Political Specialization

Transcription

1 Political Secialization Bernardo Guimaraes Kevin D. Sheedy Sao Paulo School of Economics FGV London School of Economics First draft: th December 203 This version: 7 th March 205 Abstract This aer resents a theory of olitical secialization in which some countries uhold the rule of law while others consciously choose not to do so, even though they are ex ante identical. This is borne out of two key insights: for incumbents in each country, i the first stes to the rule of law have the greatest rivate cost, and ii stes taken by some countries in the direction of the rule of law make it less attractive for others to follow the same ath. The world equilibrium features a symbiotic relationshi between desotic and rule-of-law economies: by roducing technology-intensive goods that require rotection of roerty rights, rule-of-law economies raise the relative rice of natural resources and increase incentives for desotism in other countries; while the choice of desotism entails a ositive externality because chea oil makes the rule of law more attractive elsewhere in the world. JEL classifications: D74; F2; F43; O43; P48. Keywords: olitical secialization; international trade; rule of law; ower sharing. We thank seminar articiants at the Sao Paulo School of Economics and the London School of Economics for their comments. Sao Paulo School of Economics FGV. bernardo.guimaraes@fgv.br LSE, CEP, CEPR, and CfM. k.d.sheedy@lse.ac.uk

2 Introduction It is a commonlace to claim that the world has become smaller and there are fewer and fewer differences between formerly exotic laces and the West. An unrecedented flow of goods and ideas has allowed emulation of faraway countries, resulting in a large increase in conformity across the globe. However, olitics seem to be immune to this trend. While the rule of law can be taken for granted in large arts of the world, authoritarianism revails in far too many laces, in site of its well-known negative consequences. This aer resents a theory of olitical secialization according to which some countries will uhold the rule of law with commitment to roerty rights, while others will consciously choose not to do so. This is borne out of two key insights: i the first stes to the rule of law are the hardest ones: for those in ower, the marginal rivate cost of roviding a broader reach of the rule of law are decreasing; and ii strategic substitutability: stes taken towards the rule of law by some countries make it less desirable for other countries to follow the same ath because of the effect of countries olitical choices on the international rices of goods. The combination of these two insights leads to divergence in olitical choices even if all countries are ex ante identical. Central to the theory is a model where ower sharing enables commitment to rules that would otherwise be time inconsistent. Power sharing suorts the rule of law because it increases the number of otential losers from changes to the status quo, and thus raises the number of eole willing to defend the status quo against threats from both inside and outside the grou in ower. However, sharing ower requires sharing the rents associated with holding ositions of ower, which goes against the interests of incumbents and drives a wedge between the social return to investments and the return erceived by incumbents, who must make a credible commitment to honour investors roerty rights. One imlication of the model is that the cost to incumbents of sharing ower and thus rents is related to the ratio of incumbents incomes to the incomes of those outside the grou in ower. This ratio is lower in economies with more ower sharing, which imlies that incumbents have less to lose by increasing ower sharing even further. In contrast, incumbents in economies where ower is highly concentrated face substantial losses if they were to share ower more widely. That is why the first stes to the rule of law have the greatest rivate cost to incumbents. From the oint of view of incumbents, there are increasing returns to extending the reach of the rule of law through sharing ower. The imact of the rule of law on economic activity varies between different tyes of goods. Some roduction occurs even in desotic countries where individuals have no rotection against exroriation, for examle, extraction of natural resources. However, roduction of goods that require long-term investments in hysical caital or research and develoment is sensitive to whether investors exect roerty rights to be enforced. Imortantly, international trade allows the exchange of rule-of-law intensive goods for those goods whose roduction is less sensitive to the olitical system. This means that desotic countries can enjoy consumtion of rule-of-law intensive goods even though these cannot be roduced domestically, breaking the link between a country s olitical

3 system and the range of goods available for consumtion. International trade thus oens the door to secialization in olitical systems. Some countries increase ower sharing and fully embrace the rule of law to suort an economically efficient level of roduction. Others become desotisms with minimal ower sharing. Incumbents in countries with the rule of law gain from secialization because it allows them to exloit fully the increasing returns to sharing ower. However, not all countries will take this ath. The choices of olitical regimes are strategic substitutes since an exogenous increase in the number of countries uholding the rule of law would reduce the relative rice of rule-of-law intensive goods and thus increase the gains from turning to desotism for incumbents in other countries. In equilibrium, incumbents of ex-ante identical countries are indifferent between the choice of the rule of law and desotism, and they always gain from the ossibility of trading internationally. However, the ensuing olitical secialization leads to economic divergence as well. The economies that adot the rule of law become substantially richer than desotisms that roduce no rule-of-law intensive goods. International trade thus benefits some countries but harms others. The world equilibrium features a symbiotic relationshi between rule-of-law economies and desotisms. By roducing goods that require rotection of roerty rights, rule-of-law economies raise the relative rice of other goods such as natural resources and thus increase incentives for desotism in other countries. Conversely, desotisms have a ositive externality on other countries because chea oil makes ower sharing and the rule of law more attractive elsewhere in the world. The baseline model redicts that olitical divergence arises even in a world of ex-ante identical economies. When ex-ante heterogeneity across countries is considered, comarative advantage determines which countries secialize in which olitical system, with desotism taking hold in countries with a comarative advantage in less rule-of-law intensive goods. A natural resource curse arises owing to the effects of a comarative advantage in natural resources on the incentives for incumbents to forsake sharing ower. The model has some imortant lessons on how the roblem of bad institutions should be addressed. One rediction is that exogenous imrovements in one country s olitical institutions, erhas brought about by well-intentioned international ressure or intervention, will tend to be counteracted by an increase in incentives for desotism in other countries. However, this does not reclude a role for international olicy because the total amount of desotism in the world is affected by the relative rice of rule-of-law intensive goods, which is in turn influenced by atterns of demand. The model thus suggests that channelling resources to the study and develoment of technology-intensive alternative fuels would be more effective in curbing desotism than efforts directed to affect the olitical systems of articular countries. Since the mechanism for olitical secialization relies on international trade, an imlication of the model is that the ossibility of trade drives countries aart, economically and olitically. Williamson 20 shows that economic divergence did indeed follow the first wave of globalization in the early 9 th century, when the third world fell behind. While those countries with a comarative advantage in rimary goods grew more than in revious centuries, the ga between rich and oor countries widened. In terms of olitics, by the early 9 th century, the rule of law was becoming established in 2

