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Alfred Greiner · Bettina Fincke
Public Debt, Sustainability and Economic Growth Theory and Empirics AlfredGreiner•BettinaFincke PublicDebt,Sustainability andEconomicGrowth TheoryandEmpirics AlfredGreiner
FacultyofEconomics
BielefeldUniversity
Bielefeld Germany
BettinaFincke FacultyofEconomics
BielefeldUniversity
Bielefeld Germany
ISBN978-3-319-09347-5ISBN978-3-319-09348-2(eBook) DOI10.1007/978-3-319-09348-2
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2014952604
©SpringerInternationalPublishingSwitzerland2015
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Preface Thefinancialcrisesthathadbegunasasub-primecrisisintheUSAin2007 hadplungedagreatmanyeconomiesthroughouttheworldintodeepeconomic recessions.Itseemedthattheslumphadbeenovercomeby2010whensome countriesreachedtheirpre-crisislevelof production.However,thesub-primecrisis turnedintoapublicdebtcrisisbecausethebail-outofprivatefinancialinstitutions bygovernmentsledtoadrasticincreaseofnationaldebttoGDPratiosinsome countries.Particularlyintheeuroarea,economiesstillfacesevereproblemsand mustbesupportedbyothercountries.This illustratesdrasticallythatpublicdebt doesaffecttheevolutionofmarketeconomiesandthequestionariseswhich mechanismsonecanidentifythatmake publicdebtinfluencetherealsideofan economy.Whereaseconomicconsequencesoftaxationcanbereadilyderived,that doesnotholdforpublicdebtsincethelatterdoesnothaveimmediateconsequences asconcernstheallocationofresources.Withthisbook,weintendtocontributetothe researchonhowpublicdebtaffectsthegrowthprocessofmarketeconomiesinthe medium-tolong-run.Inparticular,wewanttoworkoutthemechanismsthatmake publicdebtaffecttheallocationofresourcesandthatarenotsoeasilyunderstood astheeconomiceffectsofdistortionarytaxation.
Ourbookpartlybuildsonpapersbyourselvesandextendsourearlierbook (GreinerandFincke 2009).Thus,wedevelopnewtheoreticalmodelsofendogenous growth,weupdateempiricalestimationsandwepresentnewempiricalevidenceas regardstherelationbetweenpublicdebtandeconomicgrowth.Theadvantageofa monograph,comparedtopublicationsintheformofresearchpapers,isthatabook publicationallowstogetmoreintothedetailsandalsotobemorepreciseabout theeffectsthatensuewhencertainassumptionsarechangedandreplacedbyother ones,sothatonecansaymoreabouttherobustnessoftheresultsderived.Moreover, thisbookworksoutfundamentalpropertiesofpublicdebtwithinbasicmodelsof endogenouseconomicgrowth.Therefore,itisalsosuitedasatextbookforgraduate studentsstudyingtherelationbetweenpublicdebt,publicdeficitsandtheallocation ofresourcesinanintertemporalcontext.WealsooweourthankstoPeterFlaschel,
GöranKauermann,UweKöllerandWilliSemmlerfromwhomwehavebenefited throughearlierjointworkandstimulatingdiscussions.Further,weareindebtedto GabyWindhorstfortypingsomesectionsofthemanuscript.
Partsofthematerialinthisbookhavebeenpresentedatconferences,workshops anduniversityseminars.Valuablecommentsthataregratefullyacknowledged wereprovidedbyparticipantsintheInternationalWorkshoponAdvancesin MacrodynamicsatBielefeldUniversity,intheConferenceonTheInstitutional andSocialDynamicsofGrowthandDistribution,Lucca,Italy,intheWorldBank workshoponModelingFiscalPolicy,PublicExpenditureandGrowthLinkages, Washington,D.C.,intheSymposiumonNonlinearDynamicsandEconometrics, London,intheWorkshoponPublicDebtandEconomicGrowthofthe EuropeanCommission,EconomicandFinancialAffairs,Brussels,intheDIW annualworkshoponmacroeconometricmodelling,Berlin,attheUECEConference onEconomicandFinancialAdjustmentsinEurope,Lisbon,attheSPERIAnnual ConferenceBeyondAusterityvsGrowth:TheFutureoftheEuropeanPolitical Economy,Sheffield,aswellasinseminarsattheUniversitéduLuxembourg,atthe ViennaUniversityofTechnologyandattheUniversitéParis1Panthéon-Sorbonne.
Bielefeld,GermanyAlfredGreiner June2014BettinaFincke
2SustainablePublicDebt:TheoryandEmpiricalEvidence
2.1.1PublicDebtandthePrimarySurplus
2.1.2ConditionsforSustainabilityofPublicDebt
2.2Empirics:Japan,GermanyandtheUSA ...............................11
2.2.1DescriptiveHistoricalApproach
2.2.2EmpiricalApproach
2.3EmpiricalResultsforEuroAreaCountries
2.3.1France
2.3.2Ireland,PortugalandSpain
2.3.3GreeceandItaly .................................................33
2.4TheImpactofthe2007FinancialCrisis:PortugalandSpain
2.5EmpiricalEvidenceforDevelopingCountries
2.5.1TheEstimationStrategy
2.5.2EstimationResults
3DebtandGrowth:ABasicEndogenousGrowthModel
3.1TheGrowthModel
3.1.1TheHouseholdSector
3.1.2TheProductiveSector ..........................................84
3.1.3TheGovernment ................................................85
3.1.4AnalysisoftheModelStructure
3.1.5WelfareEffectsofDebtPolicy
3.2DebtCycles
3.2.1StructureoftheModel
3.2.2TheDifferentialEquations
3.2.3BalancedGovernmentBudget
3.2.4PermanentPublicDeficits
3.3TheInteractionofFiscalandMonetaryPolicy
3.3.1TheHouseholdSector ..........................................106
3.3.2TheProductiveSector
3.3.3ThePublicSector
3.3.4TheBalancedGrowthPath
3.3.5AnalysisoftheModel
3.4EffectsofWageRigiditiesandUnemployment
3.4.1TheStructureoftheGrowthModel
3.4.2TheBalancedGrowthPath
3.4.3StabilityoftheEconomy
4ProductiveGovernmentSpending,PublicDebtandGrowth
4.1TheEndogenousGrowthModelwithFullEmployment
4.1.1Households
4.1.2Firms
4.1.3TheGovernment
4.1.4EquilibriumConditionsandtheBalancedGrowthPath
4.1.5AnalyzingtheModel
4.2EffectsofaProgressiveIncomeTax
4.2.1TheModel
4.2.2TheHouseholdandtheProductiveSector
4.2.3ImplicationsoftheModel
4.3ProductivePublicSpendingasaFlow
4.3.1ThePrivateSector
4.3.2TheGovernment
4.3.3AnalysisoftheModel
4.4TheRoleofWageRigidityandUnemployment
4.4.1TheEndogenousGrowthModel
4.4.2AnalysisoftheModelwithWageFlexibility
4.4.3TheModelwithWageRigidities ...............................188
4.4.4DiscussionandComparisontotheModel
5GovernmentDebtandHumanCapitalFormation
5.1TheStructureoftheGrowthModelwithHumanCapital
5.1.1TheHouseholdandtheProductiveSector
