The Costs and Benefits of Autocracy

The Costs and Benefits of Autocracy Jiahua Che∗ Kim-Sau Chung† Xue Qiao‡ June 26, 2011

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Introduction

One of the most remarkable events the world witnessed during the last three decade was the spectacular economic development taking place in China. China’s economic development was remarkable, and to many a miracle, because the rapid economic growth sustained through the thirty years of time was made possible under a regime that monopolized the political power, constrained by no checks and balance, which we so often associate with quality governance of a nation. However, China was not alone in this respect. Turning the clock further back another thirty years, the rise of many emerging market economies, including South Korea, Taiwan, and Singapore, had all spearheaded by political regimes of similar sort. At the opposite end of this picture, however, are the conviction at various corners around the world that economic progress would not be possible without an accountable government, and with such conviction, the abandonment of authoritarian regimes by the populace, two decades ago in the former soviet bloc, and now in the Arabic world. These historical and on-going episodes require us to evaluate the autocratic regime in comparison to a democratic one. They require us to develop an understanding as to why, in some cases, autocracy seem to be able to perform reasonably well not just over a short spell of time but continuously over many generations, whereas in other instances, the same political institution has failed so miserably in so many places around the world. With the bulk of the political economy literature devoting their attention to analyzing democratic institutions, the effort to this end has largely been missing. ∗

Department of Economics, Chinese University of Hong Kong, Hong Kong; [email protected] Department of Economics, University of Minnesota, U.S.A.; [email protected] ‡ Department of Economics, Tsinghua University, China; [email protected] †

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As an attempt to fill this gap, this paper draws a comparison of the performances of these two political regimes. Our comparison begins with what we view as a defining institutional feature that sets the two regimes apart. In autocracy, the right to select the political leader rests with the incumbent leader himself, whereas in democracy the right is shared by the public through majority voting. With this perspective, we remove any possibility of political competition under autocracy, and focus instead on how each political institution selects its leader one term after another. This is not to say that political competition never matter in autocratic regimes. However, it is not what makes autocracy autocratic and we view it as distraction for truly understanding the very nature of autocracy. To this end, we set aside any political incentives motivated by the re-election concern by assuming one-term limit for each leader.1 In the “Federalist Papers”, James Madison wrote that the “aim of every political Constitution is or ought to be, first to obtain for rulers men who possess most wisdom to discern, and most virtue to pursue, the common good of society”. Following this spirit, we postulate the presence of benevolent politicians, who seek to maximize the long-term welfare of all people, alongside politicians who are self-interested in a society. While the assumed existence of benevolent politicians appears to trivialize our analysis of autocracy at the first glance, it is in fact not the case for two reasons. First, despite their presence, it is assumed that benevolent politicians can be identified only occasionally. From time to time, the society is left with self-interested politicians to choose from. Hence, autocracy in our model is never reduced to a benevolent dictatorship, and its performance hinges crucially on how self-interested leaders select their successors. Second, contrary to the common wisdom, the presence of benevolent politicians does not directly imply the superiority of autocracy over democracy. After all, since benevolent politicians may be able to raise well-being for all, their presence has the potential to improve the performance of both autocracy and democracy. Whether such a potential can be realized under each of these political institution depends on what kind of leaders these two institutions tend to select. What kind of leader these institutions will select in turn depends on how the chosen leader enacts policies after coming to power. In our model, public scrutiny may constrain a leader’s choice of policies under both autocracy and democracy. When subject to the constraint, a leader gives in to popular demand; when the constraint is weakened, however, he is free to choose at his will. For the lack of a better term, we refer to this constraint of public scrutiny as civil society. As casual observations would testify, the aforementioned examples of autocratic regimes, for better or worse, were almost all associated with weakened civil 1

According to Besely (2005), the incentive issue “has been studied at length”, but the selection issue “has received far less attention” despite the fact that the “past 200 years of political history justify an emphasis on selection”.

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society. Reflecting this, we endogenize the state of civil society by assuming that it can be either weakened or strengthened by leaders, both under autocracy and under democracy as well. As all institutions, the state of civil society is sticky and it is only because it is sticky that a strengthened civil society binds leaders’ policy choice. We therefore model a leader’s attempt to weaken or strengthen civil society as it will take effect only after the end of the leader’s term. Such a lag induces the leader, especially a self-interested one, to internalize the impact of any change in civil society. Nevertheless, it is under autocracy when a leader is equipped with the right to select his successor, that a self-interested leader can potentially neutralize the impact by putting the government office on sale. Our analysis is placed in an overlapping generation model with infinite horizon, where in each period a leader is selected to serve one term. This overlapping generation model features dynamic free-riding, which, when removed, improves well-being of all individuals over all generations, and yet in any given period is welcomed by the majority of the living population. Such a feature characterizes the popular demand for government policies and offers a room for a benevolent leader to play a role under both democracy and autocracy. It also allows us to derive, for any equilibrium, an asymptotic welfare measure that is universal to all citizens. Thus, our analysis compares the two political institutions by looking at citizens’ asymptotic welfare in equilibrium under one institution to that under another. With these basic ingredients, our analysis is able to derive, given the characteristics of an economy, a unique equilibrium outcome under each of the political institutions. This enables us to compare the performance of the two institutions, without relying upon equilibrium selection. In particular, we describe one political institution as outperforming the other for a particular economy if and only if, for such an economy, in the unique equilibrium under the former institution all citizens asymptotically enjoy a high social welfare than they do under the latter. Hence, our comparative study of the two political institutions is unambiguous. Moreover, for every economy parameterized in this model, we are able to derive the unique equilibrium outcome under each of the political institutions. In other words, our comparative study is comprehensive too. The result of this comparative study is a rich set of interesting observations. First, all democracies are alike, but autocracies differ. All economies share the same unique equilibrium outcome under democracy: civil society remains strong, self-interested leaders are selected by the general public, and populist policies are pursued. Under autocracy, however, some economies enjoy an equilibrium outcome that asymptotically dominate that under democracy, whereas some suffer from an equilibrium outcome that asymptotically is much worse than that under democracy, while other economies fare in between these

