essays on macroeconomic policy & affine term structure models

296 Pages·2014·4.04 MB·English

by  Vicente Jakas

ESSAYS ON MACROECONOMIC
POLICY & AFFINE TERM
STRUCTURE MODELS
Inaugural-Dissertation
zur Erlangung des akademischen Grades eines Doktors
der Wirtschaftswissenschaft (doctor rerum politicarum)
der Rechts- und Wirtschaftswissenschaftlichen Fakultät
der Universität des Saarlandes
vorgelegt von
M.Sc. Vicente Jakas
15. August 2013
TagdesKolloquiums:24.März 2014
Dekan: Univ.- Prof. Dr. StephanWeth
Erstgutachter: Univ.- Prof.Dr.AhokKaul
Zweitgutachter: Prof. Dr. Michael Wolf
To Ines, that tookcareof thekids andsupported meso muchduringthejourneyand
tomytwobeloveddaughters Anne & Lucia, forwhom Iwill needto catch upwithin
ordertocompensateforthetimespentwriting this thesis.
ii
Acknowledgements
Special thanks toProf.Dr.Ashok Kaul forhis great support andvaluable advice
throughout this dissertation.Iam also verygrateful tomyfatherProf.Dr. Mario
Jakas forhis critical view andscientificsupport throughout various paths of this
work.
iii
Table of Contents
Acknowledgements......................................................................................................iii
TableofContents.........................................................................................................iv
List ofTables..............................................................................................................vii
List of Figures............................................................................................................viii
1. Introduction...........................................................................................................1
Section I. Affineterm structuremodels abriefintroduction....................................8
Section II.Empirical EvidenceonAffineTerm StructureModels........................14
Section III.Whyis relevant tounderstandthe yieldcurveas part of anetworkof
macroeconomicvariables?......................................................................................16
Section IV.PublicDebt Policy: abriefintroduction..............................................22
SectionV. Inprogress foranovel theory...............................................................29
SectionVI. Links toThe Theoryof Fragilityofthe Eurofrom De Grauwe
(2013a,b).................................................................................................................31
SectionVII. Links ofthe FragilityoftheEurozone to IlliquidMarkets................36
2. Theoryofa Term StructureModel AppliedtoEuropeanData(violatingthe no-
arbitrage condition).....................................................................................................39
Section I. Introduction............................................................................................39
Section II.The BasicAssetPricingEquation.........................................................40
Section III.TheModel............................................................................................41
Section IV.TheEmpirics........................................................................................47
SectionV.TheData................................................................................................48
SectionVI.Empirical Results.................................................................................48
SectionVII.Relatedliterature................................................................................58
SectionVIII.Conclusions andFinal Remarks........................................................59
3. IntroductoryNotes onAffineTerm StructureModels: Continuous Time
Approach.....................................................................................................................61
Section I. IntroductionandMotivation...................................................................61
Section II.The BasicAsset PricingEquation.........................................................62
Section III.The BasicPricingEquationforAsset Returns....................................64
Section IV. TheHoldingPeriodReturn(hpr)........................................................65
SectionV.UnivariateCaseUnderVasicek............................................................69
SectionVI. LinkingNow toaStateSpaceSystem withanObservationEquation76
SectionVII.Univariate CaseunderCox-Ingersoll-Ross (1985)model.................77
SectionVIII.Multifactor AffineModels................................................................84
Section IX.Conclusions andfinal remarks.............................................................91
4. AffineTerm StructureModels appliedtoaMacro-FinanceModel...................92
Section I. Introduction............................................................................................92
iv
Section II.Someintroductorynotes........................................................................93
Section III.AMacro-FinanceDynamicModel......................................................95
