A Lipsetian theory of voluntary power handover

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A Lipsetian theory of voluntary power handover

Raouf Boucekkine, Paolo Piacquadio, Fabien Prieur

To cite this version:

Raouf Boucekkine, Paolo Piacquadio, Fabien Prieur. A Lipsetian theory of voluntary power handover. Journal of Economic Behavior and Organization, Elsevier, 2019, 168, pp.269-291.

�10.1016/j.jebo.2019.10.010�. �hal-02370531�

A Lipsetian theory of voluntary power handover

Raouf Boucekkine

^{a, ∗}

, Paolo G. Piacquadio

^b

, Fabien Prieur

^c

aAix-Marseille University (Aix-Marseille School of Economics), CNRS and EHESS, and Institute for Advanced Study (IMéRa), Marseille,France

bDepartment of Economics, University of Oslo, Oslo, Norway

cCEE-M, University of Montpellier, Montpellier, France

JEL classification: D72, I25, O11, O43

Keywords: Institutional change Human capital Lipset’s theory Resource curse

a b s t r a c t

Weconsideranautocracywheretherulingelitecontrolboththeresourcewealthanded-ucationpolicies.Educationpromptseconomic growthandenrichesthebudgetoftheelite.

However,educationalsoincreasesthe“awarenessofcitizens”–capturingtheirreluctance

toacceptadictatorshipandtheirlabormarketaspirations– andforcesthe elitetoex-pandredistributionorhandoverthepower.A powerhandoverleadstoamoredemocratic

regime, where the elite retains (at least partially) its economic power. This trade-off is thebackbone of our Lipsetian theory of voluntarypowerhandover.Thistheoryprovidesnew

insightsonthepositiverelationshipbetweeneconomicdevelopment,education,and de-mocratization,andonthenegative relationshipbetweeninequalityand democratization.

Finally,werevisittheresources-cursehypothesiswithinoursetting.

1. Introduction

Over the last century, a large number of regime changes has transformed the international politicalscene. Arguably, theworld isnowsignificantly moredemocraticthan before,asdocumentedby thelarge increase indemocraticcountry- wideelectionsforboththelegislatureandtheirchiefexecutives (BormannandGolder,2013).Inthispaper,weinvestigate theeconomicdeterminantsoftheseregimechanges. Moreprecisely,we proposeaLipsetiantheory ofpowerhandoverto exploretherolesofresourcewealthandhumancapitalaccumulation.

Accordingtotheresourcecursehypothesis,resourceabundanceleadsonaveragetoloweconomicgrowthandslowde- velopment(seeinparticular,SachsandWarner,1995).Oneofthekeysuggestedmechanismsisthat“resource-richcountries mayinadvertently–and perhapsdeliberately– neglectthe developmentoftheirhumanresources” (Gylfason,2001,p.850).

Then,contrarytothetraditionalhumancapital-drivendevelopment(Lucas,1988),resourceabundanceleadstounderinvest- mentineducationand,therefore,lowerlong-termgrowth.

Yet,theresource cursehypothesis fallsshortofexplainingthe observedheterogeneity intherelationship betweenre- source abundance anddevelopment, suggestingthat other factors are determinantin explaining this relationship. Anec- dotally,two resource-rich countrieslikeBotswana andthe DemocraticRepublicof Congohave experienced divergentde-

∗ Corresponding author.

E-mail addresses: raouf.boucekkine@univ-amu.fr (R. Boucekkine), p.g.piacquadio@econ.uio.no (P.G. Piacquadio), fabien.prieur@umontpellier.fr (F. Prieur).

0

Fig. 1. The relationship between GDP growth rate and resource wealth (log). Each circle represents the average GDP growth rate and resource wealth of a country over a 10-year period. All countries on the top; non-democratic countries on the bottom.

velopment paths:thefirst hasstringentdemocraticcontrolsandactive long-termeducationpolicies,while thesecond is characterizedby uncontrolledrent-seekingpracticesandlittleinvestmentineducation.Thisdivergencewascapturedbya refinementoftheresourcecurse (seeRoss, 2001),and(Tsui,2011):the“institutionalresourcecurse” arguesthatresource abundance generallyimpedesdemocracy andstrengthensautocraticregimes.However, asforthe initialformulation,also theinstitutionalversionoftheresourcecurse cannotaloneexplainobservedheterogeneity(seeAlexeevandConrad,2009, andHaberandMenaldo,2011).The largeheterogeneityisevident whenplottingthedataonresourcewealthandgrowth ratesfromtheVDEMdatabase, asinFig.1.¹ Moreover, basedontheoreticalmodels,its emergenceseems todependona numberofotherfactors,suchasthedegreeofentrenchmentofautocracies(CaselliandTesei,2016)orthesetofredistri- bution/repressionpolicieschosenbytheautocracies(Boucekkineetal.,2016).

Thispaperexploresanovelmechanismthat combinesaccesstoresources withhuman capitalaccumulation.² Thekey intuitionisthat resourceabundanceallows theautocraticregimetofundasizeableeducationsystem, whichinturnmay boosteconomicdevelopmentandultimatelyleadtodemocratization.Ourmechanismiscloselyrelatedtothe“moderniza- tiontheory” putforwardbyLipset(1959),(1960)intwohighlyinfluentialcontributions.Lipsetsuggestedthatdevelopment causesdemocratization.Hisviewisthatdemocracyrequiresasignificantcivicengagement,apoliticalcultureofnegotiation, andtherecognitionoftheneedforcompromises.Asthesevaluesare typicalofdevelopedsocieties,characterizedby high

1See Coppedge et al. (2019) for details on the Varieties of Democracy Dataset Version 9.

2For example in Boucekkine et al. (2016) , redistribution of resource windfalls takes the form of consumption subsidies and there is no public education.

Caselli and Tesei’s model is even more basic.

education,urbanization, individual mobility,andlow inequality,heconcludesthat economicdevelopmentisconducive to democratization.

Theempiricalvalidity oftheLipsetianhypothesisiscontroversial.The colonialoriginsofinstitutions issuggestivethat institutions may be the ultimate cause of development, and not the reverse (see Acemoglu et al., 2001). Moreover, the stabilityofrichdemocracies,asopposedtopoorerones,mayberesponsibleforthepositiverelationshipbetweeneconomic developmentand democratization (Przeworski et al., 2000). However, human capital andculture maybe considered an evenmorefundamentalsourceofgrowththaninstitutions (seeBarro,1999) or(Glaeseretal.,2004).As ofnow,itisfair tosaythattheempiricaldebateontheLipsetianviewisnotyetsettled.³TheVDEMdataconfirmthewell-knownpositive relationshipbetweenthe levelofdemocracy – heremeasured bythe Polyarchyindex– and the level of education– here givenby average years of educationin adult population (Fig. 2). More interestingly, when restricting to non-democratic countries(i.e.,with Polyarchy indexlessthan 0.5 inall periods) two typesof autocracies emerge (Fig. 2). The firsttype kept investmentineducation verylow (with educationlevel lessthan 4).The second type is characterized bylarge and increasinginvestmentineducation(rapidlyclosingthegaptothelevelofdemocraticcountries).

