Lecture Notes in Economics and Mathematical Systems

Transcription

1

2 Lecture Notes in Economics and Mathematical Systems 639 Founding Editors: M. Beckmann H.P. Künzi Managing Editors: Prof. Dr. G. Fandel Fachbereich Wirtschaftswissenschaften Fernuniversität Hagen Feithstr. 140/AVZ II, Hagen, Germany Prof. Dr. W. Trockel Institut für Mathematische Wirtschaftsforschung (IMW) Universität Bielefeld Universitätsstr. 25, Bielefeld, Germany Editorial Board: H. Dawid, D. Dimitrow, A. Gerber, C-J. Haake, C. Hofmann, T. Pfeiffer, R. Slowi ński, W.H.M. Zijm For further volumes:

3

4 Boris Hirsch Monopsonistic Labour Markets and the Gender Pay Gap Theory and Empirical Evidence 123

5 Dr. Boris Hirsch Friedrich-Alexander-Universität Erlangen-Nürnberg Chair of Labour and Regional Economics Lange Gasse Nürnberg Germany ISSN ISBN e-isbn DOI / Springer Heidelberg Dordrecht London New York Library of Congress Control Number: Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permissions for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: SPi Publisher Services Printed on acid-free paper Springer is part of Springer Science+Business Media (

6 To my parents and grandparents

7

8 Acknowledgements I would like to thank all those people who have helped me in the course of my research that culminated in this Ph.D. thesis. First and foremost, I am deeply indebted to my academic supervisors. My special thanks go to my principal academic supervisor Claus Schnabel for his perpetual 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 substantially to this thesis completion. Apart from my supervisors, I am particularly grateful to my co-authors Marion König, Joachim Möller, Thorsten Schank, and Claus Schnabel. Large parts of Chapters 6 and 9 are grounded on joint work with them, and I benefited a lot from their comments and suggestions. Many thanks go to my colleagues at the Friedrich Alexander Universität Erlangen Nürnberg and to the Bavarian Graduate Program in Economics and its members. The program s excellent courses and seminars proved to be instrumental in writing this thesis. The program s generosity also allowed me to spend half a year at the Centre for Economic Performance at the London School of Economics and Political Science, which has been a great stimulation in the course of writing this thesis. I would like to thank for the centre s warm hospitality and in particular Alan Manning for many fruitful conversations and helpful suggestions. My very special thanks go to Jürgen Deinhard. He not only proof-read the whole thesis (including the technical appendices) and pointed me at several inaccuracies and obscurities in the exposition but also provided me with a lot of useful econometric comments and suggestions. Last but not least, I owe my deepest gratitude to my parents and grandparents, to whom I dedicate this work. vii

9

10 Contents 1 Introduction Wage Setting vs. Wage Taking Classic vs. New Monopsony Plan of the Book... 6 Part I Spatial Monopsony 2 Simple Static Monopsony Short-Run Spatial Monopsony The Basic Assumptions The Elasticity of the Firm s Aggregate Labour Supply Convexity and Elasticity of Individual Labour Supply Convexity Relative to an Exponential Spatial Implications of Individual Labour Supply s Convexity Spatial vs. Spaceless Monopsony Firms Interactionand ConjecturalVariations The Short-Run Equilibrium Short-RunComparativeStatics Conclusions Long-Run Spatial Monopsony The Zero-ProfitLocus The Wage-Setting Curve The Long-Run Equilibrium Long-Run Comparative Statics Changes in the Position of the Zero-Profit Locus and the Wage-Setting Curve Comparative Statics in the Fixed Costs and the Worker Density Comparative Statics in the Marginal Revenue Product of Labour ComparativeStatics in the Travel Cost ix

