A Theory of Political Transition

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American Economic Association

A Theory of Political TransitionsAuthor(s): Daron Acemoglu and James A. RobinsonSource: The American Economic Review, Vol. 91, No. 4 (Sep., 2001), pp. 938-963Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/2677820

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A Theory of Political TransitionsBy DARON ACEMOGLUAND JAMESA. ROBINSON*

Wedevelopa theory of political transitions nspired by the experiences of WesternEurope and Latin America. Nondemocraticsocieties are controlled by a rich elite.The initially disenfranchisedpoor can contest power by threatening revolution,especially when the opportunitycost is low, for example, during recessions. Thethreat of revolution may force the elite to democratize. Democracy may notconsolidate because it is redistributive, nd so gives the elite an incentive to mounta coup. Highly unequal societies are less likely to consolidate democracy,and mayend up oscillating between regimes andsuffersubstantialfiscal volatility. (JELD72,D74, 015, P16)

Although economists and policy makers in-creasingly realize the importance of politicalinstitutions in shapingeconomic performance,there s relatively ittle workon what determinespolitical institutions. For instance, why aresome countries democracies while others areruled by nonrepresentative egimes? The con-trastbetween NorthernEuropeand Latin Amer-ica in this regard s quite stark.Most NorthernEuropeancountriesextended the franchise dur-ing the late nineteenth and earlytwentieth cen-turies, and succeeded in consolidating massdemocracy.For example, in Britain, followingthe first tentativereforms of 1832, voting rightswere significantly extended in 1867 and in1884. They were further expanded in 1919,when universal male suffrage was introduced,and in 1928, when all women were allowed tovote. There were no reversals in this processofdemocratization.Although many less-developed

countries, notably those in Latin America, alsobecame democraticduring the late nineteenthand early twentiethcenturies, most quickly re-vertedto nondemocraticregimes.'The recent history of many Latin Americancountries is thereforemarredby oscillations inand out of democracy.In Argentina,for exam-ple, universalmale suffragebecame effective in1912. But it was soon overthrownby a coup in1930. Democracy was reinstated in 1946, butfell to a coup in 1955, re-createdagainin 1973,subvertedagain in 1976, and finally reinstalledin 1983. Why has massdemocracybeen durablein many NorthernEuropeancountries,andwhyhas it been so hard to consolidate this set ofpolitical institutions n less-developedcountriessuch as those in LatinAmerica?This paper providesa framework or analyz-ing this question. We emphasizethat in demo-cratic societies the poor impose higher taxes onthe rich than in nondemocraticsocieties. Thismakes the poor pro-democraticwhile simulta-neously giving the rich an incentive to opposedemocracy.2 In nondemocratic societies, the

* Acemoglu: Departmentof Economics, MassachusettsInstitute of Technology, 50 Memorial Drive, Cambridge,MA 02142 (e-mail: [email protected]);Robinson: Depart-ment of Political Science, 210 Barrows Hall, University ofCalifornia, Berkeley, CA 94720 (e-mail: [email protected]).We thank two anonymous referees,AbhijitBaneijee, Fran,ois Bourguignon,RuthBerins Col-lier, Steven Durlauf, JeffryFrieden, Michael Kremer,Rob-ert Powell, Dani Rodrik, Kenneth Sokoloff, MarianoTommasi, JaumeVentura,andseminarparticipants t MIT,Wisconsin, NYU, WesternOntario,Toulouse, NBER Sum-mer Institute, IMF, Canadian Institute of Advanced Re-search, Berkeley, Princeton, and Yale Political ScienceDepartments, he conferenceon "Asset Inequalityand Pov-erty" at the Ministry of Land Reform in Brasilia,and LA-CEA 98 at the Universidaddi Tella for useful suggestions.

1Before the mass democratization f the nineteenthcen-tury, Britain had elections with a very restricted ranchise,whereas in Argentina, nondemocraticregimes have oftenbeen militaly dictatorships.We do not distinguishbetweenthese different types of nondemocraticregimes. We alsodefine any significant move toward mass democracy as"democratization."2 For example, Dani Rodrik (1999) shows that democ-racies tend to have higher wages and a higher aborshare.Inthe context of Latin America, there are many examples of

militarycoups specifically aimed atreducingredistribution,938


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 939poor are excluded from political power, butpose a revolutionarythreat, especially duringperiods of crisis. The rich (elite) will try toprevent revolution by making concessions tothe poor, for example, in the form of incomeredistribution.However, because the threat ofrevolution is often only transitory,current re-distributiondoes not guaranteefutureredistri-bution. If this temporary redistribution isinsufficient o preventa revolution, he elite willbe forced to make a credible commitment tofuture income redistribution.This is what ex-tending voting rights achieves by changingtheidentity of the future median voter.Democracies are not necessarily permanentbecause the elite may have an opportunitytomounta coup. The poor would like to commit tolow levels of future taxation to prevent this.However, because such commitments are notalways credible, the elite may prefer to retakepower, even though coups aresocially wasteful.They are more likely to do so when, because ofhigh taxes, democracy is relatively costly forthem. Taxes will be high, in turn,when inequal-ity is high. As a result,a highly unequal societyis likely to fluctuate n and out of democracy.In consolidated democracies, such as theOECD economies, the threat of coups is notimportant, o taxes aredeterminedby the usualtrade-off or the medianvoterbetween transfersand deadweight losses. There is little or novariability in the amount of redistribution.Incontrast, in highly unequal economies, fiscalpolicy is more volatile because as a societyfluctuatesbetween different political regimes,the amount of fiscal redistribution changes[MichaelGavin andRoberto Perotti(1997), forexample,show thatfiscalpolicy in LatinAmer-ica is muchmorevariable thanthat in Europe].Interestingly, although greater inequality in aconsolidateddemocracy ncreasesredistribution(e.g., Allan H. Meltzer and Scott F. Richard,1981), an unequal society is less likely to be in

the more redistributivedemocraticregime, andso may be less redistributive.Our framework emphasizes that regimechanges are more likely during recessionaryperiods because costs of political turmoil,bothto the rich and to the poor, are lower duringsuch episodes. This is in line with the broadpatterns in the data. Stephan Haggard andRobert R. Kaufman(1995), for example, docu-ment that many transitions to democracy inLatin America happened during economic cri-ses. They summarizetheir findings by writing"in Argentina, Bolivia, Brazil, Peru, Uruguayand the Philippines, democratic transitionsoc-curred n the context of severe economic diffi-culties that contributed to opposition move-ments"(1995 p. 45). Many coups also happenduringrecessionsorduringperiodsof economicdifficulties, such as those in Brazil in 1964,Chile in 1973, and Argentinain 1976. In sup-port of this Mark J. Gasiorowski (1995) andAdam Przeworskiet al. (1996) show thatreces-sions significantlyincrease the probabilityof acoup. Przeworskiet al. (1996 p. 42) conclude:"the fragility of democracy .. flows largelyfrom its vulnerability n the face of economiccrises."The relationshipbetween volatility andcoups also suggests that a possible reason forthe greatersuccess of richersocieties in consol-idating democracy is theireconomic stability.The incentives to engage in or avoid fiscalredistribution,which are generatedby underly-ing asset inequality,are a key factorin shapingpolitical transitionsn our framework.This sug-gests that redistributionof assets, if it is rela-tively costly to reverse, may be used to alterregime dynamics.For example, educationalre-forms thatincreasethe relativeearningscapac-ity of the poor and land reforms that achieve amoreegalitariandistributionof assets may con-solidatedemocracy.This is because, by promot-ing asset equality, they reducesubsequent iscalredistribution and discourage future coups.There is a dangerin radicalreforms,however;despite reducingthe futureincentive to mountcoups, their anticipationmay increasethe like-lihood of a coup during he reformperiod,as inGuatemala n 1954, Brazil in 1964, andChile in1973. We also discuss how asset redistributionmay be used by the elite to preventdemocrati-zation,how the possibility of repressionaffectstherelationshipbetweeninequalityandpolitical

including the coups in Argentinaagainst Peron,the coup inBrazil against Goulart, and the coup in Chile against Al-lende [see Thomas E. Skidmore (1967), Peter H. Smith(1978), Alfred Stepan (1978), and Michael Wallerstein(1980)]. Obviously, in practice, there are dictatorships hatare against the interests of the richersegments of society,such as socialist dictatorshipsor some Africanregimes, andthey fall outside the scope of our model.


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940 THEAMERICANECONOMICREVIEW SEPTEMBER 001transitions, and how the presence of invest-ments that have differentreturns n democraciesand nondemocraciescan lead to multiple equi-libria. Finally, our model providesa frameworkfor understanding therempiricallysalientpat-terns related to political transitions.For exam-ple, we discuss the reasons why economicdevelopment might encouragedemocraticcon-solidation, and why democracies may be lessstable in societies with presidential ystems [seePrzeworskiet al. (1996) for evidence].Although the reasons for changes in regimesarenumerous,conflict between different socialgroups appears to be important n practice. InAcemoglu and Robinson (2000), we presentedevidence suggesting that in Britain, France,Germany,and Sweden democratizationwas inlarge parta response to the threatof revolutionand social unrest. In Latin America, many in-stances of democratization, ncluding those inPeru, Uruguay,and Brazilduring he 1980's, inArgentina n 1912 and 1973, and in Venezuelain 1945 and 1958, appearto have been drivenby the same factors [see, e.g., Haggard andKaufman 1995) andRuthB. Collier (1999) forgeneral treatments;Rock (1987 Chapter 8) forthe Argentine case; and Glen L. Kolb (1974 p.175) and Daniel H. Levine (1989 p. 256) onVenezuela].In the economics literature,our paper is re-latedto the analyses of the political economy ofredistribution[see, e.g., Meltzer and Richard(1981), Alberto Alesina and Rodrik (1994),Torsten Persson and Guido Tabellini (1994),and Roland Benabou (1999)] and to models ofsocial conflict [see, e.g., John E. Roemer(1985), Herschel I. Grossman (1991), AaronTornell and Andres Velasco (1992), Jess Ben-habib and Aldo Rustichini (1995), and Al-berto Ades and Thierry Verdier (1996)].There is a large political science literatureondemocratization, starting with the work ofSeymour M. Lipset (1959) and BarringtonMoore (1966) that emphasizes the structuraldeterminants of democracy (such as incomelevel and class composition). More recentwork has focused on the strategic interactionbetween regimes and their opponents, and onpolitical rather than economic factors [see,e.g., Dankwart C. Rustow (1970), GuillermoO'Donnell and Philip C. Schmitter (1986),Przeworski (1991), and Juan J. Linz and Al-

fred Stepan (1996)]. Goran Therborn (1977)and Dietrich Rueschemeyer et al. (1992) aremore closely related because they also em-phasize the importance of the disenfranchisedpoor in democratization, although they do notdiscuss the commitment role of different po-litical regimes, which is key to our approach.In our previous work (Acemoglu and Robin-son, 2000), we emphasized democratizationas a commitment to future redistribution, butdid not discuss coups and democratic consol-idation. The literature on coups is much lessdeveloped and focuses mostly on how purelypolitical factors explain the persistence orcollapse of democratic politics [see, e.g.,Robert A. Dahl (1971) and Juan J. Linz(1978)]. This contrasts with our focus on so-cial conflict and redistribution [althoughGuillermo O'Donnell (1973) also pointed outthat many coups in Latin America were in-tended to reduce wage pressure].The paper proceeds as follows. In Section Iwe presentour basic model and study the de-terminantsof transitionsbetween regimes. InSection II we discuss how redistributionof as-sets, constitutionalprovisions and political in-stitutions, and regime-specific nvestments mayhelp consolidate democracies.In Section IIIwediscuss the strategiesof the elite to avoid de-mocratization.Section IV concludes.