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two extremes. Our observation corresponds to the empirical finding that the performances of democracies converge to the mean, whereas those of autocracies diverge, both for the better and for the worse.2 Second, there is no room for benevolent politicians under democracy. As the civil society remains strong, benevolent politicians, even if elected, are not able to play any role different from self-interested politicians do. Should the civil society ever become weakened, the dynamic free-riding attempt induces the public to embrace a self-interested politician instead of a benevolent one. Third, under democracy, because a self-interested incumbent does not have the right to appoint his own successor, he cannot put the office on sale. As a result, a self-interested leader internalizes the negative impact of a weakened civil society (allowing a self-interested successor to engage in self-dealing) and in accordance keeps the civil society strong. This, in contrast, is not the case under autocracy especially when autocracy outperforms democracy. Fourth, autocracy outperforms democracy exactly when all leaders, benevolent or selfinterested, choose to weaken the civil society and even self-interested leaders favor benevolent successors. Weakened civil society on the one hand enables benevolent leaders to defy populist pressure to correct the dynamic free-rider problem; and on the other hand allows self-interested leaders, who rise to power from time to time when benevolent politicians become unidentifiable, to engage in self-dealing. This in turn derives the next observation: Fifth, when autocracy outperforms democracy, the economy behaves volatile even asymptotically, swing from one extreme with benevolent leaders helping the nation to overcome collective action failure, to another extreme where the nation falls to the prey by selfinterested politicians. Ironically, it is exactly because a self-interested leader plunder the economy that even his self-interested predecessor will not want to appoint them should he be able to identify a benevolent successor. Meanwhile, it is the efficiency gain delivered by a benevolent successor that induces the incumbent, benevolent or self-interested, to keep a weakened civil society in order for the benevolent successor to play a role should he be identified. Sixth, despite the fact that a self-interested incumbent may hesitate to appoint a selfinterested successor, in the equilibrium where autocracy becomes terribly “bad”, such hesitance is set aside as the incumbent can be compensated through the sale of his office. In such a “bad” autocratic equilibrium, self-interested leaders keep civil society weakened so as to create room for their self-interested successors to engage in self-dealing, while at the same time charging these successors bribes in exchange for the appointment. Consequently, the economy is trapped in the worst extreme. 2

See Besley and Kudamatsu (2007).

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The last, but perhaps the most important (or troubling), observation that our analysis brings about is: even though some autocracies will be terribly bad asymptotically, they may initially behave like good autocracies. In other words, it is possible for some economies under autocracy to begin with the reign of a sequence of benevolent leaders, each maintaining weaken civil society in order to overcome dynamic free-riding problem, only to see themselves eventually succeeded by a self-interested politician; and once that happens, the “bad” autocratic equilibrium prevails. There is in fact a deep reason why good autocracies and bad autocracies may appear alike initially. Autocracy cannot outperform democracy without defying popular demand. To defy popular demand, autocracy must put aside the constraint of public opinion, which requires a weakened civil society. Good autocracies and bad autocracies therefore appear alike only when both are lucky enough to ride on benevolent leaders initially. However, when the leadership is eventually taken over by a self-interested politician, that is when a good autocracy and a bad autocracy begins to part their way. In this sense, we may conclude that what makes autocracy appealing is also what can make it terribly wrong, and vice versa. Our study complements a few notable exceptions in the political economy literature that are devoted to the understanding of non-democratic political structures. Besley and Kudamatsu (2007) make an insightful comparison between autocracy and democracy. Different from this paper, their comparison focuses on the incentive aspect rather than from the selection aspect. In particular, both under autocracy and under democracy, it is the re-election concern that offers political leaders incentives. Besley and Kudamatsu (2007) define autocracy as a political institution that allocates the right to re-elect to a group of citizens, of which the incumbent is a member. However, as in Bueno de Bueno de Mesquita, Morrow, Siverson and Smith (2003) and Miquel (2007), Besley and Kudamatsu (2007) add a key extra feature to autocracy: the right to re-elect becomes unsecured when the group decides to not re-elect the incumbent. In other words, Besley and Kudamatsu’s autocracy can be viewed as a political institution that is not functioning properly. The wellfunctioning version of Besley and Kudamatsu’s autocracy (i.e., one with a secure right to re-elect), however, always outperforms democracy. Autocracy characterized by this study allocates the right to select a political leader to the incumbent leader and the right is secure. Despite this, our autocracy outperforms democracy only occasionally. Acemoglu, Egorov, and Sonin (2010) study the issue of political selection for a large class of institutions, in which democracy and autocracy fall into the two extremes. As in this paper, autocracy, which Acemoglu, Egorov, and Sonin (2010) refer to as “extreme dictatorship”, is defined as incumbents having the right to determine who run the govern-

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ment. Different from this paper, however, there is no term limit for leaders in Acemoglu, Egorov, and Sonin (2010). Another difference is that, in Acemoglu, Egorov, and Sonin (2010), all citizens agree on the quality of candidates (in terms of competence) and all prefer the best candidate. In contrast, in this paper as well as in Besley and Kudamatsu (2007), citizens diverge in their preference for political leaders. Because of these differences, Acemoglu, Egorov, and Sonin’s democracy always delivers the best government, whereas their autocracy can be anything, depending on who “happen” to be in the government.3 Democracy also dominates autocracy according to McGuire and Olson (1996). McGuire and Olson highlight an important difference between autocracy and democracy when it comes to the government fiscal policy. Under autocracy, a self-interested dictator decides how much to tax the general public without applying the same tax to himself; whereas under democracy, the majority chooses the tax rate applicable to the general public including themselves. Because tax is distortionary, the majority internalizes part of the social cost in redistribution. As a result, democracy is less redistributive than autocracy. In essence, McGuire and Olson’s democracy removes the discretion of political leaders, and hence the possibility of any wrong-doing in high office. Thus, the issues of political selection and accountability are not part of McGuire and Olson (1996).

