When will a dictator be good?
by Ling Shen
Handout prepared by team Dixit:
Denzel
Diego
Pawel Table of Contents 1 Introduction ...... 3 Background ...... 3 2 The Model...... 3 3 The Exogenous Growth Model ...... 6 3.1 Dictatorship ...... 6 3.2 Democracy ...... 9 4 Democratization ...... 13 4.1 The incentive of political transition in the bad dictatorship ...... 13 4.2 The incentive of political transition in the good dictatorship ...... 15 5 External effect and endogenous growth ...... 17 Conclusion ...... 20 Criticisms and extensions ...... 21
1 Introduction
Background Economists have realized the importance of political institutions in shaping economic performance. Most academic studies of political economy (e.g., Shepsleand Weingast 1995; Cox 1997; Persson and Tabellini 2000, 2003) focus on the democratic political system, where formal political institutions, such as the constitution, the rule of law, and the election system, are already well advanced. However, few studies shed light on dictatorship, although most people on earth live in such regimes. A puzzling phenomenon in dictatorial economies is that they can achieve dramatically different economic growth rates.
Good and Bad Dictators Good dictators will: o Invest in public education, infrastructure o Establish rule of law to encourage private investment, subsidizes R&D, etc Bad dictators will: o Transfers large fraction of social wealth to herself Both are willing to tax citizens
Purpose of the Paper: To provide a theoretical model that illustrates underlying determinants of a dictator’s behavior
2 The Model The model is based on three different components: o Economic growth is generated by decentralized investment . The higher the private investment, the higher the aggregate technology level . Private investment positive external effect on aggregate technology level This represents endogenous growth . **We will also consider exogenous growth in a later section o Political power affects economic performance through the redistribution policy . 2D vector- tax rate and social transfer . Social transfer policy = measurement of “goodness” “Bad” and “good” are statements about the amount of the social transfer o Democracy is growth-enhancing in the current model, because it protects decentralized investment from expropriative taxation
Sequential Process of the Model is as follows:
1. Beginning of period t, technology level 퐴푡is determined by exogenous factors (section 3), or by endogenous variables in t-1 (section 5) 2. Citizens decide whether or not to begin a revolution 3. If there is no revolution, or if the revolution fails, the ruler can keep political power. She decides her social transfer scheme (to be good or bad) 4. If revolution is successful, the ruler is killed and citizens establish democracy 5. Citizens decide whether to invest after watching dictator’s political state and behavior (i.e. 푎 is determined) 6. Citizens produce output 7. Tax rate τ determined either by dictator or democratic system. Tax revenue collected and citizens receive remaining output
Additional assumptions are included for the sake of simplicity in the model: o Tax rate is determined after production to reflects the idea that taxation is key property of dictatorship o Social transfer is paid to citizens before production o We assume there is a perfect capital market with 0% interest rate. o The more that income is taxed in dictatorship compared to democracy, the more incentive there is to democratize. o All debts cleared at the end of each period o Agents are risk neutral
. Citizen’s net income (without weapon spending): 푌푎푡 = 푦푎푡 1 − 휏푡 + 푠푎푡 − 퐼푎푡 푒퐴푡
. Ruler’s net income: 푌푟푢푙푒푟 , 푡 = 휏푡 푦푎푡 − 푠푎푡 푑a
To fully understand the mechanisms of the model, the economic and political characteristics must be defined. They are as follows:
Economic environment o The economy is an infinite horizon economy o There are two agents: the dictator and continuum Λ of citizens o Citizens and rulers live forever (if ruler isn’t killed during revolution) o Citizens born with different abilities (invariant over time) . Each citizen is distinguished by independently determined value: a휖Λ= [0,1] 퐼푎푡 o Production Function (citizen a , time t): 푦푎푡 = 퐴푡 푁푎휆 , 휆> 1 . 푦푎푡 = output of individual a in period t . 퐴푡 = aggregate technology level . N =natural resources per capita . 휆 = gross return on investment (for mathematical purposes)
. 퐼푎푡 = indicator function of investment in period t =1 if citizen a invests in time t; =0 if citizen a does not invest . a = value 휖 [0,1] that uniquely represents an individual citizen and their productive abilities These values are ordered within the continuum Λ 휖 [0,1] o 0 = no ability o 1 = perfect ability 푎 represents a certain threshold ability level, above which citizens will choose to invest; citizens with a value a <푎 will not choose to invest
o The return rate for each citizen a is (N(휆-1)a)/ e . e = the cost percentage of investing in technology
e퐴푡 represents the investment cost in technology . >1: citizen a invests
Political Environment o Assume the initial political state is dictatorship . The ruler is unproductive and can tax citizens at any rate she chooses . The ruler can redistribute tax revenue as she pleases . Dictatorship impedes growth of productivity due to taxation o Political institutions are represented by the vector (τ, s) where: . τ = tax rate; between [0, 휏 ], 휏< 1 휏< 1 reflects the sustenance (threshold tax) level of the citizens. If the tax rate exceeds this level, they will not be able to live properly and will be willing to start a revolution. . s = social transfer financed via taxation
. 푠푎 = social transfer obtained by individual a
o Bad dictator: Consumes all tax revenue; 푠푎 = 0 ∀ 푎.
o Good dictator: Shares benefits with some citizens; 푠푎 > 0 for some a . The author refers to the dictator’s partial sharing as group-specific social transfer. Only a certain portion of the citizenry will gain from the dictator’s chosen social transfer policy.
