Authoritarianism and Democracy in Rentier States. Thad Dunning Department of Political Science University of California, Berkeley

Authoritarianism and Democracy in Rentier States Thad Dunning Department of Political Science University of California, Berkeley CHAPTER THREE FORMAL MODEL 1

CHAPTER THREE 1 Introduction In Chapters One and Two, I presented the puzzle that motivates this study. An important body of mostly empirical work in political science has suggested that rents from oil and similar minerals promote authoritarianism. Yet this nding appears to contradict the claim of country experts that oil rents fostered democratic stability in Venezuela, one of the oldest oil exporters in the world. In this chapter, I develop a formal model that reconciles these competing claims. The model elucidates a mechanism through which resource wealth promotes democracy. My analysis does not contradict the assertion the resource rents promote authoritarianism because, as we will see, resources can also have an authoritarian e ect. The strength of the model is that it allows us to compare the mechanisms through which resources can lead to democracy to those through which it can lead to authoritarianism and thereby generate conjectures about when the democratic or authoritarian e ects of resource wealth will be more important. In addition, as my statistical analysis of time-series cross-section data elsewhere will show, the empirical link between resources and democracy is more general than previous analysts have suggested. Thus, understanding the link between resource rents and democracy constitutes an important agenda for research on the political e ects of resource wealth, and a central contribution of the model developed in this chapter. 2 The theoretical approach Scholars of comparative politics have developed many di erent approaches to understanding processes of democratization as well as democratic breakdown, from the extensive literature on the role of intra-elite schisms in prompting transitions to democracy (e.g., O Donnell and Schmitter 1986: 19) to the literature emphasizing the international dimensions of democratization (e.g., Huntington 1991: 40, 45-46). These traditions have generated many important insights, and I view the argument I develop here as largely complementary to, rather than competitive with, these approaches. Like most of the "transitions to democracy" literature, I emphasize the internal dynamics rather than external sources of democratization and democratic breakdown. However, building on a recent literature on the role of popular 2

mobilization "from below" and the politics of redistribution in shaping the emergence of democratic and authoritarian regimes (especially Acemoglu and Robinson 2001, 2005, Collier 1999 and Rueschemeyer, Stephens, and Stephens 1992), I also emphasize the role of economic con ict and of political cleavages based on economic divisions. My substantive wager in undertaking this study is that if resource rents are to have an in uence on the political regime type, it will be through their e ect on these economic sources of authoritarianism and democracy. The strategic environment of the model is similar in some respects to Acemoglu and Robinson (2001, 2005) and also Boix (2003). First, I conceive of politics as being de ned by the con ict between a relatively small group of elites and a relatively large group of masses whose members act to advance common interests or purposes. Second, the approach is instrumental, in the sense that preferences over policy outcomes here, economic outcomes will drive preferences over political institutions, since institutions allocate political power and thus ultimately help determine policy outcomes. Third, I will emphasize the role of inequality of wealth and income in producing economic con ict and thereby in uencing the institutional preferences of di erent groups. Finally, following the assertion of Reuschemeyer, Stephens and Stephens (1992:5) that "democratization represents rst and foremost an increase in political equality," I will assume that elites exercise more political power under authoritarianism, while the masses, who are more numerous, have more political power under democracy. This assertion does not imply that the "masses" exercise political power to the exclusion of elites in any real-world democracy: institutional and electoral rules (Beard 1913, Persson and Tabellini 2000), lobbying (Grossman and Helpman 2001), cross-cutting cleavages (Roemer 1998), and other factors can all undercut the in uence of a democratic majority. Instead, it should be understood primarily as a comparative statement about the ability of masses to in uence policy under democracy, relative to a modal authoritarian system, and as a useful building block in a theory of the emergence and persistence of democratic and authoritarian regimes. My approach also emphasizes that although institutions allocate formal political power, groups sometimes have other sources of power: in particular, the ability to take control of the state by force. For example, elites may launch coups against democracy, while subordinate groups can threaten authoritarian regimes with popular mobilization and, in the limit, with revolution. Yet opportunities for coups may be transient, and social revolutions are rare events (Skocpol 1979). In historical perspective, we have perhaps more often observed 3

political regime change that is relatively non-violent and that does not involve a dramatic transformation of state institutions. Yet why would the bene ciaries of incumbent regimes willingly relinquish power? The approach I develop here emphasizes that the threat posed by out-of-power groups to take power by force can induce both policy change and institutional reform (Acemoglu and Robinson 2000, 2001, 2005). For example, a mass mobilization against an authoritarian regime may force elites to choose between repression of the masses, which may be costly; some possibly temporary policy change aimed at defusing popular opposition; or some possibly more durable institutional change such as democratization, which tends to allocate both present and future political power to the majority. That we do not often observe the exercise of the implicit "revolutionary" threat may be precisely because elites have averted this outcome through some combination of repression, policy moderation, or institutional reform. Similarly, democratic majorities may also sometimes moderate policy, or adopt institutional reforms or informal measures that limit their own formal political power, in order to avoid a coup (see, e.g., Collier 1999 on Southern Europe, Wantchekon 1999 on El Salvador, or Londregan 2000 on Chile). Of course, whether this image of politics provides a useful analytic window on the sources of democracy and authoritarianism in resource-rich countries is an empirical question, one I take up in subsequent chapters. Given this theoretical framework, the main contribution of the model developed in this chapter is to clarify how resource rents shape economic con ict and thereby in uence the development of political institutions. Along with previous analysts, I emphasize the unique characteristics of resource rents. These rents ow directly into the scal co ers of the state at a relatively low cost of extraction, relative to other sources of revenue such as taxation, and their e ects are largely felt on the expenditure side of the scal balance (Beblawi 1987: 53-54). Yet I di er from other analysts in my assessment of the political consequences of this characteristic of resource rent. The existing literature on oil and authoritarianism emphasizes that resource rents increase the incentives of elites to block or reverse processes of democratization, because resource rents ow directly into the co ers of the state and may be appropriated by authoritarian elites and used to repress or coopt popular opposition (Ross 2001). My analysis does not necessarily contradict this claim, since, in the model, con ict over the distribution of resource rents can reduce the incidence of democracy. Yet there is also an important "indirect" e ect of resource wealth. Because resource rents are less costly to extract than taxes from citizens, resource rents displace taxation as a source of revenue for public spending. As we will see, resource rents will therefore reduce the extent 4

