A dynamic theory of the transition to democracy

Journal of Economic Behavior & Organization Vol. 52 (2003) 1–25

A dynamic theory of the transition to democracy Paul J. Zak∗ , Yi Feng School of Politics and Economics, Claremont Graduate University, Claremont, CA 91711-6165, USA Received 9 February 2000; received in revised form 28 January 2001; accepted 2 March 2002

Abstract A model of the transition to democracy is presented within a dynamic general equilibrium framework. We demonstrate that democratic transitions occur endogenously in the course of economic growth or with economic contraction, being fundamentally driven by the economic position of the “middle class.” Democratic transitions can occur rapidly or slowly because the autocrat faces an informational asymmetry regarding the effect of his policies on the political–economic environment. The model shows that the primary factors affecting the speed of democratic transitions are inequality, the planning horizon of the autocrat, the autocrat’s perceived legitimacy, and the rate of economic growth. © 2003 Elsevier Science B.V. All rights reserved. JEL classification: E13; P16 Keywords: Economic growth; Democracy; Political economy; Regime change

1. Introduction In still influential work, Lipset (1959) argues that modernization leads to democracy. Yet we have outstanding counter-examples of “modern” autocracies. Further, recent transitions from autocracy to democracy show a non-monotone relationship between levels of per capita GDP at the time of transition (Feng and Zak, 1999). To wit, some democratic transitions follow economic successes, while others arise in economic crises. This suggests that a general theory of democratic transitions that captures the dynamics of jointly evolving economic and political systems is needed to augment Lipset’s modernization thesis. In this paper, we present such a formal dynamic theory to explain why countries with similar development histories undergo transitions to democracy at different times and illustrate how the distribution of economic resources affects the timing of democratic transitions. Further, ∗ Corresponding author. Tel.: +1-909-6218788; fax: +1-909-6218460. E-mail address: [email protected] (P.J. Zak).

0167-2681/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0167-2681(03)00018-0

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the theory also characterizes the factors that cause democratic transitions during economic crises as well as during economic successes. In a recent book, Bueno de Mesquita et al. (2003) (BDMSSM) present a formal model of polity longevity that examines why autocracies with poor economic policies may be long-lived while other autocracies readily implement pro-growth policies. Their explanation is based on the relative sizes of the selectorate (those who have the right to choose the government) and the winning coalition (the subset of the selectorate whose support is essential to keep the government in power). In the BDMSSM model, there is political competition so that the incumbent must keep the winning coalition loyal to retain office. Their model shows that poor policies are implemented without affecting a regime’s longevity when the winning coalition is small and the selectorate is large. Conversely, they show that in institutional environments where the winning coalition and the selectorate are both large, regime longevity depends more closely on policy performance and implemented policies produce better economic results.1 The model in this paper is similar to BDMSSM in several ways, but considerably extends it in others. First, our model of regime change is embedded in a general equilibrium model of economic growth so that the dynamics of underlying political changes are explicit and all aspects of the model are mutually consistent. Second, as in the “dissatisfaction” models of Lohmann (1993, 1994), citizens express their discontent with the government through violent action (rather than bargaining). Besides including equilibrium dynamics, the innovations introduced here include modeling agents as heterogeneous in income and wealth as in Acemoglu and Robinson (2001), as well as characterizing the role of informational asymmetries faced by the autocrat. The former permits a precise determination of the role of inequality and the behavior of the “middle class” on the timing of democratic transitions while the latter permits the equilibrium dynamics to include rapid transitions to democracy. We characterize the factors that produce rapid or gradual democratic transitions and show that transitions in economically successful versus economically unsuccessful nations have quite different etiologies. The primary implication of the model is that a democratic transition will almost always occur with sufficient economic growth or with sufficient economic contraction. Such a transition occurs more slowly when the gains from development are unevenly shared among citizens. We also show that democratic transitions depend non-monotonically on the planning horizon of the autocrat and the regime’s legitimacy. Though legitimacy has long been posited to affect democratic transitions (Lipset, 1959; Findlay, 1990; Wantchekon, 1999), we use the model to formalize this notion in a natural way and derive implications for differing levels of legitimacy on regime longevity. A more succinct summary of our findings is that democratic transitions are determined by the evolving economic status and political mobilization of the “middle class,” both in good economic times as well as in bad. This result is consistent with a number of empirical findings (e.g. Feng and Zak, 1999; Huber et al., 1993; Roemer, 1985) and identifies the process through which individual choices lead to democracy. The inclusion of heterogeneous agents, political–economic dynamics, and the autocrat’s policy choices produces a rather complicated model, but the payoff is the rich set of factors 1

We compare our model with other formal models of political regime change in Section 3.

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that we show affect the timing of transitions to democracy. Indeed, our analysis offers an explanation for the ambiguous relationships that have been found between democracy and economic growth (Feng, 1997; Barro, 1999, 1996; Przeworski and Limongi, 1993; Sirowy and Inkeles, 1990). The resolution of this puzzle is that (i) the factors we identify that affect the timing of democratic transitions do so non-monotonically (e.g. legitimacy), and (ii) democratic transitions occur both in economies that are economically successful as well as those that are economically unsuccessful. Thus, our model predicts that there is no unambiguous cross-sectional correlation between democracy and growth. Further, the model indicates that empirical studies of democratic transitions have omitted a number of important variables when characterizing the factors that determine the timing of democratic transitions.

2. Growth and government policy in an autocracy In this section, we present a formal theory of endogenous democratic transitions in market-based economies by examining the decisions faced by various individuals in a society and by an autocratic government. It will become clear in the subsequent sections that heterogeneity of the population (in a sense defined below) is critical in the characterization of political regime transitions. The model is built in pieces by examining the choices and constraints faced by different actors that are then combined into a political–economic equilibrium. 2.1. The choices of citizens The data suggest that transitions to democracy are more likely as per capita income increases (Jackman, 1973; Dahl, 1989; Burkhart and Lewis-Beck, 1994; Feng and Zak, 1999). Nevertheless, the movement towards democracy is neither monotonic nor inexorable. In this section, we ask what it is that individuals do as the level of economic development changes that cause transitions to democracy. As a country begins to develop, some individuals benefit from the changing economic environment before others do. As documented by Kuznets (1955) and many others, the distribution of income typically widens with development; that is, differences among individuals increase with development.2 At the same time, industrialization increases urbanization causing traditional lifestyles to disappear so that historical forms of governance may no longer be applicable or acceptable to the population. For an individual living in an autocracy, changes in income, wealth, and social setting alter his or her support of the autocrat—in particular, whether he or she thinks the autocrat should remain in power. For agents living in autocracy, there are limited avenues through which dissatisfaction with the government can be expressed. To make the argument below as transparent as possible, we take the narrow view that civil liberties are the defining characteristic of 2 More recent evidence on, and models of, income distribution and development can be found in Glomm and Ravikumar (1998), Galor and Tsiddon (1996), Brenner et al. (1991) and the survey in Adelman and Robinson (1989).

