Three Essays on Labor Market Inequality and Policy Implications in Search Models

Poliy Impliations in Searh Models

Dissertation

zur Erlangung des Grades

Doktor der Wirtshaftswissenshaften (Dr.rer.pol.)

amFahbereihWirtshaftswissenshaften

der UniversitätKonstanz

vorgelegt von:

Jun Lu

Shwaketenstraÿe 100

78467 Konstanz

Tagder mündlihen Prüfung: 01 März 2011

1. Referent: Prof. Dr. LeoKaas

2. Referent: Prof. Dr. Carlos Alós-Ferrer

The dissertation was written during the time from September 2006 to Deember

2010, while I partiipated in the Dotoral Programme in Quantitative Eonomis

and Finane atthe University of Konstanz. Here, I would like toexpress my grat-

itude toallthose who helped me duringthe writingof this dissertation.

Mydeepest gratitude goesrst andforemostto mysupervisor, Mr. Prof. Dr. Kaas

for his onstant enouragement and guidane. He has taught me the knowledge of

searh theory and motivated me for the topi of labormarket inequality. Without

his illuminatinginstrution, insightful ritiism and expert guidane, this disserta-

tion ould not have reahed its present form.

Moreover, I wouldliketo extendmy sineregratitude toMr. Prof. Dr. Alós-Ferrer

and Mr. Prof. Dr. Koebel (University of Straÿbourg), who have put onsiderable

time and eort into their ommentson the draftof my dissertation.

High tribute shall be paid to my olleagues, Christian Manger, Tim Eggebreht,

AnnaZaharieva,TillGroÿmaÿ,Karsten WasilukandPetra Marotzke, fortheiruse-

ful suggestions during the internal seminar and produtive onversations. Speial

thanks toChristian Mangerfor his support duringdiult times.

Finally,Iamindebtedtomygrandparents,myparents,andmywife,fortheirloving

onsiderationsand great ondene inme allthrough these years.

Summary 1

Zusammenfassung 4

1 EqualTreatment Poliy in a Random Searh Model with Taste

Disrimination 8

1.1 Introdution . . . 9

1.2 The Model . . . 14

1.3 Laissezfaire equilibrium . . . 16

1.4 Equal pay with strit armative ation . . . 18

1.5 Equal pay without armativeation . . . 20

1.6 Mean wages and the wage gap . . . 24

1.7 Conlusion . . . 29

Appendix . . . 30

Referenes of Chapter 1 . . . 38

2 Do Equal-Treatment Poliies Redue Labor Market Inequality? - Poliy Impliations in a Direted Searh Model 41 2.1 Introdution . . . 42

2.2 The Model . . . 45

2.3 Laissezfaire equilibrium . . . 47

2.4 Equilibria under equal-treatment poliyregimes . . . 51

2.4.1 Equilibriumunder equal pay with strit armative ation . . 52

2.4.2 Equilibriumunder equal pay withoutarmativeation . . . . 54

2.5 Free-entry equilibrium . . . 63

2.6 Numerial examples. . . 63

2.6.1 Numerialresults for moderateemployers' disriminatory taste 64

2.6.2 Numerialresults for mildemployers' disriminatory taste . . 66

2.6.3 Numerialresults for strongemployers' disriminatorytaste . 68 2.7 Conlusion . . . 70

Appendix . . . 70

Referenes of Chapter 2 . . . 87

3 Natives' Soial Prejudie and Wage Disparities in a Monoentri City 90 3.1 Introdution . . . 91

3.2 The Model . . . 94

3.2.1 Urban land use market . . . 96

3.2.2 Labormarket . . . 98

3.3 Equilibrium analysis . . . 100

3.4 Numerial example and poliyimpliations . . . 108

3.4.1 Steady-state equilibrium . . . 108

3.4.2 Poliy impliations . . . 112

3.5 Conlusion . . . 116

Appendix . . . 117

Referenes of Chapter 3 . . . 124

Complete Referenes 127

2.1 Numerial example for

k = 0.5

^,

θ = 0.5

^,

p = 1

^,

σ = 0.2

^{, with free}

entry

c = 0.2

^{. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64}

2.2 Numerial example for

k = 0.65

^,

θ = 1

^,

p = 1

^,

σ = 0.2

^{, with free}

entry

c = 0.2

^{. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65}

2.3 Numerial example for

k = 0.9

^,

θ = 0.5

^,

p = 1

^,

σ = 0.2

^{, with free}

entry

c = 0.2

^{. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67}

2.4 Numerial example for

k = 0.99

^,

θ = 1

^,

p = 1

^,

σ = 0.2

^{, with free}

entry

c = 0.2

^{. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67}

2.5 Numerial example for

k = 0.1

^,

θ = 0.5

^,

p = 1

^,

σ = 0.2

^{, with free}

entry

c = 0.2

^{. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69}

2.6 Numerialexamplefor

k = 0.1

^,

θ = 1

^,

p = 1

^,

σ = 0.2

^{,with freeentry}

c = 0.2

^{. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69}

2.7 Numerialexperimentstoexplore thefeasible rangeof

k

^fordierent

parameter ombinationsof

θ

^and

σ

^{. . . . . . . . . . . . . . . . . . . 81}

3.1 Parameters . . . 109

3.2 Steady-state equilibrium . . . 110

1.1 The equilibrium wageoer density for parameters

p = 1

^,

d = .1

^,

λ = σ = .5

^,

m = 1

^{. About 89.5% of disutility rms oer wages}

w ∈ [0, .897]