I. The BasicModelThere are two groupsof agents:the poor andthe rich (the elite). The political state can bedemocratic or nondemocratic.In a democracy,the median voter sets the tax rate, and becausethepoorare morenumerous, hemedianvoterisa poor agent. In a nondemocratic egime, taxes

are set by the rich. Whenthe political system isnondemocratic, he poor can attempta revolu-tion, and the elite decide whether to establishdemocracy.When the systemis democratic, herich can mounta coup. The level of income inthis economy is stochastic,and the opportunitycosts of coups and revolutionschange with in-come. This capturesthe notion that some peri-ods, such as recessions, maybe moreconduciveto social and political unrest.It also enables usto model the fact that those in power cannotcommit to futuretax rates,which will be deter-mined in futurepolitical equilibria.


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 941A. The Environment

We consider an infinite horizon economywith a continuum1 of agents.A proportionA ofthese agentsare "poor,"whereas the remaining1 - A form a rich "elite."Throughout he papersuperscript denotespoor agent and r denotesrich agent (or memberof the elite). We treat allpoor agents as identical, and all membersof theelite are also identical.Initially, political poweris concentrated n the hands of the elite, but A >1/2,so that if there s full democracy, he medianvoter is a poor agent.Thereis a unique consumptiongood y and aunique asset with total stock h (which can bethoughtof asphysicalorhumancapitalorland).We begin our analysis of the economy at timet 0 ,whereeachpoor agenthas capitalhP andeach member of the elite has hr > hP. Thesecapital stocks are exogenous. To parameterizeinequality, let hr = (1 - O)hI(1 - A) andhP = Oh/A,where A > 0 > 0, so that a lowlevel of 0 corresponds o higher inequality.Thefinal good is producedfrom capital, and totaloutput of an agent is y' = Ath' for i = p, r,where At captures aggregate productivity. Inparticular,we assumethatAt takes two values,

Ah 1 withprobability1-sAt-l A' - a with probability s,whereAl = a < 1 is a periodof recession. Weassume that s < 1/2, so that recessions arerelativelyrare.We thereforerefer to At = Ah as"normal times." The role of recessions is tochange the opportunitycost of coups to richagentsin a democracyand of revolution o pooragents in a nondemocracy.3All agents have identical preferences repre-sented by Et lJ_= 0 fCt+j, for i = p, r, whereC' is consumptionof agent i at time t, ,B s thediscount factor, and Et is the expectations op-erator conditional on all information availableattime t. Posttax ncome is given by, 9- (1 -

T) Ath' + Tl, where T ? 0 is the tax rate onincome, and T' 0 is the lump-sum transferthat an agent of group i receives from the state.We simplifythe analysis by assumingthat taxesare linear and transfers cannot be person spe-cific, hence Tt = Tt [see the previous version,Acemoglu and Robinson (1999) for group-specific ransfers].We also assume hat t is costlyto raise taxes: at tax rate Tt. there is a dead-weight cost of c(QT)Ath,where c is twice con-tinuouslydifferentiablewith c(O) = 0, c'(0) =0, c'(T) > 0 for all T > 0, and c" ' 0. Thisformulation implies that a proportionc(T) ofpretax output is lost as a result of taxation. Ifthere were no costs of taxation, our generalresults would not be altered, although some ofthe comparative statics would not apply whenthe tax rate is at a corner (i.e., at T = 1). Toavoid keeping track of this case, we assumec' (1) = oo, which ensures an interiortax rate.The governmentbudget constraint mplies

Tt= TtAt(AhP (1 - A)h) -C(t)Ath= (Tt- C(Tt))Ath.

The society starts n nondemocracyand the Apoor agents are initially excluded from the po-litical process, althoughthey can attempta rev-olution in any period t ' 1. We assumethatifa revolution is attempted and a fraction (" c 1of the poor take part,it always succeeds. Aftera revolution, poor agents expropriatean addi-tional fraction 'n - 0 of the asset stock of theeconomy. Duringtheperiodof therevolution,afraction 1 - p > 0 of the income of the econ-omy is destroyed,so each agent obtains a per-period return of g7rAthl. After this initialperiod following revolution,eachagentreceivesa per-periodreturnof nrAthlI orever. Becausea revolutiongeneratesprivatebenefitsfor apooragent, there is no collective action problem.4

3 The previous version of the paper,Acemoglu and Rob-inson (1999), discussed the case in which the costs of coupsand recessions were directly stochastic. This could be be-cause wars, changes in the internationalbalance of power,and recessions affect the extent of the collective actionproblem or inequality. Here we focus on recessions forconcreteness.

4 Although a revolutionthat changes the political systemmight seem to have public good-like features, the existingempirical literature ubstantiates he assumptionthat revo-lutionary eaders concentrateon providing private goods topotential revolutionaries see Gordon Tullock (1971)].There could also be a coordinationproblem n which allpoor agents expect others not to take part n a revolution,sodo not take part hemselves. However, since taking part n arevolution imposes no additional costs irrespective ofwhether t succeeds or not, it is a weakly dominantstrategy,


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942 THEAMERICANECONOMICREVIEW SEPTEMBER 001We also assume that the rich lose everythingafter a revolution,so that they will alwaystry toprevent it. A low value of p implies that arevolution is relatively costly, and a low valueof 'n implies that returns from revolution arelimited.5The rich can also decide to voluntarilyextend the franchise and establish a democracy,and there are no costs in this process. If thefranchise s extended, then the society becomesa democracy, and the median voter, a pooragent, sets the tax rate.In a democracy, the elite have no specialvoting power (one-person-one-vote),but theycan attempta coup.We assume that if a coup isattemptedand a fraction r c 1 of the elite takepart, it always succeeds. After a coup, the po-litical situationreverts to the initial status quo,with the elite controlling political power. Thisformalization mplies that,as with a revolution,there is no free-riderproblemwith a coup.6Acoup causes economic disruptionand politicalturmoil, and destroys a fraction 1 - 4 of allagents' income during the period in which ittakes place. Agent i's income if a coup occursin period t is therefore4Ath'.The timing of events within a periodcan besummarizedas follows.1. The stateAt is revealed.2. If there has been a revolution n the past,thepoorreceive theirshareof income, consump-tion takes place and the period ends.If the society is in a democracy,the poor setthe tax rateTt. If the society is in a nondem-ocraticregime, the rich set Tt.3. In a nondemocraticregime, the rich decidewhether to extend the franchise; n a democ-racy, theydecidewhether o mounta coup.Ifthey extend the franchise or a coup takes

place, the party that comes to powerdecideswhether o keepthetax Tt set at stage2 or seta new tax rate.4. In a nondemocraticregime, the poor decidewhetherto initiate a revolution. If there is arevolution, they share the remainingoutputof the economy. If thereis no revolution,thetax rate decided at stage 2 or stage 3 getsimplemented.5. Consumption takes place and the periodends.

Notice that coups areonly possible starting na democraticregime, and revolutionsare onlypossible starting in a nondemocratic regime.This implies that the poor cannot undertakearevolution immediately following a coupagainst democracy.

B. Definition of EquilibriumBecause thereare no free-riderproblemsaf-fecting political action,we can treatpooragentsas one player and members of the elite as an-otherplayerin a repeatedgame. This economycan thereforebe representedas arepeatedgamebetweenthe elite and the poor.We characterizethe pure strategyMarkovperfect equilibriaofthis game in which strategies depend only onthe current state of the world and the prioractions taken within the same period.The stateS is one of (A, D), (A, E), or (A,R), whereA = Al orA = Ah. HereE denoteselite in power (nondemocraticregime), D de-notes democracy,and R denotes "revolution."The strategyof the elite is denotedby o.r(SI P)and is a function of the stateS andthe taxationdecision by the poor when S = (A, D). Thisstrategy determines the actions of the elite

which are {y, ;, Trr}. y denotesthe decision toextend the franchise,which applies only in thestate (A, E), and y = 1 correspondsto theextension of the franchise, whereas y = 0means no franchiseextension. ; is the decisionto mounta coup, which applies only in the state(A, D), and we adoptthe convention that ; =1 corresponds o a coup and ; = 0 to no coup.Finally, Tr iS the tax rate set by the elite, andthey get to set the tax rate eitherwhen S = (A,E) and y = 0, orwhen S = (A, D) and = 1.The strategyof the poor is denotedby o-P(SI ,Tr) anddependson the stateS, and the franchise

and we therefore gnore this coordinationproblemboth inthis case and in the case of coups below where a similarissue arises.5An alternative ormulation s to assume that a revolu-tion creates a temporaryperiod of low output,but eventuallyleads to a democracy. The resultsare identical in this case,but somewhatmorecomplicatedbecause the desirabilityofa revolutiondependson whetherdemocracy s consolidatedor not.6 This seems plausible. For example, in Venezuela in1948, Guatemala n 1954, and Chile in 1973, landownerswere rewarded or supporting he coup by having their land

returned o them.