Section IV.Consumerpreferences.........................................................................96
SectionV.Central Bank Policy..............................................................................99
SectionVI.TheGovernment Problem..................................................................102
SectionVII.TheTheoryoftheFragilityofthe Eurozone....................................106
SectionVIII.Conclusion andFinal Remarks.......................................................109
5. DiscreteApproachtoAffineTerm StructureModels AppliedtoGermanand
Greek Government Yields........................................................................................111
Section I. Introduction..........................................................................................111
Section II.Recallingsomebasicconcepts andintroducingnewones..................112
Section III.Multifactor AffineTerm StructureunderVasicek.............................115
Section IV.Multifactor AffineTerm StructureunderCox-Ingersoll-Ross..........119
SectionV.Generalised MultifactorAffine Term StructureDuffieandKan........123
SectionVI.CalibratingUndertheDiscrete Approach.........................................129
SectionVII.CalibratingwithGreekGovernment Bonds.....................................137
SectionVIII.Conclusions andFinal Remarks......................................................143
6. TheYieldCurveand EconomicFundamentals: A Continuous TimeModel...146
Section I. Introduction..........................................................................................146
Section II.TheModel...........................................................................................149
Section III.Results anddiscussion.......................................................................151
Section IV.PolicyImplications............................................................................165
SectionV.Conclusions andFinal Remarks..........................................................167
Appendix: Bond yields calculations....................................................................168
7. DiscreteAffineTerm StructureModels AppliedtotheGovernment Debt and
Fiscal Imbalances......................................................................................................170
Section I. Introduction..........................................................................................170
Section II.Recallingsomebasicconcepts andintroducingnewones..................172
Section III.Thetheoryof thepricelevel andrisk-freeassets: themodel ............178
Section IV.Solvingwhenthetheoryofthepricelevel is at workand when is not
...............................................................................................................................183
SectionV.Solvingbyanalysingfiscal shocks onsurplus debt rolloverrisk.......184
SectionV.I.Theeffects of surplus shocks ontotal notional debt outstanding..184
SectionV.II.Theeffect of changes intotal notionaldebt outstandingontheprice
level andcredit spread......................................................................................187
SectionV.III. ModellingGovernment’s net primarysurplus as afunctionofstate
variables............................................................................................................190
SectionVI.Empirical Analysis.............................................................................195
SectionVII.PolicyImplications, Conclusions andFinal Remarks......................213
Appendix Chapter7..............................................................................................215
I. Solvingwhenthetheory of thepricelevel is at workandwhenisnot.....215
II. Solvingthecoefficients A(N+1)andB(N+1)assuminginnovations in
government surplus influence changes intotal notional debt outstanding.......217
v
III. Solvingthecoefficients A(N+1)andB(N+1)assumingthat changes in
total notional debt outstandinginfluencetheprice level or credit spreads .....218
IV. Solvingthecoefficients A(N+1)andB(N+1)assumingnet primary
surplus is afunctionof astatevector of macroeconomicvariables.................220
8. TheTerm Structure, Latent Factors andMacroeconomicData: A LocalLinear
Level Model..............................................................................................................223
Section I. Introduction..........................................................................................223
Section II.Yields’unobservedcomponents.........................................................224
Section III.Discussionof Results.........................................................................231
Section IV.CalibratinganAffineTerm Structure Model with Latent Factors....249
SectionV.PolicyImplications.............................................................................252
SectionVI.Conclusions andFinal Remarks........................................................252