5.1.2HumanCapitalFormation ......................................208
5.1.3TheGovernment ................................................208
5.1.4EquilibriumConditionsandtheBalancedGrowthPath
5.1.5AnalysisoftheModel
ListofFigures Fig.2.1JapaneseNationalgovernmentdebtaspercentage ofGDP(1955–2006) .................................................12
Fig.2.2GermanNationalgovernmentdebtaspercentage ofGDP(1950–2007) .................................................13
Fig.2.3USFederaldebtattheendofyearaspercentage ofGDP(1940–2008) .................................................15
Fig.2.4Deviation sm.t/ fromtheaveragecoefficient for b.t 1/ forJapan ................................................18
Fig.2.5Generalgovernmentnetfinancialliabilities,Japan (1970–2006) ..........................................................19
Fig.2.6Deviation sm.t/ fromtheaveragecoefficient for b.t 1/ accountingforassetsforJapan ........................21
Fig.2.7Deviation sm.t/ fromtheaveragecoefficient for b.t 1/ forGermany ............................................23
Fig.2.8Deviation sm.t/ fromtheaveragecoefficient for b.t 1/ fortheUS ...............................................25
Fig.2.9IberianinterestratescomparedtoGermanbonds (1979–2012)in% ....................................................36
Fig.2.10PrimarysurplustoGDPratioforPortugalandSpain ..............37
Fig.2.11DebttoGDPratioforPortugalandSpain ..........................37
Fig.2.12PrimarysurplusanddebttoGDPratioforSpain (1980–2012) ..........................................................38
Fig.2.13PrimarysurplusanddebtratioforSpain(1980–2012) separatedbydecades .................................................39
Fig.2.14SmoothtermPortugal ................................................42
Fig.2.15SmoothtermSpain ...................................................42
Fig.2.16PublicdebttoGDPratioforBotswana(1978–2003) ..............46
Fig.2.17PrimarysurplustoGDPratioforBotswana (1978–2003) ..........................................................46
Fig.2.18Deviationsm(t)fromtheaveragecoefficientfor b.t 1/ forBotswana .........................................................48
Fig.2.19BudgetdeficitofBotswana(1978–2003) ...........................49
Fig.2.20PublicdebttoGDPratioforCostaRica(1970–2002) .............50
Fig.2.21PrimarysurplustoGDPratioforCostaRica (1970–2002) ..........................................................50
Fig.2.22Deviationsm(t)fromtheaveragecoefficientfor b.t 1/ forCostaRica ........................................................52
Fig.2.23BudgetdeficitofCostaRica(1970–2002) ..........................53
Fig.2.24Publicdebtto GDPratioforMauritius(1973–2005) ..............53
Fig.2.25PrimarysurplustoGDPratioforMauritius (1973–2005) ..........................................................54
Fig.2.26Deviationsm(t)fromtheaveragecoefficientfor b.t 1/ forMauritius .........................................................55
Fig.2.27BudgetdeficitofMauritius(1973–2005) ...........................56
Fig.2.28PublicdebttoGDPratioforPanama(1970–2000) ................57
Fig.2.29PrimarysurplustoGDPratioforPanama(1970–2000) ...........57
Fig.2.30Deviationsm(t)fromtheaveragecoefficientfor b.t 1/ forPanama ...........................................................58
Fig.2.31BudgetdeficitofPanama(1970–2000) .............................60
Fig.2.32PublicdebttoGDPratioforRwanda(1978–2004) ................60
Fig.2.33PrimarysurplustoGDPratioforRwanda(1978–2004) ...........61
Fig.2.34Deviationsm(t)fromtheaveragecoefficientfor b.t 1/ forRwanda ...........................................................62
Fig.2.35BudgetdeficitofRwanda(1978–2004) .............................63
Fig.2.36Rwanda’sreceivedgrantsrelativetoGDP(1978–2004) ...........64
Fig.2.37PublicdebttoGDPratioforTunisia(1972–1998) .................64
Fig.2.38PrimarysurplustoGDPratioforTunisia(1972–1998) .............65
Fig.2.39Deviationsm(t)fromtheaveragecoefficientfor b.t 1/ forTunisia ............................................................66
Fig.2.40BudgetdeficitofTunisia(1972–1998) ..............................67
Fig.2.41Plotofvariablesandsmoothtermsm(t)forFrance ................74
Fig.2.42Plotofvariablesandsmoothtermsm(t)forIreland ................75
Fig.2.43Plotofvariablesandsmoothtermsm(t)forPortugal ..............76
Fig.2.44Plotofvariablesandsmoothtermsm(t)forSpain .................77
Fig.2.45Plotofvariablesandsmoothtermsm(t)forGreece ................78
Fig.2.46Plotofvariablesandsmoothtermsm(t)forItaly ..................79
Fig.3.1Limitcycleinthe .b z c/ phasespace with D 3:7127 10 3 ..............................................104
Fig.4.1Transitionalgrowthratesofconsumption,private capitalandpubliccapitalafteratransitionfrom scenario(iii)toscenario(i)at t D 0 .................................158
Fig.4.2Averagetaxrate(constant)andmarginaltaxrate (rising)asafunctionof ............................................168
Fig.4.3TwosaddlepointstableBGPsfor 1= >1, >0 .................175
Fig.4.4Limitcycleinthe .x b c/ phasespace ..........................187
Fig.6.1Three-yearsgrowthrate ..............................................236
Fig.6.2PublicdebttoGDPratio .............................................237
Fig.6.3Pool, q D 5 ............................................................239
Fig.6.4Pool, q D 3 ............................................................240
Fig.6.5Pool, q D 1 ............................................................240
Fig.6.6Spline, q D 5 ..........................................................241
Fig.6.7Spline, q D 3 ..........................................................241
Fig.6.8Spline, q D 1 ..........................................................242
ListofTables Table2.1Equation(2.9)forJapan ............................................17
Table2.2Equation(2.9)without YVar ,Japan ................................17