An even harder challenge is to build theories incorporating the Lipsetian mechanisms. Two decades ago, Barro(1999)wrotethat:“giventhestrengthoftheLipset/Aristotlehypothesisasanempiricalregularity,itissurprisingthat convincingtheoreticalmodelsoftherelationdonotexist.” Here,wetakeupthischallengeandreexamineLipset’smodern- izationtheorybydisentanglingeconomicdevelopmentintoitscomponents–resourcewealth,education,andinequality–and byanalyzingtheirinteractionandimplicationsfordemocratization.

Westudythe paradigmaticcaseofautocraticelite withfull politicalandeconomicpower. Inline withtherecentlit- eratureondemocratizationgames(seeAcemogluandRobinson,2006)andconsistentlywithempiricalevidence(Aidtand Franck,2015),theeliteanticipateandreacttotheexistenceandextentofrevolutionarythreats.Theycanact toavoidrev- olutionsintwoways.Theelitecanintroduceappropriateredistributionandwage-settingpoliciestoplacatetheincentives torevolt ofthe citizens. Alternatively,they can start thedemocratization process andvoluntarily dismiss their power. In thelattercase, thebenefitsandcosts fortheelitearedefinedbyasharingrule,resultingfroma negotiationbetweenthe citizens(now achievingthe politicalpower) andtheeliteforthecontrolofthe naturalresources. Givenour assumptions, wecanonlystudycasesofvoluntary powerhandover.Asoutlinedby Boucekkineetal.(2019),since1960pro-democratic transitionshavebeenrecurrentbutrevolutionstendtobemuchlessfrequentthanothertypesoftransitions:only30rev- olutionsoutof227pro-democratictransitions(13%oftotal).

Citizensarehand-to-mouthworkers:theyareemployedinthenationalindustryandconsumeineachperiodtheirlabor incomeandtransfers. If their consumption–andthus life satisfaction–doesnot reacha specific threshold, workerswould revolt.Akeyingredientistoassumethisthresholdisendogenousandincreasing withrespecttothehumancapitalofthe workers.Thiscanberationalizedbytwoseparatecomponents.Thefirstcomponentisthesubsistencelevelofconsumption;

itcan also includeculturalandsocial aspects capturingthe willingnessto revolt,such asthe degree ofindividualism or collectivismofworkers(Gorodnichenko andRoland,2015,see).The second componentreliesontheideathat, ascitizens becomemoreeducated,theyalsobecomemoreawareofthepoliticalsituation(seeZaller,1992).⁴Consequently,andbesides itsinfluenceonthesharingrule,theeducationpolicysetbytheelitehastwodirectoppositeeffects.Ontheoneside,human capitalisaproductionfactorintheeconomyandtriggerseconomicgrowth.Ontheother side,ithastheabove-described awarenesscost,makingworkersmoredemanding.

Withmoderate returns to education,⁵ our theory predicts two possible scenarios. The first corresponds to elite who decidetokeepinvestmentineducationlow,relymassivelyonresourceexport,andredistributetocitizensjustenough to stayinpower.Asaresult,inequalityremains largeandtheautocracypersists.Thesecondscenarioemergeswhentheelite undertakeapathofeducationanddevelopmentleadingtoaninstitutionalchangeinafinitetimehorizon.Despitetheirfull politicalandeconomicpower,theelitemayindeedoptforamassiveeducationpolicy.Inthissecondscenario,theeconomy experiencesaprogressivereductionofthedependenceonresourceexportandthelevelofinequalitycontinuouslyshrinks.

However,theelite,facingincreasingpoliticalandredistributiveclaimsofthecitizens,willeventuallyhandoverpower.

Thesepredictionsare inlinewithLipset’stheory ofinstitutionalchange.Thedemocratization pathistriggered by the correctbalancebetweeneconomicreturnstocitizens’educationandtheirincreasingclaimsforconsumption.Inparticular, ahighlevelofhumancapitalisbotha prerequisitefor– andaconsequenceof– institutionalchange.Itisa prerequisite astheelitedismisstheir poweronlyiftheeconomyhasthepotentialtobecome richandguaranteetotheelitesufficient economicreturnsinthepost-autocraticregime.Itisaconsequencebecausetheeliteanticipatethecostsandbenefitsofthe democratizationpathandoptimallydecidewhetherornottoreachthehumancapitallevelthattriggersaregimechange.⁶

3On this econometric debate, see: Acemoglu et al. (2005) ; Epstein et al. (2006) ; Castello-Climent (2008) ; Papaioannou and Siourounis (2008) , Che et al., 2013.

4Or, as suggested by Campante and Chor (2012) to explain the Arab Spring events, they may have higher income expectations and require better working opportunities.

5This is a characteristic trait of autocratic regimes, partially explained by the low life expectancy of citizens.

6Our results are consistent with the central role of education in the post-soviet transitions: Papaioannou and Siourounis (2008) find that democratization is “more likely to emerge in affluent and especially educated societies,” while education is also a key factor determining the intensity and the pace of democratic reforms. These also provide further support to the idea that dictators may, in some circumstances, adopt growth enhancing policies, as emphasized recently by Shen (2007) ; Cervellati and Sunde (2014) , and De Luca et al. (2015) .

0

Fig. 2. The relationship between education and democracy. Each circle represents the average level of education and democracy of a country over a 10-year period. All countries on the top. Non-democratic countries on the bottom, differentiated by type: diamonds for non-investing autocracies and triangles for investing autocracies.

Finally, ourLipsetian theory has some concise implications regarding the role of naturalressources whichrationalize thecontrastingempiricalevidenceontheinstitutionalresourcecurse(seeagainAlexeevandConrad,2009),and(Haberand Menaldo,2011):resourcewealthcannotalonetriggerthedemocratizationprocess.Evenwhenacountryisresourcerich,the democratizationpathmaybesuboptimalanddominatedbypermanentdictatorship.Thiscaseemergeswhen,forexample, theeducationsectorisnotveryeffectiveand/orwhentheeliteexpectsignificantlossesfollowingtheregimechange.

Theremainderofthepaperisorganizedasfollows.Section2brieflyreviewstherelatedliteratureandputsourresearch into context. Section 3 presents the model of the economy. Sections 4 and5 study all the possible solutions and then compare them to determine the optimalchoices. Section 6 discusses extensions. Section 7 concludes.All the proofs are gatheredintheAppendix.