4 the more advanced Euroean countries as the absolute ower of monarchs was eroded by increasingly owerful arliaments. However, countries in the erihery were exeriencing none of this olitical change, desite a large increase in trade, which resumably led to greater exosure to foreign ideas. Interestingly, this attern of both economic and olitical divergence also holds for some countries that were relatively roserous in the 8 th century but which lost ground with the first wave of globalization. Russia is a case in oint. During the 8 th and early 9 th centuries, Russia was a owerful Euroean country that went through modernizing reforms both in the reign of Peter the Great and in the age of the Russian Enlightenment. 2 However, in the early 9 th century, Russia exerienced strong ositive terms-of-trade shocks and subsequently fell behind. By the end of the century, Russia was one of the oorest countries in Euroe Nafziger, In contrast to the exansion of ower sharing in other Euroean countries at the time, and consistent with the story of olitical secialization roosed here, Russia went through the 9 th century without any kind of elected arliament. 3. Related literature The theory of olitical secialization builds on the framework roosed by Guimaraes and Sheedy 205. That aer develos a model where rules allocating ower and resources are established in the interests of incumbents. Rules need to survive rebellions from both inside and outside the grou in ower. The mechanism for contesting rules is the same no matter what those rules rescribe, and there are no secial individuals in the model: everyone is ex ante identical. The model assumes no exogenous technology to rotect roerty rights, instead, ower sharing allows for the endogenous emergence of the rule of law. Here, the environment is extended to a world with two goods and many economies, and the equilibrium allocation of ower and resources is characterized, taking account of interactions between countries olitical systems. The two main theoretical results of this aer are the increasing returns to ower sharing and strategic substitutability in ower sharing when there is international trade. Following the demise of the Soviet Union and the end of the cold war in the early 990s, Fukuyama 992 famously redicted the end of history. He argued that the days of autocratic regimes were numbered and all countries would converge to Western-style democracy. Reality, however, has not been so kind. Fukuyama has since acknowledged that autocratic regimes have been stubbornly ersistent in far too many arts of the world. 4 But the lack of convergence should not be surrising if olitical regimes are strategic substitutes, as argued in this aer. Nafziger 2008 claims that understanding what inhibited Russian economic develoment in the nineteenth century is an imortant task for economic historians. 2 The exansion of the Russian emire was a sign of its ower and develoment at the time. In the early 9 th century, the Russians colonized Alaska and even founded settlements in California. Among other notable Russian sea exloration voyages, in 820, a Russian exedition discovered the continent of Antarctica. 3 Nicholas I ruled between 825 and 855, the time when Russian exorts were becoming more exensive. He resisted any kind of ower sharing and concentrated his existing owers even more, crushing demonstrations demanding ower sharing among other things and abolishing several areas of local autonomy Bessarabia, Poland, the Jewish Qahal. 4 See Fukuyama 20. The absence of convergence in olity scores is discussed in Goorha