^{and 10.5% of them oer wages}

w ∈ [.95, .953]

^{, rejeting}

B workers. . . 23

1.2 Mean and standard deviation of wages for A workers (blue) and B

workers (red) under laissez faire (solid) and equal pay (dashed) as

λ

and

σ

^{are varied (allother parametersas inFigure 1.1). . . . . . . . 26}

1.3 (a) Redution ofthe wagegap underthe poliy(negativeif wagegap

inreases,withred

< 0

^,blue

0−0.05

^,purple

0.05−0.1

^{). (b)Redution}

of mean earnings of B workers (yellow

0 − 0.05

^{, blue}

0.05 − 0.1

^{, red}

> 0.1

^{). All other parametersare asin Figure 1.1. . . . . . . . . . . . 28}

1.4 Mean earnings for A workers (blue) and B workers (red) under lais-

sez faire (solid) and equal pay (dashed) as

m

^{is inreased (all other}

parameters as inFigure 1.1). . . 29

3.1 Urban ongurationinthe andidate urbanland use equilibrium . . . 101

3.2 Bid renturvesfordierentworkergroups,withgreenforBU,yellow

for BE, purple for AE and blue for AU workers. . . 102

3.3 Equilibrium rent paid by urban residentsto absentee landlords . . . . 107

3.4 The impatof immigrationon(a) utility ofeahworker, (b)prot of

eah rm, () total rent of absentee landlords, (d) soialwelfare. . . . 111

3.5 The impat of inome tax

τ w

^on(a)

γ ^∗

^{and on(b)}

e ˆ

^{. . . . . . . . . . 112}

3.6 The impatofinometax

τ w

^{on(a) wages, (b)utilityof eahworker,}

() prot of eah rm, (d) total rent of absentee landlords. . . 113

3.7 The impat of unemployment benet

b

^on(a)

γ ^∗

^{and on(b)}

e ˆ

^{. . . . . 114}

3.8 The impat of unemployment benet

b

^on(a) reservation wage of A workers, (b) reservation wage of B workers, () unemployment rates

and (d) workers' utilities.. . . 115

3.9 The impatof unemploymentbenet

b

^{on(a) prot of eah rm and}

on (b) total rent of absentee landlords. . . 116

The dissertation was written during the time from September 2006 to Deember

2010, while I partiipated in the Dotoral Programme in Quantitative Eonomis

and Finane at the University of Konstanz. It onsists of three essays, studying

labor market inequality and labor market poliy impliations. In the labor mar-

ket minority workers, whose demographiharateristisdeviate fromthe preferred

group(usually the historiallysoio-politiallydominantgroup, e.g. majorityraes

and men), are oftenreported to have lower earnings and lower employment oppor-

tunities. The main purpose of this dissertation is thus toinvestigate how the wage

disparitiesand unemploymentdierentialsbetween dierent demographigroupsof

workers are generated through searh models. The three haptersof this thesis an

bebroadlyseparatedintotwo ategories. Chapter 1and2onentrateonanalyzing

labormarketdisriminationduetoemployers' disriminatorybehavior. Inaddition,

the eetiveness of equaltreatment poliies in ombating disrimination beomes

the fous of my analysis. Chapter 3 inorporates a ompetitive land use market

intoafritionallabormarketand examinesthe eet of natives' soialprejudieon

labormarket inequality. This setionsummarizes the main results.

Chapter 1 is the result of joint work with Mr. Prof. Dr. Leo Kaas (University of

Konstanz). The paper has been published under the title Equal-treatment Poliy

inaRandomSearhModelwith Taste DisriminationinLabor Eonomis,Vol.17,

2010, p. 699-709. We onsider a searh model of the labormarket with two types

of equally produtive workers, A and B and two types of rms, disriminatorsand

non-disriminators. The disriminators suer utility loss when employing type B

workers. Without poliy intervention, rms are free to set wage oers onditional

on worker type. In equilibrium, there is wage dispersion between and within the

two worker groups. Both disriminators and non-disriminators oer lower wages

to type B workers. However, the wage dispersion is negligible when the taste for

disriminationis small. Then, weanalyze the eet of an equal pay poliy,both in

ombinationwith armativeation and without. Ifboth equal pay and armative

ation polies an be enfored, the wage gap between A and B workers will be

ompletely eliminated. The within-group wage dispersion still exists. But it is

negligibleas long as the taste for disriminationis very small. However, suh kind

ofidealsituationmightnotexistinreality. Whenequalopportunityofhiringannot

be enfored, the equal pay poliyauses disriminatory praties of hiring of some

oralldisriminators. Overallwage dispersionisstronglyamplied, even if thetaste

for disriminationis very small. The wages for B workers fallsubstantially relative

to laissez faire. Sometimes also the wage gap between worker groups widens in

response tothe poliy.