Table2.3Equation(2.9)without GVar,Japan ................................18
Table2.4Equation(2.9)with b only,Japan ..................................18
Table2.5Equation(2.9)forJapan(netdebt) .................................20
Table2.6Without YVar,JAP(netdebt) .......................................20
Table2.7Without GVar,JAP(netdebt) ......................................20
Table2.8With b only,JAP(netdebt) .........................................20
Table2.9Equation(2.9)forGermany ........................................22
Table2.10Equation(2.9)without YVar ,GER .................................22
Table2.11Equation(2.9)without GVar,GER ................................22
Table2.12Equation(2.9)with b only,GER ...................................22
Table2.13Equation(2.9)fortheUSA .........................................24
Table2.14Equation(2.9)without YVar ,USA .................................24
Table2.15Equation(2.9)without GVar,USA ................................24
Table2.16Equation(2.9)with b only,USA ...................................24
Table2.17ADFtestforJapan(grossdebt) ....................................28
Table2.18ADFtestforJapan(netdebt) .......................................28
Table2.19ADFtestfortheUSA ...............................................28
Table2.20ADFtestforGermany ..............................................28
Table2.21CoefficientsforEq.(2.14)forFrancewithdata from1975to2008 ..................................................31
Table2.22CoefficientsforEq.(2.14)forIrelandwithdata from1975to2008 ..................................................33
Table2.23CoefficientsforEq.(2.14)forPortugalwithdata from1977to2009 ..................................................33
Table2.24CoefficientsforEq.(2.14)forSpainwithdata from1980to2009 ..................................................33
Table2.25CoefficientsforEq.(2.14)forGreecewithdatafrom 1976to2009 ........................................................34
Table2.26CoefficientsforEq.(2.14)forItalywithdatafrom 1972to2009 ........................................................34
Table2.27InterestrateandgrowthrategapforPortugalandSpain
Table2.28EstimationresultsSpain(1980–2010)
Table2.29EstimationresultsSpain(1980–2011)
Table2.30EstimationresultsPortugal
Table2.31EstimationresultsSpain
Table2.32CoefficientsforEq.(2.16)forBotswana
Table2.33ADFtestresultsforBotswana
Table2.34CoefficientsforEq.(2.16)forCostaRica
Table2.35ADFtestresultsforCostaRica
Table2.36CoefficientsforEq.(2.16)forMauritius
Table2.37ADFtestresultsforMauritius
Table2.38CoefficientsforEq.(2.16)forPanama
Table2.39ADFtestresultsforPanama
Table2.40CoefficientsforEq.(2.16)forRwanda
Table2.41ADFtestresultsforRwanda
Table2.42CoefficientsforEq.(2.16)forTunisia
Table2.43ADFtestresultsforTunisia
Table3.1Welfare F forthedifferentbudgetaryrules with D 0:25 and b.0/ D 0:32 ....................................96
Table3.2Thebalancedgrowthrate, g ,thedebttocapitalratio, v,andtheinflationrate, ,fordifferentvaluesofthe reactioncoefficient, ,ontheBGP ................................112
Table3.3Thebalancedgrowthrate, g ,thedebttocapitalratio, v,andtheinflationrate, ,fordifferentvaluesofthe nominalmoneygrowthrate, ,ontheBGP .......................113
Table3.4Thebalancedgrowthrate, g ,thedebttocapitalratio, v,andtheinflationrate, ,fordifferentnominal moneygrowthrates, ,ontheBGPwithabalanced governmentbudget ..................................................114
Table3.5Welfare, F ,fordifferentnominalmoneygrowth rates, ,withabalancedgovernmentbudget ......................115
Table3.6Welfare, F ,fordifferentvaluesofthenominalmoney growthrate, .......................................................115
Table3.7Welfare, F ,fordifferentvaluesofthereaction coefficient, ........................................................115
Table3.8Welfare, F ,forabalancedgovernmentbudget comparedtopermanentdeficits ....................................116
Table3.9Welfare F forthedifferentbudgetaryrules with D 0:25 and b.0/ D 0:5. .....................................137
Table3.10Welfare F forthedifferentbudgetaryrules with D 1 and b.0/ D 0:32 .......................................137
Table3.11Welfare F forthedifferentbudgetaryruleswith D 1 and b.0/ D 0:5 ...............................................138
Table4.1Balancedgrowthrateandthedebttoprivatecapital ratiofordifferent with D 0:05 ................................156
Table4.2Balancedgrowthrateandthedebttoprivatecapital ratiofordifferent with D 0:25 ................................157
Table4.3Welfareinscenario(iii)andwelfareresultingfrom atransitiontoscenario(ii)andscenario(i),respectively .........160
Table4.4Welfareinscenario(i)andwelfareresultingfrom atransitiontoscenario(iii)with b ? >0 ...........................160
Table4.5Welfareinscenario(i),scenario(ii)andscenario(iii) forgiveninitialconditions x.0/ D 0:03 and b.0/ D 0:02 ........161
Table4.6Long-rungrowthrate,endogenousvariables ontheBGPandeigenvaluesfordifferentvaluesof " and with D 0:015 ..............................................168
Table4.7Long-rungrowthrate,endogenousvariablesonthe BGPandeigenvaluesfordifferentvaluesof " and with D 0:015 ....................................................169
Table4.8BGPsfor 1= <1 and <0 ......................................176
Table4.9Balancedgrowthrate, g ,andeigenvaluesfordifferent with D 0:01 ....................................................186
Table4.10Balancedgrowthrate, g ,andeigenvaluesfordifferent with D 0:05 ....................................................186
Table4.11Balancedgrowthrate, g ,unemploymentrate, u, andeigenvaluesfordifferentvaluesof with D 0:01 .........189
Table4.12Balancedgrowthrate, g ,unemploymentrate, u, andeigenvaluesfordifferentvaluesof with D 0:05 .........190
Table5.1Long-rungrowthrateandendogenousvariables ontheBGPfordifferent andsmallvaluesof with ˇh D 0:75 ......................................................212
