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Externalités de revenu dans le taux d'escompte dans des modèles bi-sectoriels à générations imbriquées : analyse dynamique en autarcie et en économie ouverte, Income externalities in discounting in two-sector overlapping generations models : a dynamic analysis in autarky and under free trade

De
228 pages
Sous la direction de Alain Venditti
Thèse soutenue le 16 juin 2010: Aix Marseille 2
Cette thèse propose de formuler le taux d’escompte comme fonction du revenu individuel et classifie cette spécification comme les externalités de revenu dans le taux d’escompte. La justification de cette relation est trouvée dans la théorie de la hiérarchie des besoins humains par Abraham Maslow (Maslow (1943)) : plus le revenu d’un individu, interprété comme le pouvoir économique à consommer, est élevé, plus l’individu a tendance à penser à des besoins supérieurs, associés à une plus grande patience. Ensuite, la présente étude s’intéresse aux implications des externalités pour deux phénomènes macro-économiques : les fluctuations endogènes, et la convergence/polarisation des revenus par tête entre les pays. Les résultats obtenus indiquent que les externalités de revenu dans le taux d'escompte constituent un mécanisme qui génère des fluctuations endogènes dans une économie fermée. L’extension de ce modèle à une configuration 2x2x2 dynamique permet de conclure qu’en fonction des technologies et des préférences des consommateurs, l'intégration commerciale d'une économie volatile avec une économie stable peut avoir un effet stabilisant ou, au contraire, peut engendrer des fluctuations macro-économiques dans toute la région. Enfin, cette thèse démontre que la libéralisation des échanges commerciaux peut avoir, comme effet de long terme, soit la convergence soit la divergence des revenus par habitant. Pour un certain nombre de paramètres, les externalités génèrent la divergence. Ce résultat est compatible avec les observations empiriques et met en évidence l’importance des interventions politiques pour bénéficier de la libéralisation commerciale.
-Taux d'escompte
-Externalités de revenu
This dissertation proposes a new formulation of time discounting: discount factor as a function of individual income, referred to as income externalities in discounting. The rationale for this relationship is found in the theory of hierarchy of human needs by Abraham Maslow (Maslow (1943)): the greater is income, interpreted as economic power of individuals to consume, the higher layers of needs, associated with greater patience, individuals seek to satisfy. Then, the thesis entails an examination of the linkage between the externalities and two macroeconomic phenomena: endogenous fluctuations and convergence/polarization of per capita incomes across countries. It is established that income externalities in discounting could be a vehicle for endogenous fluctuations in an autarkic economy. In the extension of the autarkic model to a dynamic 2x2x2 framework, it is found that trade integration of a volatile economy with a stable one can make fluctuations to evanesce or, on the contrary, propel them to the whole region depending on technologies and consumer preferences. Last, it is shown that trade liberalization can result in convergence or divergence of long run per capita income. For some range of parameters, externalities produce divergence. The result is consistent with empirical observations and emphasizes the importance of policy interventions for reaping benefits from free trade.
-Discount rate
-Income externalities
Source: http://www.theses.fr/2010AIX24007/document
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UNIVERSITE DE LA MEDITERRANEE (AIX-MARSEILLE II)
FACULTE DES SCIENCES ECONOMIQUES ET DE GESTION

EcoleDoctoraledeSciencesEconomiquesetdeGestiond'Aix-Marseillen 372
Thèseprésentéeetsoutenuepubliquementpourl'obtentiondu
DoctoratèsSciencesEconomiques
le16juin2010
par
ALENA SIARHEYEVA
IncomeExternalitiesinDiscountinginTwo-Sector
OverlappingGenerationsModels:
aDynamicAnalysisinAutarkyandUnderFree
Trade
DirecteurdeThèse
ALAIN VENDITTI : DirecteurdeRechercheauC.N.R.S.
