Essays in dynamic contract theory [Elektronische Ressource] / vorgelegt von Sebastian Köhne

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Essays in Dynamic Contract TheoryInauguraldissertationzur Erlangung des akademischen Gradeseines Doktors der Wirtschaftswissenschaftender Universit¨at Mannheimvorgelegt vonSebastian K¨ohneMannheim, Mai 2010Dekan: Prof. Tom Krebs, Ph.D.Referent: Prof. Dr. Ernst-Ludwig von ThaddenKorreferent: Prof. Nicola Pavoni, Ph.D.Tag der mu¨ndlichen Pru¨fung: 28. Juni 2010iiAcknowledgementsFirst of all, I wish to thank my advisor Ernst-Ludwig von Thadden for his invaluableguidance throughout the process of writing this thesis. My research has benefited a lotfrom his deep knowledge about contract theory, the great research environment at hischair, and his very constructive feedback on my results. I am deeply indebted for theencouragement and support I have received during the last five years.IalsowishtothankNicolaPavoniforhisinvaluableadviceonmythesisandbeyond. Hissupervision during my visits to the University College London has had a huge impact onmyunderstandingofdynamicpublicfinanceandmacroeconomics. Iamdeeplyindebtedfor his continuous help and confidence in me.´ ´Moreover, I am very grateful to Arp´ad Abrah´am and Nicola Pavoni for the productiveand joyful cooperation on Chapter 4 of this thesis. I am looking forward to futurecollaborations on this topic.Ian Jewitt provided numerous constructive comments on Chapter 3 of this thesis. I amalso very grateful for his help during the job market period.
Publié le : vendredi 1 janvier 2010
Lecture(s) : 17
Source : D-NB.INFO/1004737297/34
Nombre de pages : 107
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EssaysinDynamicContractTheory

Inauguraldissertation

zurErlangungdesakademischenGrades

einesDoktorsderWirtschaftswissenschaften

derUniversita¨tMannheim

vorgelegtvon

SebastianKo¨hne

Mannheim,Mai2010

De:nak

Referent:

Korreferent:

Tagdermu¨ndlichen

Pru¨fung:

D..hP

,sbreK

moT

.froP

Thadden

Dr.Ernst-Ludwigvon

.froP

NicolaPavoni,Ph.D.

.froP

28.Juni2010

ii

Acknowledgements

Firstofall,IwishtothankmyadvisorErnst-LudwigvonThaddenforhisinvaluable
guidancethroughouttheprocessofwritingthisthesis.Myresearchhasbenetedalot
fromhisdeepknowledgeaboutcontracttheory,thegreatresearchenvironmentathis
chair,andhisveryconstructivefeedbackonmyresults.Iamdeeplyindebtedforthe
encouragementandsupportIhavereceivedduringthelastveyears.

IalsowishtothankNicolaPavoniforhisinvaluableadviceonmythesisandbeyond.His
supervisionduringmyvisitstotheUniversityCollegeLondonhashadahugeimpacton
myunderstandingofdynamicpublicnanceandmacroeconomics.Iamdeeplyindebted
forhiscontinuoushelpandcondenceinme.
Moreover,Iamverygratefulto´Arpa´d´Abraha´mandNicolaPavonifortheproductive
andjoyfulcooperationonChapter4ofthisthesis.Iamlookingforwardtofuture
collaborationsonthistopic.

IanJewittprovidednumerousconstructivecommentsonChapter3ofthisthesis.Iam
alsoverygratefulforhishelpduringthejobmarketperiod.

Inaddition,IwishtothankmyfellowgraduatestudentsattheCDSEforthewonderful
timeIexperiencedhere.Iamparticularlygratefultoallfellowsfromtheclassof2005.

Finally,Janaandmyfamilyhavebeengiantsourcesofsupport.Thankyou!

iii

vi

Contents

1Introduction

2Repeatedmoralhazardwithhistory-dependentpreferences

2.1Introduction..................................

2.2Model.....................................

2.2.1Preferences..............................

2.2.2Technology..............................

2.2.3Contracts...............................

2.2.4Optimalcontracts...........................

2.3Resultsonintertemporaloptimality.....................

2.3.1ModicationoftheInverseEulerequation.............

2.3.2Theintertemporalwedge.......................

2.4Functionalformsofhistory-dependence...................

2.4.1Weightedaverages..........................

2.4.2Cobb-Douglasaggregation......................

2.5Extensiontomulti-periodmodels......................

v

1

5

5

11

11

21

31

31

41

41

61

91

02

32

92

3

4

2.5.1Notation................................29

2.5.2Intertemporaloptimality.......................31

2.6Concludingremarks..............................36

2.AAppendix:Proofs...............................37

Therst-orderapproachtomoralhazardproblemswithhiddensaving43

3.1Introduction..................................43

3.2Model.....................................47

3.2.1Preferences..............................48

3.2.2Technology..............................48

3.2.3Contracts...............................48

3.2.4First-orderapproach.........................49

3.3Asucientconditionforconcavityoftheagent’sproblem........50

3.4Alternativesucientconditionsforconcavity...............56

3.4.1CRRAutility.............................57

3.4.2Exploitingthecurvatureofthecontract..............58

3.5Concludingremarks..............................64

3.AAppendix:Proofs...............................64

3.BAppendix:Concavewageschemes......................68

Optimalincometaxationwithassetaccumulation71

4.1Introduction..................................71

4.2Model.....................................73

iv

3.4

4.4

45.

A.4

4.2.1Preferences..............................

4.2.2Productionandendowments.....................

4.2.3Markets................................

4.2.4Contracts...............................

4.2.5Eciency...............................

4.2.6First-orderapproach.........................

4.2.7Preliminarycharacterizationofoptimalcontracts.........

Simpleresults.................................

Moreelaborateresults............................

Conclusionandoutlook............................

Appendix:Proofs...............................

iiv

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58

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Chapter1

Introduction

Thisthesisconsistsofthreemainchapters,whichcontributetotheliteratureondynamic
contracttheoryanddynamicpublicnance.Thechaptersareself-containedandcanbe
readseparately.Ashortsummaryofeachchapterisprovidedbelow.

Repeatedmoralhazardwithhistory-dependentpreferences

Chapter2introduceshistory-dependentpreferencesintotherepeatedmoralhazard
framework:theagent’sinstantaneousconsumptionutilitymaydependonbothpresent
andpastlevelsofconsumption.ThepapershowsinwhatsensetheInverseEulerequa-
tiongeneralizestothisenvironmentandderivesimplicationsfortheintertemporalwedge
betweentheprincipal’srateofreturntosavingandtheagent’sshadowrateofreturn.
Whiletheintertemporalwedgeispositiveundermildassumptionsforalltwo-period
modelswithhistory-dependence,theintertemporalwedgeisgenerallyindeterminatefor
modelswithalongertime-horizon.Finally,thepapercontrastssomespecicfunctional
formsofhistory-dependence.

2

Introduction

Therst-orderapproachtomoralhazardproblemswithhidden
saving

Moralhazardmodelswithhiddensavingdecisionsareusefultostudysuchdiverseprob-
lemsasunemploymentinsurance,incometaxation,executivecompensation,orhuman
capitalpolicies.Howcanwesolvesuchmodels?Ingeneral,thisisverydicult.Under
theconditionsderivedinChapter3,however,wecanreplacetheincentiveconstraint
withtheassociated

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