2. Relatedliterature

Despitetheabundantandmixedempiricalresults,thereareonlyfewattemptstocaptureLipset’stheoryinatheoretical framework.BourguignonandVerdier(2000)introduceanendogenouspoliticaleconomydecisionmechanismthatdepends ontheeducationofcitizens:therulingoligarchssettheeducationpolicyanticipatingtheireffectsontheeconomicgrowth, oninequality,onthepoliticalparticipationofcitizens,andonthestructureofpoliticalpower.Theyshowthatahighinitial percapitaincomeisassociatedwithalargerlikelihoodofacountrytobeinademocracyortofaceaquicktransition;ini- tialinequalityhas,instead,theoppositeeffects.InBourguignonandVerdier’smodel,theeliteoptimallychoosesthenumber ofpoortobeeducated:thisincreasesthefuturenumberofvotersanddilutes theelite’spoliticalpower, whileproviding educationalexternalities.Incontrast,wemodeleducationpoliciesasinvestmentsinhumancapitalaccumulationand,rather thanintroducingavotingsystemandaredistributivetax,weassumethat theelitemaintainfullpower,butfaces increas- ing redistributionrequests. Closely relatedto thismechanism, Eicher etal.(2009) presenta framework whereeducation raisespoliticalawareness(the electoratebecomesbetteratmonitoringthegovernment).Theauthorsfocusontheinterac- tionbetweeneducation,corruption,anddevelopmentandshow thatapovertytrapmayemergeforintermediatelevelsof education.Morerecently,Glaeseretal.(2007)conveytheideathateducationraisesthebenefitsofcivicengagementpretty muchassocialcapital,thereforeleadingtoalargersocialandpoliticalinvolvement.Theyfurtherarguethateducationdoes not only favorthe emergence of democracy, but alsohelps stabilizingit. On a similar line,Jung andSunde (2014) have investigatedthe Lipsetclaim that democracy ismore likelyin countrieswithmoreequal distributions ofresources. Two mainnoveltiescharacterizeourcontribution.First,bydisentanglingtheroleofclassiccorrelatesofeconomicdevelopment—

i.e.income,education,inequality,naturalresources—we provideanewsetofpredictionsthat canbeused toreassessthe empiricalevidence.Second, byintroducing naturalresources, webring together theliteratureon institutionalchange,the literatureoneducation-drivenendogenousgrowth,andtheliteratureonthenaturalresourcecourse.

3. Themodel

Timeiscontinuous,i.e.t∈R+;thetimeindexisomittedwherenoconfusionmayarise.

Societyconsistsofarulingeliteandworkers.Theelitehavecontrolofaconstantwindfallof(natural) resourcesR>0.⁷ Resourceshavetwoalternativeuses.Apartofitisexportedontheinternationalprimarygoodmarketandsoldattheexoge- nouspricep^x>0—letexportquantitybeX(≥0)—and,fortheremaining part,itissuppliedinternallytothemanufacturing sector—letdomesticsupplybeQ≤R−X.

The manufacturing sector is perfectlycompetitive. Firms employ resources Q and the humancapital H ofworkers to producea homogeneous commodity Y.The productionfunction is Cobb-Douglas,i.e.Y≤F(^Q,H)=AQ^αH^1−α with

α

∈(0, 1).⁸

Theresourcerentoftheelitethen consistsoftheinternationalanddomesticsalesofresources.Theuseofthisrentis threefold:a partC isallocatedfor theelite’s consumption;another part ^istransferred to (or, ifnegative, expropriates from)theworkers;theremainingpartEisinvestedineducation.Formally,theelite’sbudgetconstraintis:

p^xX+pQ≥C+

+E, (1)

wherep=

α

^YQ isthecompetitivepriceofresources.

Investment in the education sector increases human capital of the workers according to the following accumulation function:

H˙ =h

(

^E,H

)

^=hE−

δ

^{H (2)}

whereh>0measurestheeffectivenessoftheeducationinvestmentand

δ

≥0isthedepreciationrateofhumancapital.

Thetransferandtheeducationinvestmentallowtheelitetosupervisetheleveloflifesatisfactionandresentmentofthe workers.Workers—normalizedtounity—inelasticallysupplytheirhumancapitalHtothemanufacturingsectorandearnthe equilibriumwagew=(¹−

α

)^YH.Theirincomeiscompletedbythetransfer^{andisentirelyconsumedineachperiod.As} transferscanbenegative,partoftheirwageincomemightbetaxedawaybytheelite.

Theworkers’lifesatisfactionandresentmentdependontheirconsumption.Iftheirincomeisnotlargeenough,workers mightnotbe ableto affordenoughconsumption andmaydecideto contestthepowerof theelite.Moreprecisely, there isa thresholdlevel ofconsumption that triggersa revolt.This thresholdconsistsof twocomponents. Followingthe long tradition of Francois Quesnay and Adam Smith, the first component interprets a subsistence level of consumption s>0 (forarecentapplication, seeGalorandWeil, 2000).⁹ Thesecond componentcapturestheidea that,asworkersgetmore

7This is consistent with the fact that most governments of MENA countries (or Central and Eastern Euorpean transitional countries) operate large parts of the natural resource industries. While governments exercise control over these industries, this doesn’t prevent them from privitizing these sectors, as for example in Egipt (during the last years of presidency of Hosni Mubarak) or in Russia and the post-Soviet republics.

8We might have incorporated (physical) capital accumulation. But this is to a large extent irrelevant for the Lipsetian theory we want to develop. In addition, it would make the analysis much trickier and prevent us from giving a full characterization of the optimal solution.

9Subsistence need not be limited to nutrition, clothing, and housing needs. Inspired by Gorodnichenko and Roland (2015) , differences in s across coun- tries may capture cultural and social aspects such as the degree of individualism/collectivism of society. Alternatively, differences in s may also capture

andmoreeducated,theyraisetheirconsumption requirementsandresentment.Thisisconsistentwiththeidea,borrowed fromthepoliticalsciencesliterature,thateducationincreasestheworkersawarenessabouttheoppression ofadictatorial regime(seeZaller, 1992).¹⁰This“politicalawareness” componentthusdependsontheworkers’levelofhumancapital.For simplicity,it isa linearfunctionofhuman capitalwithslope

φ

>0,referred toasthepoliticalawareness parameter. Our approachisverymuchinlinewiththeliterature,seeinparticularEicheretal.(2009)whoconsider,inadifferentsetting, thateducationmakespeoplemorepoliticallyaware.¹¹ Then,workersdecisiontorevoltissummarizedasfollows:

revolt ifwH+

<s+

φ

^H

norevolt otherwise (3)

Akeyaspectofourmodelisthecapacityoftheelitetofullyinternalizeworkers’incentivestorevolt.Consequently,the elitecanalwaysavoidacostlyrevolt,butmaychoosetoleavetheofficevoluntarily,whichweinterpretasdemocratization.

LetT∈R+

{

∞

}

^{be thetimeatwhichtheautocraticregime comestoan end(permanent autocracyholdswhenT}=∞).