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democracies.3 Some individuals living in an autocracy who desire, but do not have, civil liberties are so frustrated by living under an autocratic regime that they choose to demonstrate against the government. The goal of such demonstrations is to weaken the government to induce it to grant civil liberties. Let us call this political activity. We assume that politically active agents in an autocracy engage in demonstrations against the government to enfeeble it by reducing its tax base. This is done by destroying part of the capital stock.4 We model politically active agents as receiving higher utility as more of the capital stock is destroyed during anti-government demonstrations. Thus, property rights in this model are not inviolate, and further, they are costly to protect as the government must expend resources to put down anti-government demonstrations.5 When will agents, then, engage in anti-government demonstrations? We answer this question by identifying the “types” of individuals in a country. Let us identify individuals by the index i, lying on the unit interval, which denotes their level of wealth and the wages they earn.6 Let η(ei , p) : [0, 1] × R+ → [0, 1] be the demonstration technology through which politically active agents can destroy part of the capital stock. We call η a “technology” because we presume that any actions taken by one agent can be copied by another. For example, making a Molotov cocktail is a type of technology for the destruction of capital; if one person knows how to make a Molotov cocktail, others can quite easily observe the technique and use it themselves. By assuming free imitation, we simplify the model by allowing all agents to use the same technology in demonstrating against the government. The amount of capital that can be destroyed by agent i is increasing in the time spent demonstrating, ei , ∂η(ei , p)/∂ei > 0, and exhibits diminishing marginal productivity in demonstrating, ∂2 η(ei , p)/∂(ei )2 < 0. The capital that is destroyed during anti-government demonstrations also depends on a policy chosen by the autocrat, expenditures on the police, p. The greater are the expenditures on the police, the more difficult it is to destroy capital in demonstrations, ∂η(ei , p)/∂p < 0. Let us call the aggregate impact of anti-government
1 demonstrations, 0 η(eit , pt ) dµt , the amount of instability in this country at time t, where µ is an appropriately defined probability measure defined over agents. Table 1 contains definitions of all variables used in this paper.7 3

We are ignoring issues such as elections and an unfettered media which are important in democracies (Bollen, 1993; Gastil, 1979) because our goal is to determine the factors that cause autocracies to make transitions to democracy, rather than specify how political preferences are expressed in democracies. Focusing on the existence or absence of civil liberties is sufficient for our purposes here. On the political process that results in the granting of civil liberties in democracies, see Sened (1997). Note also that we do not model the transition to democracy as a contest, where the victors divide the spoils of the fallen regime among themselves, as in Roemer (1985), Grossman (1991), and Acemoglu and Robinson (2000), because we find no empirical evidence that those agitating for democracy receive a windfall after the autocrat is deposed. 4 Rather than endow agents with a desire for democracy, we model dissatisfaction with the government as the impetus for demonstrations since those living in an autocracy only vaguely understand what a “democracy” entails. This is consistent with experimental evidence in Kahneman and Snell (1992) showing that individuals do not have fully developed preferences for goods they have not experienced. 5 On the ability to protect and enforce property rights, see Zak (2002) and Tornell (1997). 6 The index i thus reduces two dimensions of heterogeneity into a single dimension. 7 As will be shown later, in the model we ignore the physical effects that police actions may have on demonstrators such as beatings or jail sentences for simplicity’s sake. This will not change the implications of our results since, if the desire for civil liberties is strong enough, these will be endured. A discussion of how the brutality of the police will affect our findings is made after the full model is presented.

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Table 1 Notation used in the model Variable

Definition

i ei hi H η(ei , p) η¯ p γ(p) λ τ ci R ¯ R ai wi K Λi U(ci ) V(ηΛi ai ) Y ω δ ζ β µ σ α

Identifier of agent type Time spent in political activity Time spent working Aggregate hours spent working Technology to destroy capital Average destruction of capital Police expenditures Government’s protection technology Public goods expenditures Tax rate on labor income Consumption Yield on savings (1 + net interest rate) Net-of-destruction return on savings Wealth Wage Capital stock Capital not owned by agent i Utility from consuming goods Utility from the destruction of capital Aggregate output produced using production function F(K, λH) Proportion of output paid as labor earnings Physical capital depreciation rate Democracy/autocracy indicator Subjective discount factor Measure of agents Proportion of tax revenue consumed by autocrat Legitimacy of the autocrat

Presuming that demonstrating agents are rational, they will not destroy their own capital during anti-government demonstrations. If we use a to denote assets (wealth), then agent i’s wealth at time t is ati . Aggregate capital, Kt , at time t is the sum of the assets of all agents,
1 Kt = 0 ati dµt . The total capital that agent i has the potential to destroy by demonstrating against the government at time t is the difference between the aggregate capital stock and ¯ t (Kt − ati ). The interest factor R ¯ (the net interest the capital that agent i personally owns, R rate plus one less average capital losses) enters into at risk capital because the destruction of capital takes place after production has occurred and firms have paid capital owners for the use of their assets in production (which is shown below). Following the contributions of Gurr (1970, 1980), Tilly (1978), Tarrow (1989), Kuran (1989), and Lohmann (1993, 1994), we model agents as receiving utility from activities that weaken the autocrat and facilitate his demise.8 That is, agents protest because they want to change the political system. Theories of the factors motivating demonstrations include grievances against governments that suppress freedoms (Gurr, 1980), reductions in political constraints and the emergence of more open discourse (Tarrow, 1989), and signals 8

Lohmann (1994) provides an excellent review of various theories of mass political action.

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sent by current demonstrations indicating how widely represented are anti-government sentiments and reductions in the political cost of demonstrations (Kuran, 1989; Lohmann, 1994). In our model, agents participate in demonstrations to impel government change through the destruction of capital that reduces the tax base. Below we derive the optimal time spent demonstrating under various economic constraints. As in Lohmann (1994), agents do not necessarily demonstrate when they are most suppressed or when they see a political thaw. Rather, they demonstrate out of a desire to change the political system. A reduction in tax revenue is the means through which the goal of dissatisfied agents is realized. Demonstrations terminate when civil liberties are granted and a transition to democracy occurs. In the next section, we show that a democratic transition is the result of demonstrations by a sufficient number of pivotal citizens, consistent with the model of Lohmann (1994). Let V(ηΛi ai ) : R+ → R+ be a continuous and strictly increasing representation of agents’ preferences for the destruction of capital in anti-government demonstrations, with ¯ V(0) = 0, where Λi ≡ R(K − ai ) is the capital that agent i does not own that can be destroyed. The specification of preferences for demonstrating multiplies the proportion of capital agent i destroys, ηΛi , by agent i’s wealth, ai . That is, the greater is one’s wealth, the more one desires that the autocrat grants civil liberties. This construct captures the strength of the preference for freedoms by those who have access to many other “goods” that life provides. In particular, as an individual’s wealth increases, his or her feasible consumption set grows since prices act as thresholds for the consumption of expensive goods. With sufficient wealth, non-economic goods enter into one’s purview. We can consider “civil liberties” to be such goods that become ever more desirable as one’s wealth grows (Lipset, 1959). This is not to say that the poor do not desire freedoms (which we show below), but that their motivation for political activity is different from those who need not worry about meeting their daily caloric intake.9 Agents also receive utility from consuming goods. We denote agent i’s consumption of goods by ci , and the utility from consuming goods as U(ci ), where U(ci ) is strictly increasing, continuous, concave, and satisfies the Inada conditions. Combining all the aspects discussed above, we can now write down the lifetime utility maximization problem for an infinitely lived agent in an economy where there is a single good that can be either consumed or used as capital in production. Lifetime utility is maximized at time t by choosing consumption, i , and a division of time between working in production, hi , cti , next period’s wealth, at+1 t and time spent in anti-government activities, eit , with future utility flows discounted by β ∈ (0, 1). Thus, agents solve maxcti ,hit ,eit

∞  t=0

βt [U(cti ) + ζV(η(eit , pt )Λit ati )]

s.t. i ¯ t − at+1 cti = wit hit (1 − τt ) + ati R

1 = eit + hit , 9

On the disinclination of the poor to engage in public demonstrations, see Dreze and Sen (1989).