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The Model

Consider an overlapping-generation economy. At the beginning of each period t, a unit mass of young citizens are born. Each citizen live for at most two periods. With probability > 0, a typical citizen will die prematurely after one period. Therefore, in each period t, the economy is populated by a unit mass of young and a 1 − mass of old citizens. The role of is to break the symmetry between the sizes of the young and old populations, making the young citizens the majority. For most of this paper, we shall simplify algebra by treating as arbitrarily small while remaining non-zero. All payoffs will be measured in terms of a (perishable) numeraire good. At the beginning of each period, each old citizen is endowed with e units of this numeraire good, which can be thought of as income from his inelastic labor supplied when he was young. There is a government. We shall explain later how a politician is selected into its office under different political systems. The government does two things, which we shall refer to as its welfare and investment policies. First, it implements transfer payments among 3

The interesting aspect of Acemoglu, Egorov, and Sonin (2010) is their analysis of political institutions that fall in between democracy and autocracy, where incumbents have limited influence in determining who (including themselves as no term-limit is assumed) to be in the government. They show that marginally reducing incumbents’ influence may not improve the government quality.

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citizens. We assume that different young citizens have to be treated equally, and similarly for different old citizens. Therefore transfer payments can take only the form of taxing old citizens (uniformly) and transferring to young citizens (also uniformly). Transfer payments involve deadweight loss. The exact form of such loss matters little. Here, we assume that if τ units of numeraire good are taxed from the old citizens, a fraction δ ∈ (0, 1) of τ will dissipate in the process of transfer. Let λ = δe denote the total deadweight loss if each old citizen’s full endowment e is taxed away. The government is also endowed with certain amount of perishable goods at that beginning of each period, which can be thought of as income from natural resources. The second thing the government does is to invest this income. There are three ways to invest it. First, it can invest it in some long-term project, which is so long-term that none of the citizens, young or old, will live long enough to enjoy the benefit. More concretely, we assume that a long-term investment made in period t yields a public good in period t + 2, which in turn generates for each period-(t + 2) citizen a benefit equivalent to R units of the numeraire good. Second, it can invest it in some short-term project, which yield benefits immediately. More concretely, a short-term investment made in period t yields a public good in period t, which in turn generates for each period-t citizen a benefit equivalent to G units of the numeraire good. We assume G < β 2 R, where β is the discount factor. Third, it can spend it on perks given to the politician in office. The perks generate for that politician a private benefit equivalent to Z units of the numeraire good, with Z > G. We refer to the politician in office in period t as the period-t leader. The periodt leader, however he was selected, may or may not be able to choose the government’s period-t welfare and investment policies, depending on whether the civil society is strong or weak. We use the state variable ωt to denote the strength of the civil society in period t, with ωt = 1 meaning strong and ωt = 0 weak, and this is assumed to be beyond the control of the period-t leader. The period-t leader gets to choose the government’s period-t welfare and investment policies only if ωt = 0. If ωt = 1, the government’s period-t welfare and investment policies will be chosen by the majority of the society (i.e., the period-t young citizens). The period-t leader, however, can costlessly determine the strength of the civil society in the next period, ωt+1 . This amounts to assuming that the civil society is both fragile and resilient. It is fragile in the sense that the period-t leader has available many cheap dirty tricks to discourage civic activism, such as targeted enforcement of tax codes. It is also resilient in the sense that these tricks take effect with a time lag, and the frustrated civil society will rebound once the leader stops applying these tricks.

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We want to emphasize that we speak of a “strong” or “weak” civil society only in relative terms. In particular, a “strong” civil society is not strong enough to change the political system from autocracy to democracy, or vice versa; nor a “weak” civil society weak enough to allow the leader to make such changes. Similarly, a “strong” civil society is not strong protect itself from being weakened by the leader, and a “weak” civil society is not weak enough to rebound. We consider two political systems: democracy and autocracy, which we regard as differing only in their constitutional rules of how a politician is selected into office — every other difference comes from there. In democracy, the leader is elected by the citizens; in autocracy, the next leader is selected by the previous leader. We assume these constitutional rules are exogenous imposed from the onset. We do not consider more general systems such as those that allow switching back and forth between these two by way of referendums. Regardless of the political system, we assume that only young citizens are eligible to be selected into office, perhaps because old citizens are not physically fit for the job. The selection process of the period-t leader takes place at the beginning of period t. We model the selection process in democracy as one where the majority group (i.e., the period-t young citizens) act as a single selector who selects one of the eligible candidates (i.e., the period-t young citizens) into the office. As such, we ignore any collective-decision problem among them. In autocracy, the period-(t − 1) leader will serve as the selector. There are two types of citizens: the set of benevolent ones is non-empty but has measure 0, while the rest are selfish. A selfish young citizen’s utility is Ut = uyt + βuot+1 , with uyt = (1 − δ)τt + gt + rt and uot+1 = e − τt+1 + gt+1 + rt+1 , where τt is the tax imposed on the period-t old citizens, gt = G if the government makes short-term investment in period t (gt = 0 otherwise), rt = R if the government made longterm investment in period t − 2 (rt = 0 otherwise), and β is the discount factor. Total welfare in period t is (recall that almost all citizens are selfish, and that the premature death rate is arbitrarily small) wt = uyt + uot . A period-t benevolent citizen (young or old) maximizes Wt =

∞ X s=0

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β s wt+s .