Inthisscenario,whattheeliteearnatthedateoftheregime changeisdenotedby S(H(T)),withH(T)thestockofhuman capitalatthedateofvoluntarypowerhandover.Thistermcapturesthepresentvalueofthebenefitsaccruingtotheelite inthe democraticregime. It isimportantto note that hereafter,weassume that S(.)≥0. Severalargumentssupport this assumption.First,theeliteshouldexpectthattheywillkeepsomecontrolovertheeconomicactivities,andthenthattheir economicinterestswillextendoverthedemocraticregime.Giventhatwealthisanincreasingfunctionofhumancapitalin oursetting,itseemsnaturaltoassume thatS(.)isincreasing intheamountofhumancapitalavailable atthedate ofthe transition.Asecondexplanation,whichisclosertoLipset’sview,isthefollowing:asexplainedintheIntroduction,human capitalistightlyconnectedwithnegotiationandabsenceofviolence.Thus,theeliteexpectdemocratizationinaneconomy withhighlyeducatedworkerstobecharacterizedbylesspoliticalviolenceandlowereconomicexpropriation.Wewilldeal withspecificationsofS(.)thatareconsistentwithbothviews(seeRemark3below).

Tosum-up,wemodeltheelite’scapacitytocontroltheoccurrenceofaregimechangeby(i)introducingthe—norevolt—

constraint(3)inthetheiroptimizationprogram,and(ii)takingT,thedateofaregimechangeifany,asacontrolvariable.¹² Finally,theintertemporalwell-beingoftheeliteisgivenby:

U= _T

0

e^−ρtu

(

^C

)

^dt+e−ρTS

(

^H

(

^T

))

^{, (4)}

withT∞,andwheretheinstantaneousutilityfunctionisu(^C)≡ ^(C₁⁾₋¹⁻_γ^γ with

γ

∈(0,1)and

ρ

>0isthediscountrate.

Beforemovingtotheanalysis,wefurtherdiscussthreeaspectsofourmodel.

Remark1. Theeliteareparticularlypowerful.Theyareabletocontroltheconsumption/incomeofworkers,andthustheir willingnesstorevolt,inthreedifferentways:(i)directly,bysettingthetransfer^;(ii)indirectly,bydecidinghowmanyre- sourcestosupplytothenationalindustryQ;and(iii)dynamically,byinvestingmoreorlessineducationEandthussetting theirlevelofhumancapital.Furthermore,theycontrolthepoliticaltransitionprocessandchoosethetimingT(possiblyin- finite)fortheinstitutionalchange.Notethatourresultsarestrengthenedbythissimplifyingassumption:despitetheelite’s exceptionalpower,weshowthattheelitemightdecidetoleadthecountrytodemocratization.

Remark2. Theresourcewindfall needstobesufficientlylarge.Tomaketheprobleminteresting,Assumption1belowen- suresthattheelitecansustainthedictatorialregimewhenhumancapitaliszero(i.e.whentheconsumptiondemandedby theworkersissmallest).

Assumption1. p^xR>s:Thevalueofresourcesislargerthanthesubsistenceconsumptionoftheworkersandgivestheelite somefreedominhowtoallocatesuchwealth.

Remark 3. In Sections4 and5, we take a linear specificationofthe scrap value: S(^H(^T))=

π

^H(^T) ^with

π

>0.This as- sumptionisenoughtoconveythekeyideathatatthemomentoftransition,theelitebenefitfromahigherstockofhuman capitalinthecountry.The parameter

π

^canbe interpretedasasharingrulethat givesthepieceofthecakethatgoesto the elite atthe time ofa regime change. Thischoice is madefor thesake of exposure sincewe getsimple closed-form solutionsinthiscase.Analternativetothelinear,andexogenous,scrapvaluecaseisexaminedinSection6.Asannounced intheIntroduction,we providewithaNash bargainingfoundationforanendogenoussharingrule,leadingtoa generally nonlinearscrapvalue.Weultimatelyshowthatthemainpropertiesarisingfromthelinearscrapvaluecaseremainvalid.

differences in the difficulty/costs for achieving a successful revolt. Note that military power can also be introduced as a control variable of the elite to repress the workers’ hope for successful revolts. Military expenses play a similar (but opposite) role of transfers .

10Importantly, there are also arguments for the effect of education on consumption requirements and resentment being negative. There is, in fact, anec- dotical and empirical evidence that education has been used by several authoritarian regimes as an instrument to control people (mostly through indoc- trination). If “indoctrination” is sufficiently large, it may happen that also the combined effect of the listed mechanisms be negative. Importantly, this does not affect our main results, with the sole exception of the (otherwise negative) relationship between education of workers and inequality.

11In their study of the interaction between education, corruption and development, the authors indeed assume that the probability to get reelected, for a corrupt government, is decreasing in the share of educated people.

12 Accounting for the uncertainty surrounding the occurrence of a revolt, or its success, does not alter the qualitative nature of the results. We present a simple extension of the analysis to a risky world in the Appendix B.1 .

4. Permanentdictatorshipvsinstitutionalchange

Theelite seekto maximize utility (4),subjectto the budget constraint(1),equilibriumprices pandw,the dynamics ofhuman capital(2),andthe revolutiondecisions ofworkers(3). Todoso, the elitesets optimallythe useof resources Q,ownconsumption C,transfers^{,andeducationE.Yet,}substituting^{fromthenon-revoltconditionofworkers(3),the} optimizationproblem of the elite can be written as an optimal stopping problem, where T is the time until which the constraintismet.Formally:

max_{Q,E,T} T 0 e^−ρtu

p^x

(

^R−Q

)

^{+AQαH1−α−E−s−}

φ

^H

dt+e^−ρT

π

^H

(

^T

)

s.t. H˙ =hE−

δ

^H

H

(

^T

)

=HT isfree E, R−Q≥0 H

(

⁰

)

=H₀is given

MaximizingthecriterionwithrespecttonationalresourcesupplyQ,requiresthatnationalpricesequalizeinternational ones,i.e.p=p^x,andsetstheoptimalratiobetweenresourcesandhumancapital.¹³Optimalinvestmentineducationequal- izesthemarginalbenefitfromeducationwiththemarginalcostofinvestingineducation(in termsofforegoneconsump- tion).TheoptimaltimeT<∞forviolatingtheno-revoltconditionequalizestheelite’svalueofstayinginthecurrentdicta- torialregimeandthevalueofthesalvagefunction.TheoptimalityconditionsaredisplayedinAppendixA.1.

Since the optimalstopping problemis non-convex, we proceed in two steps. First, we studythe dynamics of: i) the systemwheneducationinvestmentsarestrictlypositive.Second,we studythecasesof:ii)zeroinvestmentsineducation;

andiii)alternatingperiodsofpositiveandzeroinvestments.Asbothi)andii)maybesolutionsofouroptimizationproblem (seeSection5),wealsohighlighthowthesepotentialsolutionsdependontheparametersofthemodel.

4.1. Education-driveninstitutionalchange

Defineasfollowsthe instantaneousreturnonhumancapital andtheinstantaneous returnoneducationinvestment

χ

^:

≡ ¹⁻_α^αp^x

_αA

p^x

1−¹α −

φ

^,

χ

^{≡h −}

δ

^.

Theinstantaneousreturnonhumancapitalisthedifference betweenthe(equilibrium)grossreturnofhumancapitaland thefeedbackeffectofhumancapitalonworkers’claimsfordemocracy,givenbythepoliticalawarenessparameter

φ

^.