5 The aer is related to a literature on the effects of trade on olitical institutions. 5 Milgrom, North and Weingast 990, Greif 993, and Greif, Milgrom and Weingast 994 combine historical analysis and game theory to understand how institutions in medieval times allowed merchants to solve a commitment roblem that arises in large-scale international trade. 6 Acemoglu, Johnson and Robinson 2005 and Puga and Trefler 204 study how international trade induced institutional change by enriching and emowering merchant grous. Acemoglu, Johnson and Robinson 2005 argue that the Atlantic trade led to better institutions in Euroean countries with good initial conditions, while Puga and Trefler 204 show how emowering merchants in Venice led to imortant institutional innovations u to the 3 th century, but also to olitical closure and reduced cometition afterwards. In a similar vein, secial-interest grous lay a key role in Levchenko s 203 analysis of the imact of international trade on institutional quality. 7 This aer takes a different ersective. It looks at the world economy as a whole and studies how international trade affects equilibrium ower sharing in a model of ex-ante identical individuals and ex-ante identical countries. The model shows that the world equilibrium is asymmetric, a oint that is absent from this literature. In this sense, the aer is related to Acemoglu, Robinson and Verdier 204, who study secialization in economic systems and also find an asymmetric world equilibrium. However, the question there is a very different one: understanding why we cannot all be like Scandinavians as oosed to Americans. Here, the question is why some of us must be Venezuelans. In consequence, the model here is comletely different from Acemoglu, Robinson and Verdier 204. For examle, the ower struggle lays a central role here but is absent from their analysis, while here the aer abstracts from changes in the world technological frontier, which is central to their aer. As in the new trade theory models of Krugman 979, 980, the model here redicts a substantial amount of trade between ex-ante identical economies. Those aers assume roduction technologies with increasing returns, so countries secialize in different varieties of goods to exloit economies of scale, and trade benefits all countries. Here, increasing returns from the oint of view of incumbents to extending the reach of the rule of law through sharing ower arise endogenously from the ower struggle. That leads to olitical secialization, and trade benefits those in ower anywhere in the world irresective of olitical system but not all countries gain from trade. The aer is also related to the large literature on the natural resource curse working through olitical institutions. 8 Robinson, Torvik and Verdier 2006 and Mehlum, Moene and Torvik 2006 study the role of institutions in understanding the natural resource curse. While in those aers the curse is a consequence of bad institutions, here the key institutional variable ower sharing is endogenously determined and is a consequence of having a comarative advantage in natural resources. 5 There is also a literature on the effects of institutions on trade, but much of that work takes institutions as given. The literature studies how institutions affect trade flows for examle, Anderson and Marcouiller, 2002, the attern of comarative advantage Levchenko, 2007, Nunn, 2007 and its dynamic effects Araujo, Mion and Ornelas, 204. For a recent survey, see Nunn and Trefler See also Greif See also Grossman and Helman 994 and Do and Levchenko For a discussion of the emirical evidence on the natural resource curse, see Sachs and Warner 200 and Van der Ploeg 20. 4

6 There are models in which natural resources distort rulers choices for examle, Acemoglu, Verdier and Robinson, 2004, Caselli and Cunningham, 2009, Caselli and Tesei, 20, but the distinguishing and imortant imlication of this aer is that for the world as a whole, the number of desotic countries deends on the demand for natural resources, not on the suly. There is also a large body of work based around the idea that trade hurts economies that secialize in rimary goods. One ossibility is that some sectors give rise to ositive externalities on the whole economy or within an industry through knowledge creation. 9 In this aer, trade hurts those economies that fail to adot rules conductive to develoment, but not because of any intrinsic disadvantage of roducing rimary goods. 0 The lan of the aer is as follows. Section 2 sets u the model, describing the environment and the assumtions on the ower struggle rules and rebellions. The equilibrium rules allocating ower and resources are characterized for an individual country in section 3, and section 4 studies the benchmark case of economies in autarky. The equilibrium rules in oen economies and the world equilibrium are derived in section 5. Section 6 takes u the extension of ex-ante heterogeneity between countries. Section 7 concludes. 2 Environment 2. Preferences and technologies The world comrises a measure-one continuum of ex-ante identical countries indexed by j Ω. Each country is an area containing a measure-one oulation of ex-ante identical individuals indexed by ı Ω. There are two goods in the world, an endowment good and an investment good, the names referring to how the goods are obtained. The only use of both goods is consumtion. All individuals throughout the world have the same references over these goods as reresented by the Cobb-Douglas consumtion aggregator: C = c α E cα I α α α, α where c E and c I are resectively an individual s consumtion of the endowment and investment goods, and C is the number of units of the comosite good obtained. The arameter α, satisfying 0 < α <, indicates the relative imortance of the investment good. Each individual in each country exogenously receives q units of the endowment good. investment good requires effort to be roduced, and there is a time lag between the effort cost being incurred and the good becoming available. In each country, a fraction µ of individuals exogenously receives investment oortunities at random. Each investment oortunity is the ability to roduce one unit a normalization of the investment good if an effort cost is incurred receiving and taking 9 See, for examle, Krugman 987, Rodrik 996 and Melitz There is also a large literature in sociology that attemts to exlain underdeveloment as the result of rich countries exloiting oor ones, so-called deendency theory. See, for examle, Cardoso and Faletto 979. [2.] The 5