We observe for later reference that wt ≥ e − λ =: w, and Wt ≥ w/(1 − β) =: W . The lower bound is achieved if the government always spends the public funds on the leader’s perks and implements the maximum welfare transfer. Similarly, wt ≤ e + R =: w, and Wt ≤ w/(1 − β) =: W . The upper bound is achieved if the government always spends the public funds on long-term investment and implements no welfare transfer. Types are private information. At the beginning of each period t, before the selection process takes place, an heroic event may or may not happen. We can think of it as a natural disaster, in which a benevolent young citizen will rise to the occasion and reveal credibly his type to the society. Such a heroic event happens with probability q > 0. If it happens, the selector has the option of selecting this identified benevolent candidate. The selector always has the option of selecting a random candidate, who is almost surely selfish. Bribe-taking is possible if the selector is a single person instead of the majority group. We assume benevolent selectors/candidates do not take/pay bribe. Bribe-taking hence happens only when the selector is a period-(t − 1) leader, and when he intends to select one out of infinitely many selfish period-t young citizens as his successor. We do not try to explicitly model how any bribery contract may be enforced, or how a young citizen may borrow resources to pay bribe upfront. Instead, we collapse all these and other possible obstacles into a single parameter ˆb ∈ (0, 1), which we interpret as the maximum portion of perks a candidate can credibly pledge to share with the selector. Two implications follow immediately from this specification: the maximum bribe a selector can collect from selling the office is b := ˆbZ if he has weakened the civil society, and is 0 if he has not. We summarize the time line (within period t) as below: 1. an heroic event may or may not happens; 2. the selector (the majority group in democracy; the period-(t − 1) leader in autocracy) selects the period-t leader; bribery may or may not take place; 3. if ωt = 1, the majority group choose the government’s welfare and investment policies; 4. if ωt = 0, the period-t leader chooses the government’s welfare and investment policies; 5. the period-t leader chooses ωt+1 ; 6. period-t payoffs realized.

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Analysis

Our solution concept is pure-strategy Markov-perfect equilibrium. The only payoffrelevant state variable is the strength of the civil society ωt . 9

Before we study the equilibria in democracy and in autocracy, respectively, let’s observe some common features across these equilibria. First, when ωt = 1, the majority group (i.e., the period-t young citizens) will choose the government’s welfare and investment policies. Regardless of the political system, in any Markov-perfect equilibrium, they must choose to tax the old citizens maximally (i.e., τt = e, resulting in the maximum deadweight loss of λ), and to make short-term investment (generating payoff G immediately for every citizen). We shall refer to these as the populist policies. Second, when ωt = 0, and when the period-t leader is a benevolent one (hereafter a B-leader), he must choose not to tax the old citizens (resulting in no deadweight loss), and to make long-term investment (generating payoff R for every period-(t + 2) citizens). Third, when ωt = 0, and when the period-t leader is a selfish one (hereafter an S-leader), he must choose tax the old citizens maximally (because he is himself a young citizen), and to invest in his own perks (generating immediate payoff of Z for himself). Therefore, equilibria in democracy and in autocracy differ in only two aspects: (i) how a period-t leader chooses ωt+1 , and (ii) the kind of leader selected into office. We now turn to these questions.

3.1

Democracy

Given the above observations, in democracy, an equilibrium boils down to a vector ΩB (·), ΩS (·), LY (·) , where ΩB (ωt ) (resp. ΩS (ωt )) is a (period-t) B-leader’s (resp. Sleader’s) equilibrium choice of ωt+1 when the state is ωt , and LY (ωt ) ∈ {S, B} is the (period-t) young citizens’ equilibrium choice of (period-t) leader when the state is ωt . If LY (ωt ) = S, the young citizens intend to select a selfish candidate into office, and they will succeed with probability one (recall that they can always randomly pick one of the young citizens). But if LY (ωt ) = B, they intend to select a benevolent candidate into office, and they will succeed only with probability q. With probability 1 − q, an heroic event does not happen, and they will have no means to identify a benevolent candidate. Markov-perfection requires that these choices depend only on the state but not on the history. Indeed, that the young citizens’ leader choice depends only on the state implies that ΩB and ΩS should be independent of the state; i.e., ΩB (0) = ΩB (1) = ΩB and ΩS (0) = ΩS (1) = ΩS . To characterize all pure-strategy Markov-perfect equilibria under democracy, it suffices to consider four possible cases. Case 1: ΩB = ΩS = 0 We argue that case 1 is impossible in equilibrium, because of the following two lemmas.

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Lemma 1 ΩB = ΩS implies LY (0) = S. Proof. Since uot+1 depends only on the state ωt+1 , it is unaffected by the choice of period-t leader when ΩB = ΩS . So it suffices to study how the choice of period-t leader affects uyt . By choosing a B-leader, uyt = 0 because a B-leader makes long-term investment and implements no welfare transfer. By choosing an S-leader, uyt = (1 − δ)e because an Sleader spends public funds on perks but implements maximum welfare transfer. Therefore, LY (0) = S as claimed.