• Dictator knows distribution of private ability, citizens’ investment decisions • She cannot distinguish individuals by ability; hence group specific transfer is based on investment. In other words, the rich will benefit from the dictator’s social transfer policy because they have invested the most
In the model, a democracy is formed if a revolution is successful. The following are key qualities of a democratic system:
• There is no ruler. The tax rate is determined by all citizens via “1 person, 1 vote” majority voting system 푑푒푚 • Every citizen gets the same transfer: 푠푎 = 푠 , ∀ 푎 • Social transfer is not group specific. This means no certain class of citizens will receive more benefits than the rest of society. • Allowing group specific transfer does not qualitatively change result about dictator behavior.
3 The Exogenous Growth Model
3.1 Dictatorship Assumptions:
1. Repeated game with finite periods. 2. Initial political framework is dictatorship. 3. Technology level 퐴푡 grows exogenously. 4. Tax rate is set by the dictator after production at휏푑푖푐 = 휏 regardless of whether she is good or bad. 5. Tax policy cannot be used as a tool to encourage citizens to invest (i.e. a promise to reduce the tax rate is not credible). 6. The dictator (if she is a good one) chooses the group of citizens that will receive the amount 푠푡as a social transfer. In fact only citizens who invest will receive a social transfer푠푡 = 퐴푡 푆, where푆 is the steady state of social transfer to technology level. 7. A citizen will invest if: (푒 − 푆) 푎 ≥ 푎 (푆) = 푁 1 − 휏푡 [휆 − 1]
푦푎푡 1 − 휏푡 + 푠푎푡 − 퐼푎푡 푒퐴푡 ≥ 푦푎푡 1 − 휏푡
퐴푡 푁휆푎 1 − 휏푡 + 퐴푡 푆 − 푒퐴푡 ≥ 퐴푡 푁푎 1 − 휏푡
푎[퐴푡 푁휆 1 − 휏푡 − 퐴푡 푁 1 − 휏푡 ] ≥ 푒퐴푡 − 퐴푡 푆 퐴 (푒 − 푆) 푎 ≥ 푡 퐴푡 푁 1 − 휏푡 [휆 − 1]
The investment threshold can be lowered by increasing transfer 푆. Some citizens will still invest if 푆 = 0, an assumption made to avoid corner solutions so that 푎 푆 < 1, ∀ 푆 ≥ 0. This means that when 푆 = 0,
푒 − 0 푎 0 = 푁 1 − 휏푡 휆 − 1 푒 1 > 푁 1 − 휏푡 휆 − 1 풆 ퟏ − 흉 > (퐴1) 풕 푵 흀 − ퟏ
And the net benefit of investment for the individual with 푎 = 푁 휆 − 1 1 − 휏푡 is greater than the cost of investment. Or, what is the same, the net return rate of investment is
푵[흀 − ퟏ](ퟏ − 흉 ) 풕 > 1 풆
Dictator’s Income Maximization
The dictator maximizes her income by choosing the optimal social transfer 푆,
1 푚푎푥푆 푌푟푢푙푒푟 ,푡 = 휏푡 푦푎푡 푑푎 − 1 − 푎 푆 퐴푡푆, ≡ 퐴푡 푌 푟푢푙푒푟 0 1 푠. 푡. 푌 = 휏 푁 휆 + 1 − 휆 푎 푆 2 − (1 − 푎 푆 )푆 푟푢푙푒푟 2
The first order condition with respect to S is as fallows,
푆푏푎푑 = 0, 푖푓 휏 ≤ 휏 ∗ 푆푒푥푔 = 푒 − 푁 휆 − 1 (1 − 휏 )2 푆푔표표푑 = 푡 , 푖푓 휏 > 휏 ∗ 2 − 휏푡
e Solving 푆푔표표푑 for 휏 we now obtain τ ∗ = 1 − . 푡 N(λ−1)
푒 푁 휆 − 1 1 − 휏 2 = 푡 2 − 휏푡 2 − 휏푡 푒 = 1 − 휏 2 푁 휆 − 1 푡
푒 = 1 − 휏 푁 휆 − 1 푡
푒 휏 = 1 − 푡 푁 휆 − 1
Proposition 1. If “the net benefit of investment for the individual with 푎 = 푁 휆 − 1 1 − 휏푡 is greater than the cost of investment(푒), even if he gets no transfer from the dictator,” so that the following inequality holds: 푒 1 − 휏 > 푡 푁 휆 − 1
∗ And 퐴푡 grows exogenously, the dictator will be bad if the highest tax rate is lower than 휏 ; she will be good if 휏 > 휏 ∗. The social transfer 푆푒푥푔 increases in the highest rate 휏, and decreases in the return rate of private investment (푁 휆 − 1 )/푒.
Results:
1. The dictator wants to encourage private investment if 휏 is high enough (i.e. higher than a certain threshold given by 휏 ∗ because it ensures higher revenue from taxing. 2. Social transfers are an investment for the dictator and the tax rate, her return.