7 an investment oortunity is denoted by the binary variable I {0, }. Receiving an investment oortunity is rivate information, but whether it has been taken or not becomes common knowledge when the investment good is roduced. If a fraction s of investment oortunities in a country are taken then the total amount K of the investment good roduced the caital stock is: K = µs. [2.2] All individuals throughout the world have the same references defined over consumtion C, investment I, and fighting effort F, and these references are reresented by the utility function: U = log C I log + θ log + F. [2.3] Individuals receive disutility if they exert effort in investing, where θ is a arameter secifying this cost in consumtion-equivalent units, and if they exert fighting effort F also in consumtionequivalent units, the role of which is exlained below. The substantive imlication of the functional form in [2.3] is that an individual would be willing to ut in no more than F = C C/C units of fighting effort to receive consumtion C instead of C. When countries are in contact with each other, the endowment and investment goods can be exchanged in erfectly cometitive world markets. The relative rice of the investment good in terms of the endowment good in those markets is denoted by π, which all countries take as given. A country must satisfy its international budget constraint: x E + π x I = 0, [2.4] where x E and x I resectively denote the country s net exorts of the endowment and investment goods. While goods can be mobile internationally, individuals cannot move between countries. Given roduction K of the investment good satisfying [2.2], and net exorts x E and x I of the two goods satisfying the international budget constraint [2.4], a country s resource constraints are: c E ıdı + x E = q, and c I ıdı + x I = K, [2.5] Ω Ω where c E ı and c I ı denote the non-negative quantities of the endowment and investment goods consumed by individual ı Ω. 2.2 Rules and rebellions In each country, there are rules stiulating the allocation of ower and resources, which will be determined endogenously. Rules can be contested through rebellions, which lead to new rules being established. The modelling here follows Guimaraes and Sheedy 205. Rules secify the set P of individuals currently in ower, referred to as the incumbents. Each osition of ower confers an equal advantage on its holder in the event of any conflict, as described below. Power sharing is defined as the measure of the grou P. The incumbent grou P can have any size between 0% and 50% of the oulation 0 /2. It is assumed that investment oortunities cannot be received by those individuals currently in ower, but oortunities are 6

8 otherwise received at random. The rules also secify the allocation of resources, namely the allocation of consumtion of each good and the amounts exorted and imorted. Each individual s consumtion of each good can deend on whether the individual is in ower, or on whether the individual has roduced caital. Moreover, the rules can also secify the set of individuals to whom the contingency of consumtion on roducing caital alies. Since receiving an investment oortunity is rivate information, the rules cannot directly comel individuals to invest, but through a choice of the fraction of individuals for whom investing is incentive comatible, the rules will effectively determine the amount of investment in the economy. Formally, rules are a collection R = {P, L, c E, c I, c ke, c ki, c we, c wi, x E, x I }, where c E and c I are resectively consumtions of the endowment good and the investment good by an individual in ower, c ke and c ki are similarly the consumtion allocation of the two goods for individuals who roduce caital referred to as caitalists and who are in the set L, and c we and c wi are the consumtion allocation of the two goods for all remaining individuals referred to as workers. 2 The set L is the grou of individuals who have a consumtion allocation that is contingent on roducing caital with L P =, as those in ower do not receive investment oortunities. Given that investment oortunities are randomly assigned and rivate information to those who receive them, the fraction s of investment oortunities that are taken is determined by incentive comatibility under the otentially investment-contingent consumtion allocation secified by the revailing rules. Given the utility function [2.3], s is equal to the measure of the set L if the following condition holds: C k + θc w, [2.6] otherwise s is equal to zero. Rules R must be such that the measure of P ower sharing is no more than /2, net exorts must satisfy [2.4] given the world rice π, and the non-negative consumtion allocation must satisfy [2.5] given the fraction s of investment oortunities taken imlied by incentive-comatibility [2.6]. The timing of events is deicted in Figure. In a given country, rules are established, followed by oortunities for rebellions, with new rules established if a rebellion succeeds. The rocess of establishing rules that can be contested by rebellions is referred to as the ower struggle. Once there are no rebellions, there are oortunities to invest. After individuals make investment decisions, there are again oortunities for rebellions, with new rules established if a rebellion occurs. Finally, endowments are received, and any investment goods that have been roduced become available for use. The consumtion allocation secified by the revailing rules is imlemented. Any trade With heterogeneity in the effort cost of investing between different individuals, it would be ossible for rules to affect the number of individuals for whom investing is incentive comatible through an investment-contingent consumtion allocation that alies to everyone. See Guimaraes and Sheedy 205 for an examle of how this could be done. 2 It would be ossible to extend the analysis so that rules would secify a fully individual-secific consumtion allocation, but that would add considerable comlexity without necessarily affecting the results. In a related setting, Guimaraes and Sheedy 205 allow for fully individual-secific consumtion allocations but find that in equilibrium, consumtion is only contingent on being in ower or roducing caital. 7

9 between countries occurs at this oint, with world markets clearing. The sequence of events occurs simultaneously in all countries countries only interact through erfectly cometitive world markets where each takes rices as given. Figure : Sequence of events No rules New rules New rules Rebellion? no yes Investment Rebellion? no yes Payoffs received Rebellions are the only mechanism for changing the rules. A rebellion is described by a rebel army B, an amount of non-negative fighting effort F ı for each individual ı B who belongs to the rebel army, and an incumbent army A that defends the rules. In a given rebellion, the rebel army can comrise those outside or inside the grou currently in ower, or a mixture of both. The incumbent army is drawn from those currently in ower who do not join the rebel army. Formally, a rebellion is a collection {A, B, F ı}, where the sets A and B satisfy A P and A B =. A rebellion succeeds if F ıdı > δdı, [2.7] B A which requires that the fighting strength of the rebel army exceeds the fighting strength of the incumbent army. Each army s fighting strength is the integral of the fighting strengths of its members. The fighting strength of individual ı B in the rebel army is the amount of fighting effort F ı he exerts. Each individual ı A in the incumbent army has fighting strength measured by a arameter δ the ower arameter, which is obtained at no utility cost to these individuals. 2.3 Equilibrium definition The requirements for rules to be an equilibrium are now stated. Rules must be otimal in the sense of maximizing the ayoff of incumbents, taking into account the threat of rebellions. Rebellions must be rational in the sense defined below. In what follows, denotes any asect of the rules that would be established following a rebellion and Uı is individual ı s continuation utility under a articular set of rules ignoring any ast sunk effort costs. 3 3 For an individual who exerts fighting effort in several rebellions this will be off the equilibrium ath, the utility function [2.3] is to be interreted as being additively searable between the fighting effort exerted in different rebellions. That is, the individual receives disutility l log + F l, where F l denotes fighting effort in a articular 8