MembresduJury
BERTRAND WIGNIOLLE Professeuràl'UniversitéParis1
FABRICE COLLARD DirecteurdeRechercheauC.N.R.S.;Universitéd'Adelaide
GILLES NANCY Professeuràl'UniversitéAix-MarseilleIIL'UniversitédelaMéditerranéen'entendniapprouver,nidésapprouverlesopinions
particulières du candidat : ces opinions doivent être considérées comme propres à leur
auteur.TomyparentsAbstract
This dissertation proposes a new formulation of time discounting: discount
factorasafunctionofindividualincome,referredtoasincomeexternalitiesindis-
counting. The rationale for this relationship is found in the theory of hierarchy of
human needs by Abraham Maslow (Maslow (1943)): the greater is income, inter-
preted as economic power of individuals to consume, the higher layers of needs,
associatedwithgreaterpatience,individualsseektosatisfy. Then,thethesisentails
an examination of the linkage between the externalities and two macroeconomic
phenomena: endogenous uctuations and convergence/polarization of per capita
incomes across countries. It is established that income externalities in discount-
ing could be a vehicle for endogenous uctuations in an autarkic economy. In the
extension of the autarkic model to a dynamic 2x2x2 framework, it is found that
trade integration of a volatile economy with a stable one can make uctuations to
evanesce or, on the contrary, propel them to the whole region depending on tech-
nologies and consumer preferences. Last, it is shown that trade liberalization can
result in convergence or divergence of long run per capita incomes across coun-
tries, the result consistent with empirical observations. Thus, policy interventions
areimportantforreapingbenetsfromfreetrade.
Keywords: incomeexternalitiesindiscounting,two-sectoroverlapping-generations
model,indeterminacy,endogenousuctuations,tradeliberalization,dynamicHeckscher-
Ohlinmodel,convergenceAcknowledgments
I wish to express my greatest appreciation and profound gratitude to my su-
pervisor, C.N.R.S.Research DirectorAlainVenditti, forhis professionalguidance,
highavailabilityandmotivationduringthisresearchproject.
I am very thankful to Professor Gilles Nancy, the director of DEFI, who be-
lieved in my potential and gave me an opportunity, nancial and administrative, to
accomplishmywork. Itrulyappreciateourdiscussionsatthebeginningofmydoc-
toral studies, which gave rise to the central idea of the thesis, income externalities
indiscounting.
I am indebted to Karine Gente from DEFI at the Aix-Marseille II University
forhervaluableadvisesandenthusiasticsupport.
Iwouldliketothankmyreferees,ProfessorBertrandWigniollefromtheParis
1 University and C.N.R.S. Research Director Fabrice Collard from the University
ofAdelaide,fortheirhelpfulsuggestionsthathavemademyanalysistoevolveand
tomature.
This research project was made possible thanks to the nancial support from
theFrenchGovernment.
iAcknowledgments ii
Ithanktheparticipantsoftheconference"GénérationsImbriquées,Développe-
ment et Dynamique Economique", in particular, my referee, Thomas Seegmuller
fromG.R.E.Q.A.MattheAix-MarseilleIIUniversity,forhiscomments.
ManythankstotheresearchteamofDEFI,formerlyCEDERS,MarcelAloy,
AliceFabre,MichelNormandin,DavidDiazandothermembersoftheAix-Marseille
IIUniversityfortheirsupportatvariousstagesofmywork.
IamgratefultotheadministrationoftheDoctoralSchool,PierreBatteauand
BrigitteMarcellinfortheirprofessionalmanagementandsupport.
My sincere thanks to the administrative staff, Mathilde Martelli, Armande
Poret and Jenny Ottosson for efcient management and pleasant working atmo-
sphere.
Many thanks to my colleagues and friends, Caroline Duburcq, Jean-Philippe
Garnier,ArtiomsIvlevs,FlorencePrin,CélineBreton,PaulMaarekandMohammed
Slimaniforbeinginthesameboat.
I am indebted to my parents whose moral support helped me to accomplish
my project. Last, but not least, my warmest thanks to my friend Sylvain Achard.