Investment thresholds for individual investment:
a. Under a bad dictator: This is the case presented right before proposition 1, where 푆 = 0. 풆 풂 풃풂풅 = 푵 ퟏ − 흉 풕 흀 − ퟏ
b. Under a good dictator: In this case, 푆 > 0. In fact, from the first order conditions of the maximization problem, we obtained the optimal 푆, 푒 − 푁 휆 − 1 (1 − 휏 )2 푆푔표표푑 = 푡 2 − 휏푡
Substituting in the investment threshold equation, 푎 푆 , 푒 − 푁 휆 − 1 1 − 휏 2 (푒 − ( 푡 ) 2 − 휏 푎 푔표표푑 = 푡 푁 1 − 휏푡 휆 − 1 2 푒 1 − 휏푡 + 푁 휆 − 1 1 − 휏푡 2 − 휏 푎 푔표표푑 = 푡 푁 1 − 휏푡 [휆 − 1]
풆 + 푵 흀 − ퟏ ퟏ − 흉 풂 품풐풐풅 = 풕 푵 흀 − ퟏ ퟐ − 흉 풕
It is clear that 푎 푏푎푑 > 푎 푔표표푑 , which entails that a lower proportion of the citizenry will invest under a bad dictator than other a good one. Therefore, the good dictator will have a positive impact on the her citizens (when compared to a bad one) since, (a) the earnings of the citizens that invest are enhanced by the social transfers, 푆, and (b) it is the positive social transfer the element that lowers the investment threshold for the citizenry.
Proposition 2. If condition 휏 > 휏 ∗ holds, which entails that the dictator will be good, the transition from a bad to a good dictatorship is a Pareto-improving process. More citizens invest, aggregate output increases and all agents obtain a higher (or at least the same) income.
The transition guarantees that the income of the good dictator will be higher than that of the bad dictator, and social transfers guarantee that those who invest will earn a higher return. Some of those who did not invest under the bad dictator will do so under the good one since the threshold is lower. The remaining portion of people that do not invest under neither dictator, will see no change to their income.
Table 1. Income Comparison Dictator Citizens 1 푒2 푏푎푑 푏푎푑 푏푎푑 퐴푡 푁푎 1 − 휏 , 푎 < 푎 푌푟푢푙푒푟 = 휏 퐴푡 푁 휆 − 2 2 푌푎 = 푏푎푑 2 푁 (휆 − 1)(1 − 휏 ) 퐴푡 푁푎 1 − 휏 − 푒퐴푡 , 푎 > 푎
2 푔표표푑 푔표표푑 휏 퐴푡 푁 퐴푡 (푁 휆 − 1 − 푒) 푔표표푑 퐴푡 푁푎 1 − 휏 , 푎 < 푎 푌푟푢푙푒푟 = + 푌푎 = 푔표표푑 푔표표푑 2 푁(휆 − 1)(2 − 휏 ) 퐴푡 푁휆푎 1 − 휏 − 푒퐴푡 + 푠 , 푎 > 푎
3.2 Democracy Assumptions:
1. Tax rate is determined by all citizens through a “One-person-one-vote” majority voting system. 2. Tax revenue is equality distributed and tax burden is equally shared: everyone pays the same tax rate. 3. The median voter,푌0.5,푡, is the deciding person. Income Maximization of the Median Voter
The media voter maximizes his income with respect to the budget constraint of redistribution:
퐼0.5 푚푎푥휏푌0.5,푡 = 0.5퐴푡푁휆 1 − 휏 + 푠 − 퐼0.5푒퐴푡
1 2 2 푠. 푡. 푠 = 푦푎푡 푑푎 = 0.5휏퐴푡 푁(푎 + 휆 − 휆푎 ) 0
Depending on whether the median voter’s ability is over or under the threshold, there will be three cases, two extreme and a moderate one. The latter will be stated as part 2 of proposition 3.
1. 풂 > 0.5. At this level of ability the median voter does not invest.
The income maximization problem of the median voter becomes:
2 2 푚푎푥휏푌0.5,푡 = 0.5퐴푡푁 1 − 휏 + 0.5휏퐴푡 푁(푎 + 휆 − 휆푎 )
As it can be seen in the previous expression, the median voter in this case will benefit from social transfers directly.
FOC:
휕푌 0.5,푡 = −0.5퐴 푁 + 0.5퐴 푁 푎 2 + 휆 − 휆푎 2 휕휏 푡 푡
2 = 0.5퐴푡 푁 휆 − 1)(1 − 푎 > 0
Therefore, in democracy휏푑푒푚 ,푡 = 휏 .
The investment threshold for individual investment, 푎 푑푒푚 ,1, can be found at the point where the income of a citizen who invests is equal to that of the citizen who does not.