10 Definition A rebellion A, B, F ı against the current rules R is rational given subsequent rules R if: i All individuals in the rebel army B must exect a osition of ower under the subsequent rules yielding a ayoff no lower than what the individual would receive under the current rules, and the disutility of each individual s fighting effort F ı must not exceed his anticiated gain: B = {ı P U ı Uı}, and F ı ex{u ı Uı}. [2.8a] ii The incumbent army A drawn from those currently holding ositions of ower who do not rebel comrises those who would be worse off under the subsequent rules: A = {ı P\B Uı > U ı}. iii Condition [2.7] for a successful rebellion holds. [2.8b] In a rational rebellion, the rebel army B includes only individuals who would be in ower under the subsequent rules, which is an assumtion designed to cature the incentive roblems in inducing individuals to fight. The maximum amount of fighting effort exerted by an individual in the rebel army has disutility equal to his utility gain from a change in the rules the uer bound on F ı in [2.8a] follows from the utility function [2.3]. Analogously, an individual in ower will join the incumbent army A to defend the current rules if this is in his own interest. 4 A set of rules is an equilibrium if those rules are otimal, taking account of the threat of any rational rebellions, with any subsequent rules established after a rebellion required to be equilibrium rules with any subsequent rebellions being rational, and so on. The equilibrium conditions for rules in one country take as given rices in world markets. Definition 2 Rules R are an equilibrium if the following conditions are satisfied: i Otimal rules: Rules R maximize the utility of incumbents, taking account of the threat of rebellions. ii Rational rebellion: A rebellion against rules R occurs if and only if it is rational according to Definition. iii Sequential rationality: The conditions for otimality of rules and rationality of rebellions aly to any subsequent rules and any subsequent rebellions that occur in the sequence of events in Figure. iv Markovian: At any two stages of the sequence of events in Figure where fundamental state variables are the same, the rules allocating ower and resources must be identical u to a ermutation of identities. rebellion. 4 See Guimaraes and Sheedy 205 for a discussion of the rebellion mechanism used here. 9

11 The first requirement of equilibrium is that rules must be in the interests of incumbents taking account of the threat of rebellions. The second requirement is that any rebellion must be in the interests of those who take art in it. It is never in the interests of incumbents to have rules that trigger rebellion, and since there is no uncertainty in the model, no rebellions occur in equilibrium. Nonetheless, the roblem of finding rules that maximize the ayoff of incumbents is effectively constrained by the threat of rebellions. With a slight abuse of language, the term no-rebellion constraint is used below to refer to the conditions on the rules such that there is no rational rebellion for a articular rebel army associated with a articular incumbent grou under subsequent rules. The set of no-rebellion constraints is the collection of these constraints for all ossible comositions of the rebel army associated with different subsequent incumbent grous. The nature of the threat osed by rebel armies deends on what the ost-rebellion rules would be. The third requirement of equilibrium is that ost-rebellion rules are in the interests of subsequent incumbents and further rebellions occur if and only if they are rational according to Definition. The fourth requirement of equilibrium is that rules are Markovian, in the sense of deending only on fundamental state variables fundamental in the sense of being ayoff relevant, with the excetion of individual identities. At the re-investment stage in Figure, there are no fundamental state variables, therefore the rules in any round of the ower struggle must be the same aart from changes in the identities of those in ower. At the ost-investment stage of Figure, the caital stock will be a fundamental state variable. Since individuals are ex-ante identical, there is an essential indeterminacy in the identities of the incumbents and those who are given incentives to invest. If a certain set of rules R is an equilibrium, otherwise identical rules with any ermutation of identities will also be an equilibrium. Therefore, the characterization of equilibrium rules will determine the amount of ower sharing, the fraction s of investment oortunities that are taken, and the distribution of resources, but not the secific identities of incumbents, caitalists, and workers. Finally, a world equilibrium is a set of rules in each country and a world relative rice π of the investment good such that the rules in each country are an equilibrium taking π as given, and where international markets clear at rice π : x E jdj = 0, and x I jdj = 0. [2.9] Ω Ω Note that π can adjust to ensure that both market-clearing conditions hold because countries must resect their international budget constraints [2.4] at all rices π. Throughout the aer, the following arameter restrictions are imosed: { } δ 2 + δ + δ δ + 2δ2 µ, and θ δ min,. [2.0] 22 + δ 2 + δ δ 2 The interretation of these restrictions is discussed later. 0