Lemma 2 LY (0) = S implies ΩB = 1. Proof. Suppose LY (0) = S but ΩB = 0. Let W (ωt ) be the equilibrium discounted sum of future welfare starting from the initial state ωt . A B-leader’s choice of ωt+1 affects only Wt+1 . If he chooses ωt+1 = 0, then Wt+1 = W (0) = e−λ+βW (ΩS ) = w +βW (ΩS ) because the period-(t+1) leader will be an S-leader, who will implements maximum welfare transfer and spend public funds on perks. If he chooses ωt+1 = 1, then Wt+1 = W (1). Since ΩB = 0, we have W (0) = w + βW (ΩS ) ≥ W (1). (1) But this is impossible, because W (1) = e − λ + G + β qW (ΩLY (1) ) + (1 − q)W (ΩS ) > w + βW = W , contradicting (1) regardless of whether ΩS = 0 or ΩS = 1. Since ΩB = ΩS = 0 implies that LY (0) = S (by Lemma 1) and LY (0) = B (by Lemma 2) at the same time, we have a contradiction. Case 2: ΩB = 0, ΩS = 1 We argue that case 2 is also impossible in equilibrium. Suppose it is. Then LY (0) = B by Lemma 2. In order for LY (0) = B to be part of an equilibrium, it must be that the young citizens’ payoff from selecting a B-leader, which is Ut = 0 + β qe + (1 − q)0 (where uyt = 0 because a B-leader implements no welfare transfer and makes long-term investment; and uot+1 = qe + (1 − q)0 because the period-(t + 1) leader will be a B-leader with probability q and an S-leader 1 − q), is weakly higher than their payoff from selecting an S-leader, which is Ut = (1 − δ)e + βG 11

(where uyt = (1−δ)e because an S-leader implements maximum welfare transfer and spends public funds on perks; and uot+1 = G because ΩS = 1 and populist welfare and investment policies will prevail in period t + 1). Since (1 − δ)e > 0, this implies qe > G. On the other hand, in order for ΩS = 1 to be part of an equilibrium, it must be that an S-leader weakly prefers a stronger civil society when he becomes old; i.e., βG ≥ β qe + (1 − q)0 ⇐⇒

G ≥ qe,

a contradiction. Case 3: ΩB = 1, ΩS = 0 We argue that case 3 is also impossible in equilibrium. Suppose it is. We first argue that young citizens will avoid selecting an S-leader when the state is ωt = 0 (i.e., LY (0) = B). Lemma 3 LY (0) = S implies ΩS = 1. Proof. Suppose LY (0) = S but ΩS = 0. An S-leader’s choice of ωt+1 affects only uot+1 . If he chooses ωt+1 = 0, then uot+1 = 0 because the period-(t + 1) leader will be an S-leader, who will implements maximum welfare transfer and spend public funds on perks. If he chooses ωt+1 = 1, then uot+1 = G because populist welfare and investment policies will then prevail. This contradicts ΩS = 0. In order for LY (0) = B to be part of an equilibrium, it must be that the young citizens’ payoff from selecting a B-leader, which is Ut = 0 + βG (where uyt+1 = 0 because a B-leader implements no welfare transfer and makes long-term investment; and uot+1 = G because ΩB = 1 and hence populist welfare and investment policies will prevail in period t + 1), is weakly higher than their payoff from selecting an S-leader, which is Ut = (1 − δ)e + β qe + (1 − q)0 (where uyt+1 = (1 − δ)e because an S-leader implements maximum welfare transfer and spends public funds on perks; and uot+1 = qe + (1 − q)0 because ΩS = 0 and the period12

(t+1) leader will be a B-leader with probability q and an S-leader 1−q). Since (1−δ)e > 0, this implies qe > G. On the other hand, in order for ΩS = 0 to be part of an equilibrium, it must be that an S-leader weakly prefers a weaker civil society when he becomes old; i.e., β qe + (1 − q)0 ≥ δ(G) ⇐⇒

qe ≥ G,

a contradiction. Case 4: ΩB = ΩS = 1 This is the only possible case in equilibrium. By Lemma 1, we have LY (0) = S. Anticipating that LY (0) = S, both a B-leader and an S-leader indeed will not weaken the civil society, as argued by Lemmas 2 and 3, respectively. Given these behaviors of both kinds of leaders, young citizens are indifferent between them when the state is ωt = 1. Therefore, we have the following proposition. Proposition 1 In democracy, the unique4 pure-strategy Markov-perfect equilibrium is that neither kind of leader weaken the civil society when it is strong, and both allow it to rebound when it is weak; young citizens are indifferent between the two kinds of leader when the civil society is strong, and will select an S-leader when it is weak. Regardless of the initial state ω1 , the country enters the absorbing state of ωt = 1 starting from period 2. And, subsequently, populist welfare and investment policies prevail in every period.

3.2

Autocracy

Given the observations made at the beginning of this section, in autocracy, an equilib rium boils down to a vector ΣB (·), ΣS (·) , where ΣB (ωt ) = ΩB (ωt ), LB (ωt ) ∈ {0, 1} × {B, S} is the (period-t) B-leader’s equilibrium choice of ωt+1 and (period-(t + 1)) successor when the state is ωt ; and similarly for ΣB (ωt )). Indeed, as in the case of democracy, Markov-perfection implies that ΣB and ΣS should be independent of the state; i.e., ΣB (0) = ΣB (1) = ΣB = (ΩB , LB ) and ΣS (0) = ΣS (1) = ΣS = (ΩS , LS ). Notice that, independent of B-leaders’ strategies, an S-leader is always indifferent between ΣS = (1, B) and ΣS = (1, S). His payoff when he becomes old will be G in both cases. 4

There are actually two equilibria, differing from each other in LY (1), but they are observationally indistinguishable.