AnysolutionwithstrictlypositiveeducationE>0satisfiesthefollowingnecessaryconditionsforoptimality(wherethe superscript1indicatestheregimewithpositiveeducation):

⎧ ⎪

⎨

⎪ ⎩

C¹

(

^t

)

=C₀¹e^(χ−γρ)t H¹

(

^t

)

=

H0+^h(px_χ^R−s)−_ρ−^γ_χ(^hC₁¹⁰_{−γ )}

e^χt+_ρ−^γ_χ(^hC₁¹⁰_{−γ )}e^(χ−γρ)t −^h(px_χ^R−s)

λ

¹

(

^t

)

=

(

^C10

)

^−γ

h e^{(ρ−χ )t}

(5)

Weestablishthefollowingresult.

Proposition1. Assumethatthereturnoneducationarelowerthantherateoftheelite’stimepreference:

ρ

>

χ

. (6)

(i) Thereisnosolutioncombiningpermanentdictatorshipandpositiveeducation.

(ii) Theremaybeasolutioncombininginstitutionalchangeandpositiveeducation.

(a) Thissolutionischaracterizedbytheaccumulationofhumancapital,institutionalchangeinfinitetimeT=T(^H0,R,

π

), andaend-pointstockofhumancapital:

HT= h

ρ

⁻

χ

γ (

^h

π )

^−1γ

1−

γ

^+pxR−s

>0. (7)

(b) ThenecessaryconditionfortheexistenceofsuchsolutionforallH₀∈[0,H_T]is:

p^xR−s>

(

^h

π )

^−γ1. (8)

13 The optimal resource supply of the elite to the national industry would determine a price wedge between international and internal resource prices in case of costly redistributive transfers. In this case, the elite would find it more profitable to redistribute income to workers by oversupplying resources and, indirectly, determining a wage increase. While this extension is potentially relevant for an empirical assessment, the results discussed are not affected.

(c) Sufficientconditionsfortheexistenceofauniquesolutionare(8)and

χ

>

χ

^,with

χ

∈(0,

ρ

^{)theuniquesolutionof:}

e^{ργ χ−χ} =

ρ

^[

(

¹−

γ )( ρ

−

χ (

¹−

γ ))

+

γ

²

χ

^]

(

¹−

γ )( ρ

−

χ )

^{2 . (9)}

Therankingbetween

ρ

^and

χ

^{turnstobecrucialin}understandingthenatureofthepotential solutions,underpositive education.Imposing

ρ

>

χ

^{isatthesametimenecessarytoshowtheexistenceofasolutionwith}democratizationinfinite time, andsufficient to discard an outcome featuring permanentdictatorship. Under the opposite condition

χ

≥

ρ

^,autoc-

racyistoogrowth-friendly.Theelitecaninvestineducationand,duetothehighreturns,thisstimulatesgrowthofoutput (andcitizens’consumption)whilebeingcompatiblewiththerespectoftheno-revolutionconstraint,whichisinfactnever binding.However,thesolutionwithpermanentdictatorshipandpositiveeducationisnotrelevantbecauseitwouldeither violatetheresourceconstraint,orimplyresourceimportstobecomeinfinite(withXtendingto−∞).Thus,anecessarycon- ditionfortheelitetobewillingtoleavepowerinfinitetimeisthatthereturnoneducationinvestmentisquitemoderate andtheyexhibitahighenoughlevelofimpatience.

Itisworthnotingthatthesearetwocharacteristictraitsofresource-richnon-democraticregimes.Indeed,itiswelldoc- umentedthat (small)resource-richeconomiesusuallydisplayhighdiscountratesbecauseoftheirdependenceonresource revenue (lowdiversification)and(volatile)resourceprice, andtheir politicalinstability (Nigeria,Venezuela),among other factors(seeHooper,2018,foradiscussion)).Atthesametime,andfocusingontheMENAregion,ifresource-richcountries haveinvestedheavilyineducationoverthepastdecades,itisclearthatthereturnsofthispolicy intermsofgrowthand economicdevelopmenthavebeenquitelimited. Aspointedoutby arecentworldbank reportdevotedtothisregion,the evidencedemonstrates that schoolsystems inMENAare generallyoflow quality,therebypromoting theaccumulationof lowqualityhumancapital(WorldBank,2013).Thismeansthatwecansafelyimposethat

χ

^{islow,andlowerthan}

ρ

^.

Letusnowdiscussthepredictionsofourmodelconcerning theLipsetianlinksbetweenhumancapital,education,and democratization. Theproposition establishes theincompatibility betweenpermanent dictatorshipand education(i). From theperspectiveoftheelite,humancapitalhastwoimplications:onetheonehand,itincreasestheconsumptionaspiration andwagesoftheworkers;ontheotherhand,itincreasesthereturnoftheeliteatthetimeofdemocratization.Permanent dictatorshipexcludesthesecondimplication.Asforthefirstone,sincetransferring^{totheworkersisfree,theelitefindsit} moreeffectivetoexportallresources,bringtheworkers’humancapitaltozero,andmeettheir“no-revoltconstraint” with transfers^{.Whentransfersarecostly,somepositivelevelofhumancapitalmaybeconsistentwithpermanent}dictatorship.

Thenecessaryexistenceconditionin(8)statesthatresourcewindfallsnetoftheintrinsicsubsistenceconsumptionlevel shouldbelargerthanthelevelofconsumptiontheelitejustenjoyatthedatedictatorshipceases,C¹(T).Finally,asufficient conditionforexistencerequiresthatthereturnstohumancapitalbehigherthanathreshold

χ

^{,definedby(9).Highenough}

returns to human capital logically guarantee that it is worthwhile for the elite to engage in the path of education and sustainedcapitalaccumulation.

Under

ρ

>

χ

^{,thetimepathof}consumptionisdecreasingwhereasthestockofhumancapitalisincreasing.Theintuition runsasfollows.For theelite tofindit optimalto democratizethey should be ableto accumulate a sufficientamount of humancapital,whichwilldirectlyaffectthewealththeywillholdinthepost-dictatorshipregime,andwillalsoguarantee that they can enjoy their wealth in a peaceful environment. Thus investment in human capital should be favored over consumption.Moreover,byinvesting significantlyinhumancapital,theelitefosterthedevelopmentofcitizens’claimsfor a freersystemthrough theincreasing awareness mechanism. Inorderto delaythepoliticalregime change theelitehave no otheroption buttotransfer moreandmoreresources tothe citizens,even ifthiscomesatthe expenseoftheir own consumption.

Note that under the conditionsof Proposition 1, solutions that combine positive educationand a revolution infinite timeexistforanyH₀≤H_T.Inotherwords,thestatedconditionsguaranteetheexistenceofasolutionwitheducation-driven institutionalchangeindependentlyoftheinitialendowmentinhumancapital.Thisisareasonablefeatureofourmodel:it wouldotherwise bedifficult toexplain whysome countriesaredoomed to dictatorialregimesexclusively basedon their initialstockofhumancapitalandwouldalsoraisetheissueofidentifyingthisinitialperiod(ofthedevelopmentprocess).