Table5.2Long-rungrowthrateandendogenousvariables ontheBGPfordifferent andsmallvaluesof with ˇh D 0:5 .......................................................212
Table5.3Long-rungrowthrateandendogenousvariables ontheBGPfordifferent andlargevaluesof with ˇh D 0:75 ......................................................213
Table5.4Long-rungrowthrateandendogenousvariables ontheBGPfordifferent andlargevaluesof with ˇh D 0:5 .......................................................213
Table5.5Welfareinscenario(i),scenario(ii), andscenario(iii)forgiveninitialconditions q.0/ D 0:0032;p.0/ D 0:1; z.0/ D 0:035 .......................227
Table5.6Welfareinscenario(iii)ontheBGPandwelfare resultingfromatransitiontoscenario(ii),and scenario(i),respectively ............................................227
Table5.7Balancedgrowthrate, g ,debttocapitalratio ontheBGP, b ? ,andthesignsoftheeigenvalues oftheJacobianfordifferentvaluesof and ....................232
Table5.8Balancedgrowthrate, g ,growthrateofpublicdebt, gb ,andthesignsoftheeigenvaluesoftheJacobian for D 0 andfordifferentvaluesof
Table6.1Plainpanelestimationresults
Table6.2Splineestimationresults,plainmodel
Table6.3Panelestimationresults,pooledOLS
Table6.4Panelestimationresults,randomeffects
Table6.5Modelselectiontests ................................................244
Chapter1 Introduction AfterWorldWarII,inparticularduringthe1970s,thepolitico-economicprinciples hadbeenlargelydominatedbytheKeynesianapproachaccordingtowhich governmentsmustplayanactiveroleinstabilizingmarketeconomies.Thelatter canbeachievedbypublicexpendituresinordertoraiseaggregatedemand,withthe spendingbeingfinancedbypublicdeficits.Particularly,intimesoflowaggregate demandandhighunemploymentthegovernmentmustbecomeactiveinorderto restorethefullemploymentequilibriumwhich,then,allowstoreduceoutstanding publicdebt.Inaddition,accordingtothatviewpublicdebtdoesnotposeaproblem ifthegovernmentrunsintodebtinthehomecountry.Thisholdsbecauseno resourcesarelostandpublicdeficitsjustimplyareallocationofresourcesfrom taxpayerstobondholders.
Anotherreasontoresorttodebt-financingisinter-generationalredistribution. Theaspectofinter-generationalredistributionisalsothejustificationforthe so-calledgoldenruleofpublicfinance.Accordingtothatrule,governmentsshould financepublicinvestmentsthatyieldlong-termbenefitsbypublicdeficitsinorder tomakefuturegenerationscontributeto thefinancing.Sincefuturegenerations willbenefitfromtoday’sinvestment,theircontributiontothefinancingisjustified. Otherwise,thecurrentgenerationwouldhavetobearallthecostsbutbenefitonly toacertaindegreewhichisconsideredasunfair.
AsaconsequenceofthepredominantKeynesianview,publicdebtrose considerablyinthefourthquarterofthelastcenturyand,whatismore,theincrease inpublicdebtwasevenlargerthanthegrowthrateofthegrossdomesticproduct (GDP),mainlyinmanyEuropeancountries,sothattheratioofpublicdebttoGDP grew,too.Evenintheeuroarea,wherecountriesparticipatingintheEuropean EconomicandMonetaryUnionhavesignedtheMaastrichttreatystatingthatthe publicdeficitandthepublicdebtrelativetoGDPmustnotexceed3and60%, respectively,quiteamanyeconomieshavedifficultieswiththeirdebtservice andsomeevenhadtobebailedoutbytheEuropeanStabilityMechanismto preventbankruptcy.Thisraisesthequestionofwhetherand,moregenerally,under
©SpringerInternationalPublishingSwitzerland2015 A.Greiner,B.Fincke, PublicDebt,Sustainability andEconomicGrowth, DOI10.1007/978-3-319-09348-2__1
whichconditionsagivenpathofpublicdebtissustainable.Ineconomics,modern empiricalresearchanalyzingthesustainabilityofatimeseriesofpublicdebthas begunwiththepaperbyHamiltonandFlavin(1986),whostudiedUSgovernment debtfromtheearly1960stothemid1980s.
Whenpublicdebtrisesinaneconomy,thegovernmentmustincreasefuture primarysurplusesinordertofulfillitsintertemporalbudgetconstraintunlessit acceptsthepossibilityofadefault,whichisnotagoodoptionsinceagovernment defaultisusuallyaccompaniedbysocialriotsthatcanendangerthewholepolitical system.Higherprimarysurplusescanbeachievedbyraisingtaxes,byreducing publicspendingorbyariseinGDPthatleadstomoretaxrevenueswhere,ofcourse, acombinationofallthreemeasuresisfeasible,too.Anotherpossibility,thatarises inmonetaryeconomics,isthatthecentr albankraisesthemoneysupplyandaccepts ahigherinflationratesuchthattherealvalueofpublicdebtdeclines.Intheextreme casewhentheinflationrateexceedstheinterestrateonpublicdebt,therealinterest ratebecomesnegativeleadingtoadeclineinthepublicdebttoGDPratio.
Whenamonetaryeconomyisconsidered,itisalsopossibletodistinguish betweenRicardianandnon-Ricardianregimes,whichgoesbacktoAiyagariand Gertler(1985),andthatisbasedonthefiscaltheoryofthepricelevel.According tothattheory,theintertemporalbudgetconstraintofthegovernmentmustholdfor somepathsofthepricelevelbutnotforall,incontrasttothebudgetconstraintof privateagents.Iftheintertemporalbudgetconstraintofthegovernmentdoesnot holdforanypathofthepricelevel,thegovernmentfollowsanon-Ricardianpolicy andtheintertemporalbudgetconstraintof thegovernmentonlyholdsinequilibrium. Iftheintertemporalbudgetconstraintholdsforanypricepath,andnotonlyforthe equilibriumpricepath,thegovernmentpursuesaRicardianfiscalpolicy.Thus,in anon-Ricardianregime,thegovernmentwouldnotcommititselfinthefutureto completelymatchnewpublicdebtwithfutureprimarysurpluses,becausesome partoftheadditionaldebtistobefinancedthroughmoneycreation.InaRicardian regime,theoppositeholdstrueandfuturefiscalrevenuesareexpectedtobeequalto currentpublicdebt.Forcontributionsasregardsthefiscaltheoryofthepricelevel seeforexampleLeeper(1991),Sims(1994)andWoodford(1994).However,the fiscaltheoryofthepriceleveliscontroversialandhasbeencriticized,forexample inthecontributionbyBuiter(2002)andinthepaperbyMcCallum(2003).Fora surveyofthefiscaltheoryofthepricelevelaswellasforfurtherstudiescriticizing thattheorywerefertoMcCallumandNelson(2006).