(1)

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where ζ=



1,

if the country is a non-democracy

0,

if the country is a democracy,

7

(2)

for some value of initial assets for agent i, a0i . The first constraint in (1) is the agent’s budget relation. Consumption is funded by net-of-tax labor income wit hit (1 − τt ), which is wage wi times hours worked, hi less taxes ¯ t , less the wealth held for next τ ∈ (0, 1), plus the net-of-demonstration return on wealth, ati R i period, at+1 . The second constraint is the adding-up condition for time allocated between working and demonstrating, with total time normalized to unity. The indicator variable ζ signifies whether agents live in an autocracy or a democracy, since, using our (narrow) definition of a democracy, no demonstrations for civil liberties occur in democracies since all individuals have been granted civil rights. To demonstrate against the government, agents must take time away from work, foregoing the (net-of-tax) wage wi (1 − τ). In this way, we are able to determine the strength of agents’ preferences for demonstrating against the government, V(·), since there is a well-defined cost to acquiring the utility from this activity. One of the differences between model (1) above and a standard apolitical heterogeneous agent growth model is that the return to saving is reduced by the factor 1 − η¯ ≥ 0, where ¯ ≡ R(1 − η¯ ). The term 1 − η¯ appears because demonstrations destroy part of the capital R stock that affects individual returns to investment. Rather than identify the particular agents whose wealth is destroyed in anti-government demonstrations, losses due to demonstrations are assumed proportional to one’s wealth.10 The average amount of anti-government
1 demonstrations for a given level of security expenditures is η¯ t = 0 η(eit夹 , pt ) dµt , where ei夹 is equilibrium time spent demonstrating against the government by agent i. Then, the average loss of wealth due to anti-government demonstrations is ati Rt η¯ t . In this way, it can be seen that anti-government demonstrations reduce the return to savings.11 Individuals solving the utility maximization problem (1) take the government policy triple {τ, λ, p} as given when finding a solution. There are three aspects to government policy. The government chooses funding levels for public goods, λ, and the police, p, deriving revenue from a tax on labor income, τ. In the next section, we characterize how government policies are chosen and show that public goods, λ, affect wages and the return to saving. However, from the individual’s point of view, government policy variables {τ, λ, p} are parameters that affect their consumption, savings, work, and demonstration choices.12 The time t necessary and sufficient conditions for an optimum to problem (1) for agent i at time t are given by i ¯ t+1 U  (ct+1 ) U  (cti ) = βR

(3)

10 Using proportional losses due to insurrections is standard in the general equilibrium literature on conflict (see Grossman, 1991; Grossman and Kim, 1995; Zak, 2002). 11 With a continuum of agents, the choices by any individual have no effect on equilibrium outcomes so that the agent’s choice of ei does not effect η¯ . 12 Public goods are included in the model for two reasons: (1) to permit autocrats to choose policies that both stimulate growth and raise social welfare that we show affects the timing of democratic transitions; and (2) to facilitate a comparison of our results to related models (e.g. BDMSSM) that include public goods.

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and −U  (cti )wit (1 − τt ) + ζV  (η(eit , pt )Λit ati )η1 (eit , pt )Λit ati = 0,

(4)

where η1 (eit , pt ) ≡ ∂η(eit , pt )/∂eit . The first condition, Eq. (3), determines the optimal i夹 . This choice amount of assets held from period t to period t + 1, which we will call at+1

i夹 depends on labor income, wealth, and the interest factor from t to t + 1, at+1 = a(wit hit (1 − i ¯ t+1 ). The second equation, (4), determines the amount of time spent demonstrating, τt ), at , R

eit夹 = e(wit hit (1 − τt ), ati , Λit , pt ). For agents who are living in a democracy, ζ = 0, so that eit夹 = 0. That is, for these agents, all their time is spent working and none is spent demonstrating, hit夹 = 1.13 For politically active agents living in an autocracy, the optimal time spent demonstrating eit夹 ≥ 0. Let us call an optimum in which the values of all variables are constant, a steady state, i.e. i cti = ct+1 = ci , ∀t. In order to keep the analysis as clear as possible, we initially characterize the behavior of citizen-consumers at a steady state. The following results describe optimal individual behavior at a steady state (with proofs provided in Appendix B). Proposition 1. Consider a steady state where agent i is politically active, ei > 0. If agent i’s preferences for civil liberties satisfy ¯ i )R(K ¯ ¯ − 1) −V  (η(ei , p)RΛ − ai )ai U  (ci )wi (1 − τ)(R < 1 − , ¯ i) ¯ ¯ i) V  (η(ei , p)RΛ η1 (ei , p)R(K − 2ai )V  (η(ei , p)RΛ then an increase in agent i’s wealth will increase the time he or she spends in anti-government demonstrations. Proposition 1 shows that as one’s wealth increases, dissatisfaction with the lack of civil liberties grows and, therefore, the time one spends demonstrating increases. We will call this the wealth effect on political instability.14 Since this economy has a large number of agents and aggregate asset holdings sum to the capital stock, it must be the case that K − 2ai > 0 so that the denominator of the right-hand-side term is positive. The proposition may not hold if instability is so high that the average loss of capital reduces the net-of-loss interest ¯ − 1 < 0. That is, very high instability that destroys large amounts of capital may rate R counteract the wealth effect. When instability is moderate, the result always obtains if the ¯ > 1, all terms on preference for demonstrations is convex in the capital destroyed since, if R the right-hand-side of the inequality are positive and the left-hand-side is negative. This does not mean, though, that economic growth (typically leading to increases in wealth and wages for most or all agents) necessarily causes an increase in anti-government demonstrations as the next result shows (the effect of growth on instability is addressed in Lemma 1 after we derive the optima for firms and the policy set by the autocrat). 13 For simplicity’s sake, we abstract from leisure time, though its inclusion would not change the results of the model; a related model that includes leisure time is Zak (2000a). 14 Similar, but more complicated, results can be derived off a steady state, but they add no further insights. A i夹 ¯ The first conditions is strictly increasing in wi and R. steady state exists if hi and λ are both concave in k, and at+1 i follow from the convexity of e(a ) which is discussed in Proposition 10, while the latter two conditions are assumed.

