Instant download Public debt sustainability and economic growth theory and empirics 1st edition alfr

Page 1


Visit to download the full and correct content document: https://textbookfull.com/product/public-debt-sustainability-and-economic-growth-theor y-and-empirics-1st-edition-alfred-greiner/

More products digital (pdf, epub, mobi) instant download maybe you interests ...

Sustainability and Optimality of Public Debt 2nd Edition Michael Carlberg

https://textbookfull.com/product/sustainability-and-optimalityof-public-debt-2nd-edition-michael-carlberg/

Patent Markets in the Global Knowledge Economy Theory Empirics and Public Policy Implications Madies T.

https://textbookfull.com/product/patent-markets-in-the-globalknowledge-economy-theory-empirics-and-public-policy-implicationsmadies-t/

Social Capital and Local Development: From Theory to Empirics 1st Edition Elena Pisani

https://textbookfull.com/product/social-capital-and-localdevelopment-from-theory-to-empirics-1st-edition-elena-pisani/

Public Debt Management Separation of Debt from Monetary Management in India 1st Edition Charan Singh (Eds.)

https://textbookfull.com/product/public-debt-managementseparation-of-debt-from-monetary-management-in-india-1st-editioncharan-singh-eds/

Plant Growth Promoting Rhizobacteria for Agricultural Sustainability From Theory to Practices Ashok Kumar

https://textbookfull.com/product/plant-growth-promotingrhizobacteria-for-agricultural-sustainability-from-theory-topractices-ashok-kumar/

Culture Growth and Economic Policy 1st Edition

Panagiotis E. Petrakis (Auth.)

https://textbookfull.com/product/culture-growth-and-economicpolicy-1st-edition-panagiotis-e-petrakis-auth/

Economic Growth and Demographic Transition in Third World Nations A Chaos and Complexity Theory Perspective 1st Edition ■efika ■ule Erçetin (Editor)

https://textbookfull.com/product/economic-growth-and-demographictransition-in-third-world-nations-a-chaos-and-complexity-theoryperspective-1st-edition-sefika-sule-ercetin-editor/

Public Debt Dynamics of Europe and the US 1st Edition

Dimitris N. Chorafas (Auth.)

https://textbookfull.com/product/public-debt-dynamics-of-europeand-the-us-1st-edition-dimitris-n-chorafas-auth/

Physical Limits to Economic Growth Perspectives of Economic Social and Complexity Science 1st Edition

Roberto Burlando

https://textbookfull.com/product/physical-limits-to-economicgrowth-perspectives-of-economic-social-and-complexityscience-1st-edition-roberto-burlando/

Public Debt, Sustainability and Economic Growth

Theory and Empirics

AlfredGreiner•BettinaFincke PublicDebt,Sustainability andEconomicGrowth

TheoryandEmpirics

AlfredGreiner

BielefeldUniversity

Bielefeld Germany

BielefeldUniversity

Bielefeld Germany

ISBN978-3-319-09347-5ISBN978-3-319-09348-2(eBook) DOI10.1007/978-3-319-09348-2

SpringerChamHeidelbergNewYorkDordrechtLondon

LibraryofCongressControlNumber:2014952604

©SpringerInternationalPublishingSwitzerland2015

Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection withreviewsorscholarlyanalysisormaterialsuppliedspecificallyforthepurposeofbeingentered andexecutedonacomputersystem,forexclusiveusebythepurchaserofthework.Duplicationof thispublicationorpartsthereofispermittedonlyundertheprovisionsoftheCopyrightLawofthe Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw.

Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateof publication,neithertheauthorsnortheeditorsnor thepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein.

Printedonacid-freepaper

SpringerispartofSpringerScience+BusinessMedia(www.springer.com)

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.

Another random document with no related content on Scribd:

E D

This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.

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

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

L, B, C

T A M C

P U S A

[Contents]

TO those people of the Enchanted Desert who called me “Chief,” Indians, employees,

[Contents]

missioners, traders,—whose confidence, loyalty, and devotion made my work among the Hopi and Navajo tribes possible of success; and to humbler friends, my faithful horses, Dandy and Barney Murphy, Prince and Frank, that went with me so many weary miles, and were shot, by my order, to save them from the miseries of Governmental economy, this book is dedicated. [vii]

[Contents]

ILLUSTRATIONS

A S D Frontispiece

W, P C 12

T V I H

A N F I S 16

C C, S R

C D C B 58

T O W F-T

N T W D 70

A N H I B L

O W-D, D “W-W” 84

D B L C R

T H C C-P 92

H G S-F N D

H I A K C 106

H I H K C

A B D T-P, K C 118

R 105-M T R

H N, N C M M 124

J H H I C 132

Y, A P P 162

A M R—O T H 170

A P H H

A H S 178

A H Y W I P C

T W H, S O 196

T W S, A R-L S 202 [x]

T A, E D 230

O G B F A

A Y: I 234

T P: H M P

T C R, A B- 238

O W S D 250

D E S P

T G, H R 266

A P S

T C S-P 272

T E D M B 282

I T-B C 294

S J: T N

B C: C N N 316

N O: T C P

A N B W H N B A S 322

A H R-R 336

B C: A S B--W

A H S 338

A H W C R

A K D

H M G D, H C 340

N M C C

A N S D 344

H G A D

H W C 352

A H B 358 [1]

[Contents]

INDIANS OF THE ENCHANTED DESERT

NOLENS VOLENS

It is well for a man to respect his own vocation, whatever it is, and to think himself bound to uphold it and to claim for it the respect it deserves C D

They were good fellows, cordial, modest, although somewhat shy in manner, the sort that would have been more at home perhaps among fewer men. They came out of the West, at infrequent intervals, to visit the Chief, who in those days did not keep them waiting. The course of business, filtering down through the red-taped labyrinth, brought some of them to my desk and within my survey. I wonder now what they thought of me, especially as I am about to relate how I viewed them.

Imbued as I was then with the rare efficiency of bureaucracy, I sympathized with their apparent helplessness in the transaction of Departmental business. They were always wanting to do promptly things that weren’t done. Aside from that, I found them interesting, they being from what an Easterner would term the “hinterland,” had he vision enough to know that his country has one. I thought they would have tales to tell—a hope that never materialized.

When one came to know them better, as I sometimes did, they would relate their problems in a constrained, half pathetic manner, as if, seeking something and finding it not, they were confused. The idea came to me that they were awed, if not actually bewildered, by their uncommon [4]experiences in the big city. I did not dream that they were struggling manfully, as indeed they could, to restrain a just wrath; that their seeming pathos was a sort of crude pity, inspired by the artificialities and cheap bluff that they saw around them. Their

Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.