Theresearchanalyzinghowpublicdebtaffectseconomieshashadalong tradition.InthenineteenthcenturyDavidRicardosetupwhatisnowadayscalled theRicardianequivalencetheorem.Accordingtothattheorembudgetdeficitstoday requirehighertaxesinthefuturewhenagovernmentcutstaxeswithoutchanging presentorfuturepublicspending.Giventhathouseholdsareforwardlookingthey willrealizethattheyhavetopayhighertaxesinthefuturesothattheirtotal taxburdenremainsunchanged.Asaconsequence,householdswillreducetheir consumptionandincreasesavingsinordertomeetthefuturetaxburden.The Ricardianequivalencetheoremisbasedontheintertemporalbudgetconstraintof thegovernmentandonthepermanentincomehypothesis.Thefirstprinciplestates
thatpublicdebtmustbesustainableinthesensethatoutstandingdebttodaymust beequaltothepresentvalueoffuturegovernmentprimarysurpluses.Thesecond principlestatesthathouseholdsdonotbasetheirconsumptiononcurrentincome butonpermanentincomesothattheywillnotraiseconsumptionaslongastheir incomeincreasesonlytemporarily.TheRicardianequivalencetheoremisintuitively plausiblebutrestsonassumptionsthatmaybedifficulttofindinrealworld economies,suchastheabsenceofdistortionarytaxationorthenon-consideration ofeconomicgrowth,justtomentiontwo.
Withthisbook,ourgoalistoanalyzetheeffectsofpublicdebtandtoworkout themechanismsthatmakepublicaffecttherealsideofaneconomy,usingmodern modelsofendogenouseconomicgrowththeory.Startingpointofouranalysisis theintertemporalbudgetconstraintofthegovernmenttowhichthegovernment muststick.Whendealingwiththequestionofunderwhichconditionsagivenpath ofpublicdebtissustainable,weprimarilyfocusonpublicspendingandpublic revenues,ignoringthecentralbankofaneconomyinthemajorityofcases.Wedoso becausegovernmentsshouldnotrelyoncentralbankstoreducepublicdebtthrough moneycreationsincecentralbanksareindependentandthereisnoobligationfor themtoassistgovernmentsinpursuingsustainabledebtpolicies.Thus,wemostly neglectthepossibilitythatagovernment canuseseignorageorinflationtoreduce thestockofoutstandingrealpublicdebt.
InChap. 2 westartwiththeoreticalconsiderationsdealingwiththequestionof underwhichconditionsagivenpathofpublic debtissustainable.Weputparticular emphasisontherelationbetweentheprimarysurplusandthepublicdebtrelativeto GDP,respectively,andontheratioofpublicdebttoGDP.Amongotherthings,we demonstratethatapermanentlyrisingdebttoGDPratioisnotcompatiblewitha sustainabledebtpolicy.Thelargestpartof thischapterisdedicatedtotheempirical analysisofthesustainabilityofagiventimeseriesofpublicdebtinrealeconomies. WetestJapanandtheUSAaswellasmembercountriesoftheeuroarea,where weexemplarilyshowforPortugalandSpainhowthe2007financialcrisishas affectedtheirsustainabilitypositions.Inaddition,wealsotakeabrieflookatsome developingcountries.
Abasicendogenousgrowthmodelthatallowsforpublicdebtispresentedin Chap. 3.There,westudygrowthandwelfareeffectsofdifferentdebtpoliciesand weanalyzehowthosedebtpoliciesaffect thestabilityofmarketeconomies.Westart withabasicmodelthat,then,isgeneralizedbyassumingthatitisthehistoryofpast debtthatdeterminestheprimarysurpluspolicyofagovernment.Inthatchapter,we alsoconsiderthecentralbankthatcanhelpthegovernmenttofulfillitsintertemporal budgetconstraintbymoneycreation.Weanalyzetheinterrelationbetweenfiscal andmonetarypoliciesandhowitaffectsgrowthandwelfareaswellasinflation andstabilityofaneconomy.Finally,thestructureofthisbasicmodelischanged byassumingthatthelabormarketischaracterizedbyrealwagerigiditiesthatgive risetopermanentunemployment.Theeffectsofthisassumptionwithrespectto economicgrowthandstabilityoftheeconomyarethenanalyzedandwehighlight thedifferencetothemodelwithaperfectlabormarket.
Chapter 4 extendsthebasicendogenousgrowthmodelfromChap. 3 byallowing forproductivepublicspending.Weassumethatthegovernmentinvestsina productivepubliccapitalstockthatraises aggregateproductionpossibilities.The governmentfinancesitsexpendituresbytaxrevenuesandbypublicdeficitsandwe againanalyzetheeffectsofdifferentpublicdebtpolicieswithrespecttogrowthand welfareaswellaswithrespecttothestabilityoftheeconomy.We,then,changethe taxsystemandwestudyhowthemorerealisticassumptionofaprogressiveincome taxschemeaffectstheoutcome.Inaddition,wepresentandanalyzeamodelwhere publicspendingdirectlyaffectsproductioninaneconomy,wherewepayparticular attentiontotheemergenceofunderdevelopmenttrapsandlock-ineffectsthatmay arisedependingontheinitialdebttoGDPratio.Further,wepointouttheeffects thatresultwhenthelabormarketisnotperfectbutcharacterizedbywagerigidities andunemployment.Wepresentadetailedanalysisofthatmodelandwecompareit totheoneobtainedwithaperfectlabormarket.
