that lowering \(\pi \), i.e. strengthening the competition, decreases the effect), while differentiating \(\frac{dG_1}{dp_2}\) with respect to \(\Pi \) gives \(\frac{D\Pi _{G_1}(R_e^2-RR_{ee})-\Pi \Pi _{G_1}(R_e^2-RR_{ee})[-2(H-(1-\alpha )F)\Pi _{G_1}R_{ee}]}{D^2}\), which is negative. \(\square \)

Proof of Proposition 4.4

Solving for \(n^J\), \(J=H,L\), gives the equilibrium share \(\pi =\frac{n^L}{n^H+n^L}\) of L types in the pool of opponents:

$$\begin{aligned} \begin{aligned} \pi&=\frac{1}{1+x},\\ x&\equiv \frac{V_2^Hy^L\frac{1}{2}+\xi \sigma }{V_2^Ly^H\frac{1}{2}-\xi \sigma }=\frac{(\alpha ^H\psi \tau +R) y^L\frac{1}{2}+\xi \sigma }{(\alpha ^L\psi \tau +R)y^H\frac{1}{2}-\xi \sigma }\gtrless 1. \end{aligned} \end{aligned}$$
(76)

Lastly, plugging \(\pi \) into \(\hat{\sigma }\equiv \sigma (1-2\pi )\) in (35) gives the equilibrium rents that the incumbent extracts from revenues

$$\begin{aligned} r_1^J=\tau -\xi \Big [1-\sigma \Big (\frac{1-x}{1+x}\Big )\Big ](\psi \tau +R/\alpha ^J). \end{aligned}$$
(77)

Taking the derivative of (77) and (76) with respect to \(\tau \) shows that a political resource curse manifests in two ways: higher rents (and less public goods) and the erosion of the quality of the candidate pool. That is, \(\frac{\partial r_1^J}{\partial \tau }=1+\xi \alpha (\frac{1-x}{1+x})\psi >0\) and \(\frac{\partial \pi }{\partial \tau }=\frac{-\partial x/\partial \tau }{(1+x)^2}>0\).Footnote 16 Furthermore, note that \(\frac{\partial r_1^J}{\partial \tau }=1+\xi \alpha \pi (1-x)\psi \) itself is increasing in \(\pi \) if \(x<1\). In this case, the curse of lower public good provision is exacerbated as candidate-quality is eroded. \(\square \)

Proof of Proposition 4.5

Bulte and Damania formally show that if there is no challenger (such that constraint (40) does not bind), an increase in p unambiguously decreases \(B^M\) and increases \(B^R\). (Intuitively, an increase in p enables firms in the resource sector to offer higher bribes, which induces the incumbent to move public-good spending away from the more productive manufacturing sector and towards the resource sector.) That is, with no political challengers, \(\frac{\partial B^M}{\partial p}<0,\frac{\partial B^R}{\partial p}>0\). This generates a drop in welfare, i.e. \(\frac{dW}{dp}<0\). To see this, note that when profits equalise in equilibrium, welfare \(W=N^M\pi ^M+N^R\pi ^R+wL\) reduces to \(N\pi +wL\), and hence, \(\frac{dW}{dp}=N\frac{d\pi }{dp}\). With \(\frac{\partial B^M}{\partial p}<0,\frac{\partial B^R}{\partial p}>0\), profits in the manufacturing sector decline by more than any increase in resource-sector profits (because of the sector-wide spillovers in manufacturing). Thus, in equilibrium, it must be that \(\frac{d\pi }{dp}<0\), which means that \(\frac{dW}{dp}<0\).

Now if there is a challenger such that (40) binds, the incumbent is also induced to provide more \(B^M\). (From (40), the increase in \(B^M\) is likely to be larger the smaller the cost v incurred by challengers, that is, the stronger the political competition.) Thus, with \(\frac{\partial B^R}{\partial p}>0\) and \(\frac{\partial B^M}{\partial p}>0\), profits rise in both sectors, which means that in equilibrium \(\frac{d\pi }{dp}>0\), implying that \(\frac{dW}{dp}>0\).

Thus, faced with threats from challengers, an increase in the value of resources may generate a blessing in the form of higher public goods provision and aggregate welfare. However, the authors do not draw attention to the implication that the increase in welfare may come at the expense of greater corruption. Increasing provision of \(B^R\) and \(B^M\) increases profits in both sectors, which means that all firms can afford to pay more bribes. The increase is higher for the manufacturing sector which internalises the positive effect of \(B^M\) on other firms in that sector.

Specifically, suppose constraint (40) binds such that \(\frac{\partial B^M}{\partial p}>0\) (while \(\frac{\partial B^R}{\partial p}>0\) is always true). Then if public goods sufficiently raise productivity such that (i) \(p\frac{\partial Q^R}{\partial B^R}>w\frac{\partial l^R}{\partial B^R}+\frac{\partial s^R}{\partial B^R}\), then \(\frac{\partial s^R}{\partial p}\). Similarly, if (ii) \(\frac{\partial Q^M}{\partial B^M}>w\frac{\partial l^M}{\partial B^M}+\frac{\partial s^M}{\partial B^M}\), then \(\frac{\partial s^M}{\partial p}\). (To see this, one can differentiate profit (37) with respect to \(s^R\) and profit (38) with respect to \(s^M\) and note that profits rise with \(s^R\), \(s^M\), inducing firms to increase the latter, for as long as (i) and (ii) hold.) When (i) and (ii) hold, aggregate bribes unambiguously increase. \(\square \)

Proof of Proposition 4.6

By symmetry, both candidates choose the same policy platform (and win with probability \(\frac{1}{2}\)):

$$\begin{aligned} r^I=\min \Big (R,\frac{w+R}{2\psi +1}\Big ). \end{aligned}$$
(78)