to which democratic majorities want to redistribute income away from rich elites. indirect e ect of resource wealth, working through the e ect of resource rents on taxation, will make democracy less costly for elites. This Thus, there are two contrasting political e ects of resource wealth in the model. After introducing the model in section 3, and deriving the main comparative statics implications in section 3.4, I discuss the broader implications for our interpretation of politics in resource-rich societies in section 4. 3 The model 3.1 The setting Consider an in nitely-repeated game in a society with a continuum of citizens of mass 1. Citizens belong to one of two groups, the "elites" and the "masses" (or, equivalently, the "rich" and the "poor"). These groups are distinguished both by their size and by their level of private income. First, a fraction 2 (0; 1 ) of the population is rich and a fraction (1 ) 2 is poor, so the poor are more numerous. Second, let the the fraction of total private income accruing to the rich group be, with >. Total (and average) private income is y, so the income of each rich individual is y r = y, while the income of each poor individual is y p (1 ) = y. Thus, (1 ) yr > y > y p. Citizens derive utility from private consumption and from public spending. In each period t of the game, the instantaneous utility of individual i is given by: Ut i = c i t + V (g t ) (1) where c i t is the (post-tax) consumption of individual i at time t and g t is public spending at time t. All citizens seek to maximize the (discounted) in nite-horizon sum of their 1X instantaneous utilities, t Ut i, where 2 (0; 1) is the common discount factor. t=0 Private consumption is just private income net of taxes, so c i t = (1 t )y i (2) where t is the proportional tax on income adopted in period t. Public spending, on the other hand, comes from two sources: tax revenue and resource rent. Tax revenue is collected from citizens by the central government and disbursed through public spending. Resource 5

rent ows directly into the public co ers, without any need for collection of private income from citizens. The government budget constraint in each period is given by: g t = H( t y) + R (3) where t y is total tax revenue in period t and R is the resource rent. V and H are both concave functions but they have di erent interpretations. The concavity of V captures diminishing marginal utility of public spending as well as ine ciencies involved in the provision of goods and services valued by the public. Diminishing marginal utility of public spending is a standard assumption in the public nance literature, where quasilinear utility functions of the form in equation (1) are standard. On the other hand, the concave function H captures the speci c ine ciency associated with collecting taxes relative to resource rents. Tax revenues are hard to raise: they may demand a developed and capable state bureaucracy that can monitor and enforce restrictions on tax evasion. Even in societies with comparatively capable bureaucracies, raising taxes to high enough levels may eventually cause some diversion of production into non-taxable activities and therefore some e ciency loss. Resource rents, in contrast, are more like manna from heaven. These rents ow directly into state co ers and can be converted more e ciently into public spending. Formally, the model captures this distinction between the taxation of citizens and resource rents by assuming that unlike resource rents, tax revenues cannot be converted unit-by-unit into public spending. The tax rate will be the choice variable in the model. Using the de nitions in equations (1), (2), and (3), we have that in each period t, the ideal tax rate for group i is given by: arg max(1 t )y i + V (H( t y) + R) Thus, the following rst-order condition implicitly de nes this ideal tax rate of individual i: y i + V 0 (H( i y) + R)H 0 ( i y)y = 0 (4) where for simplicity I abstract from the time subscripts (since, as we will see, the ideal tax rate of each individual or group of individuals will be the same in every period). Rearranging, we have: V 0 (H( i y) + R) = y i H 0 ( i y)y (5) 6

where i is the tax rate preferred by the group with private income y i. Since y r > y p, the rich prefer lower taxes than the poor. This is because, if the numerator on the right-hand side of equation (5) increases, either the denominator or the left-hand side of the equation must increase as well (or both), in order to maintain the equality required by the rst-order condition. By the concavity of V and H, both V 0 (H( i y) + R) and H 0 ( i y) are decreasing in i, so i must be decreasing in y i. Thus: p > r (6) that is, the poor prefer a higher tax rate and more public spending than the rich. 1 Each period of this in nite-horizon game is de ned by a "state of the world," which has two characteristics. First, society is either authoritarian or democratic; thus, P 2 fd; Ag, where "P " is for political regime, "D" is for democracy, and "A" is for authoritarianism. Under authoritarianism, elites are assumed to have political power, and therefore they choose policy, while democracy implements the preferences of the poor. Note that the median voter in the model is poor, and that the ideal tax policy p of the poor is a Condorcet winner (that is, it will defeat any other policy proposal under a pairwise vote). 2 The assumption that the elite set policy under authoritarianism and the masses set policy under democracy simply captures the idea that democracy gives political power to the majority, relative to authoritarianism. It is relatively straightforward to extend the set-up of this model to characterize "intermediate" types of democracy or authoritarianism, in which public policy can be thought of as a weighted average of the preferences of elites and masses, with a greater weight on the preferences of the poor masses under democracy than under authoritarianism. 3 The second characteristic of the state of the world determines the collective action capacities of the "out-of-power" group, which will determine their ability to pose a threat to the in-power group. Under democracy, the collective action capacity of the rich is measured by the cost of a coup: ' 2 f' L ; ' H g, with "L" for low and "H" for high. Under authoritarianism, on the other hand, the collective action capacity of the poor is measured by the 1 This a standard result of public nance models in the tradition of Romer (1975), Roberts (1977), and Meltzer and Richard (1981). 2 Thus, in the background is an unmodelled process of Downsian political competition in which democracy leads to convergence on the policy preferred by the median voter (as in, e.g., Wittman 1995). The analytic results developed in this model would be robust in a similar model in which, say, electoral rules or party systems undercut the political in uence of a poor democratic majority as long as the masses generally have more in uence under democracy than they do under authoritarianism. 3 Acemoglu and Robinson (2005) develop a probabilistic voting model which provides some microfoundations for such weights. 7

