Table Of ContentLecture Notes in Economics
and Mathematical Systems 639
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Boris Hirsch
Monopsonistic Labour
Markets and the Gender
Pay Gap
Theory and Empirical Evidence
123
Dr. Boris Hirsch
Friedrich-Alexander-Universität Erlangen-Nürnberg
Chair of Labour and Regional Economics
Lange Gasse 20
90403 Nürnberg
Germany
[email protected]
ISSN 0075-8442
ISBN 978-3-642-10408-4 e-ISBN978-3-642-10409-1
DOI10.1007/978-3-642-10409-1
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To myparentsandgrandparents
Acknowledgements
I would like to thank all those people who have helped me in the course of my
researchthatculminatedinthisPh.D.thesis.
Firstandforemost,I am deeplyindebtedto myacademicsupervisors.My spe-
cialthanksgotomyprincipalacademicsupervisorClausSchnabelforhisperpetual
guidance and encouragement and for the many insightful discussions that helped
greatly in forming this work. I am also deeply grateful to my second supervisor
Jürgen Jerger for valuable advice and many useful suggestions that contributed
substantiallytothisthesis’completion.
Apartfrommysupervisors,I amparticularlygratefultomyco-authorsMarion
König, Joachim Möller, Thorsten Schank, and Claus Schnabel. Large parts of
Chapters6and9aregroundedonjointworkwiththem,andIbenefitedalotfrom
theircommentsandsuggestions.
Many thanks go to my colleagues at the Friedrich–Alexander–Universität
Erlangen–Nürnbergand to the Bavarian Graduate Program in Economics and its
members.Theprogram’sexcellentcoursesandseminarsprovedtobeinstrumental
inwritingthisthesis.Theprogram’sgenerosityalsoallowedmetospendhalfayear
at the Centre for EconomicPerformanceat the LondonSchoolof Economicsand
Political Science, which has been a great stimulation in the course of writing this
thesis.Iwouldliketothankforthecentre’swarmhospitalityandinparticularAlan
Manningformanyfruitfulconversationsandhelpfulsuggestions.
MyveryspecialthanksgotoJürgenDeinhard.Henotonlyproof-readthewhole
thesis (includingthe technicalappendices)and pointedme at several inaccuracies
and obscuritiesin the expositionbut also providedme with a lot of usefulecono-
metriccommentsandsuggestions.Lastbutnotleast,Iowemydeepestgratitudeto
myparentsandgrandparents,towhomIdedicatethiswork.
vii
Contents
1 Introduction................................................................... 1
1.1 WageSettingvs.WageTaking........................................ 1
1.2 ‘Classic’vs.‘New’Monopsony ...................................... 3
1.3 PlanoftheBook....................................................... 6
PartI SpatialMonopsony
2 SimpleStaticMonopsony.................................................... 11
3 Short-RunSpatialMonopsony.............................................. 15
3.1 TheBasicAssumptions ............................................... 15
3.2 TheElasticityoftheFirm’sAggregateLabourSupply.............. 19
3.3 ConvexityandElasticityofIndividualLabourSupply .............. 21
3.3.1 ConvexityRelativetoanExponential........................ 21
3.3.2 SpatialImplicationsofIndividualLabour
Supply’sConvexity............................................ 27
3.4 Spatialvs.SpacelessMonopsony..................................... 28
3.5 Firms’InteractionandConjecturalVariations ....................... 31
3.6 TheShort-RunEquilibrium........................................... 35
3.7 Short-RunComparativeStatics ....................................... 38
3.8 Conclusions............................................................ 46
4 Long-RunSpatialMonopsony .............................................. 49
4.1 TheZero-ProfitLocus................................................. 50
4.2 TheWage-SettingCurve .............................................. 52
4.3 TheLong-RunEquilibrium ........................................... 55
4.4 Long-RunComparativeStatics ....................................... 60
4.4.1 Changesin thePositionoftheZero-Profit
LocusandtheWage-SettingCurve........................... 61
4.4.2 ComparativeStatics in the Fixed Costs
andtheWorkerDensity....................................... 62
4.4.3 ComparativeStaticsintheMarginalRevenue
ProductofLabour............................................. 65
4.4.4 ComparativeStaticsintheTravelCost....................... 67
ix
x Contents
4.5 Long-Run Spatial Monopsony under Linear
IndividualLabourSupply............................................. 70
4.5.1 TheLöschianEquilibrium.................................... 75
4.5.2 TheGreenhut–OhtaEquilibrium ............................. 78
4.5.3 TheHotelling–SmithiesEquilibrium......................... 79
4.6 Long-Run Spatial Monopsony with Constant
IndividualLabourSupply............................................. 82
4.6.1 The Hotelling–Smithies and the
Greenhut–OhtaEquilibrium .................................. 83
4.6.2 AllowingforVaryingParticipation........................... 87
4.6.3 TheLöschianEquilibrium.................................... 90
4.7 Conclusions............................................................ 92
5 SpatialMonopsonyandtheGenderPayGap............................. 95