Importantly,thisdoesn’tmeanthat theinitialstockofhumancapitalisirrelevanttoouranalysis.As farastheoptimality analysisisconcerned,thisvariablewillbecrucialtodeterminewhichoneoftheoptimalitycandidatesyieldstheoptimum.

Inaddition,itisworthemphasizingsome otherinterestingfeaturesofthefirstoptimalitycandidates.Theyaresumma- rizedinthenexttwocorollaries.

Corollary1. Thesolutionwitheducation-driveninstitutionalchangeispossibleonlyif,ceterisparibus,

(i) Resourcewealth,p^xR,islargeenough.

(ii) Elite’sincentivestodemocratize,thatareprovidedbytheshareofwealthaccruingtotheeliteaftertheygiveuppower,

π

^,

areimportantenough.

(iii) Theeffectivenessoftheeducation,h,needstobeimportantenoughtoo.But,incontrasttoresourcewealthandthesharing rule,itshouldnottakeanexcessivevaluesincetheinstantaneousreturnstoeducation,

χ

^{,cannotbetoohigh.}

Fig. 3. Phase diagram.

ThesepropertiesareinlinewithLipset’stheoryintwoessentialaspects:thelinkbetweendemocratizationandeduca- tion;andthelinkbetweenresources(orincome)anddemocratization.¹⁴Firstofall,themodelpredictsthatalargeamount ofresources(oroftheirexportprice)isapreconditionfortheemergenceofanon-dictatorialregimethroughhumancapital accumulation.However,theresourcewealthofacountry(measuredbyp^xR)isnottheuniquerelevantdeterminantofde- mocratization.Twofurtherfactorsmatter:asufficientreturntoinvestmentineducation,h,andasufficientrewardforthe eliteatthetimeofinstitutionalchange,

π

^.Democratizationmaynotoccurunderlargeresourcerevenuesbecauseoneofthe twolatterparametersistoosmall(leadingto violatingconditions(15)).Importantly,theinteractionbetweentheresource wealthandthesefactorsislikelytoberesponsibleforthemixedsupportforthenaturalresourcecursehypothesis(seethe debateopposingproponentsofthishypothesis,Ross(2001),andTsui(2011),anddetractors,AlexeevandConrad(2009),and HaberandMenaldo(2011))andisinlinewiththeempiricalstudiespointingatthemis-managementofeducationinseveral oil-exportingcountries(see Gylfason,2001). Finally,noticethat therole ofthe returntoeducationistricky: itshould be highenoughceterisparibusfordemocratizationviaeducationtoarise,butitshouldnotbetoohighastheinducedwealth inthehandsoftheeliteinsucha casecould besufficienttocompensate forthelarger awarenessoftheworkers.Inthis case,adevelopingdictatorshipcouldbesustained,althoughnoequilibriumpathsexist(seetheinterpretationof(8)).

Next,we highlighthow the time-to-democratization isaffected by theparameters of themodel (see thecomparative staticsexerciseattheendofAppendixA.2).

Corollary2. Theoptimaltimeforinstitutionalchange,T=T(^H0,R,

π

),is decreasingin boththeinitial endowmentin human capital,H₀,theresourcewindfall,R,andthesharingruleparameter,

π

^.

Thefirsttwofeaturesstrengthenthecorrelationbetweenwealthanddemocratizationdiscussedbefore.Thelargeristhe initial stockof humancapital (another possible measure ofhuman wealth) or thewindfall ofresources, the quicker are theeliteindrivingthecountryintoaninstitutionalchange.Whilethelargerwindfall isalsoassociatedtoalargerlevelof humancapitalatthe time ofinstitutionalchange,such aneffect isabsent fortheinitial humancapitallevel. Finally,the optimaltime-to-democratization is decreasingin

π

^{.The elite compensate a lessfavorablesharing rule by increasing the}

humancapitalofthecountryattheinstitutionalchange,H_T.Thisrequiresalongerperiodofinvestmentineducation.

Toend up this discussion, it is important to measure the elite’s payoff associated with the solution witheducation- driveninstitutionalchange.Letsuchoptimalitycandidatebereferred toasregime1;thenthepresentvalue (fortheelite) offollowingthisregimeisgivenby(hereafter,theoptimaltimeforinstitutionalchangeisexpressedintermsofH₀ only):

V¹

(

^H0

)

=e^−ρT(H0)

γ (

^h

π )

^{−(1−γγ )}

(

¹−

γ )( ρ

−

χ (

¹−

γ ))

e^(ρ−χ(

1−γ )^T(^H0)

γ −1

+

π

^HT

.

ThetypicaldynamicscorrespondingtothisfirstpossiblesolutionisdepictedinFig.3. Inthenextsectiontheotheroptimalitycandidatesarebrieflyreviewed.

14 Note that they are a direct consequence of the second necessary condition in (8) . Also note that the parameters R and π do not show up in the sufficient condition χ> χsince they don’t enter into the expressions of . In contrast, the parameters h and p ^xenter this condition through .

4.2. No-educationandpermanentdictatorship

Thegeneralsolutioncorrespondingtonoinvestmentsineducation,i.e.E=0,isgivenby(thesuperscript2referstothe regimewithnoeducation):

_C2

(

^t

)

^{=pxR−s+ H2}

(

^t

)

H²

(

^t

)

=He^−δt

λ

²

(

^t

)

=e^(ρ+δ)t

L−

C²

(

^u

)

^{−γe−(ρ+δ)udu}

withHandLconstantstobedetermined.Weestablishthefollowingresult:

Proposition2.

(i) Therealwaysexistsasolutioncombiningpermanentdictatorshipwithnoinvestmentineducation.

(ii) There may be solutions alternating periods of investment in education with periods of no investment, but these never provideacandidateforoptimality.

The solutionwithpermanentdictatorship andno educationischaracterized bya decreasingflow ofconsumption and a decreasing stockof human capital. Consumption asymptotically converges toward C²(∞)=p^xR−s, while the stock of humancapitalvanishes.Thisisthepathtakenbytheelitethat considersinvestmentinhumancapitaltoocostlyinterms ofresourcesneededbyeducated workersandintermsoftherisk ofbeingoverthrown. Solutionswithnoeducationexist foranylevelofthestockofhumancapital.Thevaluefunctioncorrespondingtotheoptimalitycandidatewithnoeducation isgivenby:

V²

(

^H0

)

=

_∞

0

1 1−

γ

p^xR−s+ H0e^−δt

1−γ e^−ρtdt.

Finally,solutions featuring aregime changefrompositive to zeroeducationcanbe disregarded becausetheseare always dominatedbyothersolutions(seeAppendixA.3).