cost of revolution to the poor: 2 f L ; H g. Empirically, groups clearly sometimes do have opportunities to stage coups or revolutions, yet such opportunities may exist only in special circumstances: for example, an economic recession, a threat of a foreign war (Skocpol 1979), or other contingent events. Thus, I assume that ' L ; L! 1, so a coup is only possible when ' = ' H and a revolution is only possible when = H. ' = ' H with probability p and ' L with probability (1 In any democratic period, p), while in any authoritarian period, = H with probability q and L with probability 1 q. To capture the idea that opportunities for coups or revolutions are rare, let p; q 1. The notation may be somewhat 2 confusing: the idea is that when the relevant variable is "high," the out-of-power group has the collective-action capacities necessary to pose a threat to the in-power group. The state space of the game is therefore S = ffd; ' H g; fd; ' L g; fa; H g; fa; L gg: The regime type P 2 fd; Ag will be determined by the history of the game, in particular, the regime type at the end of the immediately preceding period. The capacity for collective action of the out-of-power group in each period will be determined in each period by the realization of the random variable or '. The structure of the game and the distributions of and ' are all common knowledge. The timing of each stage game depends on whether the society is democratic or authoritarian. If society is democratic, then the timing of the stage game is as follows: (D1) Nature determines the realization of the random variable ' t 2 f' L ; ' H g, which is observed by both groups. (D2) The poor (who, because the society is democratic, hold political power) set a tax rate, ~ D t 2 [0; 1]. (D3) The rich decide whether to stage a coup, at a cost ' t. 4 If the rich stage a coup, they set a new tax rate ^ t 2 [0; 1], instantaneous utilities of both groups are realized, and the period ends. The next period then begins under an authoritarian regime. (D4) If the rich do not stage a coup, the tax rate ~ D t set by the poor in (D2) is implemented, utilities are realized, and the game moves to the next period under a democratic regime. 4 The sources of this cost are unmodelled here, but they involve the risks to the rich of staging an unsuccessful coup. In Venezuela, for example, coup plotters who had deposed Hugo Chávez for 48 hours in April 2002 were exiled or imprisoned after his return to power, a cost paid by similarly unsuccessful coup plotters in any number of historical instances. 8

On the other hand, if the society is authoritarian, then the stage game has the following timing: (A1) Nature determines the realization of the random variable t observed by both groups. 2 f L ; H g, which is (A2) The rich, who are in power, decide whether to repress the poor, at a cost of repression. If the rich repress the poor, they set the tax rate, utilities are realized, and the period ends. The next period then begins under an authoritarian regime. (A3) If the rich do not choose to repress the poor in (A2), the rich then have two choices: (i) They can set a tax rate ~ A t 2 [0; 1]. (ii) They can democratize, which gives political power to the poor. If the rich democratize, the poor set the tax rate, utilities are realized, and the next period of the game begins under democracy. (A4) If the rich choose to set a tax rate ~ A t as in (A3)(i), then the poor decide whether to revolt or not. If the poor mount a revolution, they control political power for the rest of the in nite-horizon game, and they set the tax rate in the current and every future period. However, revolution also carries a cost t, as described below. If the poor do not revolt, the tax rate ~ A t is implemented, utilities are realized, and the game moves to the next period under an authoritarian regime. 3.2 De nition of equilibrium The equilibrium concept used to solve the game will be pure-strategy Markov perfect equilibrium. This equilibrium concept is a re nement of sub-game perfect Nash equilibria, in which the strategies of the players can be contingent only on the payo -relevant state of the world in the current period, as well as any prior actions taken within the same period. Use of the Markov perfect solution concept has an important implication in the current context. Because strategies in every period cannot be conditioned on the history of play prior to the current period (with the exception of the current regime type, which does depend on the immediately-preceding period), both groups will have a limited capacity to commit to future policies. As we will see, in any period in which the in-power group is unconstrained by the 9