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Proposition 2. Consider a steady state where agent i is politically active, ei > 0. Then, an increase in wages wi causes agent i to decrease the time he or she spends in anti-government demonstrations if the elasticity of the marginal utility with respect to consumption, χ ≡ −U  (ci )/U  (ci )ci , exceeds the ratio of labor income to consumption, χ>

wi hi (1 − τ) . ci

The reasoning behind this result is straightforward. As wages rise, the opportunity cost of demonstrating increases, so the time spent demonstrating falls. We will call this the income effect. Note that if individuals are not sufficiently willing to give up consumption to demonstrate against the autocrat (χ is small), the result will not hold. Therefore, whether aggregate economic growth (an increase in both wages and wealth) increases or decreases dissatisfaction with the government depends on the relative strengths of the wealth and income effects. In aggregate, then, instability is determined by the evolution of the distributions of income and wealth—a point that we will return to shortly. Proposition 3. Consider a steady state where agent i is politically active, ei > 0. If an increase in police spending, p, causes the impact of the time spent in demonstrations to fall, η12 (ei , p) < 0, and ¯ i) −V  (η(ei , p)RΛ η12 (ei , p) , <  i i ¯ ) η1 (ei , p)η2 (ei , p) V (η(e , p)RΛ then police spending reduces instability. This proposition is straightforward to prove as our assumptions on η(ei , p) are that η1 (ei , p) > 0 and η2 (ei , p) < 0, so that the right-hand-side of the inequality is positive if η12 (ei , p) < 0; that is, individuals optimally adjust the time they spend demonstrating by evaluating the impact that their actions will have on the government. As in Proposition 1, Proposition 3 always obtains if V  (η(ei , p) > 0. The three propositions taken together show that the individuals who are most likely to demonstrate for democracy are those above a threshold of wealth as these agents can afford to take time away from work and have a strong desire for civil liberties, and have wages— the opportunity cost of demonstrating—that are not too high. Individuals who satisfy both conditions include students with family wealth but little income and those in the “middle class,” that is, those who have sufficient assets so that they are not worried about their next meal, but whose labor income is not so high that it dissuades them from taking time away from work to demonstrate. By adding income and wealth heterogeneity among agents, we significantly extend Feng and Zak (1998, 1999) in which it was assumed that agents become politically active when a wealth threshold is reached. The result here is subtler. A certain level of wealth is required before one becomes significantly involved in political demonstrations, but high wages militate against political activity. This leaves those in the middle income group to protest against the government. We will explore the impact of political demonstrations on regime stability once we characterize the autocrat’s choices and the profit maximization problem faced by firms.

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2.2. Choices of the autocrat Economic growth is a goal of both developmentalist autocrats as well as autocrats who seek to maximize their long-run take from the economy (McGuire and Olson, 1996). Only predatory autocrats with short time-horizons will set policies that cause the economy to contract rather than grow. As discussed above, the available government policy instruments {λ, p, τ} are, respectively, public investment, security expenditures, and an income tax rate. Public investment raises labor productivity while security expenditures raise the return to capital by reducing the destruction of capital in anti-government demonstrations. For simplicity, we consider a government that has a balanced budget each period. A portion σ ∈ [0, 1] of tax revenue is taken by the autocrat as the administrative cost of running the government. This can be considered a tribute. Let the function γ(p) : R+ → [0, 1] be the protection technology of the government that reduces the losses of capital due to anti-government demonstrations. As discussed above, police expenditures reduce the rate at which capital is destroyed, γ  (p) > 0, and we assume that continuing to increase police funding has a decreasing impact on the rate of destruction of capital, γ  (p) < 0. With perfect information about the effect of policies on the socio–political–economic environment, the government’s protection technology would coincide with aggregate demonstrations by
individuals, γ(p) = η(ei , p) dµ. Because political uprisings can emerge and dissipate quickly (Lohmann, 1994), the one-to-one mapping between policies and
outcomes does not necessarily hold in unstable polities. Accordingly, we permit γ(p) ≡ η(ei , p)dµ and use this asymmetry below to gauge when the autocrat loses political control. Indeed, an important innovation in this model (shown below) is that the autocrat does not choose to relinquish power during a transition (e.g. in a bargaining game), but is defenestrated through physical violence. Note that reducing losses of capital raises the effective return to investment as more capital remains in production and therefore raises tax revenues flowing to the autocrat. However, the police can be over-funded since raising police expenditures reduces the funding available for public goods and, by raising taxes, incomes and therefore savings fall. As a result, policies, in part, determine the growth rate of the economy. Next, we characterize the government’s optimal policy set. It seems reasonable to assume that the autocrat is not able to observe the actions of each of the large number of individuals in his country, specifically the time each spends working or demonstrating. The autocrat only observes aggregates—capital and labor hours. An autocrat who seeks to maximize the growth rate of the economy (equivalently, the present value of 15 the tribute) chooses the policy triple {λt , pt , τt }∞ t=0 by solving maxλt ,pt ,τt

Kt+1 Kt

(5)

s.t. Yt = F(Kt , (1 − σ)λt Ht )

(6) ∞

15 The present value of the tribute is t=0 στt ωYt /Πt Rt , where Πt Rt is the compounded discount factor and ω is defined in the text below, is strictly increasing in output Y which is strictly increasing in capital K (see Appendix A).

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Yt (1 − τt ω) = Ct + It

(7)

It = Kt+1 − (1 − δ)(1 − γ((1 − σ)pt ))Kt

(8)

τt ωYt = (1 − σ)[λt + pt ].

(9)

Let us describe each equation of the problem above in turn. First, consider the objective (5). When the production function, F(K, (1 − σ)λH), in Eq. (6) is homothetic, which we will assume is the case, output growth Yt+1 /Yt is proportional to growth in the capital stock Kt+1 /Kt . The autocrat in this model maximizes capital deepening, which under homotheticity is equivalent to maximizing the growth of output.16 Eq. (6) specifies the production process through which capital and labor are turned into output, Y . The relation F(K, (1 − σ)λH) is a neoclassical production function that is continuous, strictly increasing and concave in both capital, K, and efficiency hours of labor that is defined as aggregate
1 hours worked, H = 0 hi dµ, times net public goods spending (1−σ)λ, with both arguments in F(·, ·) satisfying the Inada conditions. Eq. (7) is the resource constraint faced by the autocrat that equates net-of-tax output to aggregate private consumption, C, and aggregate private investment, I. Since individuals solving (1) have two sources of income, labor earnings and investment income, with only the former being taxed, ω > 0 is the proportion of aggregate income that is earned as wages.17 Using the stock accounting method, Eq. (8) shows that investment can be written as the change in the capital stock Kt+1 − Kt correcting for capital depreciated in the process of production, δKt , where the depreciation rate δ ∈ [0, 1], and the government’s best estimate of the proportion γ((1 − σ)pt ) of capital destroyed by agents in anti-government demonstrations. The last Eq. (9) is the government’s budget constraint where tax revenue τωY is used to fund security expenditures, p, and public goods, λ, less the cut taken by the autocrat, σ. Problem (5) is a modified “planning problem” where the government allocates resources in order to maximize the growth rate of capital rather than, as in the standard case, allocations are chosen using a Pareto optimality criterion. Because the autocrat is not able to determine each individual’s behavior, the modified planning problem above is the autocrat’s approximation of the state of the economy that he uses to set policy. The descriptive literature on regime change has argued that regimes that are viewed as “legitimate” are longer lasting. We operationalize this notion by defining the ratio of government expenditures on investment λ, to total expenditures, p + λ, as the perceived legitimacy of a regime. The way we have defined legitimacy is not the only possible one, though we think it is intuitively appealing. For example, citizens in a small country with a predominate ethnic group might show high affinity for a ruling autocratic regime so that perceived regime legitimacy is high. In such a case, a larger proportion of tax revenue can be funneled into public investment as there is a sense that the group is as whole is making a sacrifice (τ > 0) to develop and anti-government demonstrations are few. When there is less of a sense of group identity, or when there are clearly defined elites who seem to 16 Using capital rather than output in the objective function simplifies the analysis because capital is the state variable observable by the government, i.e. all variables in the government’s optimization problem, including output, are functions of capital. This is clear from the definition of a political–economic equilibrium in Appendix A. 17 Under the assumption that production is homothetic, ω is constant.