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 943extension and tax rate decision of the elite in thestate (A, E) [because the elite move before thepoor in the state (A, E) according o the timingof events describedearlier].This strategydeter-mines the actions {p, Tpr}.p is the decision toinitiate a revolution when the state is (A, E),with p = 1 corresponding o revolutionandp =O o no revolution;Td iS the tax rate when thestate is (A, D). Transitionsbetween states aregiven as follows: starting rom (A, E), if thereis a revolution (i.e., p = 1), then we transit ntostate (A, R), which is an absorbingstate. Ifthere is no revolution and y = 0, the stateremains at (A, E), and if y = 1, it switches to(A, D). Starting rom(A, D), if there is a coup(i.e., ; = 1), the state transits to (A, E).

A pure strategy Markov perfect equilibriumis a strategycombinationdenotedby { .r'(SIP),6-"(Sl y, T"r)}, such that 6-P and (Jr are bestresponses to each other for all possible states.More formally, consider the following pair ofBellman equations:

(1) Vt(S) = max{ C'(6P(Sj y, Tr), fr, S),rr

+ / V(S') dP(S'j&P(Sjy, Tr), 0r, s)}and

(2) VP(S)=max{ C O(o-v rr(S| P), S)O-P

+ f VP(S') dP(S' a-P, y(S i-),S

where C'(oP, (Jr, S) denotes the consumptionof agent i as a function of the state S andstrategies o-P and Jr and P(S'jo-P, Oxr S)denotes the probabilitydistribution unction oftransition rom stateS to stateS' as a functionof the strategieso-Pand (Jr. Equations (1) and(2) are standardBellman equationsthatexpressthe net present discounted value of an agentas his current consumption plus his futurediscounted value. A pure strategyMarkovper-fect equilibrium is a strategy combination

{I r5(S IT'), 0r- (S |P, T') } such that0"r olves (1)and 6-Psolves (2).C. Analysis

The optimal tax rate for a poor agent in theabsence of a coup threat,T"n, imply maximizesthe agent's per-periodconsumptionand is inde-pendentof the state of the economy. Thus,= arg max{(I - T)A,hP+ (T - cQ(T))Ath},

T

where (1 - T)AthP s the after-tax earnedin-come for a poor agent,and(T - c(T)) Ath is thelump-sum transferTt. The first-order onditionof this problem gives

A-O(3) c''(T tn) Awhere we used the fact thathP-- Oh/A.Equa-tion (3) implies that tm is uniquelydefined anddecreasing n 0. As in the standard oting model[see, e.g., Meltzer and Richard 1981)], inequal-ity increases the preferred tax rate of pooragents. When 0 = A, so thath' = hP, we haveTm = 0. Hence, in the case of complete equal-ity, the median voter sets a zero tax rate andthere is no redistribution. Given that T' doesnot directly depend on the shock At, the taxrate would always remain constant in the ab-sence of the threat of political change. Inpractice, the tax rate will vary over time be-cause of the political constraints imposed bychanges in At.Define 8'(O)At to be the net amountof re-distribution hat a person of type i receives instateAt when the tax rateis -T'2 [i.e., 8'(O)At=Tt - TmAth'].The assumption hatthe budgetis balanced then implies Ttn = (T"'2 -c(T'))Ath. Note 6"(0) < 0 < 6P(O), so thatthere arenet transfers o the poor. Furthermore,higher inequalityraises the tax rate on the rich,while simultaneously ncreasingthe net transferto the poor.7

7 This follows because by the Envelope Theorem,di(OJ)IdO = r"'Athl(I - A) > 0, and d&P(O)/dO=_rn AthlK < 0.


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944 THEAMERICANECONOMICREVIEW SEPTEMBER 001We startby makingtwo assumptions hatwillsimplify the exposition. These assumptionswillensure that coups and revolutions are not ben-eficial whenAt = Ah. A sufficientcondition for

coups not to take place in the stateAt = Ah is:ASSUMPTION 1: (1 - ,B)(1 - 4)hr >-(1 + f3s(a - 1))8r(0).The cost of a coup for a rich agent duringnormal times is (1 - 4)hr + 6'(0), which isthe directloss resulting from turbulenceminusthe taxes that they would have paid in a democ-racy [recall5'(0) < 0], whereasthe maximumbenefitof a coupis to avoid taxation n all futureperiods.The net present value of taxation at therate T'n in the future is -,B(( 1 - s) +sa)6r(0)I(1 - f3), and comparing this to thecost (1 - 4)hr + 6'(0) gives Assumption 1.This assumption guaranteesthat there is nothreatof a coup in normaltimes.Next, define the continuationvalue (the dis-counted expected net presentvalue) of a pooragent aftera revolutionbut beforethe stateAt isrevealed as

(sa ? 1- s)-'rh(4) WPj(R)= (1-,(3)A

This expressionfollows becausea revolution spermanent,and after a revolution,the poor ob-tain a fraction'nof the total assets of the econ-omy h, and share it amongthemselves forever(and A is the fractionof the poor in the econ-omy). A fractionof 1 - s of the time, we are instateAt = Ah, so these assets have return 1, andthe remainingfraction s of the time, At = Aland the return s a < 1.If, starting in the state (At, E), the poorundertakea revolution, they would obtain

(5) VP(At,R) = ?+ 3WP(R),where At = Al = 1 orAt = Ah = 1. Thisexpressionfollows because during he periodofrevolutionthe poor receive only a fraction utkof the assets of the economy h, and obtainWP(R)thereafter.

In contrast, f, starting rom the state(At, E),

they never undertakea revolution,and there isno redistributive axation,they would obtain autility of((1 s) + sa)hPVP(At, E) = AthP+ (1

This expression follows because without taxa-tion the poor receive hP this period, hP in allfuture normal periods, and ahP in all futurerecessionperiods. VP(A h, E) is clearly a lowerbound on the utility that the poor would obtainin a nondemocracy, because in equilibriumtheremay be redistributive axation.Therefore,a sufficientconditionfor the poor not to under-take a revolution in the state (Ah, E) is thatV7P(Ah, E) is greaterthan VP(Ah, R) as givenby equation(5) evaluatedat At = Ah. This isguaranteed by the following condition onparameters:ASSUMPTION 2:

(r - O)13s(1 - a) + 0 - Puk --- ( I(10-1)'This assumptionwill imply below that in nor-mal times, thatis, whenAt = Ah, the elite willchoose no redistributionwhen in power.Because A > 1/2 n a democracy, the medianvoteris a pooragent.By Assumption1, there isno threatof a coup in normal times, so in aMarkov perfect equilibrium the agent willchoose the tax rate1Tm. The expected discountedvalue of an agentof type i = p, r in this state,denotedby Vi(Ah, D), is given simplyby usingequations(1) and (2). In this case, these give(6) V(Ah, D) = hi + 5i(0) + 3Wi(D).The agentreceives hi from his own capitaland5 (0) as net transfer rom the government.Theexpectedreturn n the next periodis the contin-uation value under democracy,(7) W'(D) = (1 - s) Vi(Ah, D) + sV'(A', D),where V (Al, D) is the value to agent i in state(Al, D). With probability1 - s, the state (Ah,


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON.THEORYOF POLITICALTRANSITIONS 945D) recursnext period, whereaswith probabilitys there is a recession, and in this state thecontinuationvalue is Vi(Al, D).The continuation value Vi(Al, D) dependson the actions of the rich, who might want toundertakea coupin the stateA, = Al. The poormay therefore reduce the tax rate to Td in thisstate in an attemptto prevent the coup-recallthat the coup decision follows the taxation de-cision of the poor. Suppose that this reducedtaxationpreventsthe coup. Then, the value ofagent i in state (Al, D) would be V1(Al, D)-v1(Al, DI ). This continuation value v1(Al,DI id) satisfies the Bellman equation;(8) v'(A', DIlTd)

= a(h' + &i(O, Td)) + I3W'(D),where

Ai(0 Td)At= Td TdAthiis the net amountof redistributionor a personof type i in state At with a tax rate of Td. Noticethat in the currentperiod, taxes are lower, Trinstead of T-", giving higherutility to the rich-that is, AP(O, Tid) < 8P(O), and L\r(0, Td) >8'(0). However, the continuationvalue is stillW1(D). This capturesthe notion that next pe-riod if the state switches to Ah, taxes will in-crease back to -: it is impossible for the poorto committo futuretaxes, unless the future alsoposes an effective coup threat.Reducing the tax rate to Td may not beenough to preventa coup, however. After ob-servingthe tax rate Td, the elite decide whetherto mount a coup,; = 1, or not,; = 0, so(9) V'(A1,D)

= max {;V'(Al, E) + (1 -;)vr(Al, DIT d)},E{0,1}

where Vr(Al, E) is the continuation value to theelite after a coup in the state (Al, E) given by(10) 'V(A', E) = 4ah 13W(E),and(11) W'(E) = (1- s)Vi(Ah, E) + sVW(A',)

is the expected continuation value with theelite in control of the political system. Thiscontinuation value depends on the strategiesthat the players will pursue in a nondemo-cratic regime. Assumption 2 ensures that inthe state (Ah, E), the rich will set zero taxes,so agent i obtains income h1, and his contin-uation value is W1(E). Hence, Vi(Ah, E) =hi + 1W1(E).In contrast,if there is a recession (Al, E),thereare threepossibilities: (i) democratization,

=y= 1; or (ii) they may choose not to democ-ratize;that s, y = 0 and set a tax rateof 1Te; andthe poor could choose p = 0 (no revolution)inresponse; or (iii) the poor may undertake arevolution, p = 1. The contination values de-pend on which of these cases applies. In thetext, we focus on 'y = 1, that is, franchiseextension, which is the case that applies alongthe equilibriumpath.8In this case,(12) V1(AI,E) = a(hi + 5i(0)) + 1W'(D).This expression follows because in this firstperiod of democracy, there is no threat of acoup, and the poor set the unconstrained taxrate 1Tm,which gives a currentconsumptionofa(h' + &'(0)). The continuation value isW1(D).The elite prefer not to carry out a coup instate (Al, D); thatis, ; = 0, if Vr(Al, E) givenby (10) is less than vi(Al, DIT d) in (8). Hence,therewill be no coup as long as(13) Wr(E) - W'(D)

a((l - 4)hr + Ar(, Td))c- [~~~~~3Equation (13) is the coup constraint. a coupoccurs if the gain to the rich of capturingpolit-ical power and reducing taxation, p3(Wr(E)Wr(D)) - alr(O, Td), is greaterthan the costof the coup, a(l - 4)hr. A coup is less likelyto be beneficial for the elite when the level of

8 To see why only the case with -y= 1 is relevant alongthe equilibriumpath, note that the society starts in a non-democraticregime. So if either -y= 0 or p = 1, there willnever be a democracyalong the equilibriumpath, and weare calculating the value of a deviationfrom democracy.