푌푎푡 푑표 푖푛푣푒푠푡 = 푌푎푡 푑표 푛표푡 푖푛푣푒푠푡
⇕
퐴푡 푁휆 1 − 휏 푎 + 푠 − 푒퐴푡 = 퐴푡 푁 1 − 휏 푎 + 푠
Solving for 푎 , we obtain,
푎 [퐴푡 푁휆 1 − 휏 −퐴푡푁 1 − 휏 ] = 푒퐴푡 푒퐴 푎 = 푡 퐴푡 푁 1 − 휏 [휆 − 1] 푒 푎 푑푒푚 ,1 = 푁 1 − 휏 [휆 − 1]
The social transfer is obtained by substituting 푎 푑푒푚 ,1in the equation for 푠,
1 1 푒 2 푒 2 푠 = 푦푎푡 푑푎 = 휏퐴푡 푁 + 휆 − 휆 0 2 푁 1 − 휏 [휆 − 1] 푁 1 − 휏 [휆 − 1]
1 푒2(휆 − 1) = 휏퐴 푁 휆 − 2 푡 푁2 1 − 휏 2[휆 − 1]2
1 푒2 푠푑푒푚 ,1 = 휏퐴 푁 휆 − 2 푡 푁2(1 − 휆)[휆 − 1]2
Having found 푎 푑푒푚 ,1 and 푠푑푒푚 ,1, we substitute the latter into the equations for the income of citizens who do and do not invest and obtain the respective incomes:
푑푒푚 ,1 푑푒푚 ,1 푑푒푚 ,1 퐴푡 푁 1 − 휏 푎 + 푠 , 푎 < 푎 푌푎푡 = 푑푒푚 ,1 푑푒푚 ,1 퐴푡 푁휆 1 − 휏 푎 + 푠 − 푒퐴푡, 푎 ≥ 푎
Results:
푒 If푎 푑푒푚 ,1 = > 0.5, which means that less than %50 of the citizens invest, democracy 푁 1−휏 [휆−1] decreases inequality when compared to the results obtained under the good dictatorship. The aggregate output is the same as the bad dictatorship. In fact, notice that the thresholds of private 푒 investment coincide 푎 푑푒푚 ,1 = = 푎 푏푎푑 , and the social transfer amount coincides with 푁 1−휏 [휆−1] the bad dictator’s income. I interpret this results and Shen’s account for the existence of a sort of ‘tyranny of the majority:’ the dictator is gone, but the masses which in this case do not invest take her place in claiming an equal amount of income in the form of social transfers. Democracy poses a trade-off between equality and further economic growth that did not exist under dictatorship, where the proportion of people that did not invest would not get social transfers.
2. 풂 < 0.5. At this level of ability the median voter invests. The income maximization problem of the median voter becomes:
2 2 푚푎푥휏푌0.5,푡 = 0.5퐴푡 푁휆 1 − 휏 − 푒퐴푡 + 0.5휏퐴푡 푁(푎 + 휆 − 휆푎 )
FOC:
휕푌 0.5,푡 = −0.5퐴 푁휆 + 0.5퐴 푁 푎 2 + 휆 − 휆푎 2 휕휏 푡 푡
2 = 0.5퐴푡푁 1 − 휆 푎 < 0
Therefore, in democracy 휏푑푒푚 ,2 = 0, and 푠푑푒푚 ,2 = 0. Once again, the condition to find the threshold is given by:
푌푎푡 푑표 푖푛푣푒푠푡 = 푌푎푡 푑표 푛표푡 푖푛푣푒푠푡
⇕ 퐴푡 푁휆푎 − 푒퐴푡 = 퐴푡 푁푎 푒 푎 푑푒푚 ,2 = 푁(휆 − 1)
Recall that the tax rate and the investment ratio (which determines social transfers) are, under democracy, subject to the behavior of the median voter. In this case the media voter does invest, so he supports a lower tax rate (in fact, the lowest). Now we obtain the income equations for citizens who do and do not invest:
푑푒푚 ,2 푑푒푚 ,2 퐴푡 푁푎, 푎 < 푎 푌푎푡 = 푑푒푚 ,2 퐴푡 푁휆푎 − 푒퐴푡, 푎 ≥ 푎
Results:
푒 If푎 푑푒푚 ,2 = ≤ 0.5, which means that more than %50 of the citizens invest, democracy 푁(휆−1) increases aggregate output with respect to dictatorship and the first case of democracy. Tax rate is at the lowest level and it is profitable for citizens to invest. It is worth nothing that even those citizens who do not invest earn a higher income in this scenario than under a good democracy.
1 1 퐴 푁휆퐼푎푡 푎 2 푌푑푒푚 ,2 = 푦 푑푎 = 푡 − 푒퐼 퐴 푡 푎푡 2 푎푡 푡 0 0
푁휆 푁휆 푒2 푒 푁 푒2 = 퐴 − 푒 − + 푒 − 푡 2 2 푁2 휆 − 1 2 푁 휆 − 1 2 푁2 휆 − 1 2
푁휆 푒2 푒2(휆 − 1) = 퐴 − 푒 + − 푡 2 푁 휆 − 1 2푁2 휆 − 1 2
푁휆 푒2 = 퐴 − 푒 + 푡 2 2푁 휆 − 1
Under democracy, therefore, two distinct states of the economy are possible: one with a higher tax rate and a positive level of social transfers 푎 푑푒푚 ,1, 휏 , 푠푑푒푚 ,1 , and another one with the lowest possible tax rate and no social transfers 푎 푑푒푚 ,2, 0, 0 .
Proposition 3.