Chapter 2 results from the working paper titled Do EqualTreatment Poliies Re-

due Labor Market Inequality? - Poliy Impliationsin a Direted Searh Model,

whereanalogous toChapter 1, the eetiveness ofequal pay poliiesand equal em-

ploymentopportunitypoliiesisanalyzed. Nevertheless,Ionsider adiretedsearh

model whih is dierent from the randomsearh models inthe sense that the pro-

ess of wage formationand mathing are endogenous. Thereexistalsotwotypesof

equallyprodutive workers, A andB inthelabormarket. Butallrmsare disrim-

inators and only have disutility when employing type B workers. Without poliy

regulation,employers'tastesresultindisriminationexpressedinexpetedwagedif-

ferentialsin amarket equilibrium. Governments an respond with equal-treatment

poliy regimes. The poliies ombining equal pay and equal employment opportu-

nitylawsahieveboth eieny and equality. Equalpay withoutarmativeation

an improvesoial equality without ineieny only under speied market ondi-

tions. Inpartiular,if governmentsimplementequalpay withoutarmativeation,

dierentequilibriumsenariosmayemerge(dependingonthestrengthofemployers'

disriminatory taste). When employers have appropriate moderate disriminatory

taste,equalpaypoliiesaloneanimprovesoialequalitywithoutineieny. How-

ever, if employers have extremely strong or small disriminatory taste, both soial

eieny and equality willbeharmed by equal pay poliies.

Chapter3inthedissertationisareprintoftheworkingpaperNatives'SoialPreju-

dieandWageDisparitiesinaMonoentriCity. Ionsideranurban-searhmodel,

withalsotwo typesofequallyprodutiveworkers, A andB.Inthe modelrmshave

no disriminatory taste. However, A workers suer utility loss for living loser to

B workers. The model inorporates aompetitive land use marketinto a fritional

labor market. In the land use market, all workers ompetitively bid rent for land

use. Inthe labormarketrms post wagesand workers searhforjobsrandomly. To

linkthe twoseemingly independent markets with eah other,I assume that the job

arrivalratesofworkers dereasewiththedistanebetweentheirresidentialloations

and jobs. It shows that ahigh enoughlevelof A workers' soialprejudietoward B

workers generateslargediereneintheirlabormarketoutomes. AssumingthatA

workers haveanaversion tolivinginproximityto Bworkers, Aworkers would oer

more rent for land use inthe areas where their own people predominantly live. So-

ialprejudieof onetypeof workers resultsinseparated residentialareasof thetwo

types. B workers end up with wage dispersion within group and with lower mean

wage. However, they experiene ashorter durationof unemployment spellsthan A

workers inthe steady-state market equilibrium. By meansof anumerial example,

the hapter also provides an overview about the marginal eets of two politial

instruments, proportionalinome tax and unemployment benet, onthe welfareof

dierent people in the eonomy. It shows that an implementation of proportional

inome tax benets rms to the detriment of other agents, whereas an inrease of

unemploymentbenetis onlyfavorablefor workers.

Die Dissertation wurde von September 2006 bis Dezember 2010 verfasst, während

ih an dem Dotoral Programme in Quantitative Eonomis and Finane an der

Universität Konstanz teilgenommen habe. Die Dissertation besteht aus drei Kapi-

teln, die die Arbeitsmarktungleihheit und die Auswirkungen der politishen Maÿ-

nahmen imArbeitsmarktuntersuhen. ImArbeitsmarktist eshäug der Fall,dass

dieMinderheiten,derendemographisheMerkmalevonderbevorzugtenGruppe(in

der Regel die historish sozial-politish dominante Gruppe, zum Beispiel die vor-

herrshenden Rassen und Männer) abweiht, niedrigere Einkommen und geringere

Beshäftigungshanen haben. Das Hauptziel dieser Dissertation ist es daher an-

hand eines Arbeitsmarkt-Suhmodells zu untersuhen, wie die Einkommens- und

Arbeitslosigkeitsuntershiede zwishen vershiedenen demograshen Gruppen von

Arbeitnehmern entstehen. Die drei Kapiteldieser Dissertation können grob in zwei

Kategorien aufgeteilt werden. Kapitel 1 und 2 konzentrieren sih auf die Analyse

derArbeitsmarktdiskriminierungaufgrundvondiskriminierendenVerhaltender Ar-

beitergeber. Darüber hinaus gehört die Wirksamkeit der Gleihstellungspolitik,die

zur Bekämpfung von Diskriminierung eingesetzt wird, auh zu dem Shwerpunkt

meiner Analyse. Im Kapitel 3 wird der Arbeitsmarkt mit einer Friktion in einem

kompetitiven Immobilienmarkt integriert. Die Wirkungen von sozialen Vorurteilen

der einheimishen Arbeitskräfte gegen Immigranten auf die Arbeitsmarktungleih-

heit werden untersuht. Dieses Kapitelfasst die wihtigsten Ergebnisse zusammen.