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946 THEAMERICANECONOMICREVIEW SEPTEMBER 001income in a recession a is high because thisdetermines he opportunity ost of political tur-moil caused by the coup. Therefore, coups areattractiveonly when a recession causes a severedrop in output,reducingthe opportunity ost ofpolitical turmoil.We can first determine a critical value ofthe cost of coup, 4(0, a, s), such that as longas 4)< 440, a, s), a coup is never beneficialfor the rich, even if the poor continue to tax atthe rate T = Tmin state (Al, D). This criticalvalue is found by solving (13) for 4)with Ti =Tm [i.e., with l\(0, Td) = 5r(0)]:(14) 4(0, a, s)

(1 - 3(1 - s))a(hr + 5r(0))+ ,3(1 - S)5r(O)

(I1-,B(l1-s))ahrWhen 4)< 4(0, a, s), the coup threat doesnot play a role, and democracy is fully con-solidated. Moreover, as we show in the Ap-pendix, a4)(0, a, s)ld0 > 0, so a less unequalsociety is more likely to achieve a fully con-solidated democracy. Intuitively, a greaterlevel of inequality makes democracy less at-tractive for the rich because it implies highertaxes. Note also that d4(0, a, s)Iaa > 0, soan increase in a, which makes recessions lesssevere, increases the opportunity cost ofmounting a coup and makes it easier to con-solidate democracy. Finally, d4(0, a, s)las> 0. An increase in the frequency of reces-sions implies that the coup constraint bindsregularly, and because in this state the richpay relatively low taxes, this makes low taxesmore "credible."Democracy is therefore lesscostly to the elite. Therefore, a coup must beless costly (4)higher) to be worthwhile.We can next determine the value of the costof coup, 4)(0, a, s) > 4(0, a, s), such that aslong as ) < (O0, a, s), the poor can stop acoup by setting a low enough tax rate in thestate (Al, D). Conversely, when 4)> 4(0, a,s), the elites' incomes fall by a sufficientlysmall amount as a result of political turmoilthat even a policy of setting Ti = 0 does notstop a coup. The threshold 4(0, a, s) isderived by solving (13) for 4)with Td = 0[i.e., Ar(0, Td) = 0]:

(15) (0, a, s)(1 - p(1 - s))ahr+ 13(1 - s(1 + a)) r(O)

(I1-p( - s))ah rThe comparative tatics areidentical to those of

0, a, s).If j(O, a, s) < 4)< (O, a, s), thendemocracy is semiconsolidated: the poor canavoid a coup by reducingthe tax rate below 1Tmin state (A , D). In particular, hey would setT= Td such that 1(W'(E) - W'(D)) = a((1- 4)hr + Ar( 0, Td)) satisfying the coupconstraint (13) as an equality. Although thesociety always remainsdemocratic, he threatofa coup is still importantand influences taxes:the tax rate Td iS less than Tm,which the poorwould have set in the absence of this threat.Inthe Appendixwe show thatT-d iS increasing n 0so that higher inequality reduces the tax ratenecessaryto preventa coup. Intuitively, higherinequalitymakes democracymore costly for therich, and the poor have to give them a bigger taxconcession to prevent a coup.Finally, if 4)> 4)(0, a, s), a coup is not verycostly to the rich, so even a strategy of settingT = 0 by the poor will not prevent it. In thiscase, society will revert to a nondemocraticregime when A, = Al, despite the social costsinvolved in this process.We next turnto the incentives to undertakearevolution in a nondemocraticsociety. If thepoor attempta revolutionin the state (Al, E),they would obtainVP(A',R) as given by equa-tion (5) evaluated at At = A'. AlthoughAssumption2 ensures that the revolutioncon-straint s not bindingin stateAh, it may bind instateAl. The elite may then choose to redistrib-ute income to the poor to preventa revolution,imposing a tax rate 1Teand giving the poor areturn VP(A', E) = ve(A', EITe). The valuevi(Al, EITe), satisfies the Bellman equation,(I 6) v (A', E|IT e)

= a(h' + -i(0, Te)) + 3W'(E),where Ni(0 Te)a Tt Teahi is the netredistributionor agenti at the tax rate Te n thestate A'. In this case, the poor receive net


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 947income (1 -T)ahP from theirown earningsandtransferTt = (Te c(T?))ah, iving thema totalincome of a(hP + 7j(O,7)). Notice thatthe con-tinuation alueis W1(E):f in the nextperiodwearestill in stateAt = Al, then redistributionon-tinues. However, if in contrast the economyswitches to At = Ah, redistribution tops. Thiscaptures he notion hatthe elite cannotcommit ofuture redistribution, nless the futurealso posesan effective revolution hreat.Also note thatT


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948 THEAMERICANECONOMICREVIEW SEPTEMBER 001Appendix, both VP(A', R) and VPj(Al,D) de-pend only on the underlyingparameters.Now we can establish the following result(proof in the Appendix):PROPOSITION1: SupposeAssumptions 1, 2,and 3 hold and the society starts in a nondem-ocratic regime. Then:1. If k < A(O,a, s), then the society remainsnondemocratic.2. If ,u > A(0, a, s) and 4)< 4(0, a, s), thenthe society democratizes the first time thestate is (Al, E), and then remains a fullyconsolidated democracy.3. If ,u > /!(0, a, s) and 4(0, a, s) < 4) /!(0, a, s) and 4)> 4)(0, a, s), thenthe society is an unconsolidateddemocracy,and continuouslyswitches regimes.

In the first type of equilibrium where ,u j(O, a,s), but 4) 4)(O,a, s). In this case, democracyis not fully consolidated; f the poor were to seta tax rate Tm in the state (Al, D), a coup wouldoccur. However, the poor can avoid a coup bysetting a lower tax T = Td in state (A', D),whichis just sufficientto dissuadetheelite frommountinga coup. Although the society alwaysremains democratic, t is in some sense "underthe shadow of a coup," as the coup threat imitsoverall redistribution.0The final ype of equilibriumnvolves k> g(O,a, s) and4)> 4)(O, , s). In thiscase, democracyis unstable:when the state moves to Al, a coup isrelatively attractive or the elite, and cannot behaltedby reducing axes.As a result, he economywill stochastically luctuatebetween democracyand elite control.Morespecifically, he economystartswith the elite in powerandtheyset T = 0.Whenever he statemoves to Al, the elite extendthe franchise.But as soon as the state goes from(Ah, D) to (Al, D), they mount a coup, regainpoliticalpower,and set T = 0. The variability ffiscal policy is thereforehighest in this equilib-rium,and the amountof redistributions less thanin cases2 and 3, but morethan n case 1. Higherinequality ncreasesredistlibutionn this regimebecause it increases the tax rate when there isdemocracy,whereas here s neverany redistribu-tion duringnondemocracies.The reasonwhy there s an inefficientequilib-rium n thiscase, in contrasto an intuitionbasedon theCoaseTheorem,s that hepoliticalsystemis unable o commiLto future axes.If thepoorandthe rich could bargainand conmiit to a pathoffuturetaxes, therewould be no coups along theequilibrium ath.Yet, in practice, uture axesaredeterminedin future political equilibria, andpromises of lower taxes in the future are notcredible- once thecoupthreatdisappears,he taxrate will rise back to fl. Forward-looking elites,realizing his, prefera coup,even though his is acostlyoutcomefor society.

'0Leonard Wantchekon 1999) argues this has been thecase in El Salvador.Thisresult s also related o Wantchekon(1999) and Matthew Elhmanand Wantchekon 2000) whoanalyze how the threatof conflict initiatedby the loser of ademocratic lection affects the votingoutcomes.


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 949Notice that when democracy is unconsoli-dated and the poor are in power, they set themaximum tax rate, fully anticipating hatredis-tribution will eventually come to an end as a

result of a coup. Thisresult may help to explainthe existence of highly redistributive,but rela-tively short-lived, populist regimes of LatinAmerica.Thisis consistentwithRobertKaufmanandBarbaraStallings's (1991) emphasison theconnection between unconsolidateddemocracyandpopulistredistribution.They write (1991 p.27) "establisheddemocracies (Venezuela, Co-lombia and Costa Rica in our study) were alsoassociated with orthodox macro policies. ... [I]twas the transitionaldemocracies(Peru, Argen-tina and Brazil) thatfollowed populistpolicies."There are four majorconclusions o be drawnfrom this analysis.The first links inequalitytoregime changes.A decrease n 0 reducesA(O,a,s), 4?(0,a, s), and 4(O, a, s). This impliesthatathigherlevels of inequality,both revolutionsandcoups are more attractive.Therefore,societieswith more initial inequalityare more likely toswitch between democracyand nondemocracy,and ess likelytohave a fullyconsolidated emoc-racy.So our resultsarein line withtheempiricalfindingsof apositiveassociation etween nequal-ity and politicalinstability see, e.g., EdwardN.Muller and Mitchell A. Seligson (1987) andAlesina and RobertoPerotti 1996)].The second conclusion pertains to the linkbetween inequality and redistribution.To seethis, fix the cost of coup 4, and define OH > OLsuch that 4;= 4(0H, a, s) and 4;= 4(0L, a,s). Moreover, suppose that k > g(O, a, s).When 0 > OH, 4 < ((O, a, s), so inequalityis sufficiently low thatdemocracy s fully con-solidated.Now consideran increasein inequal-ity (a reduction in 0). This will increase

redistributionat first as in the standardmodelsof voting over redistribution e.g., Meltzer andRichard 1981)], because a&TraIO0 . When 0falls below OH, we have 4 E (j(O, a, s), 4(O,a, s)) anddemocracy s only semiconsolidated.The poor are then forced to reduce taxes fromTm to Td in the state (Al, D). Nevertheless,overall redistribution ncreases.1"As inequality