Atthisstageoftheanalysis,weareleftwithtwooptimalitycandidates,whichmakestheoptionsavailabletotheelite very clear.Either they chooseto relyon resourcewealth andnotto investin educationinorderto keep thelabor force uneducatedanddocile.Butthisrequires sacrificingeducation-driveneconomic growth.Or,the eliteengageina policyof sustained investmentin education,which promotes theaccumulation ofhuman capital atthe cost ofgivingup political powerinfinitetimebecauseofthedevelopmentofcitizens’claimsfordemocracy.Asexpected,variableslikethereturnsto education(andhumancapital),theinitialstockofhumancapital,thediscountratebutalsotheshareofwealthaccruingto theeliteafterarevolutionwillplayacentralroleinexplainingwhatistheelite’sbestoption.

Beforedeterminingtheoptimalchoiceoftheelite,wecompareregime1and2intermsoftheirimplicationsforthelink betweeninequalityandinstitutionalchange.

4.3. Implicationsforinequality

So far, we have addressed the links income-institutional change and human capital-institutional change. In this re- spect,we have shownthat the predictionsof themodel areconsistent withLipset’s theory.It remains tostudy thelink inequalities-institutionalchange.

Asworkersareahomogeneousmassofindividuals,theonlywaytoappraiseinequalitiesinadirectandelementaryway is bytracking theconsumption ofthe elitevs. the consumptionof workers.Although thisisnot completely inthespirit ofLipset’stheoryconcerningthisaspect(seeJungandSunde,2014,foratighterconnection)),thisexerciseturnsouttobe worthwhile.Recallthattheworkers’incomeisentirelydevotedtoconsumption.Atanysolution,wehaveC_Wⁱ (^t)=s+

φ

^Hi(^t) fori=1,2.LetIⁱ(^t)≡^C_C^Wii(⁽t^t)⁾ betheindexofinequalitiesatsolutioni=1,2.Then,wecanestablishthefollowingresult.

Proposition3. Atthesolution witheducation-driveninstitutionalchange,inequalitiescontinuouslyshrink.Atthesolutionwith permanentdictatorshipandnoinvestmentineducation,theoppositeresultholdsif:

R>

(

¹−

α )

^s

φα

α

^A

p^x

₁₋¹_α

. (10)

Along thetransitionprocess to non-dictatorship, inequalities decrease.It isasifin orderto preparethe groundfora democraticregime,theelitehavetoprogressivelyreducetheincome(consumption)gapbetweenthetwogroupsuntilthe institutionalchange.Intuitively,sincetheeliteinvestinhumancapitalalongthispath,growthisstimulated.Butthepositive growtheffectisdominatedbythenegativeeffectduetoincreasingawarenessandtheelitehavenooptionbuttosacrifice partoftheirconsumptiontosatisfytheno-revoltconstraintanddelaythedateofleavingoffice.

Moreoverandnotsurprisingly,permanentdictatorshipimpliesawideningofinequalitiesifresourcewindfallsarehigh, theawarenesscostislarge,theinternationalresourcepriceishigh,andthelevelofsubsistenceconsumptionislow.Under theseconditions,thedictatorisable tofilltherevoltconstraintatlower cost.Bynot investinginhumancapital,citizens aremaintainedundercontrolwhiletheelitebecomericherandricherrelativetotheworkers.

Thenextsectioninvestigatestheoptimalityoftheabove-identifiedsolutions.

5. Optimality,povertytrap,andpolicyimplications

Theoptimality analysisboils downto astudyof therelative performanceof thesolutionwitheducation-driven insti- tutionalchange vs.the solutionwithpermanentdictatorshipandno-education. Toconductthisanalysis,we comparethe presentvaluesassociatedwithouroptimalitycandidates.Wesummarizetheresultsasfollows:

Proposition4. LetH₀∈[0,H_T].Thefollowingcasescanarise:

(i) Thesolutionwithpermanentdictatorshipandno-educationisoptimalforallH₀iff V²(H_T)>V¹(H_T); (ii) Thesolutionwitheducation-driveninstitutionalchangeisoptimalforallH₀iff V¹(0)>V²(0);

(iii) Otherwise,ahumancapitalpovertytraparises.ThereexistsH¯∈[0,H_T]suchthatthesolutionwitheducation-driveninsti- tutionalchangeisoptimaliff H₀≥H¯.

Boththe no-education regime with persistent dictatorship andthe education regime withdemocratization can arise.

Dependingontheparameters,itmightbepossiblethat: (i)thefirstalternativeischosen independentlyoftheinitialstock ofhuman capital; (ii) the second alternative is chosen independentlyof the initial stock ofhuman capital; and (iii) the regimechoicedependsontheinitialhumancapitalstock,alowstockisassociatedtono-educationinvestmentandinfinite horizondictatorshipwhilealargestockisassociatedtoeducationinvestmentanddemocratizationinfinitetime.

This result sheds light on the relationship between education, development, and democratization. First, education is necessaryforboth developmentanddemocratization: it isthe engineof economicgrowth; and, by increasing thework- ersawareness,itis alsoresponsible fortheinstitutionalchange.Second, educationinvestments mightbe optimalforthe rulingelite,despiteitmightleadtomoredemocraticinstitutions,astheirpoliticalpowergetssubstitutedbyeconomicre- turns.Third,theexistenceofapovertytrapisparticularlyinterestingforitteachesthatdevelopmentaidleadingto“small”

increasesinhumancapitalmightnotbe sufficientforaregimeswitch andthusfailsto havepermanenteffectsondevel- opmentandinstitutionsoftherecipientcountry.Indeed,ourtheorydeliversmuchmoreinthisrespect,andweshallcome backtothisimplicationbelow.

Thenextresultfurtheremphasizestheconditionsunderwhichtheelitefindthedemocratizationpathoptimal.

Proposition5. Thesolutionwitheducation-driveninstitutionalchangeisoptimalforallH₀∈[0,H_T]if:

p^xR−s>e^1+γγ

(

^h

π )

^−γ1. (11)

Thissufficientconditioncaneasilybeinterpretedonceoneobservesthatitisastrongerversionofthesecondnecessary existence condition(8).It confirmsthe previous intuition aboutwhich factorsare crucial forthe decisionofthe elite to educate thepopulation anddrive thecountry out of autocracy. Indeed,Proposition 5illustrates that institutionalchange initiatedby the elite is a matter of having the right conditions. A large stock of resources might not trigger education policiesanddemocratization iftheeducation sectordoesn’t ensuresufficient economic returnsto theelite.A permanent positiveshock tointernationalresource pricesmight give theelite the wealthneededto investineducation andhuman capitalaccumulation,butthisopportunitywillnotbetakenifthewealthprospectsatthetimeofinstitutionalchangeare notsufficientlycompelling.

Last but not least, it is important to interpret the above results in light of education aid policies. Case iii) of Proposition4indicatesthat themodelcandeliver(optimal)povertytraps.Propositions3and5—withthe associatednec- essary andsufficient conditions (8) and(11)—teach us that a massive aid policy of education systems may temporarily increasehumancapital,i.e.byimprovingaccesstoeducationandthereforeraisingtheenrollment rates.Yet,thismaynot havea permanenteconomic and institutionaleffect.One reasonis that educationaidmight be unable to improvesuffi- cientlyeducationsystems,i.e.theparameterhmightnotreachthelevelneededtoescapethepovertytrap.Anotherreason isthatinstitutionalconditionsarenotgoodenough(hereforexample,

π

^{shouldbebigenough).Thisisconsistentwiththe}

viewquestioningtheefficiencyoflargeaidtothepoorestcountries(seeKraayandRaddatz,2007,forexample).