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benefit from development at the expense of the population as a whole, the proportion of tax revenue required to keep the peace (p) is higher and legitimacy is lower. Let α denote the level of the autocrat’s legitimacy that is assumed time invariant,18 α≡

λt . pt + λ t

(10)

To simplify the notation in the autocrat’s optima, define p¯ ≡ (1 − σ)p and λ¯ ≡ (1 − σ)λ as the net-of-tribute expenditures on security and public goods. Then, the autocrat’s optimal security expenditures, found by solving (5) and using (10) satisfy, after some manipulation, αHt F2 (Kt , Ht λ¯ t ) − (1 − α)γ  (p¯ t )Kt (1 − δ) = 1.

(11)

This condition says that the growth maximizing amount of security expenditures balances the marginal benefit of security (less capital destroyed) with its cost (τ), since raising taxes reduces the funds available for public goods thus reducing the prospects for growth. Once the optimal value for security is found, the budget constraint (9) and definition of legitimacy (10) can be used to find the optimal amount of public goods expenditures and the tax rate. The next result characterizes optimal security and public goods expenditures by the autocrat. Proposition 4. Under the stated assumptions on the production function, optimal security and public goods expenditures chosen by the autocrat are increasing in the capital stock if −γ  (p¯ t )(1 − α)2 (1 − δ)Kt > −F22 (Kt , Ht λ¯ t )α2 Ht2 and (1 − α)(1 − δ)p¯ t Ht [γ  (p¯ t )Ht − γ  (p¯ t )(1 − α)Kt ] > α(1 − α)Ht [Ht F2 (Kt , Ht λ¯ t ) + F21 (Kt , Ht λ¯ t )]. The proof of this result follows directly from condition (11) and definition (10). It says that if this economy is growing rather than contracting (i.e. growth means that Kt+1 > Kt ), then optimal expenditures on security and public goods are increasing.19 Note that since output is increasing in capital, the proposition above is equivalent to saying that optimal security and public goods expenditures increase in a country’s GDP. Proposition 4 is likely to be satisfied since in both conditions of the proposition, the left-hand-side is linearly increasing in K. Thus, for moderate to high levels of GDP, optimal public goods and security expenditures are increasing in a growing autocracy. The above result begs the question of whether the choice of the autocrat’s policy will cause the economy to grow at all. If the autocrat is myopic and demands a sufficiently high tribute σ, then this economy will contract rather than grow. To demonstrate this claim requires that we characterize the dynamics of the economy as given by the individual optimality conditions 18 Assuming legitimacy to be constant over time simplifies its analysis considerably. Later in this section, we examine the implications for autocratic policy-setting when legitimacy is permitted to vary. 19 Zak (2002) provides empirical support showing that security expenditures increase in output; Feng (1997) shows that public goods expenditures increase with growth.

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(3) and (4), and the capital market clearing condition in which savings by individuals funds the investment undertaken by firms. This condition is  1 i夹 Kt+1 = at+1 dµt . (12) 0

Using the capital market clearing condition (12), the next result shows that if τ is sufficiently high (because, for example, the tribute σ or security expenditures p are high), or σ itself is high, then the economy will contract rather than grow. Thus, the government budget constraint (9) applies to both developmentalist autocrats and myopic (predatory) autocrats. The difference between these is that a predatory autocrat takes such a large tribute (or will set a high tax rate so that his take, σ[λ + p], is high) that output falls. That is, the parameter σ indicates the planning horizon of the autocrat.20 Proposition 5. If the tribute σ or the tax τ is sufficiently high, then output will contract. The proof of Proposition 5 substitutes the optimality condition for hours worked (4) into the optimal savings condition (3) and examines how these change as σ and τ change. It is straightforward to show that as τ → 1, labor income wi hi (1 − τ) → 0 and therefore i夹 at+1 → 0, ∀i. By the mean value theorem, there is some value of τ such that Kt+1 < Kt in (12) for which the economy contracts rather than grows. Now consider what happens as σ → 1. Output Y → 0 so that labor income necessarily approaches zero and again i夹 at+1 → 0. Thus, high rates of resource appropriation by the autocrat or excessively high taxes cause the economy to contract rather than grow. We have therefore shown that the policies of myopic autocrats can mire their economies at a permanently low level of income, called a poverty trap.21 Government legitimacy also affects the rate of output growth as the next two results demonstrate. Proposition 6. If p > 0, then the growth maximizing level of legitimacy, call it α夹 , is given implicitly by   (1 − σ)pα ¯ 夹 1 = . F2 K, 夹 H 1−α This result follows because a government’s perceived legitimacy determines the proportion of tax expenditures allocated to the police versus public goods. Note, though, that since the government expects some level of instability (Feng and Gizelis, 2002; Zak, 2002, 2000b), the output maximizing level of legitimacy is less than one. When the value of legitimacy satisfies α ≡ α夹 , output growth will not be at its maximum. For α < α夹 , too much revenue is spent maintaining public order and not enough is spent on public goods. For α > α夹 , public goods is overfunded so that a larger amount of capital is destroyed in anti-government 20 The tribute σ could be endogenized in our model, as in BDMSSM. For example, when an overthrow is imminent, σ would be expected to rise. 21 A survey of mechanisms that produce poverty traps can be found in Azariadis (1997).

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demonstrations than need be. Proposition 6 shows that an autocrat’s level of legitimacy is a determinant of the economy’s growth rate and, as will be shown in the next section, affects the longevity of the autocratic regime. If we allow legitimacy α to vary over time, it is straightforward to show the following. Proposition 7. If the conditions in Proposition 3 are satisfied, then output growth raises legitimacy if the growth in public goods expenditures exceeds the growth in police expenditures. Proposition 7 is quite intuitive. If an autocrat increasingly funds public goods so that its growth exceeds the growth in expenditures to maintain public order, legitimacy rises relative to an autocrat who must spend more of his resources defending his regime. We now make a simplifying assumption. Assumption 1. The autocrat chooses the policy triple {λ(Kt ), τ(Kt ), p(Kt )}∞ t=0 using (11) every period, given K0 , beginning when the autocrat takes power at t = 0, and it is maintained while the regime is in power. Assumption 1 guarantees that the government’s problem is stationary (i.e. is identical each period as given by (5)). It is consistent with both the autocrat having imperfect information when setting policy as well as the sluggishness of the government to perceive changes in the political–economic environment and adjust policy, called “governmental sclerosis” by Olson (1982), Rauch (1994), Lohmann (1996) and McGuire and Olson (1996). In particular, Assumption 1 rules out strategic changes in policy meant to sustain the autocrat in times of high instability and sets up the government to face a “prairie fire” effect where, prior to a regime change, the government is unable to react to the momentum of change as in Kuran (1991, 1989). Assumption 1 can be relaxed without changing the qualitative results we derive for regime changes, though the model’s complexity will increase substantially.

3. Democratic transitions We define a democratic transition as the point at which there is sufficient instability to overwhelm the autocrat’s policy. That is, a regime change occurs when the autocrat can no longer maintain public order.22 Equivalently, the autocrat is unable to continue ruling because he is deprived of tax revenue needed to maintain himself in power. Formally, a democratic transition occurs when  1 夹 η(eit夹 , p夹 (13) t ) dµt ≥ γ(pt ), 0

where ei夹 is the individual optimal time in political activity from (4), and p夹 is the autocrat’s optimal police expenditures from (11). A transition to democracy in this model is a “surprise” both from the autocrat’s and the population’s point of view: at some point the autocrat is 22

A similar criterion for regime change is used by Kuran (1989).