9. ConclusionandFinal Remarks.........................................................................254
Bibliography.............................................................................................................261
vi
List of Tables
TABLE2-1.EONIA,EURIBORRATES,ANDTHEGERMANGOVERNMENTYIELDCURVEASPROXIESFORTHETERM
STRUCTUREOFINTERESTRATES...........................................................................................................50
TABLE2-2.OLSMODEL:YIELDSVERSUSMACRO-FACTORSFORGERMANY,SPAIN,GREECE,ITALYANDPORTUGAL......56
TABLE2-3.OLS,ROBUSTFORMONEYMARKETYIELDSVS.MACROECONOMICDATA(DEC1999TOSEP2012)........58
TABLE5-1OLSREGRESSIONRESULTSANDSELECTEDDIAGNOSTICS..................................................................143
TABLE6-1FITTINGCOEFFICIENTSINEQ.(3)..................................................................................................155
TABLE6-2VALUEOFTHEPARAMETERSENTERINGTHEPRESENTCALCULATIONS....................................................156
TABLE8-1MONEYMARKETCURVE:EONIA,EURIBOR3M,EURIBOR6M,2YRAND5YRGERMANGOVYBOND.....232
TABLE8-2CAPITALMARKETCURVE:5,10,15,20AND30YEARGERMANGOVYBONDS....................................233
TABLE8-3OLS(ROBUST)RESULTSOFMONEYMARKETLATENTFACTORSVERSUSMACROECONOMICDATA..............237
TABLE8-4OLSRESULTSOFCAPITALMARKETLATENTFACTORSVERSUSMACROECONOMICDATA...........................237
TABLE8-5VARRESULTSOFMONEYMARKETLATENTFACTORSVERSUSMACROECONOMICDATA...........................241
TABLE8-6VARRESULTSOFCAPITAL MARKETLATENTFACTORSVERSUSMACROECONOMICDATA..........................242
TABLE8-7MONEYMARKETSGRANGERCAUSALITYTEST.................................................................................245
TABLE8-8CAPITALMARKETSGRANGERCAUSALITYTEST................................................................................246
vii
List of Figures
FIGURE1-1.YIELDSANDDEBTRATIOSFROM GIIPSCOUNTRIESANDGERMANY....................................................32
FIGURE1-2.SURPLUSASA%OFGDPFROMGIIPSCOUNTRIESANDGERMANY....................................................33
FIGURE1-3.THECASEOFSPAINVERSUSGREECEPROBLEM...............................................................................34
FIGURE1-4.2YEARBONDYIELDSVERSUSDEBT-TO-GDPRATIOSGIIPCOUNTRIESANDGERMANY...........................35
FIGURE1-5.MARKETDYNAMICSANDILLIQUIDMARKETS..................................................................................36
FIGURE1-6.CONTRACTIONINTHESUPPLYOFLIQUIDITY...................................................................................37
FIGURE1-7.FINALORCLOSINGBID-ASK(BID-OFFER)SPREADS............................................................................38
FIGURE2-1.COMPARISONOFBENCHMARKMODELUSINGOLSVERSUSOBSERVEDVALUES......................................52
FIGURE2-2.ESTIMATEDOLSFORB(N)/NCOEFFICIENTSUSINGEQUATION(11)...................................................52
FIGURE2-3IMPULSERESPONSEANALYSISONTHEEONIARATE..........................................................................54
FIGURE2-4.IMPULSERESPONSEANALYSISONTHE5YEARGERMANGOVERNMENTBOND........................................55
FIGURE4-1.THETHEORYOFTHEFRAGILITYOFTHEEUROZONEFROMDEGRAUWE(2011A,B)ANDKOPF(2011)....107
FIGURE5-1ANALYSISOFTHEB(N)COEFFICIENTSUNDEROLS,VASICEKANDCIRMODELS....................................131
I
FIGURE5-2ANALYSISOFTHEINTERCEPTA(N)COEFFICIENTUNDEROLS,VASICEKANDCIRMODELS.......................131
FIGURE5-3FITTINGTHEYIELDCURVE..........................................................................................................133
FIGURE5-4VASICEKFITTEDVERSUSOBSERVEDYIELDS.....................................................................................135
FIGURE5-5CIRFITTEDVERSUSOBSERVEDYIELDS...........................................................................................136
FIGURE5-6GREEKGOVERNMENTBONDYIELD-CURVECIR-FITTEDVERSUSOBSERVED...........................................138
FIGURE5-7GREEKGOVERNMENTBONDYIELDS,CIR-FITTEDVERSUSOBSERVEDTIMESERIES..................................139
FIGURE5-8GREEKGOVERNMENTBONDSOLSFITTEDVERSUSOBSERVEDTIMESERIES..........................................140
FIGURE5-9GREEKGOVERNMENTBONDSAFFINE-CIRESTIMATED....................................................................142
FIGURE6-1STATEVARIABLESUSEDINTHISESSAY...........................................................................................153
FIGURE6-2RISK-FREEINTERESTORSHORTRATE(EONIA)ASAFUNCTIONOFTIME(STARTINGONDEC.1999).........154
FIGURE6-3COEFFICIENTSA(N)/NANDB(N)/NINEQ.(2),OBTAINEDBYFITTINGTOEURIBORANDGERMAN
GOVERNMENTBONDS......................................................................................................................158
FIGURE6-4THREE-ANDSIX-MONTHEURIBORRATE.......................................................................................160
FIGURE6-5TWO-,FIVE-,TEN-,FIFTEEN-,TWENTY-ANDTHIRTY-YEARGERMANGOVERNMENTBONDS....................161
FIGURE6-6AVERAGEBONDSYIELDASAFUNCTIONOFMATURITY......................................................................162