Kapitel1 istdas Ergebniseiner gemeinsamenArbeitmitHerrn Prof.Dr. LeoKaas

(Universität Konstanz). Das Papier wurde unter dem Titel Equal-treatment Po-

liy in a Random Searh Model with Taste Disrimination in Labor Eonomis,

Vol.17, 2010, S.699-709 veröentliht. Wir betrahten ein Suhmodell im Arbeits-

marktmitzweiTypen gleihermaÿenproduktiverArbeiter,AundBundzweiArten

vonUnternehmen,diskriminierendeund nihtdiskriminierende. DieDiskriminieren-

denerleideneinenWohlfahrtsverlustbeiderEinstellung vonB-Arbeitnehmern.Oh-

ne politishenEingri,sind dieUnternehmenfrei,Lohnangebotegemäÿdem Typus

derArbeitnehmerzu setzen. ImGleihgewihtbestehtLohndispersionzwishenden

beiden Gruppen und innerhalb der jeweiligen Gruppe der Arbeitnehmer. Diskri-

minierende und nihtdiskrimierende Unternehmen bieten niedrigere Löhne für B-

Arbeitnehmer.Dohdie Lohndispersionistvernahlässigbar, wenn das Ausmaÿdes

Wohlfahrtverlustes bei Einstellung von B-Arbeitnehmern nur gering ist. Weiterhin

analysieren wir die Wirkung einer Gleiher-Lohn-Politik in Kombination mit und

ohne Armative-Ation-Politik. Wenn die Gleiher-Lohn-Politik und Armative-

Ation-Politik gleihzeitig durhgesetzt werden können, wird das Lohngefälle zwi-

shenA-undB-Arbeitnehmernvollständigeliminiert.DieLohndispersioninnerhalb

der Gruppe existiert noh.Sie istjedohvernahlässigbar, solange das Ausmaÿ des

WohlfahrtverlustesbeiEinstellung vonB-Arbeitnehmernnurgeringist.Eine solhe

Art idealer Situation ist in der Realität mögliherweise niht ereihbar. Falls glei-

he Beshäftigungshanen nihtgarantiertwerden können,verursahtdie Gleiher-

Lohn-Politik diskriminierendes Verhalten von einigen oder allen diskriminierenden

Unternehmen bei der Einstellung von Arbeitnehmen. Insgesamt wird die Lohndi-

spersion stark vergröÿert, auh wenn der Wohlfahrtverluste bei Einstellung von

B-Arbeitnehmern nur gering ist. Die Löhne für B-Arbeitnehmer fallen wesentlih

imVergleih zum Laissez-faire-Fall.Manhmal wird auh das Lohngefälle zwishen

beiden Gruppen der Arbeitnehmer alsFolge der Politik vergröÿert.

Kapitel 2 ergibt sih aus dem Arbeitspapier mit dem Titel Do EqualTreatment

PoliiesRedueLaborMarketInequality?-PoliyImpliationsinaDiretedSearh

Model, indenen analog zum Kapitel1, die Wirksamkeitder Gleiher-Lohn-Politik

und die Verpihtung zur gleihberehtigtenEinstellung analysiertwird. Allerdings

betrahte ih hier ein Modell mit zielgerihteter Suhe, bei der im Gegensatz zur

nihtzielgerihteten Suhe die Lohnsetzung und das Aufeinandertreen vonArbeit-

gebern und Arbeitnehmern endogen sind. Auh hier existieren zwei Typen von

gleihmaÿen produktiven Arbeitnehmern, A und B, auf dem Arbeitsmarkt. Nun

aber sind alle Firmen diskriminierend und erleiden einen Wohlfahrtsverlust beim

Einsatz der B-Arbeitnehmer. Ohne Politikeingri führt dieser Umstand zu Diskri-

minierung, welhe sih in Untershieden imErwartungslohn in einem Marktgleih-

gewiht auszeihnet.Regierungenkönnenmiteiner Gleihstellungspolitikreagieren.

Solh eine Politik, die gleihe Bezahlung und gleihe Einstellungshanen garan-

tiert, erreiht Ezienz und Gleihheit. Nurwenn spezishe Marktbedingungen er-

fülltsind,kanndie Gleiher-Lohn-PolitikohneArmative-Ation-Politikdiesoziale

Ungleihheit verbessern ohne die Ezienz zu beeinträhtigen. Insbesondere dann,

wenn RegierungenGleiher-Lohn-Politikohne Armative-Ation-Politikeinsetzen,

könnenvershiedene Gleihgewihtszenarienentstehen (abhängigvonderStärkeder

Vorurteilstendenz der Arbeitgeber). Fallsdie Arbeitgeber diskriminierendauf mitt-

leremNiveausind,kannGleiher-Lohn-Politikalleindie sozialeUngleihheitverbes-

sernohneEzienzverlustezu verursahen.WennArbeitgeberdagegen extremstark

oder shwah diskriminierendsind, werden sowohl Ezienzverluste alsauh soziale

Ungleihheit durhdie Gleiher-Lohn-Politikvergröÿert.