Theroleofhumancapitalaccumulationforeconomicgrowthisanalyzedin Chap. 5.There,itissupposedthatthegovernmenthiresteachersandfinancesadditionalteachingmaterialtobuilduphuman capitalinaneconomy.Thegovernment hasaccesstothecreditmarketandcanfinanceitsspendingbyrunningadeficitand withadistortionaryincometax.Wedefineappropriateequilibriumconditionsand abalancedgrowthpathandwestudyeffectsofdifferentpublicdebtpolicies.That model,then,ismademoreelaboratebyallowingforastockofknowledgecapital thatresultsasaby-productofproduction(learning-by-doing).However,knowledge accumulationisonlypossibleifworkersdisposeofacertainamountofeducationso thathumancapitalaccumulationisanindispensablepreconditionforthegeneration ofknowledgeand,thus,foreconomicgrowth.
Finally,Chap. 6 presentsempiricalestimationsanalyzingthecorrelationbetween economicgrowthandpublicdebt.Inthatchapterweperformpaneldataestimations includingselectedEuropeaneconomiesandtheUSAforthetimeperiodfrom1970 to2012.Weestimatebothapooledregressionmodelandtherandomeffectsmodel withtheGDPgrowthrateasthedependentvariablethatisexplainedbythepublic debttoGDPratioatthebeginningoftheperiodunderconsiderationandbyother controlvariables,suchastheinitialGDPandinflationforexample.TheGDP growthrateiscomputedfora1yeartimeperiod,fora3-yearstimeintervaland fora5-yearsinterval.Wealsotestfor non-linearitiesbyapplyingpenalizedspline estimationasinChap. 2.
Chapter 7 summarizesthemainfindingsofthisbookandpointsoutinbrief theeffectsofpublicdebtandhowitaffectstheallocationofresourcesinmarket economies.
Chapter2 SustainablePublicDebt:TheoryandEmpirical Evidence 2.1TheoreticalConsiderations Modernresearchonsustainabilityofdebtpoliciesthatappliesstatisticaltestshas startedwiththecontributionbyHamiltonandFlavin(1986)whoanalyzedwhether theseriesofpublicdebtintheUSAcontainsabubbleterm.Sincethenagreat manypapershavebeenwrittenthattrytoanswerthequestionofwhethergiven debtpoliciescanbeconsideredassustainable.Theinterestinthatquestionisin partduetothefactthatthelatterquestionisnotonlyofacademicinterestbut thatithaspracticalrelevance,too.Hence,iftestsreachtheconclusionthatgiven debtpoliciescannotbeconsideredassustainablegovernmentsshouldundertake correctiveactions.
Animportantroleinmanyofthosestudiesonsustainabilityplaystheinterest rate,anaspectthatwaspointedoutbyWilcox(1989)forexample.Recallingthat theintertemporalbudgetconstraintofthegovernmentrequiresthatthepresentvalue ofpublicdebtasymptoticallyconvergestozero,theroleoftheinterestratethatis resortedtoinordertodiscountthestreamofpublicdebtbecomesimmediately clear.Therefore,testshavebeenconceivedthatreachresultswhichareindependent oftheinterestrate.Onesuchtestistoanalyzewhetherpublicdeficitsinclusiveof interestpaymentsgrowatmostlinearly,assuggestedbyTrehanandWalsh(1991). Ifthatpropertyisfulfilledagivenseriesofpublicdebtissustainablebecauseany timeseriesthatgrowslinearlyconvergestozeroifitisexponentiallydiscounted, providedtherealinterestrateispositive.Denotingby B publicdebtandby r theinterestrate,anothertestproposedbyTrehanandWalsh(1991)istoanalyze whetheraquasi-differenceofpublicdebt, Bt #Bt 1 with 0 #<1 C r , isstationaryandwhetherpublicdebtandprimarysurplusesareco-integrated. Ifgovernmentdebtisquasi-differencestationaryandpublicdebtandprimary surplusesarecointegrated,publicdebtissustainable.Hence,thesetwotestspresent alternativeswheretheoutcomeisindependentoftheexactnumericalvalueofthe
©SpringerInternationalPublishingSwitzerland2015 A.Greiner,B.Fincke, PublicDebt,Sustainability andEconomicGrowth, DOI10.1007/978-3-319-09348-2__2
interestrate.Asurveyofanalysesthattestedonsustainabilityofdebtpoliciescan befoundinAfonso(2005),NeckandSturm(2008)orBohn(2008).
Anothertestthathasreceivedgreatattentionintheeconomicsliteratureisthe oneproposedbyBohn(1995).There,itissuggestedtotestwhethertheprimary surplusrelativetoGDPisapositivefunctionofthedebttoGDPratio.Ifthat propertyholds,agivenpublicdebtpolicycanbeshowntobesustainable.This testisveryplausiblebecauseithasaniceeconomicintuition:ifgovernmentsrun intodebttodaytheyhavetotakecorrectiveactionsinthefuturebyincreasingthe primarysurplus.Otherwise,publicdebtwillnotbesustainable.Testingrealworld debtpoliciesforthatpropertyonecanindeedfindevidencethatcountriesbehave likethat(seeforexampleBohn 1998,fortheUSAandBallabrigaandMartinezMongay 2005,Greineretal. 2007,orFinckeandGreiner 2008,FinckeandGreiner 2011b,forselectedcountriesoftheeuroarea).
Fromastatisticalpointofview,ariseinprimarysurplusesasaresponseto highergovernmentdebtimpliesthattheseriesofpublicdebtrelativetoGDP shouldbecomeamean-revertingprocess. Thisholdsbecausehigherdebtratios leadtoanincreaseintheprimarysurplusrelativetoGDP,makingthedebtratio declineandreturntoitsmean.However,mean-reversiononlyholdsifthereaction coefficient,determininghowstronglytheprimarysurplusreactsaspublicdebtrises, issufficientlylarge,aswillbeshownindetailinthissection.
Inthissection,ourgoalistoelaborateonthattestfromatheoreticalpointof view.Inparticular,weareinterestedinthebehaviorofthedebttoGDPratiowhen governmentspursuesustainabledebtpolicies.Forexample,onequestionweaddress iswhetherasustainabledebtpolicyiscompatiblewitharisingdebttoGDPratio. Anotherquestionwestudyiswhethersustainabilitycanbegivenifthegovernment doesnotreacttorisingdebtratiosandwhetherthereprobablyexistsacriticalinitial debtratiothatmakesasustainabledebtpolicyimpossible.