threat of a coup or a revolution from the out-of-power group, it will always be optimal for the in-power group to impose its ideal tax policy. For states of the world such that P = D, so the society is democratic, the action set of the poor consists of a tax rate ~ D : f' L ; ' H g! [0; 1], while the action set of the rich consists of a coup decision : f' L ; ' H g [0; 1]! f0; 1g, with = 1 indicating a coup. For example, (' H ; ~ D ) is a mapping from the "high" state and the tax rate proposed by the poor into a coup decision. For states such that P = A; so the society is authoritarian, the action set of the rich consists of a repression decision : f L ; H g! f0; 1g, where = 1 indicates a decision to repress, a democratization decision : f L ; H g! f0; 1g, where 1 indicates a decision to democratize, and a tax rate ~ A : f L ; H g! [0; 1]. The action set of the poor under authoritarianism consists of a decision to revolt, : f L ; H g f0; 1g 2 [0; 1]! f0; 1g, where 1 indicates a decision to revolt, so that (; ; ; ~ A ) is the mapping of the state variable and the actions of the rich into a revolution decision. A strategy pro le for the poor is then de ned as p f~ D (); ()g, while a strategy pro le for the rich is de ned as r f(); (); (); ~ A ()g. A Markov perfect equilibrium is a strategy combination, f~ p ; ~ r g, such that ~ p and ~ r are mutual best-responses for all states in the state space S. 3.3 Analysis I characterize the Markov perfect equilibria outcomes of the game in Proposition I at the end of this sub-section. The approach is to de ne Bellman equations that express the value functions for each group in each state of the world. I then compare these Bellman equations to de ne critical threshold values of ' H, H, and (the repression cost), which I will employ to characterize the equilibria in Proposition I. These critical values will also be useful for developing the comparative statics results of section 3.4. Assume without loss of generality that society is initially authoritarian but has reached the state fd; ' L g, that is, society has democratized at some previous point and we are in a "low" state in the current period. Because a coup is prohibitively costly for the rich when ' = ' L, the poor can set their ideal tax rate in the current period, unconstrained by the threat of a coup, and society will remain democratic in the following period. The instantaneous utilities of the rich and the poor in this period will therefore be de ned at p, the ideal tax rate of the poor. However, the value function of each individual today 10

will also depend on what will happen tomorrow. Members of both groups know that with probability p, the state tomorrow will be fd; ' H g. In this case, the rich may want to stage a coup (or, the poor may want to set a tax rate di erent from p in order to avoid a coup). On the other hand, with probability (1 p) the state tomorrow will be fd; ' L g. Then, the game looking into the in nite horizon will look exactly like the game looking into the in nite horizon today, because ' is stationary. The following Bellman equations therefore de ne the value functions of each group in the state fd; ' L g: and U r (D; ' L ) = (1 p )y r + V (H( p y) + R) + [pu r (D; ' H ) + (1 p)u r (D; ' L )] (7) U p (D; ' L ) = (1 p )y p + V (H( p y) + R) + [pu p (D; ' H ) + (1 p)u p (D; ' L )] (8) These Bellman equations have a form that will recur throughout the analysis below. The rst set of terms on the right-hand side of each equation is the instantaneous utility of each group in the present period, de ned at the tax rate p. For example, in equation (7), (1 p )y r + V (H( p y) + R) is the instantaneous utility of the rich, who have income y r, de ned at the tax rate p. Next, the set of terms in brackets is the continuation value of living under democracy tomorrow, which is discounted by (because it occurs tomorrow). This continuation value is the weighted sum of the value of living under democracy when ' = ' H and living under democracy when ' = ' L, where the weights are the probability p that ' = ' H tomorrow and the probability (1 p) that ' = ' L tomorrow. However, to de ne the value functions in equations (7) and (8), we will have to know U r (D; ' H ) and U p (D; ' H ). That is, what is the continuation value of living under democracy when the state is fd; ' H g and the rich may therefore want to stage a coup? To answer this question, rst suppose the poor follow a strategy of setting a tax rate ~ D in any period in which ' = ' H and that the rich do not stage a coup, given this tax rate. Then the payo s to living under democracy when the state is fd; ' H g will be: U r (D; ' H ; ~ D ) = (1 ~ D )y r + V (H(~ D y) + R) + [pu r (D; ' H ; ~ D ) + (1 p)u r (D; ' L )] (9) and 11

U p (D; ' H ; ~ D ) = (1 ~ D )y p +V (H(~ D y)+r)+[pu p (D; ' H ; ~ D )+(1 p)u p (D; ' L )] (10) On the other hand, rather than accept the tax rate ~ D that the poor o er, the rich may prefer to stage a coup. What is the payo to a coup? Let U r (A; L ) be the payo to the rich under authoritarianism in any period in which = L (we will de ne this payo below), and note that in any such period, the rich can set their unconstrained preferred tax rate r, and society will remain authoritarian in the following period. But the payo to the rich under authoritarianism when the state is L is identical to the payo to the rich of staging a coup, net of the cost of a coup, since in both cases the rich can set their unconstrained preferred tax rate for one period and the society is authoritarian in the following period. So, the payo of the rich in any period in which they stage a coup is simply U r (A; L ) ' H. Putting this discussion together, we can de ne the continuation values U r (D; ' H ) and U p (D; ' H ) in equations (7) and (8) as follows: U r (D; ' H ) = max [U r (A; L ) ' H ] + (1 )U r (D; ' H ; ~ D ) (11) =f0;1g U p (D; ' H ) = [U p (A; L )] + (1 )U p (D; ' H ; ~ D ) (12) where = f0; 1g is an indicator function describing the decision to stage a coup (with 1 indicating that a coup takes place). If staging a coup maximizes the utility of the rich in equation (11), then = 1 and U r (D; ' H ) = U r (A; L ) ' H. On the other hand, if the rich are better o not staging a coup and accepting ~ D, then = 0 in equation (11) and U r (D; ' H ) = U r (D; ' H ; ~ D ). I assume that if the rich are indi erent between these options, = 0, so society remains democratic. Equation (12) gives the utility of the poor under democracy as a function of the coup decision of the rich. We can now begin to de ne several key threshold values of the coup cost that will be useful both for characterizing the equilibria of the game and for analyzing how resource rents in uence the incentives of the rich to stage coups against democracy in Section 3.4. First, let the coup constraint be binding in any period in which ' = ' H if the rich prefer staging a coup to living forever in an unconstrained democracy in which the poor always set ~ D = p, regardless of the realization of '. The coup constraint therefore binds if 12