Hisunderstanding,patience,encouragementandnancialsupportwereinestimable
fortheadvancementandaccomplishmentofthislongproject.Contents
Contents.........................................................................iii
Preface............................................................................1
1. BackgroundandKeyConcepts ................................................. 1
2. Motivation....................................................................13
3. Summary.....................................................................18
1 WhatDeterminesIndividualImpatience? .............................. 22
1.1 Introduction................................................................23
1.2 TheDUmodel .............................................................25
1.3 RecursiveUtilityFunctions .................................................29
1.4 ConsumptionExternalitiesinDiscounting ...................................32
1.5 Income,WealthandImpatience .............................................34
1.6 TimeDiscountingasaFunctionofWealthandIncomeinGrowthModels.....50
1.7 Conclusion.................................................................59
2 Trade and Convergence in Two-Sector Overlapping-
GenerationsModels: aReview ........................................... 61
2.1 Introduction................................................................62
2.2 AutarkicEconomy .........................................................63
2.3 TheOpeningofTrade ......................................................75
iiiContents iv
2.4 ImplicationsforConvergence ...............................................84
2.5 Conclusion.................................................................86
2.A Proofoflemma5...........................................................87
3 Income Externalities in Discounting and Endogenous
FluctuationsinanAutarkicOverlappingGenerationsEconomy.... 88
3.1 Introduction................................................................89
3.2 TheModel .................................................................91
3.3 DynamicalSystem .........................................................98
3.4 DynamicPropertiesoftheNSS ............................................102
3.5 ANumericalExample .....................................................116
3.6 Conclusion ...............................................................120
3.A ACharacterizationofT(k;y;l) ............................................122
3.B Realinterestrate ..........................................................125
3.C CrossDerivativesandElasticities ..........................................126
3.D Theshareofcapital........................................................130
3.E CharacteristicPolynomial..................................................132
3.F Proofoflemma7..........................................................135
3.G Proofoflemma8..........................................................136
3.H Proofoflemma9..........................................................137
13.I Locationof" withrespecttotheothercriticalbounds" ...................138
4 IncomeExternalitiesinDiscountinginaDynamic2x2x2Model:
StabilizingEffectofRegionalIntegration? ............................140
4.1 Introduction...............................................................141
4.2 TheModel ................................................................142Contents v
4.3 PerfectForesightEquilibriumoftheGlobalEconomy.......................146
4.4 TheDynamicalSystemoftheGlobalEconomy .............................148
4.5 LocalPropertiesoftheNSS................................................150
4.6 ANumericalExample ....................................................158
4.7 Conclusion................................................................163
4.A Proofoflemma10 ........................................................166
4.B Proofoflemma11 ........................................................170
4.C Proofoflemma12 ........................................................171
4.D Proofoflemma13 ........................................................172
5 Income Externalities in Discounting and Trade: Implications
forCross-CountryPerCapitaIncomeConvergence .................173
5.1 Introduction...............................................................174
5.2 AutarkicEconomy ........................................................176
5.3 OpeningUptoTrade ......................................................181
5.4 Discussion ................................................................189
5.5 Conclusion................................................................191
5.A ProofofProposition9 .....................................................194
5.B Proofof10 ....................................................198
GeneralConclusion..........................................................205
References ....................................................................211Preface
“Ifweallworkedontheassumptionthat
whatisacceptedastrueisreallytrue,
therewouldbelittlehopeofadvance”
OrvilleWright
Thisthesisbringsintofocusthemannerinwhichincomeinuencesindividualimpa-
tience,referredtoasincomeexternalitiesindiscounting;andentailsanexaminationofthe
implicationsofthisrelationfori)macroeconomicstabilityofanautarkiceconomyaswell
as for ii) outcomes of trade liberalization, more specically, macroeconomic stabilization
andconvergenceofpercapitaincomesacrosscountries.
In section 1, we present the background and key concepts used in this dissertation.
We state the motivation for this research in section 2 and give an executive summary in
section3.
1. BackgroundandKeyConcepts
1.1. Evolution of Neoclassical Thinking
Economic science has sought to build itself on the example of natural sciences. For the
purpose of establishment of a “pure” discipline, mathematical formalization, introduced
by the founding fathers of neoclassical thinking, Léon Walras, Stanley Jevons and Carl
Menger,hasbecomeanunavoidabletoolofeconomics.
Notwithstandingthisvirtueofscience,economicsisasocialdiscipline. Theprimary
objectofeconomicthinkingistogainanunderstandingofaparticularsetofcircumstances
1