Economic Growth, 2nd Edition

673 Pages·2003·6.73 MB·english

by  Robert J. Barro

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ECONOMIC GROWTH C
Second Edition
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Robert J. Barro Xavier Sala-i-Martin
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This graduate level text on economic growth surveys neoclassical and more recent growth theories, stressing
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their empirical implications and the relation of theory to data and evidence. The authors have undertaken a ECONOMIC GROWTH
I Second Edition
major revision for the long-awaited second edition of this widely used text, the first modern textbook devoted C
to growth theory. The book has been expanded in many areas and incorporates the latest research. Robert J. Barro Xavier Sala-i-Martin
G AND
After an introductory discussion of economic growth, the book examines neoclassical growth theories, from
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Solow–Swan in the 1950s and Cass–Koopmans in the 1960s to more recent refinements; this is followed by a
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discussion of extensions to the model, with expanded treatment in this edition of heterogeneity of households.
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The book then turns to endogenous growth theory, discussing, among other topics, models of endogenous tech-
nological progress (with an expanded discussion in this edition of the role of outside competition in the growth T
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process), technological diffusion, and an endogenous determination of labor supply and population. The authors
then explain the essentials of growth accounting and apply this framework to endogenous growth models. The
final chapters cover empirical analysis of regions and empirical evidence on economic growth for a broad panel
of countries from 1960 to 2000. The updated treatment of cross-country growth regressions for this edition uses
the new Summers–Heston data set on world income distribution compiled through 2000.
Robert J. Barro is Robert C. Waggoner Professor of Economics at Harvard University and senior fellow of
the Hoover Institution at Stanford University. He is the author of Nothing Is Sacred: Economic Ideas for the New S
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Millennium(MIT Press, 2002), Getting It Right(MIT Press, 1997), and Determinants of Economic Growth(MIT c
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Press, 1998). Xavier Sala-i-Martin is Professor of Economics at Columbia University and visiting professor at the n
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University of Pompeu Fabra, Barcelona. E
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“Barro and Sala-i-Martin’s valuable and readable book brings the student quickly to the frontiers of modern n 7
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growth theory.” —Robert E. Lucas, Jr., John Dewey Distinguished Service Professor, The University of Chicago, 9
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1995 Nobel Laureate in Economic Sciences 4
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“Barro and Sala-i-Martin provide an outstanding and comprehensive treatment of growth theory and empir- a /
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ics—an instant classic! I learn something new every time I pull my copy from the shelf.” —Charles I. Jones, rr 6
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Department of Economics, University of California, Berkeley
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“This is an invaluable book for a first graduate course in economic growth. The exposition is clear and easy to D
follow, but also rigorous. It is an excellent stepping stone for research in the field.” —K. Daron Acemoglu, S
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Professor of Economics, MIT
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“Barro and Sala-i-Martin have done a superb job of synthesizing much of the existing theoretical and empir- i
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ical research on the mechanisms and determinants of economic growth and convergence. Though it incor- M
porates much new material, this updated version is fully accessible to a third year undergraduate student, a
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while remaining of invaluable use to any research scholar seriously interested in growth and development t
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economics.” —Phillipe Aghion, Department of Economics, Harvard University n
Cover image: Soft Watch by Salvador Dalí, © 2003 Salvador Dalí, Gala-Salvador Dalí Foundation/Artists Rights Society (ARS), New York
The MIT Press Massachusetts Institute of Technology Cambridge, Massachusetts 02142 http://mitpress.mit.edu 0-262-02553-1
,!7IA2G2-acffdj!:t;K;k;K;k
EconomicGrowth
SecondEdition
RobertJ.Barro
XavierSala-i-Martin
TheMITPress
Cambridge,Massachusetts
London,England
(cid:1)c 2004MassachusettsInstituteofTechnology
Allrightsreserved.Nopartofthisbookmaybereproducedinanyformbyanyelectronicormechanicalmeans
(includingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromthe
publisher.
ThisbookwassetinTimesRomanbyICCTypesettingandwasprintedandboundintheUnitedStatesof
America.
LibraryofCongressCataloging-in-PublicationData
Barro,RobertJ.
Economicgrowth/RobertJ.Barro,XavierSala-i-Martin—2nded.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN0-262-02553-1
1.Economicdevelopment—Mathematicalmodels. I.Sala-i-Martin,Xavier. II.Title.