U r (A; L ) ' H > U r (D; ' H ; ~ D = p ) (13) Clearly, if the poor set ~ D = p whenever ' = ' H, they will also do so when ' = ' L. Thus, the instantaneous utility of the rich in every democratic period will be (1 p )y r + V (H( p y)+r). The value of receiving this instantaneous utility forever, beginning in period t, is therefore: U r (D; ' H ; p ) = which gives the right-hand side of (13). 1X t [(1 p )y r + V (H( p y) + R) (14) t=0 = (1 p )y r + V (H( p y) + R) 1 On the other hand, U r (A; L ) on left-hand side of (13) is: (15) U r (A; L ) = (1 r )y r + V (H( r y) + R) + [qu r (A; H ) + (1 q)u r (A; L )] (16) Now, solving equation (16) for U r (A; L ) will involve de ning an expression for U r (A; H ). That is, the value function of the rich in equation (16) will depend on what the rich expect to happen under authoritarianism when the state = H is reached. Since the society was initially authoritarian, and since we are considering the coup constraint (in which the rich weigh the costs and bene ts of a coup against democracy), we are considering a society in which democratization must have occurred in a prior period in the state H. Thus, if society previously democratized in the state S t = fa; H g, we must be in the part of the parameter space in which society will democratize again when H is reached. Recall that if society democratizes, the poor can set their preferred tax rate in the current period before the game moves to the next period under democracy. The continuation payo of the rich in any period in which the state fa; H g is reached is therefore equivalent to their continuation payo to democracy when the threat state is low and the poor can set their unconstrained ideal tax policy in the current period. Thus, we can set U r (A; H ) = U r (D; ' L ) in equation (16), where U r (D; ' L ) is de ned by equation (7). Finally, to de ne the coup constraint in terms of the parameters of the model, note that equation (7) involves U r (D; ' H ), which is in turn de ned by equation (11). That is, the utility of the rich under democracy, in periods when they cannot threaten a coup, will 13

depend on what will happen in future periods when they do have the ability to threaten a coup. We will therefore also have to put some restrictions on what happens after the society redemocratizes and the state ' = ' H is reached again. One possible approach is to assume that since a coup previously occurred in the state fd; ' H g, the solution to the maximization problem of the rich in equation (11) must be = 1, so another coup will occur when this state is reached again. Then, with U r (D; ' H ) = U r (A; L ) ' H and U r (A; H ) = U r (D; ' L ), equations (7) and (16) make up a system of two equations which we can solve for the two unknowns U r (D; ' L ) and U r (A; L ). A di erent approach is to use the "one-shot deviation" principle (Fudenberg and Tirole 1991: 108-110), in which we assume that although a coup previously occurred at ' H, it will not occur again after redemocratization. It turns out that these two approaches have identical implications for the critical threshold value developed below (see Acemoglu and Robinson 2005: 203-204 for a discussion) and since it is simpler to work with the "oneshot deviation" approach here, I adopt this approach. Thus, I assume that once society redemocratizes and reaches the state (D; H ), it will remain democratic, and there will be no further coups. Using equation (14), we therefore have: U r (A; H ) = U r (D; ' H ; ~ D = p ) = (1 p )y r + V (H( p y) + R) 1 Now, substituting this expression for U r (A; H ) into equation (16), solving for U r (A; L ), substituting into equation (13) and using equation (14) gives the following de nition of the coup constraint: [(1 r )y r + V (H( r y) + R) ((1 p )y r + V (H( p y) + R))] 1 (1 q) (17) > ' H (18) If this coup constraint binds, the poor cannot set their ideal tax rate in all periods without incurring a coup. Instead, if they want to avoid a coup, they will have to moderate the tax rate they set in periods in which ' = ' H. Note that the numerator of the coup constraint in equation (18) is simply the di erence between the utility of the rich at their ideal point, r, and the utility of the rich at the ideal point of the poor, p. Let U r ( r (R); R) = (1 r )y r + V (H( r y) + R) (19) be the utility of the rich at their ideal tax policy, and let 14

U r ( p (R); R) = (1 p )y r + V (H( p y) + R) (20) be the utility of the rich at the ideal policy of the poor, where in writing U r ( r (R); R) and U r ( p (R); R) I have made the dependence of the ideal tax rate on R explicit. Then we can rewrite the coup constraint as: U r ( r (R); R) U r ( p (R); R) 1 (1 q) > ' H (21) As we will see, the various critical thresholds of the coup and repression costs developed below will all depend in some way on this utility di erence. This is intuitive because, under democracy, the poor will always be able to impose p in the state fd; ' L g, while under authoritarianism the rich will always be able to impose r in the state fa; L g. So looking into the future, each group will take into account its utilities in these two states, discounted by the probabilities of being in each state. For example, note that the denominator in equation (21) is 1 (1 q) because the rich take into account the fact that under authoritarianism, society will democratize once the state reaches H, which occurs with probability (1 If the inequality in expression (18) (or equivalently, 21) holds, then if the poor want to avoid a coup, they will sometimes have to set the tax rate at some point di erent from their ideal point, that is, they will have to set ~ D 2 [ r ; p ). However, another question is whether the poor will be able to avoid a coup by setting ~ D 6= p when ' = ' H. q). If the poor will ever be able to induce the rich not to stage a coup, it will be by setting the tax rate at the ideal point of the rich when threatened by a coup (since they cannot o er the rich greater utility than the utility of the rich at their ideal point). Note, however, that the poor cannot credibly promise to set ~ D = r when ' = ' L, because in any Markovian equilibria, the poor will set ~ D = p whenever they are unconstrained by the threat of a coup. Thus, setting ~ D = r when ' = ' H and ~ D = p when ' = ' L is the minimum amount of taxation that the poor can credibly promise. Suppose, then, that the poor follow a strategy of setting ~ D = r when ' = ' H ~ D = p when ' = ' L. Given this strategy by the poor, the rich will stage a coup whenever U r (A; L ) ' H > U r (D; ' H ; ~ D = r ). We can therefore de ne a threshold value of ' H, which we will call the critical coup cost, which is the cost of a coup such that the rich are just indi erent between staging a coup in a high period and living under democracy. critical coup cost will satisfy the following equality: and This 15