푒 1−휏 푒 1 1. If ≤ , then democracy can increase aggregate output, and if > , then 푁[휆−1] 2 푁[휆−1] 2 democracy can only decrease inequality. 1−휏 푒 1 2. In the moderate case < ≤ , the impact is ambiguous and two possibilities 2 푁[휆−1] 2 exits: 1 a. The median voter is willing to choose 푎 푑푒푚 ,2, 0, 0 , if 휏 ≥ 2 1 b. The median voter is willing to choose 푎 푑푒푚 ,1, 휏 , 푠푑푒푚 ,1 , if 휏 < 2 Intuitive proof. For the first part, look at case 2 and case 1 respectively. Notice that, for the first condition, the lower the tax rate, the higher aggregate output becomes. For the second condition, notice that it is the opposite of the condition stated in case 2. It means that the less %50 of the people will invest so that the vote of the medium voter will back higher taxes and higher social transfers, thereby decreasing inequality. Shen’s proof of the second part of the proposition is 1 not very intuitive, except probably for the last line: “Thus, the sufficient condition is휏 ≥ , i.e. the 2 median voter will choose 푎 푑푒푚 ,2, 0, 0 if the highest tax rate is high enough” p. 355 .
The Goodness Assumption and Democracy
푒 1 1 In what follows, Shen assumes ≤ and휏 ≥ , conditions consistent with the median voter 푁[휆−1] 2 2 choosing 푎 푑푒푚 ,2, 0, 0 . This assumption allows to focus on the case in which democracy has a positive aggregate effect on economic performance, which is the only case under which democratization is possible in the model. This new assumption, in conjunction with A1 from create:
푒 1 ≤ 1 − 휏 ≤ (퐴2) 푁(휆 − 1) 푡 2
Adding one more condition, A2 transforms into the “goodness” assumption, the sufficient condition for democracy:
푒 1 1 − 휏 2 < ≤ 1 − 휏 ≤ (퐴3) 푡 푁(휆 − 1) 푡 2
This condition has the positive aggregate effect on economic performance that democracy brings and is also the condition on a good dictatorship.
4 Democratization Assumptions:
1. Two stage sequential game with perfect information: first citizens decide whether to revolt, then dictator decides whether to repress. 2. Revolution and repression require weapons. 3. Citizens overtake a revolution if they expect a higher level of income could be earned in democracy. The analysis follows a comparison of the highest payments of both players for weapons, named the incentives for political transition. Shen considers two possible movements of democratization: (1) from a bad dictatorship directly to democracy, and (2) from a bad dictatorship indirectly to democracy through a good dictatorship.
4.1 The incentive of political transition in the bad dictatorship The highest payment of a citizen 푎 under a bad dictatorship in period 푡 is the difference between incomes in the bad dictatorship and the democratic society:
푏푎푑 퐴푡 푁휆푎휏 , 푎 ≥ 푎 푏푎푑 푑푒푚 푏푎푑 푃푎푡 퐴푡 푁푎 휆 − 1 − 푒퐴푡 + 퐴푡 푁푎휏 , 푎 ∈ 푎 , 푎 푔표표푑 퐴푡 푁푎휏 , 푎 ≤ 푎
The first line consists of those who invest in both political states:
퐴푡 푁휆푎 − 푒퐴푡 − 퐴푡 푁휆푎 1 − 휏 − 푒퐴푡 = 퐴푡 푁휆푎 − 푒퐴푡 − 퐴푡 푁휆푎 + 퐴푡 푁휆푎휏 + 푒퐴푡
= 퐴푡 푁휆푎휏
The second line consists of those who invest in democracy but do not invest in dictatorship:
퐴푡 푁휆푎 − 푒퐴푡 − 퐴푡 푁푎 1 − 휏 = 퐴푡 푁휆푎 − 푒퐴푡 − 퐴푡 푁푎 + 퐴푡 푁푎휏
= 퐴푡 푁푎 휆 − 1 − 푒퐴푡 + 퐴푡 푁푎휏
The third and last line consists of those who invest under neither political state:
퐴푡 푁푎 − 퐴푡 푁푎 1 − 휏 = 퐴푡 푁푎 − 퐴푡 푁푎 + 퐴푡 푁푎휏
= 퐴푡 푁푎휏
These differences show the benefits that await the citizens once they achieve the state of democracy: freedom from an expropriating tax퐴푡 푁푎휏 , and the investment return 퐴푡 푁푎 휆 − 1 − 푒퐴푡 . Even a citizen that does no invest regardless of the political state, will be freed from paying the expropriating tax.
Highest expenditure on weapons
The sum of the individual offers of payments minus the cost 푐 of revolution is the highest expenditure on weapons:
1 2 푏푎푑 푏푎푑 퐴푡 푁휆휏 퐴푡 휏 푒 푃푐푖푡푖푧푒푛 ,푡 = 푃푎푡 푑푎 − 푐 = − − 푐 0 2 푁 1 − 휏푡 휆 − 1 The ruler will spend at most the entirety of her income, since allowing the revolution to occur would entail losing her whole income:
1 푒2 푃푏푎푑 = 푌푏푎푑 = 휏 퐴 푁 휆 − 푟푢푙푒푟 ,푡 푟푢푙푒푟 2 푡 푁2(휆 − 1)(1 − 휏 )2
The difference between the payments of the citizens and the dictator will determine the success of the revolution:
푏푎푑 푏푎푑 푏푎푑 Δ푡 = 푃푐푖푡푖푧푒푛 ,푡 − 푃푟푢푙푒푟 ,푡
2 2 퐴푡 푁휆휏 퐴푡 휏 푒 1 푒 = − − 푐 − 휏 퐴푡 푁 휆 − 2 2 2 2푁 1 − 휏푡 휆 − 1 2 푁 (휆 − 1)(1 − 휏 )
2 2 퐴푡 휏 푒 퐴푡 휏 푒 = − 푐 − 2 2푁 1 − 휏푡 휆 − 1 2푁 휆 − 1 1 − 휏
퐴 휏 2푒2 = 푡 − 푐 2푁 휆 − 1 1 − 휏 2
푏푎푑 If Δ푡 ≥ 0, then the highest payment (for weapons) of the citizens exceed that of the dictator. Therefore, citizens will choose revolution and, since the ruler know her repression will not succeed, then there will be no repression.