HD75.5.B37 2003
338.9(cid:1)001(cid:1)51—dc22
2003059392
ToRachel
—RobertJ.Barro
Alamemo`riadelsmeusestimatsJoanMart´ınPujoliRamonOriolMart´ınMontemayor
—XavierSala-i-Martin

Contents
Preface xv
AbouttheAuthors xvii
Introduction 1
I.1 TheImportanceofGrowth 1
I.2 TheWorldIncomeDistribution 6
I.3 EmpiricalRegularitiesaboutEconomicGrowth 12
I.4 ABriefHistoryofModernGrowthTheory 16
I.5 SomeHighlightsoftheSecondEdition 21
1 GrowthModelswithExogenousSavingRates
(theSolow–SwanModel) 23
1.1 TheBasicStructure 23
1.2 TheNeoclassicalModelofSolowandSwan 26
1.2.1 TheNeoclassicalProductionFunction 26
1.2.2 TheFundamentalEquationoftheSolow–SwanModel 30
1.2.3 Markets 31
1.2.4 TheSteadyState 33
1.2.5 TheGoldenRuleofCapitalAccumulation
andDynamicInefficiency 34
1.2.6 TransitionalDynamics 37
1.2.7 BehaviorofInputPricesDuringtheTransition 40
1.2.8 PolicyExperiments 41
1.2.9 AnExample:Cobb–DouglasTechnology 43
1.2.10 AbsoluteandConditionalConvergence 44
1.2.11 ConvergenceandtheDispersionofPerCapitaIncome 50
1.2.12 TechnologicalProgress 51
1.2.13 AQuantitativeMeasureoftheSpeedofConvergence 56
1.3 ModelsofEndogenousGrowth 61
1.3.1 TheoreticalDissatisfactionwithNeoclassicalTheory 61
1.3.2 TheAKModel 63
1.3.3 EndogenousGrowthwithTransitionalDynamics 66
1.3.4 Constant-Elasticity-of-SubstitutionProductionFunctions 68
1.4 OtherProductionFunctions...OtherGrowthTheories 71
1.4.1 TheLeontiefProductionFunctionand
theHarrod–DomarControversy 71
1.4.2 GrowthModelswithPovertyTraps 74
vi Contents
1.5 Appendix:ProofsofVariousPropositions 77
1.5.1 ProofThatEachInputIsEssentialforProduction
withaNeoclassicalProductionFunction 77
1.5.2 PropertiesoftheConvergenceCoefficient
intheSolow–SwanModel 78
1.5.3 ProofThatTechnologicalProgressMust
BeLaborAugmenting 78
1.5.4 PropertiesoftheCESProductionFunction 80
1.6 Problems 81
2 GrowthModelswithConsumerOptimization
(theRamseyModel) 85
2.1 Households 86
2.1.1 SetupoftheModel 86
2.1.2 First-OrderConditions 89
2.2 Firms 94
2.3 Equilibrium 97
2.4 AlternativeEnvironments 98
2.5 TheSteadyState 99
2.6 TransitionalDynamics 102
2.6.1 ThePhaseDiagram 102
2.6.2 TheImportanceoftheTransversalityCondition 104
2.6.3 TheShapeoftheStableArm 105
2.6.4 BehavioroftheSavingRate 106
2.6.5 ThePathsoftheCapitalStockandOutput 110
2.6.6 SpeedsofConvergence 111
2.6.7 HouseholdHeterogeneity 118
2.7 NonconstantTime-PreferenceRates 121
2.7.1 ResultsunderCommitment 123
2.7.2 ResultswithoutCommitmentunderLogUtility 124
2.7.3 PopulationGrowthandTechnologicalProgress 129
2.7.4 ResultsunderIsoelasticUtility 130
2.7.5 TheDegreeofCommitment 132
2.8 Appendix2A:Log-LinearizationoftheRamseyModel 132
2.9 Appendix2B:IrreversibleInvestment 134
Contents vii
2.10 Appendix2C:BehavioroftheSavingRate 135
2.11 Appendix2D:ProofThatγκˆ DeclinesMonotonically
IftheEconomyStartsfromkˆ(0)<kˆ∗ 137
2.12 Problems 139
3 ExtensionsoftheRamseyGrowthModel 143
3.1 Government 143
3.1.1 ModificationsoftheRamseyFramework 143
3.1.2 EffectsofTaxRates 146
3.1.3 EffectsofGovernmentPurchases 147
3.2 AdjustmentCostsforInvestment 152
3.2.1 TheBehaviorofFirms 152
3.2.2 EquilibriumwithaGivenInterestRate 155
3.2.3 EquilibriumforaClosedEconomywithaFixed
SavingRate 159
3.3 AnOpen-EconomyRamseyModel 161