11 x Contents 4.5 Long-Run Spatial Monopsony under Linear Individual Labour Supply The Löschian Equilibrium The Greenhut Ohta Equilibrium The Hotelling Smithies Equilibrium Long-Run Spatial Monopsony with Constant Individual Labour Supply The Hotelling Smithies and the Greenhut Ohta Equilibrium Allowingfor VaryingParticipation The Löschian Equilibrium Conclusions Spatial Monopsony and the Gender Pay Gap The Gender Pay Gap and Beckerian vs. Robinsonian Discrimination The Model The Basic Assumptions Firm-Level Labour Supply and Firms Wage-Setting Behaviour The Equilibrium and Its Properties Conclusions Spatial Monopsony and Regional Differences in the Gender Pay Gap TheoreticalConsiderations EmpiricalSpecification Data DescriptiveEvidence MultivariateEvidence Conclusions Part II Dynamic Monopsony 7 Simple Dynamic Monopsony A General Equilibrium Model of Dynamic Monopsony Some Introductory Remarks The Model The Basic Assumptions Workers ReservationWage Firms Steady-State Labour Supply The Steady-State Equilibrium and Its Properties Some ConcludingRemarks...148

12 Contents xi 9 Dynamic Monopsony and the Gender Pay Gap A Simple Measureof On-the-JobSearch Frictions A Semi-Structural Estimation Approach to the Firm-Level Labour Supply Elasticity Combining Simple Dynamic Monopsony and the Burdett MortensenModel Introducing Stochastic Job-to-Job Transitions Introducing Elastic Transitions fromand to Non-Employment Procedure for Identifying the Long-Run Labour Supply Elasticity at the Level of the Firm EmpiricalSpecification Related EmpiricalLiterature Data GenderDifferencesin Search Frictions Estimates of the Gender Difference in Long-Run Firm-Level Labour Supply Elasticities Transition to Employment Transition to Non-Employment Hiringfrom Employment Estimates of the Long-Run Firm-Level Labour Supply Elasticities Conclusions Concluding Remarks A Appendix: Spatial Monopsony A.1 Proofof Remark A.2 Proofof Example A.3 Proof of Proposition A.4 Proof of Proposition A.5 The Slope of the Zero-Profit Locus in the Löschian Long-Run Equilibrium A.6 Proofof Lemma A.7 Proofof Lemma A.8 Comparative Statics under Linear Spatial Monopsony A.9 The Implicit Solution for the Long-Run Hotelling Smithies Equilibrium Wage in the Linear Model A.10 Proofof Corollary A.11 Appendixto Chapter B Appendix: Dynamic Monopsony B.1 The Relation between the Firm s Short- and Long-Run Labour Supply Elasticity...231

13 xii Contents B.2 Workers OptimalReservation Wage B.3 Proof of Proposition 8.1: Workers Expected Wage B.4 Proofof Equation(9.1) B.5 Proofof Equation(9.12) B.6 Proofof Equation(9.17) B.7 Appendixto Chapter References Index...257

14 List of Figures 2.1 Wage and employment chosen by a non-discriminating monopsonist Wage reactions of the firm s rival under Löschian, Hotelling Smithies, and Greenhut Ohta competition and the associated changesin the firm s marketradius Perceived labour supply curves for a labour market consisting of market areas of a given radius 0<X<X M under Löschian, Hotelling Smithies, and Greenhut Ohta competition The zero-profit locus in the.x; w/-plane The wage-setting curves and a family of zero-profit loci for different levels of fixed costs under strictly log-concave individual labour supply The existence and uniqueness of the long-run equilibrium under Greenhut Ohta competition The long-run equilibrium under strictly log-convex individual labour supply The long-run equilibrium under strictly log-concave individual labour supply The long-run equilibrium under log-linear individual labour supply The impact of an increase in the fixed costs or a decrease in the worker density on the long-run equilibrium wage and market radius under Greenhut Ohta competition The impact of an increase in the fixed costs or a decrease in the worker density on the long-run equilibrium wage and market radius under Hotelling Smithies competition if individual labour supply is strictly log-concave and competition is fierce The impact of an increase in the fixed costs or a decrease in the worker density on the long-run equilibrium wage and market radius under Löschian competition if individual labour supply is strictly log-concave xiii