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unable to maintain the protection of capital, his tax base shrinks, and along with it his hold on power.23 The primary result of this paper is shown below. Proposition 8. A transition from autocracy to democracy occurs when • the economy contracts sufficiently; • the conditions in Propositions 1–3 are satisfied and the economy grows sufficiently with   1  1 ∂η(ei , p) wi (K) + ai (K) ∂η(ei , p)   dµ ≥ γ dµ. (p)p (K) − i  ∂e p (K) ∂p 0 0 When the economy is contracting, the income effect on demonstrations strengthens as wages fall, eventually overwhelming the autocrat’s attempt to maintain order γ(p).24 The model shows that economic crises in autocracies always lead to democratic transitions since citizens have “nothing to lose” by demonstrating for a better government. Examples of this type of regime change are the former Soviet Union and its satellites and the Philippines in 1986 under Marcos. If a democracy emerges out of economic crisis and is successful in sustaining economic growth, no further regime changes will occur. Conversely, if a democratic regime is unsuccessful economically, a regime change will be made, perhaps to autocracy.25 In the case of a growing economy, the conditions in Proposition 8 indicate that the destabilizing effects of growth eventually dominate the effects of greater police spending (for p (K) > 0). The reasoning behind this part of the proposition can be gleaned from the following lemma. Lemma 1. Consider a non-trivial steady state of the political–economic system described by (1) when agent i is politically active, ei > 0 and the conditions in Propositions 1 and 2 are satisfied. Then, positive output growth causes agent i to increase the time he or she spends in anti-government demonstrations. 23

Note that the model only includes one (important) type of democratic transition, that arising from physical violence. Criterion (13) and indeed the model does not apply to other methods through which democracy emerges, such as military coups that lead to elections, or extensions of the franchise (Acemoglu and Robinson, 2000). 24 By analyzing the profit maximization problem of firms (Appendix A), we show that wages, wi , and the return to savings, R, depend on aggregate capital, public goods, and the effective labor hours in production, L = (1−σ)λH, Rt+1 = F1 (Kt , Lt ) + 1 − δ, wit = ,i F2 (Kt , Lt ), where the vector , = [,1 , ,2 , . . . , ,N ] is a set of parameters which identify the productivity of agents who are grouped in a finite number of groups, N. 25 Revolutions and coups are not the focus here, though the model predicts that these are more likely to occur in economic downturns (i.e. if the tax or tribute are high, or public investment is low), and in societies with unequal distributions of income. This is shown formally in Feng and Zak (1998) and matches the predictions of Acemoglu and Robinson’s (2001) model of redistribution and regime change. Supporting empirical evidence can be found in Gasiorowski (1995) and Przeworski and Limongi (1997).

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That is, in growing economies, the wealth effect dominates the income effect on demonstrations. Because civil liberties are increasingly desired as wealth increases, demonstrations increase with growth, even though growth raises wages and the income effect works to decrease demonstrations. This is the reason why in many countries, such as South Korea and Taiwan, sufficient growth leads to transitions to democracy in which increasing wealth raises the proportion of the population who desire freedoms, leading to an increase in anti-government demonstrations. In order to fix the notion that the income effect dominates the wealth effect only when capital is very low, we construct a simple example to show this. The general condition for de夹 /da > |de夹 /dw|, which holds under the conditions of Propositions 1 and 2, is ¯ 2 (K − ai )(K − 2ai )ai + U  (1 − τ) −V  ηη1 R ¯ ¯ − 1] + V  η1 R(K < −U  wi (1 − τ)[h(1 − τ) + R − 2ai ).

(14)

¯ i )) = Bη(ei , p)RΛ ¯ i , for A, B > 0. Now the condition Let U(c) = Ac and V((η(ei , p)RΛ that guarantees that the wealth effect dominates the income effect is 1−τ<

B ¯ − 2ai ). η1 R(K A

(15)

¯ is bounded above, and noting that by the capital market clearing condition (12) as If R K → 0 necessarily ai → 0, inequality (15) is satisfied for all K except for K near zero. Thus, the wealth effect on anti-government demonstrations exceeds the income effect unless income (equivalently, capital) is very low. As a result, in a growing economy, demonstrations increase as development raises wealth levels. Conversely, in a contracting economy, the income effect eventually dominates the wealth effect, leading to an increase in demonstrations. Thus, sufficient growth or contraction of the economy causes a democratic transition. Another implication of Proposition 8 is that transitions to democracy are retarded when growth is slow but positive. Slow growth occurs with high taxes, low public goods spending, or a high tribute taken by the autocrat. Transitions to democracy are also slow when preferences for demonstrations against the government V(·) are weak. Some societies may value freedoms more than others and are willing to demonstrate to express this preference while others are less strongly motivated by freedoms. In addition, the closer a country’s legitimacy is to the growth maximizing level, the faster will a democratic transition occur. Since, given a level of instability, a country may or may not be at the growth maximizing level of legitimacy, legitimacy has a non-monotone impact on the speed of democratic transitions. Economically successful autocrats that are viewed as legitimate will have high growth rates and will make transitions to democracy early in their development history. For economically stagnating countries, autocrats will remain in power without a transition to democracy because of their poor mix of implemented policies. On the other hand, policies that raise growth rates such as public goods spending or lead to greater wealth equality will hasten transitions to democracy.26 26 Feng and Zak (1999) provide empirical support showing that education expenditures increase the probability of a democratic transition.

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3.1. The distributions of income and wealth and democratic transitions Perhaps the most interesting result coming from the model is that the distributions of income and wealth affect the speed of democratic transitions. Following the propositions above characterizing political activity for individuals of various income and wealth levels, the definition of a democratic transition indicates that aggregate instability increases as the mass of moderate income and wealth individuals increases. As a result, regime transitions are primarily determined by the political activity of those in the middle income and wealth groups. While the wealthy and poor engage in anti-government demonstrations (for quite different reasons), until they are joined by the “middle class,” there will be insufficient aggregate instability to cause a regime change. Consider what happens in a growing autocracy where the maintenance of public order leads to rapid development but causes increasing discontent due to the lack of civil liberties. The democracy threshold is reached when a sufficient mass of the middle wealth agents joins the wealthy in anti-government activity (the wealth effect dominates). Conversely, an autocracy in which wages are falling will drive an increasing proportion of middle income agents into poverty, raising anti-government demonstrations and causing the government to be overthrown (the income effect dominates).27 Therefore, the model predicts that it is the “middle class” who will drive regime transitions, both in good economic times and in bad. Furthermore, the “modernization” effect that propels democratic transitions in growing economies is actually a wealth-driven impetus to political activity. Fig. 1 illustrates democratic transitions with both economic growth and contraction, showing how these shift the distribution of wealth causing political activity to increase (the distribution of income is not shown in the figure). Next, we formalize how changes in the distributions of income and wealth affect the pace of democratic transitions, holding aggregate capital constant (i.e. absent growth effects). These characterizations depend on variations in the strengths of political activity among all agents in the economy. In particular, we examine an increase in the variance of the income and wealth distributions, holding the mean constant. This is known as a (simple) mean preserving spread of the base distributions (Rothschild and Stiglitz, 1970). Two of the novel results that come out of the model are Proposition 9. If the conditions of Proposition 2 are satisfied and ∂2 ei夹 /∂(wi )2 > 0, then a mean preserving spread of the distribution of wages decreases instability, and Proposition 10. If the conditions of Proposition 1 are satisfied and ∂2 ei夹 /∂(ai )2 > 0, then a mean preserving spread of the distribution of wealth increases instability. Proposition 9 shows that if the income effect on demonstrations declines at a decreasing rate, then a less egalitarian distribution of wages decreases the amount of political activity. 27 Note that there is no collective action problem to be solved as in Olson (1965, 1992) since individuals act in a privately optimal manner without having to coordinate their actions with others. If agents coordinate their actions or value civil liberties directly, democratic transitions will occur more rapidly.