FIGURE6-7PREDICTINGEURIBORANDGERMANBONDSYIELDSVALUESUSINGCURRENTSTATEVARIABLES................164
FIGURE7-1DEVELOPMENTOFTHEEONIA,BREAKEVENINFLATIONANDREALINTERESTRATEOBSERVEDFROMEURO1
YEARINFLATIONSWAP.....................................................................................................................197
FIGURE7-2REPLICATIONOFEONIAUSINGASSTATEVARIABLESTHEREALINTERESTRATESANDTHEBREAKEVENINFLATION
RATESFROMOBSERVEDINFLATIONSSWAPSDATA..................................................................................197
FIGURE7-3FIGURE3.BLOOMBERGEUGOVERNMENTYIELDS(BLOOMBERGINDEX),OBSERVEDVS.FITTEDUSING
OBSERVEDBREAKEVENINFLATIONANDREALINTERESTRATESFROMTHEEUROINFLATION(CPI)SWAPCURVE..199
FIGURE7-4BLOOMBERGGERMANGOVERNMENTYIELDS(BLOOMBERGINDEX),OBSERVEDVS.FITTEDUSINGOBSERVED
BREAKEVENINFLATIONANDREALINTERESTRATESFROMTHEEUROINFLATION(CPI)SWAPCURVE.................200
FIGURE7-5BLOOMBERGGREEKGOVERNMENTYIELDS,OBSERVEDVS.FITTEDUSINGOBSERVEDBREAKEVENINFLATION
ANDREALINTERESTRATESFROMTHEEUROINFLATION(CPI)SWAPCURVE................................................201
FIGURE7-6BLOOMBERGSPANISHGOVERNMENTYIELDS,OBSERVEDVS.FITTEDUSINGOBSERVEDBREAKEVENINFLATION
ANDREALINTERESTRATESFROMTHEEUROINFLATION(CPI)SWAPCURVE................................................202
FIGURE7-7FITTINGBYINCORPORATINGTHESPREADASINEQUATION(26).BLOOMBERGGREEKGOVERNMENTCURVES,
OBSERVEDVS.FITTEDUSINGTHEOBSERVEDCREDITSPREADS,BREAKEVENINFLATIONANDREALINTERESTRATES
FROMTHEEUROINFLATION(CPI)SWAPCURVE...................................................................................203
FIGURE7-8FITTINGEQUATION(26).BLOOMBERGSPANISHGOVERNMENTCURVES,OBSERVEDVS.FITTEDUSINGTHE
OBSERVEDCREDITSPREADS,BREAKEVENINFLATIONANDREALINTERESTRATESFROMTHEEUROINFLATION(CPI)
SWAPCURVE.................................................................................................................................204
viii
FIGURE7-9FITTINGEQUATION(22).REPLICATIONOFPRODUCTIONPRICEINDICES(PPI)FORTHEEURO-ZONE,
GERMANY,SPAINANDGREECE.OBSERVEDVS.FITTEDVALUESUSINGTHEOBSERVEDTOTALGOVERNMENTDEBT
OUTSTANDINGAVAILABLEINBLOOMBERG...........................................................................................205
FIGURE7-10REPLICATIONOF2YSPANISHGOVERNMENTYIELDAPPLYINGTWOFACTORS,SPANISHCUMULATED
GOVERNMENTDEFICITANDUNEMPLOYMENTRATES:OBSERVEDVS.FITTEDVALUES.....................................206
FIGURE7-11EUROBREAKEVENINFLATIONOBSERVEDVS.AFFINEFITTEDVALUES.................................................207
FIGURE7-12SPANISHANDGREEKGOVERNMENTSPREADSAFFINEFITTED..........................................................207
FIGURE7-13AFFINETERMSTRUCTURESENSITIVITIESOFTHESPANISHANDGREEKGOVERNMENTSPREADS..............208
FIGURE7-14.CUMULATEDGOVERNMENTEXPENSESTOCUMULATEDGOVERNMENTREVENUESRATIOS(COST-INCOME-
RATIOS)FORGERMANY,SPAINANDGREECE........................................................................................209
FIGURE7-15.CUMULATEDGOVERNMENTEXPENSEAND CUMULATEDGOVERNMENTREVENUESFORGERMANY,SPAIN
ANDGREECE..................................................................................................................................210
FIGURE7-16SENSITIVITIESOFTAXREVENUESANDEXPENDITURETOUNEMPLOYMENTRATES................................212
FIGURE8-1LATENTFACTORSLEVEL,SLOPE,CURVATUREANDRATESFORMONEYMARKETSANDCAPITALMARKETS
RATES...........................................................................................................................................234
FIGURE8-2FITTEDVERSUSOBSERVEDMONEYMARKETYIELDS.......................................................................235
FIGURE8-3FITTEDVERSUSOBSERVEDCAPITALMARKETYIELDS.......................................................................236
FIGURE8-4LEVEL,SLOPE,SEASONALCOMPONENTSANDTHEIREMPIRICALCOUNTERPARTS....................................239
FIGURE8-5IMPULSERESPONSEFUNCTIONSFORMONEYMARKETLATENT ANDMACROECONOMICVARIABLES........243
FIGURE8-6IMPULSERESPONSEFUNCTIONSFORCAPITALMARKETLATENT ANDMACROECONOMICVARIABLES........244
FIGURE8-7FORECASTVARIANCEDECOMPOSITIONTOCHOLESKYORTHOGONALSHOCKSFORMONEYMARKETLATENT
ANDMACROECONOMICVARIABLES.....................................................................................................247
FIGURE8-8FORECASTVARIANCEDECOMPOSITIONTOCHOLESKYORTHOGONAL SHOCKSFORCAPITALMARKETLATENT
ANDMACROECONOMICVARIABLES.....................................................................................................248
FIGURE8-9YIELDCURVEFITTEDWITHANAFFINETERMSTRUCTUREMODELUSINGLATENTFACTORSASSTATEVARIABLES.
...................................................................................................................................................250
FIGURE8-10YIELDCURVEFITTEDWITHANAFFINETERMSTRUCTUREMODELUSINGLATENTFACTORSASSTATEVARIABLES.
...................................................................................................................................................251
FIGURE8-11FITTEDCOEFFICIENTS A(N) /N AND B( N ) / N ASINEQUATION(17)..............................251
i i
ix