푏푎푑 If Δ푡 < 0, then citizens know that the revolution will be repressed, so they do not revolt. This is the case at the beginning of period 푡 = 1.
Democratization and the “Status Quo” Assumption:
퐴 휏 2푒2 푡 < 푐 (퐴4) 2푁 휆 − 1 1 − 휏 2
The first portion of the equation represents the investment return of the ‘middle class,’ which invests in democracy but do not do it under dictatorship. The citizens of this class have a higher incentive to revolt with a lower 푒, and/or higher 휆 and 푁. From this equation we obtain the following results:
The higher휏 , the greater the incentive for citizens to revolt.\ Lipset/Aristotle Hypothesis: democracy follows the good economic performance, given here by the exogenous growth rate of aggregate technology level 퐴푡. The more beneficial an investment project is (lower 푒, and/or higher 휆 and 푁), the lower the incentive to democratize. Notice that this is the exact opposite from what the middle class experiences. The size of the group 푎 푏푎푑 − 푎 푑푒푚 decreases in 휆 and 푁, i.e. the middle class shrinks with highly profitable investments such as oil.
Proposition 4.
In the bad dictatorship, the incentive of democratization increases in the technology level 퐴푡, and decreases in the natural resource N. The higher the taxation level 휏 , the greater is the incentive of revolution. The net social incentive of democratization decreases in the return of the investment project and increases in its cost. 4.2 The incentive of political transition in the good dictatorship The good dictator sees social transfers as an investment that brings a positive return in the form of higher tax revenues. Her income will be higher than that of the bad dictator precisely because of those “investment returns”. This, however, also means that the highest payment she is willing to make on purchasing weapons and suppressing a revolution will be higher than that by the bad dictator.
2 퐴푡 푁휏 퐴푡 푁 휆 − 1 − 푒 푃푔표표푑 = 푌푔표표푑 = + 푟푢푙푒푟 ,푡 푟푢푙푒푟 2 2푁 휆 − 1 (2 − 휏)
Depending on the level of ability, under the good dictator the citizen a will be willing to face the following highest payment P in order to democratize:
푔표표푑 푔표표푑 퐴푡 푁휆푎휏 − 푠 , 푎 ≥ 푎 푔표표푑 푑푒푚 푔표표푑 푃푎푡 = 퐴푡 푁 휆 − 1 푎 − 푒퐴푡 + 퐴푡 푁푎휏, 푎 ∈ (푎 , 푎 ) 푑푒푚 퐴푡 푁푎휏, 푎 ≤ 푎
Let us consider the three “groups” of citizens who face differing incentives to democratize. For both the poor and the middle class (so those whose 푎 < 푎 푔표표푑 ) this number is positive, that is, they are better off in a democracy. For the rich (those who have 푎 ≥ 푎 푔표표푑 ) this is unclear because 푔표표푑 퐴푡 푁휆푎휏 − 푠 can take both positive and negative values.
Proposition 5 The citizen with the highest ability 1 always supports democracy, whereas some of the rich, who invest both in the good dictatorship and democracy, could support the dictatorship under certain conditions.
Proof: 푔표표푑 푔표표푑 푃1,푡 = 퐴푡 푁휆푎휏 − 푠 푔표표푑 = 퐴푡 푁휆푎휏 − 퐴푡 푆 푒 − 푁 휆 − 1 1 − 휏 2 = 퐴 푁휆휏 − 푡 2 − 휏
푁 휆−1 푎 An individual invests when > 1. We know, however, that this will be true for the highest 푒 ability individual. Hence, if 푎 = 1, it is true that 푁 휆 − 1 > 푒. Therefore we can place a lower bound on this equation by substituting 푁 휆 − 1 for e.
푁 휆 − 1 − 푁 휆 − 1 1 − 휏 2 ≥ 퐴 푁휆휏 − 푡 2 − 휏 1 − 1 − 휏 2 = 퐴 푁휆휏 − 푁 휆 − 1 푡 2 − 휏 1 − 1 − 2휏 + 휏2 = 퐴 푁휆휏 − 푁 휆 − 1 푡 2 − 휏 2 − 휏 = 퐴 푁휆휏 − 푁 휆 − 1 휏 푡 2 − 휏 = 퐴푡 푁휏 휆 − 휆 − 1
= 퐴푡 푁휏 > 0 Q.E.D.