U r (A; L ) ' H = U r (D; ' H ; ~ D = r ) (22) The left-hand side of equation (22) is the value to the rich of imposing authoritarianism, net of the critical coup cost ' H which de nes the value of ' H at which equation (22) is satis ed. The right-hand side of equation (22), on the other hand, is the value to the rich of living under democracy when the poor follow the strategy of setting ~ D = r when ' = ' H and setting ~ D = p when ' = ' L. Note that if the left-hand side of equation (22) is greater than the right-hand side, the poor will never be able to induce the rich not to stage a coup. Thus, the poor cannot avoid a coup for any ' H < ' H. For purposes of the analysis below, it is also useful to develop the critical coup cost under the following set of suppositions. Suppose we are in the part of the parameter space in which the cost of revolution is such that if the society is authoritarian, the rich are unconstrained by a threat of revolution from a poor (in other words, the revolution constraint, to be de ned below, does not bind), but there has been a deviation in a previous period of the game, such that we have somehow reached the state fd; ' H g. Again, the rich will be indi erent between a coup and no coup if U r (A; L ) coup cost de ned under this supposition. ^' H = U r (D; ' H ; ~ D = r ), where ^' H is the critical Because the rich will be unconstrained by the threat of a revolution, returning to authoritarianism will allow the rich to impose their ideal point in every period. Thus: U r (A; L ) = (1 r )y r + V (R + r y) 1 The value of living under democracy, on the other hand, will be de ned by U r (D; ' H ; ~ D = r ), which is the value function of the rich under democracy given that the poor set ~ D = r when ' = ' H and set ~ D = p when ' = ' L. Note that equations (7) and (9), with U r (D; ' H ) = U r (D; ' H ; ~ D = r ), constitute a system of two equations in the two unknowns U r (D; ' L ) and U r (D; ' H ; ~ D = r ). substituting into equation (9), we have: (23) So, solving equation (7) for U r (D; ' H ; ~ D = r ) and U r (D; ' H ; ~ D = r ) = (1 (1 p))[(1 r )y r + V (H( r y) + R] + (1 p)[(1 p )y r V (H( p y) + R] 1 (24) 16

This expression tells us the minimum level of redistribution to which the poor can credibly commit themselves over time. Notice that this level of redistribution is limited by the commitment problem of the poor. To see this, suppose, instead, that the poor could credibly promise to set the tax rate at r in every period, whether the state is low or high. Since the rich would receive instantaneous utility de ned at r in every period, the value function of the rich under such a strategy by the poor would simply be: U r (D; ~ D = r ) = [(1 r )y r + V (H( r y) + R) (25) 1 which is the same as equation (23), the utility of the rich from living under an authoritarianism where they are unconstrained by the threat of revolution. (In writing equation 25, I have not entered ' as an argument to utility because we are temporarily imagining that the poor follow the same strategy in every period, whether ' = ' H or ' = ' L ). Clearly, by the de nition of r as the solution to the maximization problem of the rich, equation (25) is greater than equation (24). What this implies is that if the poor could somehow promise to set a tax rate lower than p in periods when ' = ' L, they could promise more to the rich than equation (24), but this is not possible in any Markovian equilibria. Thus, by U r (A; L ) ^' H = U r (D; ' H ; ~ D = r ) and the de nitions of U r (A; L ) in equation (23) and U r (D; ' H ; ~ D = r ) in equation (24), the critical coup cost ^' H will be de ned by: ^' H = [(1 p)][(1 r )y r + V (H( r y) + R) (1 p )y r V (H( p y) + R)] (1 (1 q)) Notice that as in the de nition of the coup constraint in equations (18) and (21), the numerator of this critical coup cost involves the di erence between the utility of the rich at their optimal policy and the utility of the rich at the optimal policy of the poor. Here, this utility di erence is multiplied by the (discounted) probability that the state tomorrow is ' L, because the rich take into account that if they do not stage a coup, society will be democratic tomorrow and with probability (1 ~ D = r from the poor. (26) p) they will not be able to extract a concession of Now, to de ne the equilibria of the game, we will also need to characterize the payo s of the rich and the poor under authoritarianism. First, note that revolution is an "absorbing state" in the model; once a revolution takes place, society never reverts to authoritarianism or democracy. The payo s to revolution to the poor will simply be 17