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Fig. 1. Shifts in the distribution of wealth lead to democratic transitions.

The condition in the proposition guarantees that when there are more agents in the tails of the income distribution, the increase in political activity by poor agents is less than the reduction in political activity by high wage agents. The import of this proposition is that, holding all else constant, countries with less equal distributions of income make transitions to democracy more slowly than those with more equal income distributions. Equivalently, if the distribution of income in a certain country is egalitarian, transitions to democracy occur for lower values of per capita income than in countries that are less egalitarian. Proposition 9 also implies that countries with an unequal wage distribution, for example because of ethnic discrimination, undergo transitions to democracy more slowly that in “fairer” countries.28 Proposition 10 examines the impact of changes in the distribution of wealth on instability, showing that greater inequality in wealth increases agitation for democracy. Proposition 10 and Lemma 1 reinforce Proposition 8 by showing that growing autocracies in which the distribution of wealth is becoming more unequal will have increasing instability, resulting in a democratic transition.29 Observe that the democracy threshold (13) may never be met if security expenditures p are sufficiently high, the government’s protection technology γ(p) is efficacious, or the evolution of the economy limits the mass of wealthy agents to be small and does not 28 Discrimination can be easily built into the model be permitting the wage allocation vector , to determine the allocation of total wages based not on productivity, but on other factors, such as ethnicity. See Zak and Knack (2001) for an examination of the relationship between fairness, discrimination, and economic growth. 29 The effect of changes in both the distributions of income and wealth on the speed of democratic transitions is ambiguous.

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impoverish a large proportion of the population (by Propositions 1 and 2). The autocrat can more effectively maintain order for a given level of police spending if the police are especially brutal or the area to be protected is geographically small (e.g. Singapore). In most cases, though, there will be two democracy thresholds given by (13): one for autocracies that are growing, and one for contracting economies, as Fig. 1 depicts. More generally, the model reveals that growth, government policies, the distributions of income and wealth, and an autocrat’s legitimacy all determine the speed of democratic transitions. This significantly extends Lipset’s modernization hypothesis by showing that income alone does not necessarily cause transitions to democracy.

4. Discussion The model in this paper demonstrates that the economic position of the “middle class” determines the rate of transition from autocracy to democracy.30 If a sufficient number of those in the “middle class” become rich or poor, a transition to democracy will occur. The growth rate of output—either positive or negative—also affects the pace of democratic transitions and is determined by individuals’ saving decisions and government policies, including the amount the autocrat extracts from production as a tribute. As the economic environment evolves, citizens are driven to political activity, either to weaken the government in order to compel it to grant civil liberties with positive growth (the wealth effect) or to protest low incomes resulting from economic mismanagement (the income effect). The theory’s focus on changes in support for a government by the “middle class” is consistent with a large literature on regime transitions. Roemer (1985) posits a game between the proletariat and the Tsar in which the “middle class” determines whether the Tsar is defenestrated. Huber et al. (1993) argue that the size of the “middle class” determines the political balance of power and thus regime stability. Haggard and Kaufman (1995) show that most political regime changes occur in economic crises when there is loss of political power, consistent with the model here. Though unlike the unified theory we present, Haggard and Kaufman call non-crisis political transitions “anomalous.” Consistent with our results, Lohmann (1993, 1994) argues that demonstrations lead to meaningful political change only if “people with relatively moderate opinions participate in the initial stages of a mass protest movement” (Lohmann, 1994, p. 53). In our model, the middle class represents such a critical mass. The model in this paper is related to BDMSSM as both models focus on the distribution of economic resources as the source of conflict and cause of regime change. We see the results of BDMSSM and those from our model as being highly complementary; while BDMSSM focus on coalitions of support for an autocrat, our focus is on how the transformation of the economic environment changes the incentives to protest against the ruling regime. In addition, our model includes explicit dynamics, driven by saving by individuals and government policy, that determine the rate of evolution of the level and 30 “Middle class” is a term we dislike for it connotes something more than partitioning agents by levels of income or wealth, though it is commonly used in the literature. For example, see the survey of the literature on the growth of the “middle class” and regime change in Trebilock (1995).

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distribution of resources. Our theory can be also be interpreted as a model of an emerging civil society.31 The model in this paper also contributes to the literature on the speed of political regime changes. Following Kuran (1989), let us call the prairie fire effect a situation in which a small change in economic fundamentals induces a large change in political instability. When the distributions of wages and wealth are egalitarian, the prairie fire effect is more likely to occur. More precisely, if the distribution of income (or wealth) is relatively egalitarian, then a small change in K will induce a large change in the amount of anti-government demonstrations under Lemma 1. Thus, countries with more egalitarian distributions of income (or wealth) are more likely to undergo rapid regime changes. Inequality slows the transition to democracy, a result also found in the static model of Acemoglu and Robinson (2001). One of the novel aspects of the model is the derivation of government policies for autocrats and the implications of how these affect the timing of democratic transitions. Consider the case of Poland. Per capita incomes were quite low in the late 1980s, with a large mass of the population being impoverished. When anti-government demonstrations began, a response from their Soviet overseers was expected. In the nomenclature of the model, the signal that the Soviets would not intervene in the fomenting revolution of Poland was a shift in the γ(p) curve in Fig. 1 downward, leading to a rapid transition to democracy. Lastly, note the theory exposited here does not rule out democracy in poor countries. If these democracies are able to sustain income growth for a reasonable proportion of the population, there is no reason that democracy cannot be maintained. Conversely, Feng and Zak (1998) show that a democracy that is unsuccessful economically will make a transition away from democracy and to another form of government. If the government is unable to engineer a sustained development program, irregular government change will ensue until a government that is economically successful appears.32 In sum, the growth and distribution of the gains from economic development, the autocrat’s policies, planning horizon, and legitimacy all determine whether and when a transition to democracy will occur in the jointly intertwined dynamics of economic and political development. Though such a transition can occur without any overt policy response by the government, policies that speed growth and encourage equality will hasten the transition to democracy.

Acknowledgements We thank Jacek Kugler, Michael Spagat, an anonymous referee, an associate editor of this Journal and seminar participants at the Claremont Graduate University Conference on 31 Our model can also be understood in light of the “great man” (or “person”) theory of regime change. Some individuals may have innate preferences for civil liberties that are more intense than others. For example, Aun San Suu Kyi has demonstrated for democracy in Burma at risk of her life. Our model specifies the political–economic environment that is conducive to the rise of a charismatic opposition leader. The theory shows that either in economic success or severe crisis, such a leader is more likely to have a sufficient number of followers to lead in protests against the government. 32 Londregan and Poole (1990) call the multitude of government changes of economically unsuccessful governments the ‘coup trap.’

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Democratic Transitions for astute comments that have substantially improved our exposition. All remaining errors are the sole responsibility of the authors.