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How S-leaders break ties, however, will have implications on the long-run performance of autocracy. In this paper, we assume that they always break ties by favoring (1, B) over (1, S). This can be justified by a weak-dominance argument: if there is any risk that the period-(t + 1) civil society is weaker than expected, then a B-successor will deliver a higher uot+1 than an S-successor will. We also observe for later reference that, in any equilibrium, LB = B. This is because the preferences of a B-leader and a B-successor are congruent. The dynamics in autocracy is much richer than that in democracy. Depending on parameters, different equilibria may arise. However, as we shall see, pure-strategy Markovperfect equilibrium always exists, and for generic parameter values it is also unique. We find it helpful to visualize the absorbing dynamics of any given equilibrium with a picture such as Figure 1. In Figure 1, the entries (1, B) in row B represent ΣB = (1, B). Similarly, the entry (0, B) in row S represent ΣS = (0, B). These together describe a candidate equilibrium, which we shall see shortly is indeed an equilibrium for certain parameter range. In Figure 1, each cell corresponds to a generalized state. For example, the cell in row B and column ω = 1 corresponds to the generalized state where, in a given period t, the civil society is strong, and a B-leader is in office. The arrows coming out of that cell tell us which generalized states the economy will be in in period t + 1. The dotted arrow corresponds to the evolution conditional on an heroic event, which happens with probability q; the solid arrow that conditional on the complementary event. There are totally four generalized states, and in Figure 1 they all communicate with each other.

ω =1

ω =0

B

(1,B)

(1,B)

S

(0,B)

(0,B)

Figure 1: the “mostly-bad” dynamics

There are totally four generalized states, and in Figure 1 they all commute with each other. This is not always true in other possible absorbing dynamics. It is easy to show that there can only be five different absorbing dynamics (see the Appendix). Besides the one shown in Figure 1, the other four are shown in Figure 2. Of particular interest are Figures 2a, 2b, and 2c.

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ω =1

ω =0

ω =1

ω =0

B

(1,B)

B

(0,B)

S

(1,B)

S

(0,B)

(a) the “democratic” dynamics

ω =1

(b) the “good dynamics

B (0,S)

S

ω =1

ω =0

B

(0,B)

(0,B)

S

(1,B)

(1,B)

ω =0

(c) the “bad” dynamics

(d) the “mostly-democratic” dynamics

Figure 2: the other four possible absorbing dynamics 3.2.1

The “Democratic” Dynamics

We call the absorbing dynamics in Figure 2a the “democratic” dynamics. Its corresponding welfare performance is the same as that under democracy. In every period, regardless of the type of the leader in office, he refrains from weakening the civil society, and tries to select a B-successor whenever possible. Since civil society is always strong, populist welfare and investment policies always prevail. This economy, albeit being an autocratic one, is observationally indistinguishable from a democratic one. When will ΣB = ΣS = (1, B) arise as an equilibrium? For a B leader not to deviate to ΣB = (0, B), anticipating that any future leader will continue to play the equilibrium strategy, it must be that weakening the civil society for one period generates no greater expected welfare then the populist policies do: e − λ + G ≥ q(e + β 2 R) + (1 − q)(e − λ) ⇐⇒

G ≥ q(λ + β 2 R) =: Q.

For an S-leader not to deviate to ΣS = (0, S), it must be that the bribe he can collect from selling the office is no greater than the loss of short-term public good: G ≥ b.

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For an S-leader not to deviate to ΣS = (0, B), it must be that the benefit of having a Bsuccessor implementing no welfare transfer does not compensate for the loss of short-term public good: G ≥ qe + (1 − q)b. Proposition 2 The “democratic” dynamics is generated by the equilibrium ΣB = ΣS = (1, B), which arises when G ≥ Q and G ≥ max{e, b}. The economy is observationally indistinguishable from a democratic one, with welfare wdem = e − λ + G generated in each period. 3.2.2

The “Bad” Dynamics

We call the absorbing dynamics in Figure 2c the “bad” dynamics. In every period, the leader selected into office is an S-leader, who implements maximum welfare transfer, spends public funds on perks, weakens next-period’s civil society, and sell the office to an S-successor. In every period, welfare is the lowest possible in this model: wbad = w = e − λ. When will ΣS = (0, S) arise in equilibrium? For an S-Leader not to deviate to ΣS = (0, B), it must be that, by allowing the civil society to rebound and populist policies to prevail in the next period, his gain in short-term public good cannot compensate for his loss in bribery income: b ≥ G. Similarly, for him not to deviate to ΣS = (0, B), it must be that the benefit of having a B-successor implementing no welfare transfer cannot compensate for the loss in bribery income: b ≥ qe + (1 − q)b ⇐⇒ b ≥ e. As long as b ≥ max{G, e}, and hence ΣS = (0, S), whether ΣB = (1, B) or ΣB = (0, B) does not affect the absorbing dynamics. In the appendix we show that either one will arise in equilibrium, depending on whether G ≥ Q or Q ≥ G, respectively. Proposition 3 When b ≥ max{G, e}, either ΣB = (1, B), ΣS = (0, S) or ΣB = (0, B), ΣS = (0, S) will arise as an equilibrium, depending on whether G ≥ Q or Q ≥ G, respectively. Both equilibria generate the “bad” dynamics, with welfare wbad < wdem generated in each period. 3.2.3