5.1 TheGenderPayGapandBeckerianvs.Robinsonian
Discrimination......................................................... 95
5.2 TheModel.............................................................. 98
5.2.1 TheBasicAssumptions....................................... 98
5.2.2 Firm-LevelLabour Supply and Firms’
Wage-SettingBehaviour ......................................100
5.2.3 TheEquilibriumandItsProperties...........................103
5.3 Conclusions............................................................108
6 SpatialMonopsony and RegionalDifferencesin the
GenderPayGap..............................................................113
6.1 TheoreticalConsiderations............................................114
6.2 EmpiricalSpecification................................................116
6.3 Data.....................................................................119
6.4 DescriptiveEvidence..................................................123
6.5 MultivariateEvidence.................................................125
6.6 Conclusions............................................................128
PartII DynamicMonopsony
7 SimpleDynamicMonopsony................................................133
8 AGeneralEquilibriumModelofDynamicMonopsony .................137
8.1 SomeIntroductoryRemarks ..........................................137
8.2 TheModel..............................................................139
8.2.1 TheBasicAssumptions.......................................139
8.2.2 Workers’ReservationWage ..................................141
8.2.3 Firms’Steady-StateLabourSupply..........................143
8.2.4 TheSteady-StateEquilibriumandItsProperties ............144
8.3 SomeConcludingRemarks ...........................................148
Contents xi
9 DynamicMonopsonyandtheGenderPayGap...........................151
9.1 ASimpleMeasureofOn-the-JobSearchFrictions..................153
9.2 A Semi-StructuralEstimation Approachto the
Firm-LevelLabourSupplyElasticity.................................155
9.2.1 CombiningSimple DynamicMonopsony
andtheBurdett–MortensenModel...........................155
9.2.2 IntroducingStochasticJob-to-JobTransitions...............157
9.2.3 Introducing Elastic Transitions
fromandtoNon-Employment................................158
9.2.4 Procedurefor Identifyingthe Long-Run
LabourSupplyElasticityattheLeveloftheFirm...........160
9.2.5 EmpiricalSpecification .......................................160
9.2.6 RelatedEmpiricalLiterature..................................163
9.3 Data.....................................................................164
9.4 GenderDifferencesinSearchFrictions ..............................168
9.5 EstimatesoftheGenderDifferencein Long-Run
Firm-LevelLabourSupplyElasticities...............................173
9.5.1 TransitiontoEmployment ....................................174
9.5.2 TransitiontoNon-Employment...............................181
9.5.3 HiringfromEmployment.....................................187
9.5.4 EstimatesoftheLong-RunFirm-LevelLabour
SupplyElasticities.............................................192
9.6 Conclusions............................................................199
10 ConcludingRemarks.........................................................201
A Appendix:SpatialMonopsony..............................................207
A.1 ProofofRemark3.2...................................................207
A.2 ProofofExample3.5..................................................208
A.3 ProofofProposition3.3...............................................210
A.4 ProofofProposition3.5...............................................217
A.5 TheSlopeoftheZero-ProfitLocusintheLöschian
Long-RunEquilibrium ................................................220
A.6 ProofofLemma4.1 ...................................................220
A.7 ProofofLemma4.3 ...................................................222
A.8 ComparativeStaticsunderLinearSpatialMonopsony ..............226
A.9 TheImplicitSolutionfortheLong-RunHotelling–
Smithies Equilibrium Wage in the Linear
Model...................................................................227
A.10 ProofofCorollary5.3.................................................228
A.11 AppendixtoChapter6 ................................................229
B Appendix:DynamicMonopsony............................................231
B.1 TheRelationbetweentheFirm’sShort-andLong-Run
LabourSupplyElasticity..............................................231
xii Contents
B.2 Workers’OptimalReservationWage.................................232
B.3 ProofofProposition8.1:Workers’ExpectedWage .................233
B.4 ProofofEquation(9.1)................................................233
B.5 ProofofEquation(9.12)...............................................235
B.6 ProofofEquation(9.17)...............................................236
B.7 AppendixtoChapter9 ................................................236
References...........................................................................245
Index.................................................................................257