U p (R; ) = (1 p )y p + V (H( p y) + R) 1 Equation (27) expresses the payo to the poor when the poor set their unconstrained ideal policy in each period forever (and thus = p ), net of the cost of revolution which is 2 f L ; H g. (27) The value of depends on the state in the period in which revolution takes place (which is why revolution never takes place when = L, because L! 1). Note that by equation (27), revolution is costly not just today but also in future periods. The idea is that although revolution allows the poor to set policy as they like for the rest of the game, it also destroys a part of economic output permanently (perhaps by encouraging economic ight by the rich). For the rich, revolution is assumed to be the costliest outcome, because after a revolution they no longer exert any in uence over policy. payo to the rich of revolution at zero: U r (R; ) = 0 To model this idea, I simply normalize the It is worth emphasizing that we do not not know much empirically about public nance or redistributive policy in the wake of a revolution in a resource-rich country, because revolution is a rare event among both resource-poor and resource-rich countries (Skocpol 1979). we will see, however, revolution is also o the equilibrium path in this model: it is mainly the threat of revolution that will induce a change in the policies adopted by the rich. In order to begin to characterize the incentives of the rich and the poor under authoritarianism, we will rst want to know the condition under which a revolutionary threat will constrain the tax policy adopted by the rich. As Let ~ A be the tax rate chosen by the rich in any stage game under authoritarianism, and suppose that the rich set ~ A = r in every period, whether the state is high or low. Then the payo to the poor is: U p (A; H ; ~ A = r ) = (1 r )y p + V (H( r y) + R) 1 The revolution constraint will bind in the state H when U p (R; H ) > U p (A; H ; ~ A = r ); or using equation (27), (28) H < (1 p )y p + V (H( p y) + R) (1 r )y p V (H( r y) + R) (29) 18

If the inequality in (29) holds, the rich may want to avoid a revolution by using temporary redistribution at some rate ~ A 2 ( r ; p ], that is, by o ering a tax rate that is better for the poor than the ideal tax rate of the rich. A key question is therefore whether the rich will be able to avoid a revolution simply by o ering some tax rate ~ A 2 ( r ; p ]. To answer this question, suppose the rich o er ~ A = p, that is, the ideal point of the poor. Clearly, the rich will always set ~ A = r whenever = L, since in such periods the poor cannot mount a credible revolutionary threat. Thus, if the rich can ever avoid a revolution through redistribution, they will be able to do so by setting ~ A = p when = H and setting ~ A = r when = L. Let U p (A; H ; ~ A = p ) be the continuation value of authoritarianism to the poor, given that the rich follow this strategy. Then whenever the state is high, so that = H, the poor will be indi erent between a revolution and accepting the o er ~ A = p at the critical revolution cost H such that U p (A; H ; ~ A = p ) = U p (R; H ). The latter term is given by equation (27) with = H. For any H < H, the rich will not be able to avoid a revolution by setting a tax rate higher than their ideal point. Note, however, that U p (A; H ; ~ A = p ) is not the same as equation (28) with ~ A = p, since now, in every period in which = L, the rich will set ~ A = r. Thus, in order to de ne the critical revolution cost, we must develop an expression for U p (A; H ; ~ A = p ). This expression is: U p (A; H ; ~ A = p ) = (1 p )y p +V (H( p y)+r)+[qu p (A; H ; ~ A = p )+(1 q)u p (A; L ; ~ A = r )] (30) where the rst set of terms is the instantaneous utility of the poor at the tax rate p and second set of terms de ne the continuation values to the poor of living under authoritarianism. The payo to the poor in a low period is de ned analogously as: U p (A; L ; ~ A = r ) = (1 r )y p +V (H( r y)+r)+[qu p (A; H ; ~ A = p )+(1 q)u p (A; L ; ~ A = r )] (31) Thus, equations (30) and (31) constitute a system of two linear equations in the unknowns U p (A; H ; ~ A = p ) and U p (A; L ; ~ A = r ). We can then substitute to solve for U p (A; H ; ~ A = p ), which gives: 19

U p (A; H ; ~ A = p ) = (1 (1 q))[(1 p )y p + V (H( p y) + R] + (1 q)[(1 r )y p + V (H( r y) + R)] (1 ) (32) Equating this expression to equation (27) and setting = H then gives the critical revolution cost: H = (1 q)[(1 p )y p + V (H( p y) + R) (1 r )y p V (H( r y) + R)] (33) which is just the di erence between the utility of the poor at the tax rates p and r, multiplied by the (discounted) probability (1-q) that there is no revolutionary threat tomorrow and the rich can therefore set ~ A = r. For any H < H, the rich will be unable to avoid a revolution through temporary redistribution at the rate ~ A = p in states H : Suppose equation (33) does not hold, and H < H, so that the rich cannot avoid a revolution by changing tax policy. The rich may then want to democratize. Democratization is a more credible way to commit to a higher future tax rate for the rich, because under democracy, the poor can implement their preferred tax rate p in any period in which the state is low (whereas, under authoritarianism, when the state is low the rich implement r ). However, we have not yet analyzed the incentives of elites to redistribute at a tax rate ~ A 6= r, to democratize, or, alternatively, to repress the poor. I now turn to the analysis of this question, which is the nal issue for analysis prior to characterizing the equilibria of the game. First, consider the case in which the revolution constraint binds but H H ; that is, there exists some ~ A = ^ A 2 ( r ; p ] such that the poor are indi erent between revolution and accepting this temporary redistribution at the rate ^ A. Then the question is whether the rich will prefer to a strategy in which they adopt ^ A in all periods in which the state is H (and adopt ~ A = r whenever the state is L ) or will instead prefer a strategy of repression. Using the analogues to equations (30) and (31), now de ned for the rich rather than the poor, and solving by substitution, we have that the payo to the former strategy in the high state is: U r (A; H ; ~ A = ^ A ) = 20