2.1.1PublicDebtandthePrimarySurplus Weconsiderarealeconomyandwepositherethatthegovernmentcannotuse seignorageorinflationtoreduceitsoutstandingdebt.Wedothisbecausemodern economiesarecharacterizedbyindependentcentralbankssothatgovernments cannotcontrolthemoneysupply.Thus,governmentsshouldnotrelyonmoney creationtoreducetherealvalueofoutstandingpublicdebt.
Startingpointfortheanalysisofsustainabilityofpublicdebt,then,isthe accountingidentitydescribingtheaccumulationofpublicdebtincontinuoustime describedbythefollowingdifferentialequation:
with B.t/ realpublicdebt1 attime t , r.t/ therealinterestrate, S.t/ thereal governmentsurplusexclusiveofinterestpaymentsonpublicdebtandthedotover avariablestandsforthederivativewithrespecttotime d=dt.Agovernmentissaid tofollowasustainabledebtpolicyifthepresentvalueofpublicdebtconverges tozeroasymptotically,thatisifitdoesnotplayaPonzigame.Thisimpliesthat limt !1 e C1 .t/B.t/ D 0 holds,with C1.t/ D R t 0 r. /d thediscountrate(seefor exampleBlanchardandFischer 1989,chapter2).
Now,assumethatthegovernmentintheeconomychoosestheprimarysurplus toGDPratio, s.t/ D S.t/=Y.t/; suchthatitisapositivelinearfunctionofthedebt toGDPratio, b.t/ D B.t/=Y.t/; andofatermthatisindependentofpublicdebt, .t/ (seeBohn 1995, 1998;Canzoneri,Cumby,andDiba 2001,orGreiner 2008a). Theprimarysurplusratio,then,canbewrittenas
where .t/ isthecoefficientdetermininghowstrongtheprimarysurplusreactsto changesinthepublicdebtratioandthatistime-varying.Itshouldbenotedthat anynon-linearmodelcanbeapproximatedbyalinearmodelwithtime-varying coefficients.Further,theapproximationisgoodiftheparameterchangessmoothly (cf.Granger 2008).Thus,themodelingin(2.2)canbejustifiedandtheredoesnot seemtobetheneedforamoregeneralfunctiondescribingtheresponseofthe primarysurplustopublicdebt.
Theterm .t/ isalsotimedependentanditisinfluencedbyothereconomic variables,suchassocialspendingortransitorygovernmentexpendituresingeneral. Asconcerns .t/ wesupposethatitisboundedfromaboveandbelowbyacertain finitenumberthatisconstantovertime.Since .t/ givestheautonomouspart oftheprimarysurplusrelativetoGDP,thatassumptionisobviousandrealistic. Weshouldalsoliketopointoutthat .t/ cannotbecompletelycontrolledbythe government.Thegovernmentcaninfluencethatparametertoacertaindegreebutit hasnotcompletecontroloveritbecause .t/ isalsoaffectedbythebusinesscycle forexamplethatcanaffecttemporarygovernmentoutlays.
Inthenextsubsection,weanalyzeconditionsthatmustbefulfilledsuchthatthe intertemporalbudgetconstraintofthegovernmentholdsandhowthedebttoGDP ratioevolvesinthatcase.
2.1.2ConditionsforSustainabilityofPublicDebt Beforewestartouranalysiswemaketwoadditionalassumptions.First,weposit thattheinterestrateongovernmentbondsexceedsthegrowthrateofGDPon averagesothat R r. /d > R g. /d ; with g denotingthegrowthrateofGDP.
1 Strictlyspeaking, B shouldberealpublicnetdebt.
Wemakethisassumptionbecauseotherwisetheintertemporalbudgetconstraint wouldnotposeaproblemforthegovernmentsinceitcangrowoutofdebtinthat case.Inaddition,thisconditionisfulfilledforcountriesoftheeuroareaatleast sincethe1980s.Second,weneglectthecasewherepublicdebtbecomesnegative meaningthatthegovernmentwouldbeanetlender.Thisisdoneforreasonsof realismbecauseasituationwithnegativepublicdebtisoflessrelevanceforreal worldeconomies.
Inouranalysisofsustainabledebtpoliciesweareparticularlyinterestedunder whichconditionssustainabilityofpublicdebt isgivenandinthequestionofwhether asustainabledebtpolicyiscompatiblewitharisingdebttoGDPratio.Tostudy thosequestions,wedistinguishbetweentwocases.First,weanalyzethesituation wherethegovernmentsetstheprimarysurplusaccordingtoEq.(2.2),with .t/ ¤ 0.Second,westudythecasewheretheprimarysurplusdoesnotreacttovariations inthedebtratio,implyingthat .t/ D 0 holds.Inthelattercase,wepositinaddition thatthegovernmentsetstheprimarysurplusrelativetoGDPequaltoitsmaximum value.
ThePrimarySurplusasaFunctionofPublicDebt
Inthissubsection,wepositthattheprimarysurplusisgivenbyEq.(2.2),with .t/ ¤ 0.Tostudysustainabilityofpublicdebt,wecombineEqs.(2.1)and(2.2) yielding
With(2.3),thedebttoGDPratioevolvesaccordingto
whichisequivalentto
Withthesetwoequations,wecanderiveourfirstresultinProposition 1.2 Proposition1 AssumethattheupperboundoftheprimarysurplustoGDPratio isnotbinding.Then,astrictlypositivereactioncoefficientonaveragesothat R t 0 . /d D1 holdsfor t !1 guaranteessustainabilityofpublicdebt.
2 Inthisbookweconsiderdeterministiceconomies. Sustainabilityofpublic debtwithanadditive stochastictermisbrieflydiscussedintheappendixtothischapter.
For R t 0 . /d > R t 0 .r. / g. //d ,thedebttoGDPratioconverges toaconstantanditdivergestoplusorminusinfinityfor R t 0 . /d
R t 0 .r. / g. //d ; for t !1 respectively.
Proof Seetheappendixtothischapter.