Here richness is synonymous with ability. The richest will always support democracy but some of the rich (whose a is closer to 푎 푔표표푑 than to 1), because they receive social transfers, may support the dictator. The conditions under which this will happen are listed in Appendix 2 and will not be discussed here in order to keep this handout concise. These conditions state the level of both e and 휆 above which the rich citizens will support the good dictator.
The overall level of highest payment the citizens are willing to devote to overthrowing the dictator is 푔표표푑 1 푔표표푑 the sum of those individual levels for all citizens and thus equal to 푃푐푖푡푖푧푒푛 ,푡 = 0 푃푎푡 푑푎 − 푐, where c is the revolution cost. Therefore the citizens will find it beneficial to overthrow the dictator at period t if and only if 푔표표푑 푔표표푑 푃푐푖푡푖푧푒푛 ,푡 ≥ 푃푟푢푙푒푟 ,푡.
This will happen when the net social incentive of democratization will be positive, that is:
푁 휆 − 1 − 푒 2 1 − 휏 2 Δ푔표표푑 = 푃푔표표푑 − 푃푔표표푑 = 퐴 − 푐 > 0 푡 푐푖푡푖푧푒푛 ,푡 푟푢푙푒푟 ,푡 푡 2푁 휆 − 1 2 − 휏 2
Proposition 6 1. In the good dictatorship, the incentive of democratization increases in the aggregate technology level. The higher the taxation level, the less the incentive of revolution is. The net social incentive of democratization increases in natural resources and the return of the investment project and decreases in its cost. 2. Because of Pareto-improving social transfer the incentive of democratization in the good dictatorship is lower than in the bad one.
The first part of Proposition 6 is straightforward and can be seen by taking partial derivatives of the 푔표표푑 net social incentive of democratization Δ푡 with respect to 퐴푡 , 휏, 푁, 휆 and e.
The second part of Proposition 6 comes from the comparison of the net social incentive to 푏푎푑 푔표표푑 democratize under good and bad ruler. It follows that Δ푡 > Δ푡 .
Interestingly, in contrast to the bad dictatorship, Shen argues that the good dictatorship would 푔표표푑 휕Δ푏푎푑 휕Δ democratize faster in the presence of natural resources ( 푡 < 0 but 푡 > 0). 휕푁 휕푁 The general implication of this sub-section is such that in the short-run it is more difficult to democratize when a country shifts from bad dictatorship to good dictatorship. However, a good dictatorship allows for more investment in the aggregate technology level which will eventually make democratization more likely.
5 External effect and endogenous growth This section considers the situation when investment has a positive external effect on the aggregate technology level. Thus economic growth is considered endogenous.
From now on Shen standardizes natural resources per capita to equal one, that is 푁 = 1.
Assume that private investment in aggregate technology level creates positive externalities.
퐴푡 = 퐴푡−1(1 + 퐺 푎 푡−1 )
퐺 푎 푡−1 is the rate of growth of the aggregate technology level. Since 1 − 푎 is the proportion of citizens who will invest, the rate of growth will be increasing as this proportion rises. Since this proportion rises in the level of social transfer S, the growth rate of 퐴푡 will also increase with social transfers from the previous period.
However, we also know that under both the good and bad dictatorship the net social incentive to democratize increases with 퐴푡. Hence the dictator faces a trade-off: higher growth means more revenue in the short-run but it also means that democratization will occur faster.
The dictator will live until the first period in which the net social incentive to democratize is positive. Then he will not live any longer.
This will happen at such period t when
푎 푑푖푐
Δ푡 = 퐴푡 휆 − 1 푎 − 푒 푑푎 − 푐 ≥ 0 푎 푑푒푚
To simplify the analysis, Shen considers a three-period model in which at the latest in the last period the dictator is killed and democracy is instituted. This happens because always Δ3 > 0.
Hence
푎 푑푖푐
퐴3 휆 − 1 푎 − 푒 푑푎 − 푐 ≥ 0 푎 푑푒푚
Then he assumes that even if 푆2 and 푆3 both equal 0 the revolution will take place in period 3. Because 퐴3 = 퐴2(1 + 푔 0 ) and 퐴2 = 퐴1(1 + 푔 0 ), it follows that:
푎 푑푖푐 2 퐴1 1 + 푔 0 휆 − 1 푎 − 푒 푑푎 ≥ 푐 푎 푑푒푚
푎 푑푖푐 2 푐 1 + 푔 0 휆 − 1 푎 − 푒 푑푎 ≥ 퐴1 푎 푑푒푚
The dictator knows that in period 3 he will die and thus period 2 is his last period under any circumstances. When the dictator knows that the given period will be his last, he will act in this period the same as he would in the exogenous growth model, thus choosing the level of social transfer 푆푒푥푔 . However, in the periods before the last period, the dictator will chose the social transfer in line with the endogenous model.
In period 1, given the endogenous growth model, the dictator considers the two effects – on the one hand, higher social transfer means that citizens will invest more and the dictator will have a higher income in this period. However, this also means that the level of technology in the next period 퐴2 will be higher, raising Δ2 and making revolution more likely to happen in that period. But then, if the revolution will take place, period 1 will in fact be the last period for the dictator.