12 3 Equilibrium The world equilibrium is found in several stes. Taking as given the world rice π, the equilibrium rules in a country are characterized. The analysis roceeds by working backwards through the sequence of events in Figure. Once the equilibrium rules in any given country are known, the equilibrium world rice can be determined. The analysis begins with some basic features of the equilibrium rules in any country. It turns out that equilibrium rules are always consistent with free exchange of the two goods within economies and free trade between economies. 3. Domestic market allocation The rules secify a consumtion allocation {c E, c I, c ke, c ki, c we, c wi } of the endowment and investment goods that deends on whether an individual is an incumbent, a caitalist, or a worker. It turns out that the allocation of consumtion between goods for these individuals under a set of equilibrium rules is always consistent with the consumtion demands each individual would choose facing erfectly cometitive markets for the two goods and a given level of income. The equilibrium rules are therefore consistent with free exchange of goods domestically. To be recise, suose Y is the income in terms of the endowment good as numeraire of a given individual who can choose consumtion c E and c I freely subject to a budget constraint: c E + πc I = Y, [3.] where π is the relative rice of the investment good in terms of the endowment good. Maximizing the consumtion aggregator [2.] subject to [3.] imlies demand functions: c E = αy, and c I = αy π, [3.2] and the maximized consumtion aggregator is: C = Y π α. [3.3] The consumtion allocations associated with any equilibrium rules are solutions [3.2] of the utility-maximization roblem subject to some individual incomes Y ı and a rice π given by: π = αq x E αk x I, which deends on the caital stock K and the net exorts x E and x I determined by the rules. The individual incomes Y ı must sum to national income Y calculated using rice π from [3.4]: Y ıdı = Y, where Y = q x E + πk x I. [3.5] Ω The rice π in [3.4] is the market-clearing rice given the demand functions [3.2] the market-clearing conditions are the resource constraints in [2.5]. The domestic resource constraints [2.5] for the two goods hold given that individual incomes satisfy [3.5] and the rice is π from [3.4]. [3.4]

13 3.2 International trade The rules secify net exorts {x E, x I } subject to the international budget constraint [2.4] and a given world relative rice π of the investment good. It turns out that net exorts under a set of equilibrium rules are always consistent with what would revail if the country were oen to international trade with no restrictions on the flow of goods, which brings the domestic marketclearing rice π into line with the world rice π. The equilibrium rules are therefore consistent with free trade internationally. Consider a consumtion allocation consistent with free exchange domestically as characterized in [3.2], [3.4], and [3.5], and suose the domestic market-clearing rice π is equalized to the world rice π. The international budget constraint [2.4] together with the equation for national income in [3.5] imlies: Y = q + πk. [3.6] Using the domestic resource constraints [2.5] and the individual demand functions [3.2], net exorts are: x E = αq απ K, and x I = αk αq π, [3.7] which deend on the caital stock K. Equivalently, note that net exorts [3.7] imly that π = π using equation [3.4]. 3.3 Rules following a ost-investment rebellion The next ste in characterizing the equilibrium is to work backwards through the sequence of events in Figure. Suose a rebellion haens after investment decisions have been made this will be off the equilibrium ath. This means that the amount K of the investment good roduced is now a state variable, and continuation value U = log C log + F of the utility function [2.3] does not include any sunk effort costs of investing. New rules must maximize incumbent utility subject to the resource constraints [2.4] and [2.5] and a set of no-rebellion constraints. Taking as given and U that secify ower sharing and the incumbent ayoff following a further rebellion, for all sets P with measure, the absence of a rational rebellion according to Definition requires: max{ex{u Uı}, 0}dı δ [U > U ı]dı, [3.8] P P where [ ] is the indicator function. The roblem of determining the equilibrium rules at this stage is simlified by the results in the roosition below. Proosition Equilibrium rules at the ost-investment stage of the sequence of events in Figure have the following features: i Free exchange of goods domestically: The consumtion allocations for all individuals are solutions [3.2] of the utility-maximization roblem in section 3. given the market-clearing rice π in [3.4], and incomes Y, Y w, Y k for incumbents, workers, and caitalists. 2