Plugging \(r^I\) back into \(U_D^I\) and using \(p^I=\frac{1}{2}\), the per-period expected utility of running in the election is

$$\begin{aligned} U_D^I=\min \Big (\frac{1}{2}R,\frac{w+R}{2(2\psi +1)}\Big ), \end{aligned}$$
(79)

and the expected value of losing in the election is

$$\begin{aligned} V_D^I=\frac{\beta }{1-\beta }\Big (\frac{w+R}{2(2\psi +1)}\Big ). \end{aligned}$$
(80)

Thus, the necessary condition for self-enforcing democracy, \(V_D^I>V_C^I\), is \(\frac{\beta }{1-\beta }(\frac{w+R}{2(2\psi +1)})>\frac{\frac{1}{4}R-wF}{1-\beta }\), or, simplifying:

$$\begin{aligned} \beta +F(4\psi +2)>\left( \psi +\frac{1}{2}-\beta \right) \frac{R}{w}. \end{aligned}$$
(81)

Restrict attention to the case when \(\psi +\frac{1}{2}>\beta \). Then condition (81) is less likely to be satisfied when R is large and F and w are low. \(\square \)

Proof of Proposition 4.7

Define \(Z=\frac{R-G}{w}\). Then equilibrium fighting efforts are

$$\begin{aligned} L^{I*}= & {} \arg \max _{L^I} 2w\{[1-\theta -\gamma (L^O,L^I;\xi )(1-2\theta )][Z-L^I]\} \end{aligned}$$
(82)
$$\begin{aligned} L^{O*}= & {} \arg \max _{L^O} w\{2[\theta +\gamma (L^O,L^I;\xi )(1-2\theta )][Z-L^I]-L^O\}, \end{aligned}$$
(83)

which are both increasing in R (for \(\theta <\frac{1}{2}\)).

Besley and Persson derive thresholds \(Z^I\) and \(Z^O\), \(Z^I<Z^O\), such that:

  1. (i)

    for \(Z\le Z^I\), \(L^{O*}=L^{I*}=0\).

  2. (ii)

    for \(Z\in (Z^I,Z^O)\), \(L^{I*}>L^{O*}=0\).

  3. (iii)

    for \(Z\ge Z^O\), \(L^{I*},L^{O*}>0\).

Case (i) captures a peace equilibrium as neither group fights; case (ii) captures repression in that only the incumbent engages in violence; and case (iii) captures civil conflict since both groups fight. (That it requires a smaller value of Z for the incumbent to start engaging in violence intuitively follows from the assumption that the incumbent funds its fighting efforts out of government revenues and thus has a cost advantage over the opposition.) The result holds since Z is increasing in R and decreasing in w. \(\square \)

Proof of Proposition 4.8

As in Tsui, one can then plug the constraints (61) and (62) into (59). For case 1, one can then impose \(\tau _{R,t}^*=1\) into (60) to get an expression for \(\tau _{y,t}\) which is also plugged into (59).Footnote 17 The optimisation problem then becomes

$$\begin{aligned} \max _{g_t,b_t,r_t}\frac{(b+t_w)[\gamma r_t-\beta (b_t)][y(g_t)+\frac{R}{\delta }-\frac{p}{\delta }g_t-\frac{r_t}{\delta }]}{V_{t+1}[(1-\tau _{y,t+1})y(g_{t+1})+(1-\tau _{R,t+1})R]}, \end{aligned}$$
(84)

which implies that \(g_t^*=\arg \max _{g_t}y(g_t)-\frac{p}{\delta }g_t\).

The respective FOCs for \(r_t^*\) and \(b_t^*\) are

$$\begin{aligned}&\gamma \left[ y(g_t^*)+\frac{R}{\delta }-\frac{p}{\delta }g_t^* -\frac{r_t^*}{\delta }\right] -\frac{\gamma r_t^*-\beta (b_t^*)}{\delta }=0 \end{aligned}$$
(85)
$$\begin{aligned}&[\gamma r_t^*-\beta (b_t^*)]-\beta _b(b_t^*)(b_t^*+w)=0. \end{aligned}$$
(86)

Differentiating the latter gives

$$\begin{aligned} \frac{\partial b_t^*}{\partial R}=\frac{\gamma }{3\beta _b+2\beta _bb(b_t^*+w)}>0. \end{aligned}$$
(87)

Furthermore, in a stationary equilibrium, \(V_t=V_{t+1}\), which means \(h_t=1\). Imposing these and using (86) in the objective function in (59) gives the value of governing in equilibrium

$$\begin{aligned} V^*=\sqrt{\beta _b}(b^*+w), \end{aligned}$$
(88)

which gives the equilibrium number of challengers

$$\begin{aligned} c^*=\frac{V}{b^*+w}-\frac{i}{h}=\sqrt{\beta _b}-i, \end{aligned}$$
(89)

Let \(\beta _{bb}>0\) such that \(\beta _b\) is a function of b. Since b increases with R, then \(\beta _b\) and, hence, \(c^*\), are increasing in R. Thus, \(\frac{\partial b^*}{\partial R},\frac{\partial c^*}{\partial R}>0\). (Since \(\beta \) increases with b, then an increase in b is readily interpreted as an increase in repression/counterinsurgency.) Note by (87) that a higher wage rate dampens the effect of R on b and, hence, also the effect on \(c^*\). \(\square \)

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Desierto, D.A. Formal models of the political resource curse. Econ Gov 19, 225–259 (2018). https://doi.org/10.1007/s10101-018-0207-2

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Keywords

  • Resource curse
  • Political rent-seeking
  • Misappropriation of resource revenues

JEL Classification

  • D72
  • D73
  • D74
  • H41
  • O5