The ruler will thus live for one or two periods, and will die in that period t when Δ푡 ≥ 0, which will be either period 2 or period 3. The lifetime income of the dictator evaluated at period 1 will be equal to
푉1, where 휌 ∈ 0,1 is a discount factor.
푒푥푔 푌푟푢푙푒푟 푆1 + 휌푌푟푢푙푒푟 (퐴2 푆1 , 푆 ), Δ2(푆1) ≤ 0 푉1 = 푌푟푢푙푒푟 푆1 , Δ2(푆1) > 0
푟 Then Shen defines a threshold value 푆1 with which the net social benefit of overthrowing the 푟 dictator will be equal to 0, i.e. Δ2 푆1 = 0.
This is the value that makes the following equality hold:
푎 푑푖푐 푟 푐 1 + 푔 푆1 휆 − 1 푎 − 푒 푑푎 = 퐴1 푎 푑푒푚
For values of 푆1 which will be greater than the threshold level, revolution will occur in the second period because the net social benefit of a revolution will be positive. But since the ruler will know that, the ruler will chose the same level of transfers as in the exogenous model. If 푆1 will be below that threshold level, the ruler will die only in period 3. Hence period 2 will be the last period and that is when the ruler will choose 푆푒푥푔 and in period 1 the ruler will chose the social transfer level in ∗ accordance with the endogenous model. This level 푆1 will be such so that:
푒푥푔 푟 max 푌푟푢푙푒푟 ,1 푆1 + 휌푌푟푢푙푒푟 ,2 퐴2 푆1 , 푆 , 푠. 푡. 푆1 ≤ 푆1
Shen defines the unconstrained optimal social transfer as 푆 1 which is the outcome of the following optimization problem:
푑푌 푑푔 푟푢푙푒푟 + 휌푌 푆푒푥푔 = 0 푆1= 푆 1 푆1= 푆 1 푟푢푙푒푟 푑푆1 푑푆1
∗ 푟 Hence the dictator will choose such level of the social transfers so that 푆1 = min{푆1 , 푆 1}. The optimal choice will depend on whether picking 푆 1 will make dictator get killed or not. If so, then he 푟 will choose 푆1 instead.
Proposition 7 In the endogenous growth model, the dictator chooses the social transfer as follows: 1. In the last period of her life-time, the dictator acts the same as in the exogenous growth model. 2. In the period before, the dictator sets 푆∗ = 푚푖푛{푆푟 , 푆 }. 푆푟 increases in the revolution cost c and ∗ 푟 푒푥푔 decreases in the initial technology level 퐴1. 푆 = 푚푖푛{푆 , 푆 } could be smaller than 푆 .
Source: Shen (2007)
Figure 1 above shows how the choice of social transfers affects the life-time income of the dictator and the life-time itself.
Conclusion
Throughout this paper, Shen discusses the determinants of the dictator’s incentive to be good in the sense that she would like to share the tax income with certain citizens. Two important effects of private investment are emphasized: the individual effect which improves private output, and the positive externality on the aggregate technology level. The dictator is more likely to be good if the individual faces a less profitable investment project. The dictator’s incentive to be is to tax more through encouraging citizens to invest more.
After endogenizing the growth rate, two different effects of economic performance on democratization are found. The good dictator is capable of reducing the incentive of a revolution (in the short run) through increasing the citizens’ investment ratio and their income, but it also possible that democratization will occur earlier due to higher economic growth rates. Since the effect of revolutionary costs on the behavior is non-linear, a long life span does not necessarily lead to a good dictator.
Criticisms and extensions
Shen argues that resource rich countries under a bad dictatorship will have a lower incentive to democratize because oil wealth increases the average rate of return to private investment. However, most empirical literature on the effect of natural resources argues the existence of a “resource curse” or “the Dutch disease”. The central argument of those papers is that the natural resources sector is highly capital-intensive and thus investment in this sector will raise the cost of capital for other sectors (in Shen’s model, variable e). This would suggest that the effect of natural resource on the private rate of return to investment would be ambiguous, depending on the relative change in variables N and e.
The author also claims that under the good dictator some of the rich would support him. Hence a logical addition to the model would be to “allow them” to spend money on weapons on the side of the dictator, thus making political transition less likely.
Shen argues that the citizens will base their decision whether to revolt or not based on whether their gain from a transition to democracy will be greater than the cost c. However, he does not consider the possibility that the citizens will be concerned about the gain over their entire life-time from transition to democracy. In fact, he assumes this out by saying that all debts will have to be cleared after the end of the round. This means that they could not borrow in period t to cover the cost c in lieu of their future increased incomes under a democratic system. This assumption is quite strong, although likely implemented for the purpose of simplifying the already complex analysis.
In his model, Shen includes a revolutionary period in which citizens and the dictator pay P for weapons and incur cost c for engaging in a revolution. A significant aspect of revolution that is overlooked is the possibility of foreign aid. There are countless revolutions whose conclusion was heavily affected by the significant amount of foreign support for a faction in the conflict. This aspect of revolution could be represented in the weapon price P and revolutionary cost c. The assumption that P is fixed should be relaxed so that the citizens and the ruler can be susceptible to exogenous shocks that will raise or lower P. The citizens and ruler could also face different values of c that can be affected by exogenous shocks to represent the possibility of foreign support in preparing for a revolution.