(1 (1 q))[(1 ^ A )y r + V (H(^ A y) + R] + (1 q)[(1 r )y r + V (H( r y) + R)] 1 (34) Repression, on the other hand, allows the rich to set ~ A = r in every period, whether the state is high or low, but it carries a cost of. Thus the payo to repression is given by: U r (O; H ; ) = (1 r )y r +V (R+ r y) +[qu r (O; H ; )+(1 q)u r (O; L ; ~ = r )] (35) (where the notation "O" stands for "oppression," since I already used "R" for revolution). What is the interpretation of equation (35)? As with the other Bellman equations, the rst term captures the instantaneous utility, here the utility of the rich evaluated at r, net of the cost of repression. The nal terms capture the continuation value to the rich. With probability q, the state tomorrow is also H, and the revolution constraint will bind tomorrow as well. Now, if the rich found it optimal to repress in a Markovian equilibrium today, they may clearly nd it optimal tomorrow; I will therefore restrict the analysis to strategies in which the continuation value in the next period will again be U r (O; H ; ). However, with probability (1 q), the state tomorrow is L, and the poor cannot threaten a revolution. The rich will clearly not pay the repression cost in this case, and they will set ~ = r. Thus, the continuation value of the low state will be: U r (O; ~ A = r ; L ) = (1 r )y r + V (R + r y) + [qu r (O; H ; ) + (1 q)u r (O; ~ = r ; L )] We can then solve for U r (O; H ; ) by substitution: (36) U r (O; H ; ) = (1 r )y r + V (R + r y) (1 (1 q)) 1 The interpretation of this expression is as follows. (37) Because the elite will always repress when faced with a threat of revolution from the poor, they can set their preferred tax policy in any period. However, they will only need to pay the repression cost in periods in which = H, which occurs with probability q. So the present discounted value of playing the repressive strategy in any high period is not the payo to imposing r minus the repression cost, divided by 1, but rather the payo to imposing r minus the smaller quantity (1 (1 q)), divided by 1. That the numerator is larger than the payo to r minus 21

the repression cost stems from the fact that the rich will not have to pay the repression cost in all periods. We can con rm that as q! 1, the numerator of equation (37) approaches the payo to imposing r minus the repression cost. Using equations (29) and (37), I now de ne the critical value of the repression cost at which the rich will be indi erent between repression and redistribution at a tax rate ^ A in the high state. This critical repression cost will satisfy U r (A; H ; ~ A = ^ A ) = U r (O; H ; ), or: (^ A ) = [(1 r )y r + V (H( r y) + R) (1 ^ A )y r V (H(^ A y) + R)] (38) where I have written ^ A as an argument to make explicit the dependence of this critical repression cost on the rate at which the rich must redistribute to the poor to avoid a revolution. For any < (^ A ), the rich will prefer to repress the poor in high periods rather than redistribute to the poor at a rate ^ A. It is straightforward to show that is increasing in ^ A ; that is, the more the rich have to raise taxes in order to buy o a revolutionary threat, the greater their incentives to repress. Consider, then, the choice of the rich in the part of the parameter space where H < H. Here, the rich will not be able to avoid a revolution through temporary redistribution at any tax rate ~ A. The rich therefore have a choice between repression and democratization. One way to derive the critical threshold at which the rich will be indi erent between these choices, develop analogies to equations (30) and (31) for the continuation payo s of the rich, which after substitutions, gives: U r (D; ' L ) = (1 (1 q))[(1 p )y r + V (R + p y)] + p[(1 r )y r + V (R + r y)] (1 (1 q))(1 (1 p)) pq The critical cost of repression at which the rich are indi erent between repression and democratization is therefore the cost ^ at which: U r (O; H ; ^) = U r (D; ' L ) (39) It will be useful for the analysis below to develop an expression for the critical repression cost under a di erent set of suppositions. Assume that we are in the part of the parameter space in which, once society democratizes, it remains democratic forever, no matter what policy the poor set (that is, the coup constraint does not bind). This is the case in which 22

the rich will be most unlikely to want to democratize, since democratization is at its most costly for the rich: the poor will be able to set their ideal tax rate in every period of the game after democratization. The payo to the rich from democratization, given that we are in a part of the parameter space in which the coup constraint will not bind, will be: U r (D; ' L ) = (1 As above, the payo from repression will be: p )y r + V (R + p y) 1 U r (O; H ; ) = (1 r )y r + V (R + r y) (1 (1 q)) 1 Now let be the critical cost of repression at which these two value functions are equated, and thus the rich are indi erent between repression and democratization. After some algebra, we have: = (1 r )y r + V (R + r y) [(1 p )y r + V (R + p y)] (1 (1 q)) I now use the de nitions of the critical thresholds developed above to state the Markov perfect equilibrium outcomes of the fully dynamic game. (40) Proposition 1 The outcomes of a Markov perfect equilibrium of the game developed above are as follows: (1) If the revolution constraint in equation (29) does not bind, the society remains authoritarian forever, and the rich set ~ A = r in every period. (2) If the revolution constraint binds, then there are several possibilities: (a) If H H in equation (33) and (^ A ) in equation (38), at the ^ A at which the poor are indi erent between revolution and redistribution, then society remains authoritarian forever but the rich redistribute at the rate ^ A in periods where = H. In periods where = L, the rich set their ideal tax rate r. (b) If H H but < (^ A ), the society remains authoritarian forever but the rich use repression in periods where the state is = H. In every period, the rich set their preferred tax rate r. (c) If H < H but the cost of repression is less than the critical cost which the equality in equation (39) is satis ed, the society remains authoritarian forever but the rich 23