Kapitel3derDissertationisteinNahdruk desArbeitspapiersNatives'SoialPre-

judieandWageDisparitiesinaMonoentri City.IhbetrahteeinArbeitsmarkt-

Suhmodell mitzwei Arten von gleihermaÿen produktiven Arbeitnehmern, A und

B. Bei diesem Modell gibt es keine Diskriminierung seitens der Arbeitgeber, al-

lerdings erleiden Arbeitnehmer des Typs A einen Wohlfahrtsverlust durh enges

Nebeneinanderwohnen mitB-Arbeitnehmern.Das Modellkombiniert einenkompe-

titiven urbanen Immobilienmarktmiteinem ArbeitsmarktmitFriktionen.Aufdem

ImmobilienmarktbietenalleArbeitnehmerWettbewerbspreisefürdieLandnutzung.

Auf dem Arbeitsmarkt shreiben die Firmen Jobangebote mit festen Löhnen aus,

wobei die Arbeitnehmer Arbeitsstellen nah dem Zufallsprinzip suhen. Um eine

Verbindung zwishen dem Immobilienmarkt und dem Arbeitsmarkt herzustellen,

tree ih die Annahme, dass die Chanen der Arbeitnehmer einen Job zu nden,

negativ mit dem Abstand zwishen ihren Wohnorten und den Arbeitsplätzen im

Zentrum korrelieren. Es stellt sih heraus, dass ein gewisses Grad an Diskriminie-

rung von A-Arbeitnehmern gegenüber B-Arbeitnehmern groÿe Untershiede beim

jeweiligen Erfolgauf demArbeitmarktzur Folge haben. Aufgrund ihrer Abneigung

gegenüberdenB-Arbeitnehmern,bevorzugenA-Arbeitnehmeresweiterentferntvon

B-Arbeitnehmern zu leben. Deshalb sind A-Arbeitnehmer bereit eine höhereMiete

fürdieLandnutzungineinerGegend,inderüberwiegendA-Arbeitnehmerleben,an-

zubieten. Durh die Diskrimierung seitens eines Typs der Arbeitnehmer ergibt sih

eine vollständige Trennung der Wohngebiete der beiden Arbeitnehmer-Typen. B-

Arbeitnehmerweiseneine LohndispersioninnerhalbihrerGruppesowie einengerin-

gerenDurhshnittslohnalsA-Arbeitnehmerauf.AllerdingsistdieerwarteteDauer

der Arbeitslosigkeit im Steady-state-Marktgleihgewiht für sie kürzer, als für A-

Arbeitnehmer. Mithilfe eines numerishen Beispiels, gibt das Kapitel zudem einen

ÜberbliküberdiemarginalenAuswirkungeneinerproportionalenEinkommenssteu-

erundArbeitslosigkeitsentshädigungaufdieWohlfahrtder vershiedenenAgenten.

Es zeigt sih, dass der Einsatz einer proportionalen Einkommensteuer auf Kosten

der Arbeitnehmer und Vermieter den Unternehmen zu Gute kommt; während von

einer Erhöhung des Arbeitslosengeldesnur die Arbeitnehmer protieren.

with Taste Disrimination

1.1 Introdution

Thereare persistentwage gaps between demographigroupsthat annotberelated

toobservableprodutivitydierenes. Manyresearhersandpoliymakersattribute

suhgapstodisriminatorybehaviorofemployers. Itisthereforenotsurprisingthat

severalountrieshaveimplementedlegislationtoombatdisriminationinthelabor

market. In priniple two types of equaltreatment poliies an be distinguished.

Thereare equal pay laws, demanding equal remuneration for equal work,and there

are equal employment opportunity laws, overing hiring and promotion praties.

But even in the United States, where suh legislation has been introdued more

than forty years ago, onsiderable earning gaps between raes and genders remain,

and the evidene onthe impat of equaltreatment poliyon inequality is mixed.

1

This hapteranalyzes the eetiveness of equaltreatment poliyin asearhmodel

where a wage dierential between two groups of equally produtive workers arises

due to a disriminatory taste of a fration of employers. Prejudie on the side of

employers (or oworkers/ustomers) is one of the two prominent theoretial ex-

planations for labor market disrimination whih goes bak to Beker (1957).

2

It

is a well known result that tastebased disrimination an only our temporar-

ily but not permanently if all goods and fator markets are perfetly ompetitive

(see e.g. Cain (1986)). In light of suh ndings, one may be tempted to onlude

that there is no need for poliy ombating disrimination; to the ontrary, market

deregulationalonewillbeenoughtothrowdisriminatingemployersoutofbusiness.