3.3.1 SetupoftheModel 161
3.3.2 BehaviorofaSmallEconomy’sCapitalStockandOutput 162
3.3.3 BehaviorofaSmallEconomy’sConsumptionandAssets 163
3.3.4 TheWorldEquilibrium 164
3.4 TheWorldEconomywithaConstraintonInternationalCredit 165
3.4.1 SetupofaModelwithPhysicalandHumanCapital 166
3.4.2 TheClosedEconomy 167
3.4.3 TheOpenEconomy 168
3.5 VariationsinPreferenceParameters 177
3.6 EconomicGrowthinaModelwithFiniteHorizons 179
3.6.1 ChoicesinaModelwithFiniteHorizons 179
3.6.2 TheFinite-HorizonModelofaClosedEconomy 183
3.6.3 TheFinite-HorizonModelofanOpenEconomy 186
3.7 SomeConclusions 189
3.8 Appendix:Overlapping-GenerationsModels 190
3.8.1 Households 190
3.8.2 Firms 192
3.8.3 Equilibrium 193
3.9 Problems 200
viii Contents
4 One-SectorModelsofEndogenousGrowth 205
4.1 TheAKModel 205
4.1.1 BehaviorofHouseholds 205
4.1.2 BehaviorofFirms 206
4.1.3 Equilibrium 207
4.1.4 TransitionalDynamics 208
4.1.5 ThePhaseDiagram 209
4.1.6 DeterminantsoftheGrowthRate 210
4.2 AOne-SectorModelwithPhysicalandHumanCapital 211
4.3 ModelswithLearningbyDoingandKnowledgeSpillovers 212
4.3.1 Technology 212
4.3.2 Equilibrium 216
4.3.3 ParetoNonoptimalityandPolicyImplications 216
4.3.4 ACobb–DouglasExample 217
4.3.5 ScaleEffects 218
4.4 PublicServicesandEndogenousGrowth 220
4.4.1 APublic-GoodsModel 220
4.4.2 ACongestionModel 223
4.5 TransitionalDynamics,EndogenousGrowth 226
4.5.1 ACobb–DouglasExample 226
4.5.2 ACESExample 230
4.6 ConcludingObservations 232
4.7 Appendix:EndogenousGrowthintheOne-SectorModel 232
4.8 Problems 235
5 Two-SectorModelsofEndogenousGrowth(withSpecial
AttentiontotheRoleofHumanCapital) 239
5.1 AOne-SectorModelwithPhysicalandHumanCapital 240
5.1.1 TheBasicSetup 240
5.1.2 TheConstraintofNonnegativeGrossInvestment 242
5.2 DifferentTechnologiesforProductionandEducation 247
5.2.1 TheModelwithTwoSectorsofProduction 247
5.2.2 TheUzawa–LucasModel 251
5.2.3 TheGeneralizedUzawa–LucasModel 266
5.2.4 TheModelwithReversedFactorIntensities 267
5.3 ConditionsforEndogenousGrowth 268
Contents ix
5.4 SummaryObservations 271
5.5 Appendix5A:TransitionalDynamicswithInequalityRestrictions
onGrossInvestmentintheOne-SectorModel 271
5.6 Appendix5B:SolutionoftheUzawa–LucasModel 274
5.7 Appendix5C:TheModelwithReversedFactorIntensities 280
5.8 Problems 282
6 TechnologicalChange:ModelswithanExpandingVariety
ofProducts 285
6.1 ABaselineModelwithaVarietyofProducts 285
6.1.1 TheProducersofFinalOutput 285
6.1.2 ResearchFirms 289
6.1.3 Households 295
6.1.4 GeneralEquilibrium 295
6.1.5 DeterminantsoftheGrowthRate 297
6.1.6 ParetoOptimality 297
6.1.7 ScaleEffectsandtheCostofR&D 300
6.1.8 ARisingCostofR&D 303
6.2 ErosionofMonopolyPower,Competition 305
6.3 Romer’sModelofTechnologicalChange 310
6.4 ConcludingObservations 313
6.5 Problems 313
7 TechnologicalChange:SchumpeterianModels
ofQualityLadders 317
7.1 SketchoftheModel 317
7.2 TheModel 319
7.2.1 TheProducersofFinalOutput:LevelsofQuality
intheProductionTechnology 319
7.2.2 TheResearchSector 321
7.2.3 Consumers 328
7.2.4 BehavioroftheAggregateQualityIndex
andEndogenousGrowth 329
7.2.5 ScaleEffectsAgain 331
7.3 InnovationbytheLeader 333
7.3.1 InteractionsBetweentheLeaderandtheOutsiders 333
7.3.2 TheLeaderasaMonopolyResearcher 336