increases further, it will eventually fall belowOL. When 0 < OL, we have 4 > 4(O, a, s),and democracy s now unconsolidated.So in thestate (A', D), there is a coup followed by aperiod of nondemocracy and no taxation. Theincrease n inequality n the neighborhoodof OLtherefore reduces overall redistribution.As aresult, there is a nonmonotonicrelationshipbe-tween inequalityand redistribution,with soci-eties at intermediate levels of inequalityredistributingmore than both very equal andvery unequal societies.The third implication of our analysis is re-lated to fiscal volatility. The relationshipbe-tween fiscal volatility and inequality s likely tobe increasing. Within each regime, higher in-equality leads to more variability. Moreover,higher inequality makes case 4, which has thehighest amountof fiscal variability,more likely.This may explain why fiscal policy has beenmuch more volatile in Latin America than n theOECD (Gavin and Perotti, 1997).The fourth implication is that the costs ofredistributionwill also have an impact on theequilibrium political system. Suppose that thecost of taxation becomes less convex, so thatC(T-') is unchanged,but c'(T ...) decreases.Be-cause deadweight osses from taxation are nowlower, the median voter will choose a higherlevel of taxation. However, as T7" increases, sowill -5&(0), hence democracybecomes morecostly to the elite, and hence less likely to beconsolidated.This implies that in societies inwhich taxation creates less economic distor-tions-for example, in societies where a largefraction of the GDP is generatedfrom naturalresources- democracies may be harder toconsolidate.Finally,it is interesting o brieflyconsidertheimplicationsof our model for political develop-ment. A large empirical literaturebeginningwith Lipset (1959) has found that democracytends to be correlatedwith high per capita in-come. In our model, holding inequality andother parameters constant, rich countries areno more likely to be democratic than poor

" Overall redistribution (average redistribution) is-[(1 - s)3r(0) + saAr(0, Td)]lhr becauseinstateA" nettransfers rom the rich are equal to - 5"(0), and in stateA',

they are equal to -r((0, Td)lhr. Solving for A"(0, Ti)lhr interms of 3'(O)lh' from (A2) in the Appendix, and using thefact that a[5'(O)/h']/aO > 0, we find that overall redistri-bution increases with inequality.


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950 THEAMERICANECONOMICREVIEW SEPTEMBER 001countries. This is because an increase in hleaves both the revolution and coup constraintsunchanged. However, there are a number ofplausible ways in which such a connection canbe introduced nto the analysis. First, it is quitelikely thatGDP is more volatile and recessionsrelativelyworse in poorcountries see Acemogluand Fabrizio Zilibotti (1997) for theory andevidence]. This would imply that a is lower inpoor countries, so they suffer more severe re-cessions, leading to greaterpolitical turmoil.Asa result, democracywould tend to be less stablein poor countries.12 econd, development s of-ten associated with structuralchanges in theeconomy, and these changes may affect thecosts and benefits of coups and revolutions.Most important,richereconomies are typicallymore urbanized,and urbanization ncreasesthepowerof the poor segments of the society. Thismay make democratization more likely, andcoups less likely, contributing o the long-runtrendsobserved by Lipset.

II. Consolidating DemocracyWe now discuss ways in which unconsoli-dated democracies may be consolidated. Onemethod of consolidating a democracyis assetredistribution.Asset inequality determinesthelevel of taxation and the costs and benefits ofcoups. If asset inequality can be reducedper-manently, the benefits of a future coup to theelite would be lower becausedemocracywouldbe less redistributive.Althoughassetredistribu-tions, such as educationand land reforms, mayin the long run consolidatedemocracy,we showthat the anticipationof such reforms will createpolitical instabilityin the short run because theelite will have a greater ncentive to undertakea

coup. We then show how constitutional imitson taxation and political institutions may beuseful in consolidatingdemocracy. Finally, wediscuss the effects of investments when returns

depend on political regime, and demonstrate hepossibility of multiple equilibria.A. Asset Redistributionunder DemocracyUnlike fiscalredistribution,f asset inequalityis reduced, it is permanent'3 and cannot bereversed,althoughit also has permanentcosts.We model the costs by assuming that assetredistributioneducesthe total stock of assets inthe economy. If h is the initial stock, then thepostredistributiontock is H(0), where H is aconcave twice continuously differentiable de-creasing function [i.e., H'(-) < 0 andH"(-) 00, and assume 4 > 4(00, a, s),so thatwithoutanyasset redistributionheecon-omy would oscillate between regimes. Hence,for democracy to be (semi)consolidated, in-equalityneeds to be reduced(i.e., 00needs to beraised to OL). Also supposethatOR > 00, wherey = (OR, a, s), and that OR is very high, sothatit can be ignoredfor now.Following the same argumentsas in the pre-vious section, we can write the value to a pooragent of unconsolidated democracy startingfrom stateAl as vPl'(AI,Di0) [see the Appendixandequation (A4)]. This value functionapplieswhencoupsoccuralongtheequilibriumpath.Incontrast, f 0 0L, coups can be stopped,andwe can use equations (6), (7), and (8) to writethe correspondingvalue for consolidated de-mocracy, again startingfrom stateAl, denotedvP(A', D| 0) (see Appendix for theexpressions).To determine equilibrium asset redistribu-tion, let 0' = argmax, vP(A', DI0), bearing nmindthatwe mightbe at a corner solution with0' = 00 where no asset redistributions chosen.2 Interestingly, f output becomes less volatile becauseof a reduction in s, the effect is ambiguous. On the onehand, a lower s makes recessions less frequent,and hencethe society becomes more stable. Onthe otherhand, a lowers, by making recessionsless likely, reduces "the credibilityof future concessions" both by democracies and nonde-mocracies, and may increasethe attractiveness f coups and

revolutions.

13 For our general results to hold, asset redistributiondoes not need to be permanent; t only needs to be harder oreverse than fiscal redistribution.In practice, it may beeasier to reverseasset distributions handemocracy,but thisis ultimately an empirical question.


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 951

VP

'I

V I

o 0L 07"FIGURE1. VP1APPLIESWHEN DEMOCRACYS UNCONSOLIDATED,NDVP2APPLIESWHENDEMOCRACYS CONSOLIDATEDDEMOCRACYS CONSOLIDATEDHEN 0 2 0L

VI'

| ,,,AV~~~~2

I~~~~~~~~~~~~~~~I\'0 0,0" , OL

FIGURE2. V1APPLIESWHEN DEMOCRACYS UNCONSOLIDATED,ND V2 APPLIESWHENDEMOCRACYS CONSOLIDATEDDEMOCRACYS CONSOLIDATED HEN 0 2 OL

Also, let C' = argmax, vP Al, DO0).Then wecan see that:1. If 0"t > oL, the poor will redistributeassetsup to 0".Intuitively, n this case, the level ofredistribution hat the poor prefer ignoringthe coup constraintalso preventscoups.This

case is illustrated n Figure 1.

2. If 0"t< 0L, and vP(A', D| 0') > vP(A',DI0L), then the poor will redistribute o 0',and coups will occur along the equilibriumpath.3. Otherwise,the level of redistributionwill beOL.This case, shown in Figure 2, is probablythe most interesting one for our purposesbecause it illustratesthat, to prevent coups,


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952 THE AMERICANECONOMICREVIEW SEPTEMBER 001thepoor may choose a level of redistributionhigher than that which would maximize theirincomein the absence of the threatof a coup.

A key comparative tatic pertains o the levelof inequality:if 00 ? 0L, there will not be amotive to redistributeassets to prevent a coup(thoughtheremay be an incentive to redistrib-ute assets to increasethe income of the poor ina consolidated democracy). We may thereforeexpect asset redistribution to emerge as amethod of consolidating democracy, especiallyin relatively unequal democratic regimes thatare expected to be threatened n the future.Overall, the mainimplicationof this analysisis that asset redistribution an help to consoli-date democracy. Whenever the choice of thepoor is OL or greater, coups no longer occuralong the equilibriumpathbecause asset redis-tributionhas permanentlychanged the level ofinequality, and made coups less attractiveforthe elite.In practice, asset redistributionappears tohave played such a role in a number of in-stances. In Acemoglu and Robinson (2000),we argued that educational expansion innineteenth-century Britain and France was inpart a result of democratization, and StanleyL. Engerman et al. (1998) argue the same forLatinAmerica.In BritainandFrance,these andotherpolicies reduced nequalityand therewereno significantreversals n theprocessof democ-ratization. In Costa Rica, the educational andland reforms that reduced both earnings andland inequality after the democratizationin1948 appear o have helped with the consolida-tion of democracy [see Deborah J. Yashar(1997) for this argumentand Carlos M. Vilas(1995) for some numbers]. The situation inVenezuela after the return to democracy in1958, which led to a land reformredistributing19.3 percent of agricultural and, also providessome support o this view [see John D. Powell(1971) and Table 10.2 in Eliana Cardoso andAnn Helwege (1992)].

B. AnticipatedAsset RedistributionandPolitical InstabilityBecause asset redistributions permanentandcostly to the elite, the anticipationof such re-

distributionmay make a coup more attractive

and create political turmoil. We now analyzethis using a simple extension of our model.Suppose that h(00, a, s) < 4 < 4(00, a, s)(i.e., OH > 0 > OL) so that democracy is(semi)consolidatedwithout asset redistribution.Consider the first period of democracyin stateAl. The poor may want to redistributeassets,this time not to consolidate democracy but toincrease their incomes. However, we now as-sume that there is a one-perioddelay betweenthe legislation and the implementationof assetredistribution.For example, land reforms in-volve administrativedelays. If, during this pe-riod, the state stays in A, = Al, then the richmay mount a coup to avoid asset redistributionbefore it is implemented.