Yet, todaythereisbroadagreementbetweenlaboreonomiststhattheompetitive,

fritionlessmodelisinadequatetodealwithmanylabormarketphenomena,suhas

unemploymentandwagedispersion. Searhandmathingmodelsarethemostom-

mon alternative (see Rogerson, Shimer, and Wright (2005) for a reent overview),

1

Exploiting statelevel variation in antidisrimination statutes, Neumark and Stok (2001)

showthatthereisnoevideneofapositiveeetofequaltreatmentlegislationonrelativeearnings

ofblakmales,althoughthereseemstobeamodestpositiveeetontheearningsofblakfemales

relativetowhitemales.

2

Theotherisstatistialdisrimination(Phelps(1972)andArrow(1973))whihisnotonsidered

here.

and these models have also been used to address disrimination; see the literature

overview below. However, although wage gaps between equally produtive workers

anpersistinfritionallabormarkets,poliyonlusionsarefarfromobvious. Con-

ventional wisdom suggests the usual tradeo between equality and eieny, so

thatitisup tothe politialpreferenesofsoiety todeidetheappropriatestrength

of antidisrimination enforement. We argue in this hapter that this intuition

angowrong: inmany irumstanesequalpaypoliyan both harmequalityand

eieny. Related literature on adverse poliy eets of equaltreatment poliy is

disussed below.

Weonsider aBurdettandJudd (1983)modelofthe labormarket, withtwogroups

of workers (A and B) and two types of rms, some with a disriminatory taste

against type B workers. Without poliy intervention, the equilibrium exhibits a

positive wage gap between the two worker groups and there is also withingroup

wagedispersion. Byassumingthateahworkersendsseveralappliations,weensure

that inequality is negligible if the disutility taste is small. In fat, our model gives

risetotheperfetlyompetitive(Bertrand)outomeintheabseneofdisriminatory

behavior, but to nonompetitive outomes otherwise. We then disuss two types

of equaltreatment legislation. On the one hand, there is an equalpay law (EPL)

whihrequiresthatanyrmpaysthesamewagetoitsworkers(whoareallemployed

in the same oupation). We assume throughout that this poliy an be enfored

perfetly. Ontheotherhand,thereisanequalemploymentopportunitylaw(EEOL)

whihrequiresthatanyrm'sworkforemustrepresentthepopulationsharesofthe

twoworkergroupssuiently.

3

Hereweontrasttwooppositesenarios. Intherst,

EEOLanbeperfetlyenfored. Unsurprisingly,insuhsituationstheombination

of the two poliy measures redues the wage gap to zero, although some within

group wage dispersion stillremains.

TheothersenarioistheompleteabseneofEEOL,or,equivalently,theimpossibil-

itytoenforesuhlegislation. Certainly,inpratiethereare enforementproblems

3

In the U.S., EPL is embodied in the Equal Pay At of 1963, and EEOL is formulated in

title VII of the Civil Rights At of 1964, and enfored by the Equal Employment Opportunity

Commission(EEOC),establishedin1965.

for both equalpay and equalemploymentlaws. The poliyregime where EPLop-

erates eetively and EEOL does not is learly an abstration; it reets the view

that equalityof employment opportunitiesis perhaps morediultto enfore than

equality of pay within the same rm. Indeed, nonompliant behavior is hard to

monitorand punish; private rms an easily deidenot toinviteunfavored job ap-

pliantsforaninterviewwithoutbeinghargedwithviolationofEEOL.Armative

ationand employmentquotas are, ifat all,appliedtoa smallsegment ofthe labor

marketonly,suh aspubliemployers orgovernment ontrators.

4

Thereisalsodi-

retevideneofhiringdisriminationfromeldexperiments,whihfurthersupports

the viewthat enforement of equal employmentopportunity is far fromperfet.

5

The main result of this hapter is that the ombination of EPL without perfet

enforementofEEOLinreasesinequalitydramatially;relativetolaissezfaire,wage

dispersionunambiguouslyinreases and mean wages for minority workers generally

fall. Beausealsowages formajorityworkers are lower, theeet onthe meanwage

gapbetweenthetwoworkergroupsisambiguous. Nevertheless, wealsodemonstrate

that the wage gap an even inrease inreation toequal pay poliy, partiularlyin

labor markets where the number of minority workers is low and the number of

disriminating employers is large. The intuition for the adverse poliy impat on

inequality is as follows. Some disriminating employers who are not allowed to

disriminateinpay deidetodisriminateinhiring. Heneminorityworkers reeive

fewerjoboers, sothattheirlaborsupplybeomeslesselastithanthelaborsupply

ofmajorityworkers. Inturn, therms'wage ompetitionbeomeslessere,wage

oer distributions shift to the left, with a support that is muh larger than under

laissez faire. We also nd that not all disriminating rms disriminate in hiring:

4

IntheU.S.,allrmswithmorethan100employeesarerequiredtosubmitemploymentreports

totheEEOCwhoisauthorizedtoinitiatelawsuitsonthebasisofunderrepresentationofminorities.

However,suhlawsuitsarerare(HolzerandNeumark(2000)),andrmswhowanttodisriminate

against some group (e.g. blak males) an easily irumvent the EEOC requirements by hiring

moremembersofanotherprotetedgroup(e.g.whitefemales). Forevideneonthislastissue,see

BispingandFain(2000).