14 ii Free exchange of goods internationally: Net exorts are given in equation [3.7] and the marketclearing rice π in [3.4] is equal to the world rice π. iii Full exroriation of caital: The income levels of all non-incumbents are equalized, that is, Y k = Y w = Y n. iv Only one no-rebellion constraint corresonding to a rebel army comrising only non-incumbents is needed to characterize the equilibrium rules: C C n δ, where C n is the consumtion of non-incumbents. [3.9] Proof See aendix A.. The first and second statements in the roosition show that no inefficiency arises in the allocation of a given quantity of the two goods. No-rebellion constraints effectively lace lower bounds on all individuals utilities and thus Pareto-imroving reallocations of goods are in the interests of the incumbents, and these are recisely the exchanges that are brought about by free markets. Crucially, these exchanges do not affect any asect of the ower struggle. Note that although the equilibrium rules allow for free exchange of goods, this is not the same as individuals being allowed to kee all of what they roduce: overall levels of income consistent with the equilibrium rules will involve taxes and transfers between workers, caitalists, and incumbents. The full exroriation of caital that occurs when new rules are established at the ost-investment stage is a consequence of not needing to rovide incentives for investment after the fact, alongside incumbents desire for ayoff equalization among those individuals with equal ower. The intuition for ayoff equalization is that the most dangerous rebel army comrises the individuals with the greatest incentive to fight. Since any effort costs of investment are sunk at this oint, the maximum fighting effort of all non-incumbents deends only on their current consumtion. As a consequence, if there were ayoff inequality among non-incumbents, the most dangerous rebel army would not include those who receive a relatively high ayoff. The incumbents could then reduce the effectiveness of this rebel army by redistributing from relatively well-off non-incumbents to the worse off, which slackens the no-rebellion constraints and allows incumbents to achieve a higher ayoff for themselves. The fourth statement shows that the only relevant no-rebellion constraint corresonds to a rebel army comrising only non-incumbents. At this stage of the sequence of events in Figure, the choice of rules is effectively not constrained by the threat of rebellion from insiders because the environment does not change between rounds of the ower struggle, so in equilibrium, incumbents can do no better under subsequent rules. Given linearity of the conflict technology the condition [2.7] for a successful rebellion, a rebel army comrising a mixture of incumbents and non-incumbents cannot be more dangerous than a rebel army formed only by non-incumbents. Note also that the no-rebellion constraint [3.9] can be stated with reference only to consumtion rather than utility 3

15 because no further rebellions will occur in equilibrium, hence no further fighting effort F ı will be exerted by any individual. Given consumtion C and C n for incumbents and non-incumbents, resectively, and given the free exchange of goods domestically and internationally, the country s resource constraint can be stated as follows using [3.3], [3.5], and [3.6]: C + C n = C, where aggregate consumtion C is given by: C = q + πk. [3.0] π α At this stage, K and π have already been determined, aggregate consumtion C is taken as given in this maximization roblem. The resource constraint and the binding no-rebellion constraint [3.9] imly that the consumtion of incumbents C can be written as: C = C C. δ + With the asects and C of any ost-rebellion rules taken as given, there is only one remaining choice variable, ower sharing. Thus, after taking account of the binding no-rebellion constraint, the key decision incumbents must make is how widely to share ower. It can be shown that the exression for C is quasi-concave in, so the maximum is found by taking the first-order condition. After simlification, this yields C = C δ + + C δ δ + 2. Imosing the equilibrium conditions = and C = C see Definition 2 and rearranging leads to the amount of ower sharing secified by the equilibrium rules: = 2 + δ. [3.] The suerscrit denotes the equilibrium rules following a rebellion after investment decisions have been made in the sequence of events from Figure. Power sharing after a ost-investment rebellion is indeendent of the endowment q and the caital stock K. It is decreasing in the incumbent ower arameter δ and always smaller than /2. Sharing ower strengthen the incumbent grou and allows higher taxes to be extracted from non-incumbents, but also sreads the revenue more thinly among a larger grou of individuals. Aggregate consumtion C is distributed among individuals so that: C = 2 + δ 2 C, and C n = 2 + δ C. [3.2] 2 + δ Half of aggregate consumtion is shared among the incumbents, and the remaining individuals share the other half. Although a ost-investment rebellion will never occur on the equilibrium ath, the amount of ower sharing and the consumtion of incumbents C according to the rules that would be established following such a rebellion are imortant in understanding incentives to 4

16 rebel after investments have been made. 3.4 Power sharing at the re-investment stage At the re-investment stage, rules maximize incumbents utility U subject to no-rebellion constraints whenever there are oortunities for rebellions before and after investments have been made, and taking into account that individuals will take investment oortunities only if it is incentive comatible. By resecting the incentive comatibility constraint in [2.6] and aroriately choosing the size of the set L, incumbents can determine the fraction s of investment oortunities that will be taken. by: At the re-investment stage of Figure, the no-rebellion constraint see Definition is given max{ex{u Uı}, 0}dı δ P P [U > U ı]dı, [3.3] for all P with measure, where denotes rules that would be established after the first oortunity for rebellion. fundamental state variables. Any rebellions that occur before investments have been made have no effect on Incumbents also anticiate the threat of rebellions after investment has been made. Given the equilibrium rules that would be established after a rebellion at the ost-investment stage of Figure, as characterized in section 3.3, the constraint for no rebellions at the ost-investment stage is given by: max{ex{u Uı}, 0}dı δ P for all P with measure, where is given in [3.]. P [U > U ı]dı, [3.4] The following roosition establishes that the equilibrium rules feature a link between the fraction s of investment oortunities undertaken, the amount of ower sharing, and the rents received by incumbents. Proosition 2 Irresective of the value of s in equilibrium, the equilibrium rules must have the following roerties: i Free exchange of goods domestically and internationally, as in Proosition. ii The incentive constraint for investment in [2.6] always binds. The ost-investment no-rebellion constraint in [3.4] for workers only always binds. The ost-investment no-rebellion constraint for incumbents only binds in case δ < /2. All other no-rebellion constraints are redundant or slack. iii The relationshi between ower sharing and the fraction of investment oortunities that are undertaken is given by s = σ, where: δ δ + if δ < /2 µθ δ+ δ σ =. δ + if δ /2 µθ 2δ+ 5