Suppose that the poor legislate a redistribu-tion of assets changing inequalityfrom 00to 0.The elite will not undertakea coup during theadministrativedelay of the asset redistributionif the state is at At andwr(E| 00) - w'(DIO)

At[(l - p)hr(00) + A'(00, Td)]

where w"(EI ) is the continuationvalue to theelite in nondemocracyas a function of the dis-tributionof assets 0. Hence wr(E|00) = W"(E)will be theirvalue if they reestablishcontrolofthe political system andkeep the distributionofassets at 00. Similarly,wr(DLI) is the value tothe elite of democracyafter the distributionofassets changesto 0. Notice that the poor wouldnever redistributeo a level 0 such that the eliteundertakea coup in stateAh becausethis wouldimply that there will necessarilybe a coup fol-lowing asset redistribution.The poor may un-dertake enough redistribution, however, tocause a coup in a recession (state A'). Thecriticalvalue of 4, 4, such thatwhen 4 < 4, acoup in stateAl can be prevented, s definedby

wr(El0o) - wr(DI 3) = a(l - j)hr(0O)Therefore,when 4> 4 therewill be a coup ifthere is a recession following asset redistribu-tion. In contrast,recall that 4, the critical value


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 953of the cost of a coup without asset redistribu-tion, is given by

w'(EIO) - wr(DI o) = a(1 - O)hr(00)Given that wr(D|I) < wr(D|0O), we have< 4. This implies that there are values of4 E (4), such that without asset redistri-bution, democracyis consolidated, but if, dur-ing the period of administrative delay afterasset redistribution, the state remains in Al,the elite will attempt a coup. If s, the proba-bility that the state remains in Al, is lowenough, the poor may prefer to enact assetredistribution despite its potentially destabi-lizing effects. Therefore, the main conclusionof this subsection is that asset redistribution,which is generally in the interest of the poorand often useful in consolidating democracy,may create a temporary period of instabilityfor a democracy.A numberof coups in Latin America appearto have been motivated by a desire to preventradical land reform. For example, in Brazil, acentralaim of the coup in 1964 was to preventtheattemptby theleft-wing PresidentGoulart obypass the veto of the Congressand use othermeans to push through agrarianreform [see,e.g., Skidmore(1967) and Wallerstein(1980)].Similarly,most scholarsarguethat the agrarianreform after 1952 in Guatemalawas the mainmotivation or the coup of 1954 (JamesHandy,1984;RobertTrudeau, 993), and hat he increas-ingradicalizationf Allende'spolicies,especiallyon landreform,precipitatedhe coup of 1973 inChile (see Arturo Valenzuela, 1989). MarionBrown(1989 p. 236), for example,writes "a sec-ond generationof [agrarian]eform was clearlygainingmomentumn the latterpartof Allende'sadministration-afact that was not lost on coun-terreform lements thatultimatelysupportedPi-nochet's coup d'6tat." In fact, of the landoriginallyexpropriatedy Allende'sgovernment,43 percentwas returned o previousowners orexcluded from the reformby othermeans .[seeLovell S. Jarvis 1989 p. 249)].Thesame s true nVenezuela,where the 1948 land reform aw wasimmediatelyrepealed by the incoming militarygovernment see Powell (1971) and PeterDomer(1992 p. 47)].

C. ConstitutionalLimitationson TaxationIn our economy, coups arise because democ-racies cannot commit not to levy high taxes on

the rich in stateAh. Even though governmentsmay be unable to commit to future taxes, soci-ety may be able to adopt a constitution thatlimitshow taxes are set. Forexample, before theSixteenth Amendment to the U.S. Constitu-tion in 1913, the government was unable touse income taxes because of constitutionalrestrictions [see Sven Steinmo (1993 pp. 74-76)]. Such restrictions may help democracyconsolidate by reducing the fear of the richthat they will be heavily taxed in state Ah.More generally, our model suggests that thestructure of democratic institutions may becrucial for consolidation because they influ-ence what types of policies can arise inequilibrium.To capture these ideas, consider the casewhere 4 > 4(O, a, s), so that democracyisunconsolidated.Nevertheless,there will exist alevel of transfers rom the rich, 8'(0) > 8'( 0)[recall that 8'(0) < 0], such that when netredistribution wayfromthe rich in the stateA,his V'(0), and zero in the stateAl, they will beindifferentbetween undertakinga coup andre-mainingin democracy. By reasoningsimilartothat above [especially equation (15)], this levelof redistribution, r(0), satisfies

(1 - 3(1 - s))ah'+ ,3(1 - s(1 + a))8r(0)

(I- 3(1-s))ahrLet the tax rate that leads to Vr(0) be , whereobviously TK< Tm. Now imagine that in thestate (Al, D), the median voter-a pooragent-has an option to introducean irrevers-ible constitutional estrictionon taxes, suchthata tax rategreaterthan T- is unconstitutional.Byconstruction,once this irreversibleconstitutionis in place and the poor cut the tax rate in thisstate (Al, D) to 0, the rich will be indifferentbetween undertakinga coup and living underdemocracy.Because therewas output oss in theprocess of coups, this immediately implies thatthe introduction f theconstitution mprovesthewelfare of the poor. Intuitively, using the con-stitution, hey committo low taxes in thefuture,


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954 THEAMERICANECONOMICREVIEW SEPTEMBER 001which discouragesthe elite from undertakingacoup.A natural oncern s that constitutionsmay bechanged or amended.Althoughin manycases asupermajoritys required o change a constitu-tion, constitutional estrictionson taxes may notalways be crediblecommitments o low taxes inthe future. The importance of constitutional,and more generallyinstitutional,restrictionsontaxation in consolidating democracy thereforedepends on how durable they are expected tobe. This remains an importantquestion for fu-ture research.Constitutional estrictionson the tax rate arejust one example of how the structureof polit-ical institutionshas important mplications forthe consolidation of democracyin our model.Anothermuch discussedidea is thatpresidentialsystems may lead to more instabilitythan par-liamentary systems. Przeworski et al. (1996)present evidence supporting this hypothesis.This pattern s also consistent with our frame-work. Presidential systems concentrate morepowerin the executive relative to parliamentarysystems, and hence may makedemocracymorethreatening o the rich, and coups more attrac-tive. In line with this view, Linz (1978), forexample, has arguedthat presidential systems"raise he stakes"of thepolitical game.It is alsointerestingthat JamesMadison and the writersof the U.S. Constitution were aware of thesedangers, and constrained the powers of presi-dent by institutinga separationof powers (seeMadison, 1788).

D. Investmentand Multiple EquilibriaThe only economic actions we have consid-ered so far have been taxation decisions. Our

interestin political institutions s in partmoti-vated by our belief that these affect a rangeofeconomic decisions, including investment andgrowth. Here,we brieflydiscuss the interactionbetween investment and political transitions,pointing out a possible source of multipleequilibria.Suppose now that an agent of type i canundertakean investment of value k1 at costhTF(k1),whereF is increasingandconvex, withF(O) = 0. The cost is incurredonly once, andthis investmentraises the return n democracyforeverby a factorof 1 + ki, but has no effect

on income in a nondemocraticregime. The de-sirability of the investment therefore dependson the expected duration of democracy. Theassumption hat the investmenthas no return na nondemocracy s not essential. The importantfeature is that the returnto a range of invest-ments is higher in democracies than that innondemocracies.Plausible examples includein-vestments in sectors that trade with other coun-tries, which may reduce tradefollowing a coup,investments in long-run projects that requireguarantees against future expropriation thatmay be better provided by democracies, andalso investmentsin political participation,par-ties, and unions. We now show that the durationof democracy is affected by the amount of in-vestment,as well as affecting the profitability finvestment. As a result, if agents believe thatdemocracywill persist, they will invest more,and this will in turn increase the durability ofdemocracy. Thus there may be multipleequilibria.Notice first that because all agents face thesame marginal ax rate and because both returnsand costs are multiplied by hi, they will allchoose the same level of investment, k1 = k.Now let us now define v'l Al, D|k) as the valueto an agent in an unconsolidateddemocracystarting n stateAl and withinvestmentk. Let usdefine k as the investment level when democ-racy is expected to be unconsolidated.This in-vestmentlevel is given by k = arg maxk vi (Al,D|k).In contrast, in a semiconsolidated democ-racy, the investment is productive also duringperiods of recession. Now define v'(A', Dlk)to be the value to an agent in a semiconsoli-dated democracy, startingin stateAl and withinvestment k. The investment level that willbe chosen by the agents in this case, k*, willbe different, and in particular, will satisfyk* = arg maxkv (A', D|k). Notice thatwhendemocracy is consolidated, the investment isproductive in all future periods. Therefore,k* > k, because the cost of investment isindependentof the political regime, but whendemocracy is consolidated, the expected re-turn is higher.Now considerthe coup constraint onditionalon the level of investment k. In particular,de-fine +(k) as the critical value of 4 such thatwhen 4 < +(k), and the level of investment s


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 955k, a coup can be prevented n the state Al. Ourusual arguments mply that the critical value is+(k) given by

wr(Ejk) w2(Djk) = a(l - 4(k))hrwhere w"(DIk) is the expected continuationvalue, conditional on k, when democracy isconsolidated[definedby (A8) in theAppendix],andw"(Elk) is the expectedcontinuationvaluein nondemocracy.The reason why the valuefunctionwr(DIk) features n the coup constraintis thatthe elite compareI3wr(DIk), which is thevalue of remaining n a democracy orever,withthat of mountinga coup, which is ,Bw(Elk) -a(1 - k(k))hr. Notice thatk* is themaximizerof wr(DIk), so wr(Dlk*) > wr(D k), andhence 4(k*) > +(k). Intuitively, a greaterlevel of investmentmakesa coup less attractivebecause thepoliticalturmoilassociatedwith thecoup creates a greateroutputloss.This analysis implies thatthere arevalues of4 such that 4 E (+(k), 4(k*)). When 4 E(+(k), 4(k*)), democracywill be consolidatedwhen all agents invest up to k*, and whendemocracy is consolidated, they will indeedprefer to invest kV. There is another equilib-rium,however,where all agents expectdemoc-racynot to be consolidated,so invest only up tok. This level investment, in turn, is not highenough to consolidatedemocracy. The generalimplication is that when there are investmentswhose payoffs are higher in democracies, ex-pectationsabouthow durable hese democraciesare can be self-reinforcing, eading to multipleequilibria with different political regimes, out-put levels, and economic welfare.