Thispropositiondemonstratesthatapositiveandsufficientlylargereaction coefficientonaverageissufficientforsustainabilityofpublicdebt.Ifthereaction coefficientisstrictlynegativeonaverage,thediscountedvalueofpublicdebt divergestoinfinity.ButProposition 1 alsoshowsthatapositivevalueofthe reactioncoefficientdoesnotnecessarilyimplythatthedebttoGDPratioremains constantorthatitasymptoticallyconvergestozero.Onlyifthereactioncoefficient exceedsthepositivedifferencebetweentheinterestrateandtheGDPgrowthrateon average,convergencecanbeguaranteed.Otherwise,thedebttoGDPratiodiverges toinfinity.
WiththeresultofProposition 1,onecouldreachtheconclusionthatasustainable debtpolicyiscompatiblewithacontinuouslyrisingdebttoGDPratio,incasethe reactioncoefficient ispositiveonaveragebutsmallerthanthedifferencebetween theaverageinterestrateandtheaveragegrowthrate, r g .However,whenthe governmentsetstheprimary surplusaccordingtorule(2.2),thatpossibilityisnot givenasProposition 2 demonstrates.
Proposition2 Ifthegovernmentpursuesasustainabledebtpolicyandsetsthe primarysurplusaccordingtotherulegivenby (2.2),thedebttoGDPratioremains bounded.
Proof Assumethat b.t/ !1.Accordingto(2.2)thisimplies s.t/ !1 which, however,isexcludedbecausetheprimary surpluscannotbecomelargerthanGDP implyingthat s.t/<1 mustalwayshold. u
TheresultinProposition 2 issimplyduetothefactthattheprimarysurplusmust befinancedoutoftheGDPsothattheratiooftheprimarysurplustoGDPmust besmallerthanacertainfinitenumberthatislowerone.Consequently,whenthe governmentpursuesasustainabledebtpolicyandraisestheprimarysurplusrelative toGDPasthedebttoGDPratioincreases,thedebtratiomustremainboundedin thelong-run.
Hence,asituationmaybeobservedwherethedebttoGDPratiorisesovera certaintimeperiodalthoughtheprimarysurpluspositivelyreactstohigherpublic debt.Suchanevolutionofpublicdebtmaybecompatiblewithasustainabledebt policybutitcannotgoonforever.Soonerorlater,thepublicdebttoGDPratiomust becomeconstantordecline.Otherwise,sustainabilityisnotgiven.
ThePrimarySurplusIndependentofPublicDebt Inourconsiderationsuptonow,itwasassumedthatthegovernmentsetstheprimary surplusaccordingtotherulespecifiedinEq.(2.2).However,onecouldarguethat
governmentscanperformsustainabledebtpolicieswithoutreactingtohigherpublic debtiftheyonlychosetheprimarysurplussufficientlyhigh,independentofpublic debt.Further,asituationisfeasiblewherethegovernmentcannotreacttohigher debtsincethereisnoscopeforitbecausetheprimarysurplusrelativetoGDPhas alreadyreacheditsupperbound.Inbothcasesthereactioncoefficient .t/ would bezero.
Inordertoanalyzethatcaseweset .t/ D 0 andwedenoteby m<1 the constantupperboundoftheprimarysurplustoGDPratio.Inaddition,weassume thatthegovernmentsetstheprimarysurplustoGDPratioequaltothatmaximum valueforalltimes,thatis s.t/ D m forall t .Thus,theevolutionofpublicdebtis describedby
andthedebttoGDPratioevolvesaccordingto
GivenEqs.(2.6)and(2.7),wecanderiveProposition 3
Proposition3 AssumethattheinitialdebttoGDPratioexceedsacertainthreshold,givenby bcrit D m R 1 0 e .C1. / C2 . //d ; with C1 .
, C2. / D R0 g. /d .Then,asustainabledebtpolicyisexcluded.
IftheinitialdebttoGDPratioissmallerthanorequaltothecriticalthreshold, thegovernmentcanpursueasustainabledebtpolicy.Inthiscase,thedebttoGDP ratioconvergestoaconstant.
Proof Seetheappendixtothischapter.
Proposition 3 statesthatasustainabledebtpolicycannotbepursuediftheinitial debttoGDPratioislargerthanacertaincriticalvalue.Thecriticalvalue bcrit dependsonhowlargetheprimarysurplusrelativetoGDPcanmaximallybecome, m; andontheaveragedifferencebetween theinterestrateandthegrowthrate, r g .Hence,countriesthatdonotstabilizetheirdebttoGDPratiobutinsteadlet itgrowforalongertimeperiodfacetheriskthattheyfindthemselvesinasituation wheretheycannotreacttohigherdebttoGDP ratiosbyraisingtheirprimarysurplus relativetoGDP.Then,itmaybecomeimpossibletopursueasustainabledebtpolicy, independentofhowlargetheprimarysurplusrelativetoGDPisset.Inthiscase,the publicdebttoGDPratiobecomesunboundedasymptotically.
Thepropositionalsodemonstratesthat thegovernmentcancontrolpublicdebt ifitchoosesthemaximallypossiblevalueoftheprimarysurplus, m,providedthe initialdebttoGDPratioisnottoolarge,thatisifitissmallerthanthecriticalvalue bcrit .Inthatcase,sustainabilityofpublicdebtisguaranteedandthedebttoGDP ratioasymptoticallyconvergestoaconstant.Ofcourse,convergencetoaconstantis onlygivenifthegovernmentalwayssetstheprimarysurplusequaltoitsmaximum value m anddoesnotswitchtoadifferentdebtpolicy.
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Title: Indians of the Enchanted Desert
Author: Leo Crane
Release date: July 2, 2022 [eBook #68445]
Language: English
Original publication: United States: Little, Brown, and Company, 1925
Credits: Jeroen Hellingman and the Online Distributed Proofreading Team at https://www.pgdp.net/ for Project Gutenberg (This file was produced from images generously made available by The Internet Archive/American Libraries.) *** START OF THE PROJECT GUTENBERG EBOOK INDIANS OF THE ENCHANTED DESERT ***
[Contents]
[Contents] INDIANS OF THE ENCHANTED DESERT [Contents]
Photo. by W. C. Wilson
ANNOUNCING THE SNAKE DANCE
Priest at sunset removing kiva signal
INDIANS OF THE ENCHANTED DESERT BY LEO CRANE
WITH ILLUSTRATIONS BOSTON LITTLE, BROWN, AND COMPANY 1925
[Contents]
Copyright, 1925,
B L , B , C
All rights reserved
Published September, 1925
First Impression September, 1925
T A M P P