The “Good” Dynamics

When most people think about autocracy, the “bad” dynamics is likely what appears in their mind. But it is not the only possible absorbing dynamics. Under certain param16

eter ranges, not only that autocracy can be as good as democracy (see the “democratic” dynamics above), it can even outperform democracy. The possibility of the latter case is demonstrated in Figure 2b, which we call the “good” dynamics. In every period, regardless of the type of the leader in office, he weakens the civil society and tries to select a B-successor whenever possible. Civil society is persistently weak, and the type of leader in office is an i.i.d. draw every period. With probability q he will be a B-leader, implementing no welfare transfer and makes long-term investment. With probability 1 − q he will be an S-leader, implementing maximum welfare transfer and spends public funds on perks. Single-period welfare, wt , swings wildly between the highest possible, w, and the lowest possible, w, levels. Occasionally, wt takes the intermediate levels of e − λ + R (if the period-(t − 2) and period-t leaders are a B- and an S-leader, respectively) and e (if the period-(t − 2) and period-t leaders are a B- and an S-leader, respectively). In the limiting distribution,5 the expected single-period welfare is wgood = e + qR − (1 − q)λ. At first glance it is not obvious that wgood > wdem . But we shall see that ΣB = ΣS = (0, B) arises as an equilibrium only if wgood > wdem . For a B-leader not to deviate to ΣB = (1, B), anticipating that future leaders will follow the equilibrium strategies, it must be that allowing the civil society to rebound for one period generates no greater expected welfare: q(e + β 2 R) + (1 − q)(e − λ) ≥ e − λ + G ⇐⇒

q(λ + β 2 R) = Q ≥ G.

The last inequality implies q(λ + R) > G, which in turn guarantees that wgood = e + qR − (1 − q)λ = e − λ + q(λ + R) > e − λ + G = wdem . Similarly, for an S-leader not to deviate to ΣS = (1, B) or ΣS = (0, S), it must be that neither the benefit of short-term public good nor the bribery income from selling the office suffices to compensate for his loss from maximum welfare transfer: e ≥ max{G, b}. Proposition 4 The “good” dynamics is generated by the equilibrium ΣB = ΣS = (0, B), which arises when Q ≥ G and e ≥ max{G, b}. The performance of the economy fluctuates period by period, but on average is strictly better than that in democracy: wgood > wdem 5

In the expression of expected single-period welfare, where the expectation is taken with respect to the limiting distribution, the benefit of a long-term investment, R, is not discounted by β 2 . The intuition is that a long-term public good appears q of the time on average.

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3.2.4

The “Mostly-Democratic” Dynamics

We call the absorbing dynamics in Figure 2d the “mostly-democratic” dynamics because, under the reasonable assumption that q < 1/2, the economy spends most (more precisely, 1 − q > 1/2) of the time in the state of strong civil society, where populist policies prevail and the economy resembles one in democracy. In every period, regardless of the type of the leader, he tries to select a B-successor whenever possible. The type of leader in office is hence an i.i.d. draw every period. A B-leader always weakens the civil society, while an S-leader allows it to rebound. In the limiting distribution,6 the expected single-period welfare is wmd = (1 − q)(e − λ + G) + q 2 (e + R) + q(1 − q)(e − λ). Similar to the case of the “good” dynamics, although at first glance it is difficult to com pare wmd with wdem , we shall see that ΣB ) = (0, B), ΣS = (1, B) arises as an equilibrium only if wmd > wdem . Proposition 5 The “mostly-democratic” dynamics is generated by the equilibrium ΣB ) = (0, B), ΣS = (1, B) , which arises when Q ≥ G and G ≥ max{e, b}. The performance of the economy fluctuates period by period, but on average is strictly better than that in democracy (i.e., wmd > wdem ), although also strictly worse than that in the “good” dynamics (i.e., wmd < wgood ). 3.2.5

The “Mostly-Bad” Dynamics

We call the absorbing dynamics in Figure 1 the “mostly-bad” dynamics because, for q small enough, the economy spends most (more precisely, (1 − q)2 ) of the time in the worst situation of having an S-leader who, being unconstrained by the civil society, implements maximum welfare transfer and spends public funds on perks. In every period, regardless of the type of the leader, he tries to select a B-successor whenever possible. The type of leader in office is hence an i.i.d. draw every period. An B-leader always weakens the civil society, while a B-leader allows it to rebound. In the limiting distribution,7 the expected single-period welfare is wmb = q(e − λ + G) + q(1 − q)(e + R) + (1 − q)2 (e − λ). 6 7

See Footnote 5. See Footnote 5.

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Unlike in the cases of the “good” and the “mostly-democratic” dynamics, the comparison between wmb with wdem is ambiguous. Proposition 6 The “mostly-bad” dynamics is generated by the equilibrium ΣB ) = (1, B), ΣS = (0, B) , which arises when G ≥ Q and b ≥ max{e, G}. The performance of the economy fluctuates period by period, and on average is strictly worse than that in democracy (i.e., wmb < wdem ) if G > q(λ + R), although also strictly better than that in the “bad” dynamics (i.e., wmb > wbad ).

4

Conclusion [to be completed]

Appendix A: Equilibria in Autocracy We first verify that the five absorbing dynamics are the only possible absorbing dynamics in any pure-strategy Markov-perfect equilibrium. To see that, observe that for every absorbing dynamics there is a corresponding subset of generalized states that communicate with each other. If the communicating subset contains all four generalized states, then the absorbing dynamics can take only two forms, which are already depicted in Figures 1 and 2d. Lemma 4 In any equilibrium, if the corresponding communicating subset contains the generalized state (1, B) (resp. (0, B)), then it contains (1, S) (resp. (0, S)) as well. Proof. Suppose (1, B) is reached infinitely often. Then Σi = (1, B) for some i = B, S, and an i-leader is selected into office infinitely often. But whenever an i-leader is in office in period t, with probability 1 − q, the period-(t + 1) leader will be an S-leader. Hence (1, S) is reached infinitely often as well. The case for (0, B) is the same. No tripleton communicating subset is possible. By Lemma 4, any tripleton communicating subset must contain both (1, S) and (0, S). If it also contains (1, B), then ΣS = (1, B), otherwise (1, B) will not be reached again once an S-leader takes office. But if it contains (1, B) then it does not contain (0, B), so ΣB = (1, B). But ΣS = ΣB = (1, B) means the communicating subset can be further reduced to the doubleton {(1, B), (1, S)}, a contradiction. Similar arguments apply to the case where the tripleton communicating subset contains (0, B). 19