5

FortheU.S.,seee.g.theauditstudyofNeumarketal.(1996)andtheorrespondenetestof

BertrandandMullainnathan(2004). SeealsothesurveyofRiahandRih(2002).

thereare highwagerms whorejet minorityappliantsbut atthesame timelow

wage rms who hire them despite their distaste.

There are other ontributions exploring disrimination in searh models. In the

model of Blak (1995), minority workers reeive lower wages beause it is assumed

that these workers do not reeive job oers from disriminatingemployers. In on-

trast, in our model employment disrimination does not our under laissez faire;

it is the endogenous equilibrium response to the equalpay poliy, and there are

also disriminating rms who make wage oers to minority workers, albeit at low

wages. Closely related to our model is Bowlus and Ekstein (2002) who onsider

taste disrimination in a Burdett and Mortensen (1998) model of the labor mar-

ket, both with and without equalpay legislation. They also show that this poliy

doesnot eliminatewage gaps,but againthey assume thatminorityworkers are dis-

riminated in hiring, uniformlyaross all disutility rms. Our model, in ontrast,

derives hiring strategies endogenously and they are not uniform aross rms. In

ontrast to these wageposting models, Rosen (2003) onsiders a model with wage

bargainingand nds that disriminatingrms an ahieve higherprots than non

disriminatingrms, thus arguing that disriminatingemployers are more likely to

surviveinthelongrun. Inourmodel,asintheothersdisussedabove,thisisnotthe

ase: disriminatingemployersearnlowerprotsthannondisriminatingemployers.

Nevertheless, we show that disriminators' prots an inrease in response to the

poliy. Finally, Lang, Manove, and Dikens (2005) onsider a model where searh

is direted rather than random. Assuming that rms annot disriminatein pay, a

nonnegligiblewage gap ariseseven whenthe disutilitytaste isarbitrarilysmall. In

their model, all rms have disriminatory preferenes, ranking majority appliants

before minority appliants. Minority workers do not apply to rms posting high

wages where hiring hanes are very low sine only these jobs attrat majority ap-

pliants. In equilibrium, thus, omplete market segregation arises. However, rms

rarelypostwages publilyinthe realworld, andalthough segregationisaprevalent

phenomenon, it isfar fromperfet.

6

6

Shi(2006)alsodisusses betweengroupwageinequalityin adireted searh framework. He

arguesthat atual wagedierentialsamong similar workersmay notbe avalid indiator of dis-

Of ourse, this hapter is not the rst showing that equaltreatment poliies an

hurt the disriminatedgroup. Welh(1976)demonstratesthatarmativeationin

ombination with an equalpay poliy entails an alloative eieny loss. In our

model, in ontrast, poliies donot distort alloative eieny sine all workers are

equally produtive and there is only one type of job. More importantly, it is the

absene of armative ation that hurts minority workers who do not nd employ-

ment at highwage rms speialized in hiring majority workers. Coate and Loury

(1993)arguethatarmativeationpoliiesneednotpromoteequalitybeauseofa

patronizationproblem: protetedworkers antiipatethattheiremploymenthanes

are good even if they do not invest in produtive skills. In our model, workers

do not invest in skills; instead, the adverse impat of equalpay poliy is driven

by the harmed employment perspetivesof disriminatedworkers whih ultimately

weakens wage ompetition by rms.

7

A similar mehanism is also at work in the

model of Kaas (2009) who analyzes the impat of anequalpay poliy in a spatial

labormarketmodelofmonopsonistiompetition. Inhismodel,however, thepoliy

always redues the wage gap and it tends to eliminatethe withingroup wage dis-

persion for minority workers. Finally, Bowlus and Ekstein (2002) demonstrate in

aBurdettMortensen searh model with taste disriminationhowequalpay poliy

hurtsminorityworkerswhenrmspratiehiringdisrimination. Theruialdier-

ene is that they assume that rms disriminate inhiring, whereas hiring praties

are equilibrium responses of disutility rms inour model.

The remainder of the hapter is organized as follows. The next setion introdues

the model. Setion 1.3 derives equilibrium without poliy regulation, and Setion

1.4disusses the senariowhereequal paypoliyisombinedwithstrit armative

ation. Setion 1.5 onsiders the eet of an equalpay poliy when equal opportu-

nity of employment annot be enfored. Setion 1.6 analyzes the poliy impat on

meanwages and onthe wage gap in numerialexamples. Setion1.7 onludes.

rimination. Whatreallymattersareexpetedwageswhihinludejobndinghanes.

7

Ofourse,byabstratingfrominvestmentinhumanapital,ourmodelalsodismissespotential

eienygains fromequalpaypoliies,suhastheonesdisussedbyLundbergandStartz(1983).

1.2 The Model

We onsider a Burdett and Judd (1983) model of the labormarket, with heteroge-

nous workers and with a disriminatory taste disturbing the preferenes of some

employers. There is a ontinuum

[0, 1]

^{of workers divided into two types; fration}

(1 − σ)

^{are type A and fration}

σ

^{are type B workers. Bothworker types are non}

negligible, i.e.