15 xiv List of Figures 4.10 The impact of an increase in the fixed costs or a decrease in the worker density on the long-run equilibrium wage and market radius under Löschian competition if individual labour supply is log-linear The impact of an increase in the marginal revenue product of labour on the long-run equilibrium wage and market radius under Greenhut Ohta competition The impact of an increase in the marginal revenue product of labour on the long-run equilibrium wage and market radius under Löschian competition if individual labour supply is strictly log-concave The impact of an increase in the travel cost on the long-run equilibrium wage and market radius under Greenhut Ohta competition The impact of an increase in the travel cost on the long-run equilibrium wage and market radius under Hotelling Smithies competition if individual labour supply is strictly log-concave and competition is weak A family of zero-profit loci for different fixed costs f 1 <f 2 <f 3 <f max A family of zero-profit loci for different fixed costs f 1 <f 2 <f 3 <f max and the wage-setting curves under Löschian, Hotelling Smithies, and Greenhut Ohta competition The Löschian long-run equilibrium under linear individual labour supply for different levels of fixed costs f 1 <f 2 <f 3 <f max The Greenhut Ohta long-run equilibrium under linear individual labour supply for different levels of fixed costs f 1 <f 2 <f 3 <f max The Hotelling Smithies long-run equilibrium under linear individual labour supply for different levels of fixed costs f 1 <f 2 <f 3 <f max The Löschian, the Hotelling Smithies, and the Greenhut Ohta long-run equilibrium under constant individual labour supply The impact of an increase in the travel cost on the Hotelling Smithies long-run equilibrium under constant individual labour supply The impact of an increase in the worker density (or a decrease in the fixed costs) on the Hotelling Smithies long-run equilibrium under constant individual labour supply The impact of an increase in the marginal revenue product of labour on the Hotelling Smithies long-run equilibrium under constant individual labour supply... 87

16 List of Figures xv 6.1 The gender wage differentials 1 w and 0 w for segmented female and male labour markets with worker densities D 1 and D 0 with D 1 >D Hot spots and ruralareas Average wages and raw gender pay gaps at the NUTS 3 regional level by population density Average raw gender pay gaps in hot spots and rural areas Unexplained gender pay gaps in hot spots and rural areas using nearest neighbour matching without replacement Unexplained gender pay gaps in hot spots and rural areas using kernel matching Unexplained gender pay gaps in hot spots and rural areas using the Oaxaca Blinder decomposition Transitionsof men Transitionsof women A.1 Unexplained gender pay gaps in hot spots and rural areas using three-nearest neighbour matching with replacement A.2 Unexplained gender pay gaps using only individuals without change of regional type of first appearance in the labour market and nearest neighbour matching without replacement...230

17

18 List of Tables 3.1 Wage and market radius responses under Löschian, Hotelling Smithies, and Greenhut Ohta competition Comparative static effects on the short-run equilibrium wage The impact of changes in the market conditions on the position of the zero-profit locus and the wage-setting curve Comparative static effects on the long-run equilibrium wage Comparative static effects on the long-run equilibrium wage under linear individual labour supply Comparative static effects on the long-run equilibrium wage under constant individual labour supply Determinants of the probability of being hired from non-employment Determinantsof males instantaneousseparationrate to employment Determinants of females instantaneous separation rate to employment Determinants of males instantaneous separation rate to non-employment Determinants of females instantaneous separation rate to non-employment Determinants of males probability of being hired from employment Determinants of females probability of being hired from employment Estimates of the long-run firm-level elasticity of female and male labour supplies when tenure is not controlled for Estimates of the long-run firm-level elasticity of female and male labour supplies when tenure is controlled for B.1 Descriptivestatistics forthe whole sample B.2 Descriptivestatistics forthe recruitmentsample B.3 Wage regressions B.4 Estimates of the long-run firm-level elasticity of female and male labour supplies when tenure is not controlled for and downsizingestablishments are excluded xvii

19

20 List of Abbreviations BBR c.d.f. GO HS IAB IAB-REG LIAB Lö NUTS WSC ZPL Federal Office for Building and Regional Planning (Bundesamt für Bauwesen und Raumordnung) cumulative distribution function Greenhut Ohta Hotelling Smithies Institute for Employment Research (Institut für Arbeitsmarkt- und Berufsforschung) of the Federal Employment Agency (Bundesagentur für Arbeit) Regional File of the IAB Employment Samples (IABS) Linked Employer Employee Data Set of the Institute for Employment Research (Institut für Arbeitsmarkt- und Berufsforschung) Löschian nomenclature des unités territoriales statistiques wage-setting curve zero-profit locus xix