By Lemma 4, there can only be two possible doubleton communicating subsets, which are already depicted in Figures 2a and 2b. By Lemma 4, there can only be two possible singleton communicating subsets: {(1, S)} and {(0, S)}. We have ruled out {(1, S)} with our earlier tie-breaking assumption that ΣS 6= (1, S); whereas {(0, S)} is already depicted in Figure 2c. Proof of Proposition 3 Consider the equilibrium ΣB = (1, B), ΣS = (0, S) first. Suppose a B-leader is in office in period t. Let W be the discounted welfare from period t + 1 onward in equilibrium:8 W = q(e − λ + G + βW ) + (1 − q)(e − λ + G + βW ) where the discounted welfare from period t + 2 onward will be W and W if the period(t + 1) leader is a B- and an S-leader, respectively. If the B-leader deviates to ΣB = (0, B), anticipating that future leaders will follow the equilibrium strategies, the discounted welfare from period t + 1 onward will become: W 0 = q(e + β 2 R + βW ) + (1 − q)(e − λ + βW ). Deviation is unprofitable iff W ≥ W 0 , which is equivalent to G ≥ q(λ + β 2 R) = Q. Similarly, consider the the equilibrium ΣB = (0, B), ΣS = (0, S) . Suppose a B-leader is in office in period t. Let W be the discounted welfare from period t + 1 onward in equilibrium: W = q(e + β 2 R + βW ) + (1 − q)(e − λ + βW ) where the discounted welfare from period t + 2 onward will be W and W if the period(t + 1) leader is a B- and an S-leader, respectively. If the B-leader deviates to ΣB = (1, B), anticipating that future leaders will follow the equilibrium strategies, the discounted welfare from period t + 1 onward will become: W 0 = q(e − λ + G + βW ) + (1 − q)(e − λ + G + βW ). Deviation is unprofitable iff W ≥ W 0 , which is equivalent to q(λ + β 2 R) = Q ≥ G. Proof of Proposition 5

Suppose a B-leader is in office in period t. Let W be the

8

For notational simplicity, we ignore any occurrence of R that may arise due to any long-term investment made in periods t − 1 and t, as this is irrelevant for incentives.

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discounted welfare from period t + 1 onward in equilibrium:9 W = q(e + β 2 R + βW ) + (1 − q)(e − λ + βW 0 ) where the discounted welfare from period t+2 onward will be W and W 0 if the period-(t+1) leader is a B- and an S-leader, respectively; and W 0 is given by W 0 = q(e − λ + G + βW ) + (1 − q)(e − λ + G + βW 0 ). If the B-leader deviates to ΣB = (1, B), anticipating that future leaders will follow the equilibrium strategies, the discounted welfare from period t + 1 onward will become W 0 . Deviation is unprofitable iff W ≥ W 0 , which is equivalent to q(λ + β 2 R) = Q ≥ G. This last inequality also implies q(λ + R) > G, which in turn guarantees that wmd − wdem = q q(λ + R) − G > q q(λ + β 2 R) − G = q(Q − G) ≥ 0. Finally, for an S-leader not to deviate to ΣS = (0, B) or ΣS = (0, S), it must be that neither the benefit of no old-citizen taxation nor the bribery income from selling the office suffices to compensate for his loss of short-term public good: G ≥ max{e, b}. Proof of Proposition 6 Suppose a B-leader is in office in period t. Let W be the discounted welfare from period t + 1 onward in equilibrium:10 W = q(e − λ + G + βW ) + (1 − q)(e − λ + G + βW 0 ) where the discounted welfare from period t+2 onward will be W and W 0 if the period-(t+1) leader is a B- and an S-leader, respectively; and W 0 is given by W 0 = q(e + β 2 R + βW ) + (1 − q)(e − λ + βW 0 ). If the B-leader deviates to ΣB = (0, B), anticipating that future leaders will follow the equilibrium strategies, the discounted welfare from period t + 1 onward will become W 0 . Deviation is unprofitable iff W ≥ W 0 , which is equivalent to G ≥ q(λ + β 2 R) = Q. This 9 10

See Footnote 8. See Footnote 8.

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last inequality, however, is consistent with both wmb > wdem and wmb < wdem . Indeed, wmb − wdem = (1 − q) q(λ + R) − G , and hence wmb > wdem if q(λ + R) > G ≥ Q; and wmb < wdem if G is sufficiently large. Finally, for an S-leader not to deviate to ΣS = (0, B) or ΣS = (0, S), it must be that neither the benefit of no old-citizen taxation nor the bribery income from selling the office suffices to compensate for his loss of short-term public good: G ≥ max{e, b}.

References [1] Acemoglu, Daron, Egorov, Georgy, and Konstantin Sonin (2010), “Political Selection and Persistence of Bad Governments”, MIT working paper [2] Besley, Timothy (2005), “Political Selection” Journal of Economic Perspectives, 19(3), 43-60. [3] Besley, Timothy and Masayuki Kudamatsu (2007), “Making Autocracy Work”, LSE working Paper [4] Bueno de Mesquita, Bruce, Morrow, James, Siverson, Randolph, and Alastair Smith (2003), The Logic of Political Survival, Cambridge, MA: MIT Press, 2003. [5] McGuire and Olson (1996), “The Economics of Autocracy and Majority Rule: The Invisible Hand and he Use of Force”, Journal of Economic Literature, 34(1), 72-96. [6] Miquel, Gerard Padro (2007), “The Control of Politicians in Divided Societies: The Politics of Fear”, Review of Economic Studies , 74, 1259-1274.

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