III. ConsolidatingNondemocracyA. Asset Redistribution nNondemocraticRegimes

The elite may also wish to undertakeassetredistribution o stop a revolutionor democra-tization. To illustrate the role of asset redistri-bution in preventing democracy in a simpleway, assumept > ,A(00,a, s), or equivalently,OR > O, where recallthatOR is definedby pt=(OR, a, s). This implies that without asset

distribution, herewill be democratization.Sup-pose also that 4 < (00, a, s), so democracy,if created, will be fully consolidated. We alsoassume thatredistribution way from thepoor isnot possible (i.e., 0 ' 00).With these assumptions,democratizationwilltake place the firsttime we are in state (Al, E).The assumption4 < k(00, a, s) also ensuresthat 4 < (0, a, s) for any 0 ' 00, sodemocracy,once created,will always be fullyconsolidated. Let the return o the rich underaconsolidateddemocracy, starting rom state Al,be v"(Al, DI0). In this case, the elite may wishto undertake asset redistribution to reduce8Y(0), depending on whether asset or fiscalredistributions more costly to them. In whatfollows, we assume that asset redistributionssufficientlycostly that the elites will notdo this,so arg max v'(A', DI0) = Oo.14In contrast, asset redistributioncan also beused to avoid democratizationby increasing 0to OR (i.e., reducing asset inequality). Denotethe value of the elite in state (Al, E) by v`(A',El0) in this case.Whether the elite will choose asset redistri-bution is determined simply by comparinmvr(Al, D|00) and v3(Al, ElOR). If v"(A,D O0) < v3(Al, ElOR), then the elite prefertoprevent democratization and will choose theminimumredistributionufficient o preventde-mocratization, hatis, 0 = OR. Otherwise, theywill choose not to redistribute, o 0 = 00, andtherewill be democratization.In practice, two cases appear o fit the impli-cation that the elite may choose to redistributeassets to preventdemocratization.'5 n a 1949reform,South Korearedistributed 0 percentofthe agricultural and in Korea. Haggard (1990p. 55) argues that the reforms were aimed atdefusing rural insurrections and counteractingthe destabilizing spillovers from land reformin North Korea. Taiwanese land reforms of

14 Formally, -H(00)I(1 - A) + (1 - 00)H'(00)I(1 -A) + 6r (0O) c 0.15 This result is related to previous analyses of landreform,such as Andrew W. Horowitz (1993) and Grossman(1994), which argue land reform can prevent revolution,though these papers do not compare asset and fiscal redis-tribution.Also in contrastto these papers, asset redistribu-tion in our economy may prevent not only a revolutionbut

also democratization.


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956 THEAMERICANECONOMICREVIEW SEPTEMBER 0011949-1953 that redistributed 4.6 percentof theland(SamuelHo, 1978 p. 163)alsoappear o havebeen an attempt o defuseruralprotest see AliceH. Amsden,1985).Inthe wordsof Ch'en Ch'eng,thegovernorof Taiwanat the time of thereforms,"the situationon the Chinesemainlandwas be-comingcriticaland the villageson theislandwereshowingmarked igns of unrestandinstability. twas feared that the Communistsmighttake ad-vantage of the rapidly deteriorating ituation"(quotedin Haggard, 1990 p. 82). Interestingly,untilveiy recentlybothSouth KoreaandTaiwanremained relatively nondemocratic, especiallycomparedo othercountrieswith similarper cap-ita income levels.Asset redistribution s a method of prevent-ing democratization s more likely to emergewhen 6'(0), the transfersaway fromthe rich ina democracy,are larger.This result may helpexplain why asset redistributionemerged inSouth Korea and Taiwan, where the threat ofcommunism made social unrestvery costly tothe elite, but not in the Philippines, where thethreatwas less serious.Finally, although we have modeled the eliteas distributingassets equally amongthe poor, adifferent interpretations as a strategy of co-opting. In particular, he elite may redistributeassets selectively to groupsamongthepoorwhoare importantfor the threat of revolution andwho can be persuaded o switch sides with suchtransfers.This is equivalentto ourformulation,but this interpretationmay fit the example ofMexico in the 1930's better,wheresmallgroupsof peasantsthatsupported he ruling partyweregiven land.

B. RepressionAn alternative trategy or the elite wishingtoprevent democratization s to use repression.Such repression s observedin many cases, forexample, in Indonesia n 1965 andin El Salva-dor in 1932. We now return to the simplermodel of Section I with an exogenous distribu-tion of assets, and consider the possibility ofrepression.The main result is that in very un-equal societies, the elite may have so much tolose from democratization as to prefer a re-pression strategy to suppress revolution andprevent democratization.Therefore, the rela-

tionshipbetweeninequalityandregime changes

is potentially nonmonotonic; societies with in-termediate evels of inequality are more likelyto democratize.Nevertheless, we show thatonlysocieties with limited inequality will achievedemocratic consolidation. Furthermore,politi-cal instability is more likely in more unequalsocieties also, as long as social unrest sup-pressed by repression is counted as "politicalinstability" n the data.To analyze these issues in the simplest pos-sible way, suppose that the elite are in power,and we have - > g(0, a, s) and 4 < 4)(0, a,s), so that if the society democratizes,it willremain so forever, and the rich will obtain thevalue Vr(Al, E) as given by (12) in Section I.Assume also that the richcan hire an army withthe sole purpose of suppressing revolutionarythreats,atper periodcost M for each memberofthe elite, and that this strategy completelyavoids the threatof revolution.16 It is clear thatwith this strategy,in the state (Al, E) the richwill have a returnofVr(AI E)

((1 -,B(1-s))a + p3(1 s))(h -M)- ~~1-13

ComparingVr(Al, E) to Vr(Al, E) as given by(12) immediately mplies that the rich will findit beneficial to use repression fM < - (O)

This conditionwill be satisfied f inequalitys suf-ficiently high, in particular, f 0 < eM where0I = 6' (-M). Define ORas above [i.e., - =-(OR, a, s)]. Thus the elite cannot prevent a

revolutionwith redistribution f 0 < OR. Thisimplies that in the case where 0R OM, therewill be no equilibriumdemocratization: levelof inequalitythat is large enough to make de-mocratizationnecessarywill also makemilitaryrepressiondesirable.The case of OR > OM is moreinterestingandillustrates the nonmonotonic relationship be-

16 For example, the armymay be financedby taxation, nwhich case M is the tax paid by each memberof the elite forthis purpose.


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 957tween inequalityand democratization.A societywith 0 E (0M, OR) will democratize becausesocial unrest cannot be preventedby redistribu-tion and military repression is too costly. Incontrast,if 0 < OM, then inequalityis so highthat the elite are willing to pay for militaryrepression to prevent democratization.Finally,if 0 > OR, then therewill be no democratizationeither, this time because the elite can preventsocial unrestby redistribution.With this extension, it is still truethat amongthe countries that democratize, those withgreater nequalityare less likely to consolidatedemocracyand will thereforeoscillate betweendemocracy and nondemocracy.However, it isonly those with 0 E (0M, OR) and4 < 4(0, a,s) that transit to and consolidate democracy.The condition4 < 4(0, a, s) requires nequal-ity to be low. Therefore, our main result thatlow levels of inequality are conducive to theconsolidationof democracycontinuesto hold inthis model with repression.Political instability,either n the form of frequentregimechangesorrepression, s also more likely when inequalityis high.

IV. Concluding RemarksIn this paper, we have developed a simpletheory of political transitions. Our theory em-phasizesthe role of the threatof revolution andsocial unrestin leading to democratizationandthe desireof the richelite to limit redistributionin causing switches to nondemocraticregimes.Inequalityemerges as a crucialdeterminantofpolitical instability because it encourages therich to contest power in democracies,and alsooftenencouragessocialunrest n nondemocraticsocieties. Therefore, democracyis more likely

to be consolidatedif the level of inequalityislimited,whereashigh inequality s likely to leadto political instability, either in the form offrequentregime changesor repressionof socialunrest.Inequality s also likely to lead to fiscal vol-atility,as the redistributive egimechangeswithpoliticaltransitions.Nevertheless, nequalitydoesnot necessarily ead to more redistribution.Un-equal societies switch between regimes and innondemocraticegimes, here s no redistribution.Ourtheorysuggests hatasset redistributions aybe used to stabilizebothdemocratic nd nondem-

ocraticregimes,but the anticipation f a radicalasset redistribution,uch as a land reform, maydestabilizean otherwiseconsolidateddemocracybecause he elite may mounta coup specifically oavoid the reforms.Our approachalso suggests a numberof ave-nues for futureempiricalwork. First,a more sys-tematicanalysisof whether edistributiveaxationincreasesafterdemocratizationsnddeclinesaftercoups s necessary.Second, twouldbe interestingto investigatewhether he reasonwhy parliamen-tarydemocraciesappearmore stable thanpresi-dential democracies s that they lead to lowerand/oress variable axes,as suggestedpreviously.Finally,a numberof issues requireboth empiricaland further heoreticalwork.For example, whatarethe major actors hat ncrease he likelihoodofdemocracyas an economy develops? Also, ourtheory suggeststhatredistributionhroughassetsis more likely to consolidate democracy;why,then,do many populist regimes,such as that ofPeronin Argentina,use mainly fiscal and labormarket edistribution?

APPENDIX

We now present in more detail the deriva-tions culminatingin Proposition 1 and sketchthe proof of our mainresult. We also explicitlyderive the value functionsdiscussed in SectionII where we restrictedourselves to a more in-tuitive approach.The Coup Constraint

In the state (Al, E), thereare threepossibil-ities as we noted in the text. The continuationvalues dependon which of these cases applies.In the text we consideredthe case where y = 1where the franchise s extended.An alternativeis for the rich to choose y = 0 (no franchiseextension), set a tax rate of Tre, and the poorcould choose p = 0 (no revolution) n response.In this case, instead of (12) the relevantcontin-uation value is(Al) V'(A', E)

a(h' + 4q'(0, Tre)) + f3W'(E),where a -'(0, Te) = a((e - C(Te))h - Tehi)is net redistribution t the tax rateTe in the state


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958 THEAMERICANECONOMICREVIEW SEPTEMBER 001A'. In the next period, the continuation valueW'(E) applies because the society is still in anondemocraticregime. Finally, the poor maychoose p = 1, undertakinga revolution, inwhich case V'(AI, E) = V'(A', R) and V'(A',R) is given by (5). We focused in the text on thecase where y = 1 in the state (Al, E) becausethis is the one that will apply along the equilib-rium path. The algebra for the other cases issimilar, andis useful only forcharacterizingheoff-the-equilibriumpath behavior.ComparativeStatics of +(O, a, s), Td, and Te

To derive the properties of 4(O, a, s) dis-cussedin thetext,observethatthesign of a4(O,a, s)/aO is the same as the sign of a[8(O)/hh]/aO. Using the fact that 8r(O)/aO = TmAthl(1 - A), we have

aE ( )/hr Tm 5r(O)ao 1-0 (1-0)2h/(l-A)

(Ti - C(Tm))(1 - A) > 0,(1 - 0)2

as argued in the text. The other comparativestatics follow by straightforward ifferentiation.Comparingthe expression for +(O, a, s) and4(0, a, s) shows that the comparativestaticsfor 4(0, a, s) are identicalto thosejust derived.If 4(0, a, s) < 4 < (O, a, s), a coup canbe avoided by cutting the tax rate to Td whenthereis a recession. Td is derivedby solving thecoup constraintand is implicitly definedby(A2) (1-p(1 -s))a(4-- 1)

A'(0, T7d)- hr a((1-Jp3(1 -s)) +13s)

Br(O)+ hr (l-s -as)where recall that Ai(O,Td)At- - dA hi.Implicitdifferentiationof (A2) implies that,be-cause as shown above a[Br(0)lh r]iO > 0, wemust also have a[Ar(O, Td)lhr]/ao < 0. Thisimplies that Td must be increasing in 0 asclaimed in the text.