17 The function σ is strictly increasing and strictly convex in in both cases, with σ = 0 and σ = for and with < /2: = δδ+2+δµθ+ δδ+2+δµθ 2 +δ+2δδ+2+δµθ if δ < /2 δ+2δ2+δ, and =. 2 + δ 3δ +2+δµθ+ 3δ +2+δµθ 2 +8 δδ+2+δµθ if δ /2 4δ2+δ Note that =, where the latter is given in [3.]. iv A worker s share ψ w = C w /C is given by: ψ w = 2δ +. An incumbent s share ψ = C /C is given by: if δ < /2 2δ+ δ ψ =. +2δ if δ /2 22δ+ Rents ϱ = ψ ψ w /ψ w received by an incumbent as a fraction of consumtion are strictly ositive and strictly decreasing in in all cases. Proof See aendix A.2. The intuition for the free exchange of goods both domestically and internationally is the same as in Proosition. With incumbents, µs caitalists, and µs workers, the resource constraint can then be written as: C + µsc k + µsc w = C, where aggregate consumtion C is as defined in [3.0]. Using the binding incentive constraint [2.6] and the definitions of the worker and incumbent shares ψ w and ψ leads to: ψ + + µθsψ w =. [3.5] The second statement in the roosition imlies that the re-investment no-rebellion constraint does not bind. Intuitively, at the re-investment stage, roduction of the investment good requires roviding incentives for investment, while at the ost-investment stage, any effort costs of investment are sunk. The gains to rebels whether currently workers or incumbents from a change to the rules at the ost-investment stage are thus larger than at the re-investment stage of Figure. In some cases, only the threat of rebellion from workers is binding at the ost-investment stage, while for some values of δ, incumbents also need to consider the ossibility of a cou d etat from within their own ranks again, at the ost-investment stage. The results in the third art of the roosition relate to the choice of ower sharing given the fraction s of investment oortunities undertaken the equilibrium conditions will also determine s, but it is taken as given at this stage of the analysis. When δ < /2, the amount of ower sharing is determined by the binding no-rebellion constraints and the resource constraint, given a value of s. The exressions for ψ w and ψ are the binding no-rebellion constraints for workers 6

18 and incumbents, resectively. When δ > /2, the no-rebellion constraint for incumbents does not bind and consequently the exression for σ and ψ is derived from the first-order condition for maximizing the incumbent ayoff with resect to, taking account of the binding no-rebellion constraint. While these two cases lead to different formulas, the qualitative features of both cases are the same and no imortant result deends on the value of δ. The third statement of the roosition imlies there is a ositive relationshi between investment and ower sharing. When =, σ is zero, imlying no investment will take lace in equilibrium. Intuitively, when =, a rebellion from incumbents is costless ower sharing after the rebellion will be, and since =, all current incumbents can take art in the rebellion, hence there is no way to sustain a commitment to rotecting roerty rights. A susension of the constitution and consequent confiscation and redistribution of investment goods would benefit all but the caitalists, who have already incurred the sunk investment cost by then, and thus would not have a greater incentive to rebel than a worker. This case is referred to as desotism, denoted by the suerscrit. An increase in s raises incentives for rebellions for all grous. As increases above, the fighting effort required for a rebellion increases for all grous as well. This exlains the increasing relationshi between investment s and ower sharing. As in Guimaraes and Sheedy 205, ower sharing allows for commitment to rules that would otherwise be time inconsistent. If the increase in ower sharing goes all the way to then s =. This case is referred to as an economy with the rule of law because everyone who receives an investment oortunity has the fruits of their investment credibly rotected by the equilibrium rules. Crucially, σ is not only increasing, but is also a convex function as deicted in Figure 2, imlying there are increasing returns to ower sharing in terms of roviding incentives for investors extending the reach of the rule of law. In order to understand this result, note that the exression in [3.5] can be written as: σ = µθ ψ w + ϱ, where incumbent rents ϱ and the worker share ψ w are as characterized in Proosition 2. Owing to the utility function, the term /ψ w is linear in, hence the convexity of σ is due entirely to the behaviour of the total rents ϱ. If rents ϱ were constant, total rents would also be linear in and σ would not be strictly convex. Since ϱ is decreasing in, total rents ϱ rise less than roortionally with, imlying σ is strictly convex. Intuitively, as ower is shared more broadly, individuals in ower are receiving a lower share of the total ie, which imlies that more resources can be credibly ledged to offer incentives to investors. The increasing returns to ower sharing are thus exlained by rents ϱ being a decreasing function of ower sharing as deicted in Figure 2. Insection of the exressions for ψ w and ψ in Proosition 2 shows that an increase in leads to a decrease in a worker s share ψ w, but an even larger reduction in the share of an incumbent ψ. While this is true for all values of δ, the intuition for the cases δ < /2 and δ /2 is somewhat different. In the case δ < /2, the intuition comes from the relative effects of an increase in on the no-rebellion constraints for workers and incumbents: the value of being in ower is smaller in case 7