Appendix A. Profit maximization by firms, and the definition and properties of equilibrium Wages, wi , and the rate of return to investment, r, are determined by a large number of identical firms operating in competitive markets. Firms in the economy take government policy, a determinant of labor supply by (4), as given when maximizing profits. Output is produced using private capital, K, and aggregate effective labor hours, L ≡ (1 − σ)λH, through production process F(K, L). The profit maximization problem for a representative firm is maxK,L F(Kt , Lt ) − rt Kt − wt Lt .

(A.1)

Note that the destruction of capital occurs after the production decision and thus does not affect firms’ choices. Factor prices are given by rt = F1 (Kt , Lt ),

(A.2)

wt = F2 (Kt , Lt ),

(A.3)

where wt is the total aggregate wage bill paid at time t. Partitioning the space of agents into N subintervals where agents within a subinterval are equally productive, wages of a type i agent are given by wit = ,i F2 (Kt , Lt ).

(A.4)

The vector , = [,1 , ,2 , . . . , ,N ] is a set of parameters which distributes  the iproportion of the wage bill to each type of agent based on his or her productivity, N i=1 , = 1. Lastly, the interest factor Rt+1 is given by the net-of-depreciation marginal product of capital, Rt+1 = rt+1 + 1 − δ. A political–economic equilibrium is a sequence of wages and interest rates {wit , rt+1 }∞ t=0 , i = 1, 2, . . . , N, government policies {λt , τt , pt }∞ and an initial distribution of assets t=0
1 among agents at t = 0, a 0 with 0 a0i dµ = K0 , such that, taking wages, interest rates and government policy as given, agents maximize lifetime utility using (3) and (4), firms maximize profits via (A.2) and (A.3), and the capital, labor and goods markets clear. Market ¯ t+1 by (12) and the labor market clearing in the capital market obtains at time t for price R clears for price wt when  1 Lt = (1 − σ)λt hit dµt , (A.5) 0

where Lt is firm demand for labor found by inverting (A.3). The goods market clears by Walras’ Law. The equilibrium in this model is a second-best solution for two reasons. First, in most cases, the autocrat does not operate the government costlessly, taking resources out of the

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economy for his own use (σ ≥ 0). Even if σ = 0 indicating that the autocrat is perfectly efficient and uninterested in his own income, the equilibrium is still second-best since the autocrat chooses optima in (5) with imperfect information regarding agents’ actions.

Appendix B. Proofs The proofs to selected propositions in the text are included when the results are novel or the proofs are instructive. Proofs to other results in the paper are simply sketched, with full proofs available from the authors on request. The proofs to Propositions 1–3 are found by totally differentiating first order condition (4) and solving subject to ∂ei /∂ai > 0, ∂ei /∂wi > 0, and ∂ei /∂p > 0, respectively. Proposition 4 is proved in a similar way using first order condition (11) and the definition of legitimacy (10). The proof to Proposition 5 is sketched in the text. Proof of Proposition 6. Using the autocrat’s policy-choice problem (5) where, instead of solving for policies, one solves for the value of α that maximizes capital deepening, leads to the first order condition (with time subscripts are suppressed) F2 (K, (1 − σ)p/1 ¯ − α) p¯ − = 0. 2 (1 − α) (1 − α)2 Rearrangement produces the condition in the proposition, but it still remains to be shown that this is a maximum, not a minimum. Differentiating the first order condition above with respect to α and making the substitution HF2 (K, (1 − σ)pα ¯ 夹 /(1 − α夹 )) = 1, the second order condition evaluated at the optimal value of α is negative. Thus, α夹 is indeed is a maximum. 䊐 Proof of Proposition 7. The growth in public goods spending exceeds the growth in police spending if λ p > , λ p where for all variables x, x ≡ x (K). This condition is equivalent to λ p + λ λ − λ λ − λp > 0, which can be written as λ (p + λ) − λ(p + λ ) = α (K) > 0, (p + λ)2 using the definition of legitimacy (10). Therefore, economic growth raises legitimacy if the growth in public goods expenditures exceeds the growth in police expenditures. 䊐
1 Proof of Proposition 8. Observe that as K → 0, 0 η(eit夹 , pt ) dµ > 0 and γ(pt ) → 0. Therefore, democratic transitions occur in economic crises. The proof of the second part

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of the Proposition uses Lemma 1 which is proved straightforwardly by showing that the conditions in Propositions 1 and 2 imply that ∂ei /∂ai > |∂ei /∂wi |. This proof is simple so we save the reader its exposition. Proceeding to the proof of the Proposition, note that
1 as K → ∞, 0 η(eit夹 , pt ) dµ > 0 and γ(pt ) ≥ 0, so that economic growth does not necessarily guarantee that a transition to democracy will occur. Writing the criterion for a
1 democratic transition as 0 η(eit夹 , pt ) dµ − γ(pt ) = 0 and differentiating using Leibnitz’s rule produces    1  1  ∂η(ei , p) wi (K) + ai (K) ∂η(ei , p)   dµ ≥ γ dµ. (p)p (K) − ∂ei p (K) ∂p 0 0 If this condition is satisfied, growth leads to a democratic transition. By Lemma 1 and Proposition 3, the left-hand-side of the above inequality is strictly positive. Under the assumptions on γ(p) and η(ei , p), γ  (p) > 0 and ∂η(ei , p)/∂p < 0 so that the first term on the right-hand-side of the inequality above is positive and the second term is positive. Therefore, growth raises instability if the inequality is satisfied. 䊐 Proposition 9 is proved in a manner analogous to Proposition 10 below, so the proof is omitted. Proof of Proposition 10. A simple mean preserving spread (MPS) of the distribution of wealth increases the mass of agents in the tails of the distribution without changing the mean. Under the assumption that ei夹 is convex in ai , we can apply the result of Rothschild and Stiglitz (1970) on the integration of convex functions to show that the increase in demonstrations by the greater mass of high wealth agents in the spread distribution is less than the decrease in demonstrations by the low wealth agents. 䊐 References Acemoglu, D., Robinson, J.A., 2000. Why did the west extend the franchise? Democracy, inequality and growth in historical perspective. Quarterly Journal of Economics 115 (4), 1167–1199. Acemoglu, D., Robinson, J.A., 2001. A theory of political transitions. American Economic Review 91 (4), 938– 963. Adelman, I., Robinson, S., 1989. Income distribution and development. In: Chenery, H., Srinivasan, T.N. (Eds.), Handbook of Development Economics, vol. 2. North-Holland, Amsterdam, pp. 949–1003. Azariadis, C., 1997. The economics of poverty traps, part one: complete markets. Journal of Economic Growth 1 (4), 449–486. Barro, R., 1996. Democracy and growth. Journal of Economic Growth 1 (1), 1–27. Barro, R., 1999. Determinants of democracy. Journal of Political Economy 107 (6), S158–S183. Bollen, K.A., 1993. Liberal democracy: validity and method factors in cross-national measures. American Journal of Political Science 37, 1207–1230. Brenner, Y.S., Kaelble, K., Thomas, M., 1991. Income Distribution in Historical Perspective. Cambridge University Press, Cambridge. Bueno de Mesquita, B., Smith, A., Siverson, R., Morrow, J., 2003. The Logic of Political Survival. MIT Press, Cambridge. Burkhart, R.E., Lewis-Beck, M.S., 1994. Comparative democracy: the economic development thesis. American Political Science Review 88, 903–910.

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