When pt < ft(O, a, s) so that the elite canavoid havingto democratizeby redistributingnstate (Al, E) thetax ratethat ensuresV(A', E) =vP(A', Ele) is(A3) (1 - (3(1 - s))

0 Tea 0Xa (+ (T -C(Te))a A0+f(1-s) X

_ ((l -f3)pta + f(sa + 1-s))A

Te is increasing in p,, and decreasing in 0 (i.e.,increasing n the level of inequality).Notice thatthe tax rate ,re, which the elite set to preventarevolution can be as high as the maximum taxrateT, whereas the tax raterd, which the poorset in a recession to preventa coup, can be aslow as zero. This tax rate 7e is increasing n p,anddecreasing n 0 (i.e., increasing n the levelof inequality). This implies that, despite theirmore redistributive tendencies, democraciesmay sometimes set lower taxes than nondemoc-racies because of political constraints.Valueof an UnconsolidatedDemocracy

Finally, to establish Proposition1, it is nec-essary to assume thatdemocracyis sufficientlyredistributive hat it is more attractive for thepoorthana revolution.To makethisassumptionexplicitwe combine (6), (7), (10), (11), and(12)to calculate the value to the poor of an uncon-solidated democracy.This gives(A4) VP(Al,D) = p(1-s)hP

(1 - (1 - s))[f(1 - s)+ (1 - f(1 - s))a]lP(O)

(1 - B(1 - S))2 - 2S2

(1 - (1 - s))[APS+ (1 - p(1 - s))]ahP

(1-

p(1- S))2- -2S2


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VOL. 91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 959Assumption3 is equivalent to comparing (A4)to VP(A', R) given by (5) and is a simplerestrictionon underlyingparameters.PROOF OF PROPOSITION 1:We now prove Proposition1. Recall that theeconomy initially starts in nondemocracyandthata purestrategyMarkovperfect equilibriumis a strategy combination {6r0(S|IP), 6e(S|y,T7)} where 0jrsolves (1) and exI solves (2).Let us startwith the case in which ,u < I(0,a, s). We can solve for the complete set ofMarkov perfect equilibriaby backward nduc-tion. In nondemocracy, he rich move first,andthen the poor respond. So let us consider theactions of the poor following the decisions ofthe rich { y, Tr}. By Assumption2, the uniquebest response for the poorin the state(Al', E) isto choose eJ(Ah, Ely = 0, Tr = * ) = {p =0}, that is, they will never undertakea revolu-tion duringnormal imes. Next, in the state(Ah,E), the poor agents' uniqueoptimalstrategyis(A5) e(Al, E,y= O, iT" = )

p = 0 if y= 0 andT? Te1l if y=0andT< Te{ pH0 if y ,= 1where Te is given by equation(A3) above. Theoptimality of (A5) follows immediately since

Te, given by equation (A3), is by constructionthe tax rate that makes the poor indifferentbetween revolution and no revolution, and byAssumption 3, they prefer democracyto revo-lution. It is then clear that the unique best re-sponse of the elite is (6r(Ah, El ) = {y = 0,T= 0} and ^'(Al, El * ) = {y = 0 rTe This completes the proof of part 1.

To prove parts2, 3, and 4, considerthe casein which pL> g!(0, a, s). Now eP(Ah, E>y =0 Tr = * ) = {p = 0} is still the uniquebestresponse in the state (Ah, E). The unique bestresponse in state (Al, E) in contrast s(A6) &xP(A19ly5=0 T = )

p= 1 ifY=0-t p=O if 'y=l,9

becauseby construction,n this case no amountof redistributive axationcan make nondemoc-

racy preferred o revolution.It immediately ol-lows thatthe best response or the elite is Y(A"I,El * ) = {y = 0, 7 = 0} and6'(Al, El * ) = {y =1}, andin the state (Al, E) therewill be democ-ratization,and the state will transit to (Al, D).Also, because thereis no constraint n the poorimmediatelyafterdemocratization,hey set i" =i' in theperiod ollowingdemocratization,hererm s themost preferredax rate or the poorgivenby (3) in the text. Now consider tate Ah, D), anddo backward nduction his time startingwith theactionsof the elite, who move after hepoorin ademocracy. Assumption 1 ensures that 6r(Ah,

DI * ) = U = 0}, that is, the elite will neverundertake coup duringnormal imes. This im-mediately mpliesa uniquebest responsefor thepoor as 6P(Ah, DI ) = {1' = {'}, since T7 istheirmostpreferredax rate.Next consider democracy in the state (Al,D), and supposethat4 < 0(0, a, s). Thenbyconstruction, the revolution constraint neverbinds, so the uniquebest responseof the elite is(or(Al, D| ) = = 0}, andthe bestresponseof the poor is e'(A', DI * ) = { = Tim}. Soas claimedin the proposition, he society is in afully consolidateddemocracy,and the taxrate salways equal to 7m.Next supposethat4(0, a, s) < 4 < 4(0, a,s). Now the uniquebest responseof the elite is~= 0 if T ?i Td(A7) 0r Al, DLrP = T) ={ -= 1 if T > Tdwhere rd iS given by equation(A2) above. Theoptimality of (A7) follows because Td is byconstruction the tax rate that makes the eliteindifferent between coup and no coup. Theuniquebest responseof the poorto (A7) is theneJ(Ah, DI * ) = {7P = Td}. Any lower taxwould createless redistribution, ndany highertax would lead to a coup, which is costly for thepoor. Hence, the society alwaysremainsdemo-cratic,but it is a semiconsolidateddemocracy,in thatthe tax ratehas to fall to Td in the state(Al, D) to preventa coup.Finally, when 4 > 4(0, a, s), the uniquebestresponseof the elite is Or9(Al,DIP = ) ={ = 1}, for any T, so the economy will un-dergoa coupin the state(Al, D), taking t to thestate (A', E). As soon as they resume power,the elite set Te = 0, and then follow the optimalstrategy characterizedabove, so the economy


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960 THEAMERICANECONOMICREVIEW SEPTEMBER 001continues to switch between democracy andnondemocracy. This completes the proof ofProposition1.

Details for Sections II and I1We now derivesome of the formulasthat weused in Section II. In Section II, subsectionA,A, we use (A4) from the previous section towrite the value to a poor agent of unconsoli-dated democracy starting from state Al asvFj(A',D|0). This is

1(1 -s)OH(0)IA

(1 -f3(1 -s))[13(1 -s)+ + (1-,B(1-s))2a]P(3 )(1 _ ,B(l - S))2 - p2S2(1 -f3(1 - s))[APs

+ + (1-f(1-s))]a0H(0)/A(1 - ,B(l - S))2_- p2S2where 6P(0) = 7t9 - 7mAthPs defined as inthe previous section and hP OH(0)/A. Thecorrespondingvalue for consolidated democ-racy, again startingfrom state Al, is

v2P(Al,DJO) = 1(1 - s)[0H(0)/A + 6P(0)](1 - 1(1 - s))a[0H(0)/A + AP(0, Td)]+ 1-13

where AP(0, Td)At td- TdAthPs definedas in the previous section [and AP(0, Td) =6P(0) if 4 < 4(0, a, s), i.e., when 0 ' OH].In Section II, subsection B, wr(D|0), thevalue of democracyto the elite with asset dis-tribution0 iswr(DI)

(1 - s)[(l - A)H(0)/(1 - A) + 6r(A)]1-13

sa[(1 - 0)H(A)/(1- A) + Ar(& d)]+s1-13

Next, in Section II, subsection C, recall thatv'(Al, D|k) is the value to an agent in anunconsolidated democracy startingin state Aland with investment k. Our assumption im-plies that duringdemocracythe flow payoff isAt(h' + 51(0)) (1 + k) (so that if k = 0income is unchanged), but once the regimeswitches to nondemocracy, all agents produceonly A h'. Therefore, the value starting fromstate A' conditional on investment k with un-consolidated democracy is v (Al, D|k), givenby

vI(Al, Dlk) = a(h' + 6'(0))(1 + k)+ fwil(D|k) - h'F(k),

where(hi + 6'(0))(1 + k)

w'(D|k) = (1- l3(1 -ss))2 _ s322sh'[4a(l - p(1 - s)) + B(1 - s)]

(1 - ,(1 - S))2_ - 2S2

is the continuationvalue in an unconsolidateddemocracy with investmentk.In contrast,when democracyis consolidatedthe flow payoff is (hi + 61(0))(1 + k) duringnormal imes anda(h1 + A'(0))(1 + k) duringrecessions. In this case, the value functionv'(A', D|k) will bevi(A1, DIk) = a(h' + 6'(0))(1 + k)

+ 3w2(Dlk) - hF(k),where(A8) w'(DIk) = (1 -s)(hi+ 6(0))(1 +k)

sa(hi + A(0))(1 + k)+ 1 - ,is the continuationvalue in a semiconsolidateddemocracywith investment k.

Finally, considerour analysis in Section IV.


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VOL.91 NO. 4 ACEMOGLUAND ROBINSON:THEORYOF POLITICALTRANSITIONS 961The return to the rich under a consolidateddemocracy, starting rom state Al, is(A9) Vr(A',DI0)

= [a(l-13(1-s)) +13(l-s)][(1 - O)H(0)/(1 -A) + 6r(O)]X 1 -1j3

The value of the elite in state (A', E) is vr(A',El 0):

v"(A',EI0)3(1 s))(1 -O)H(0)/(1 - A)

a(l - B(l -s))[(l - O)H(O)/(1 - A) + r (O)]+ 1-13

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