Thus, aid programs should target education efficiencyat the same time as educational outcomes, especially in those economieswheretheresourcewealthislimited.Ourtheoryproducesaclearhierarchyinthisrespect:ifeducationefficiency (our parameter h) is above a certain threshold value foreducation, developmentand democratization will turn optimal ceterisparibusirrespectiveoftheinitialvalueofcapital(H₀)andeventhoughthecountryisrunbyanautocraticregime(as onecaninferfromProposition5).Thisresultsuggestsaclear-cutwaytosettlethetraditionaltradeoff betweenexpanding schoolenrollmentsversusimprovingschoolqualityfacedbydevelopmentagencies.

6. Extension:Non-linearandendogenousscrapvalue

InthisSection,we goonestepfurtherinthedescriptionofwhatisgoingonatthedateoftheregimechange.Assume thatapoliticaltransitiontodemocracyarisesatadateT.Then,thenewlycreateddemocraticgovernmenthastodecidehow tosharethenaturalresourcewindfall betweentheeliteandtheworkers.¹⁵ Therearetwopossibleformulationsofsuch a

15 It is worth noting that there is nothing more to bargain over than windfall resources, p ^xR : the final good sector is competitive, resulting in zero profits at the equilibrium, and we can easily think of the public education sector as a non-profit organization.

problemintheliterature:lobbyingmodels(seeforexample,GrossmanandHelpman,1994,orEstebanandRay,1999)and Nashbargainingmodels(seeBinmore,2011).Whilethetwomodelingstrategiesarenotstrictlyequivalentasveryrecently outlined by Voss andSchopf (2018), they share essentially the same implications when it comes to policy choice. Here, we assumethat thesharingruleresultsfromNashbargainingsolution,wheretheoutsideoptionisnormalizedtozero.¹⁶ ConsistentwiththeLipsetiantheory,the negotiationpoweroftheelite isincreasing withrespect totheworkers’ human capitalH_T (theelite can expecta largerpartof thecakeby interactingwithmoreeducated people). Let

ε

∈(0, 1) bethe share of resources the elite is assigned andlet

σ

^(H(T))∈(0, 1) be the elite bargainingpower, where

σ

^(.)>0. The Nash bargainingsolutionis:

ε

^∗=argmax

ε

^{σ (H(T))}

(

¹⁻

ε )

^{1−σ (H(T))}

=

σ (

^H

(

^T

))

^.

Whenthebargainingpowertakesthelinearform

σ

(^H(^T))=

σ

^H(^T),assuming thattheeliteconsumetheir entirerev- enue

σ

^{(H(T))pxRfromTon,weobtainthescrapvalue:17}

S

(

^HT

)

=

πζ

1−

γ ⁽

^H

⁽

^T

⁾⁾

^{1−γ with}

ζ

⁼

⁽ σ

^pxR

)

^1−γ

πρ

^{. (12)}

Usingthisalternativeformulation,wecanestablishthecounterpartofthemainexistenceandoptimalityresultsasstated inPropositions1and5.Importantly,themainconclusionsremainqualitativelythesame(seethecorresponding proofsin theAppendixB.2).Thenextpropositiondealswiththeexistenceissueinthisextendedframework.

Proposition6.

(i) Thereisnosolutioncombiningpermanentdictatorshipandpositiveeducation.

(ii) Theremaybeasolutioncombininginstitutionalchangeandpositiveeducation.

(a) Thissolutionischaracterizedbyaccumulationofhumancapital,institutionalchangeinfinitetimeT=T(^H0,R,

π

),anda correspondingend-pointstockofhumancapital:

HT= h

(

¹⁻

γ )(

^pxR−s

) ρ

⁻

χ (

¹⁻

γ )

⁻

γ

^h

(

^h

πζ )

^−γ1.

(b)NecessaryconditionsfortheexistenceofasolutionforallH₀∈[0,H_T]are:

ρ

^>

χ

p^xR−s>

(

^h

πζ )

^−1γHT⇔

( ρ

⁻

χ (

¹−

γ )) ρ

^−γ1

( σ

^pxR

)

^1−γγ >h

(

^h

π )

^−1γ. (13) (c)Sufficientconditionsfortheexistenceofauniquesolutionare(13)and

χ

>

χ

^,with

χ

∈(0,

ρ

^{)theuniquesolutionof:}

e^ρχγ−χ =

ρ ρ

−

χ

^.

Asfarasoptimalityisconcerned,wecanshowthefollowing:

Proposition7. Thesolutionwitheducation-driveninstitutionalchangeisoptimalforallH₀∈[0,H_T]if:

p^xR−s>

(

^h

πζ )

^−γ1HTe^1+γγ ⇔

( ρ

⁻

χ (

¹−

γ )) ρ

^−1γ

( σ

^pxR

)

^1−γγ >h

(

^h

π )

^−γ1

( γ

⁺

(

¹+

γ )

^e1+γγ

)

. (14) Importantly,theseresultshighlightthat: (i)theexistence andoptimalityanalyses caneasily beextendedto the(more general)non-linearscrapvaluefunction;and(ii)theexistenceandoptimalityconditionshavethesameshapeandinterpre- tationasthe oneswe getwitha linearscrap value. Finally,theresults corresponding toPropositions2, 3, and4remain unchanged(seeAppendixB.2).

7. Conclusion

We have proposed a Lipsetian theory ofvoluntary powerhandover. The democratization is in particular triggered by the tradeoff betweeneconomicreturns tocitizens’ educationandtheir increasing claimstoconsumption. Ahighlevelof humancapitalisbothaprerequisiteandaconsequenceofinstitutionalchange.Thenegativecorrelationbetweeninequal- ityanddemocratization followsfromthe citizensbecomingmoreawareanddemandingastheir humancapitalincreases.

Furthermore,consistentlywithLipset’stheory,we showthathigherresourcewealthis(weakly)favorabletodemocratiza- tion.Indeed,resourcewealthcannotalonetriggerdemocratizationinoursetting:democratizationmaybe suboptimaland

16As opportunely mentioned in Voss and Schopf (2018) , while the Nash bargaining solution may be questionable as a positive theory, it is used as such in dozens of articles. There is an underlying evolution-based justification for that emphasized by Binmore (2011) : evolution has provided humans with fairness norms which favor cooperation even in situations where actual bargaining cannot take place. Therefore, if the Nash bargaining solution is plausible as a fairness norm, it can be considered as a positive model.

17Note that the parameter πnow has a different interpretation. Indeed, we may argue that even if the elite deliberately choose to leave power, the transition can be fierce and they can be killed with probability 1 −π. So the regime shift is peaceful and the bargaining stage takes place only with probability π^.