σ ∈ (0, 1)

^{. When employed, all workers have the same} produtivity

p > 0

^{and the} reservation wage is ommontoall workers and normalizedto zero.

There isa large number

N

^{of rms, eah of whih an hire anarbitrary numberof}

workers to produe output

p

^{per worker. Fration}

λ

^{of rms are disutility rms}

who derive linear disutility

d

^{for every B worker in their workfore. These rms}

maximize prot net of disutility from B employment. The disutility taste is low

enough so that these rms are willing to hire B workers at a suiently low wage;

that is,

d < p

^{. The remaining}

(1 − λ)N

^{rms are} onventional prot maximizers;

they are indierent between hiring A or B workers. We assume that

N

^{is suh a}

large number that eah rm, regardless of its type, pereives (approximately) that

afration

λ

^{ofitsompetitorsareagaindisutilityrms.} Importantly,although eah rm is small relative to its ompetitors, it is large relative to workers; partiularly,

eah rm ends up employing aninnity of workers.

Intheabsene ofpoliyregulation(laissezfaire),thesequeneofeventsisasfollows.

Stage I Every worker appliesatexatly

1 + m

^{randomrms, where}

1 ≤ m ≪ N

^is

exogenouslygiven.

Stage IIEvery rm

j

^{oers jobs atwage}

w ^j _A

^{toA appliantsand atwage}

w _B ^j

^toB

appliants.

Stage III Workers aept the best oer as long as the oer is at least as high as

theirzeroreservationwage. Ifaworkerhas twoormoreequal oers, heaepts any

of them with the same hane.

Fourremarksareinorder. First,althoughrmsoerwagesafterworkersapply,this

framework is equivalent toone where rms ommitto wages before the appliation

stageandwheresearhisrandom,asistheaseinBurdettandJudd(1983). Seond,

therms' wagepoliiesarerestrited toruleout withingroupwagedisrimination.

This is not a ritial requirement. Even if rms were allowed to wage disriminate

between workers of the same type, they need not exerise this option.

8

Third, the

assumption that eah worker sends

1 + m ≪ N

appliations (rather than applying atallrms)apturesthesearhfritionsinthis modelwhiheventuallygivesriseto

nonompetitivewages. Notethat whenallworkers andjobsare idential(whihis

theasewhen

d = 0

^or

σ = 0

^or

λ = 0

^),twoormoreappliationsareenoughtoyield theperfetlyompetitiveoutome throughBertrandwageompetition.

9

Otherwise,

however, rms an exerise market power, wages for B workers dier from their

marginalprodut,and thereiswage dispersion. Fourth,the atualnumber

N

^turns

out to be irrelevant for equilibrium sine there are no apaity onstraints at any

rm. Instead,the appropriatemeasure of the strength of ompetitioninthis model

is the number of appliations per worker. Indeed, it is reasonable to imagine that

1 + m

^inreases proportionately withthe number of ativerms.

10

Atthe seondstage,rmsmaximizetheirpayoby settingwages forAworkers and

B workers respetively, taking the wage oer distributions of ompetitors as given.

The payo of anondisutility rm oering wages

(w A , w B )

^{issimplyits prot}

(p − w A )l ^A (w A ) + (p − w B )l ^B (w B ) ,

where

l ^s (w s )

^{is labor supply of type}

s = A, B

^{workers to a partiular rm oering}

8

Althoughit may happen that rms are indierent betweenseveral wageoers, theassump-

tionthat thereis nowithinrmwagedispersion(among workersof thesametype) restritsthe

equilibriumsetonlytrivially. Allwagedispersion,ifany,happensarossrmsinthismodel. This

isalsoinlinewiththeempirialregularitythatmostwagedispersionisbetweenrmsratherthan

withinrms.

9

ThisisLemma 2(ii) ofBurdettand Judd(1983). If workerswouldsend onlyoneappliation

with positive probability less than one, there would be wage dispersion even with homogenous

workers.

10

For example, think of aspatial model where workerslivein anareaof size

L

^{and that eah}

workerappliesatallrmsinaregionofsize

εL

^{aroundhishome. Ifrmsareuniformly}distributed arossarea

L

^{,eahworkerappliesat}

1 + m ≈ εN

^rms.

wage

w s

^{. The payo of a disutility rm oering}

(w A , w B )

^{is prot minus linear}

disutility of B employment:

(p − w A )l ^A (w A ) + (p − d − w B )l ^B (w B ) .

Sine searh is random, the number of appliations of workers of a given type at

anyrm isthe same. Consequently, expeted employmentof A (orB) workers only

depends on the wage oer but is independent of the rm type. Let

F _d ^s (w s )

^and

F _n ^s (w s )

^{denote the umulativewage oer} distributions to workers of type

s = A, B

bydisutilityand nondisutilityrms, respetively. ThenemploymentlevelsofAand

B workers at arm oering

(w _A , w _B )

^are11

l ^A (w A ) = (1 + m)(1 − σ)

N

h

λF _d ^A (w A ) + (1 − λ)F _n ^A (w A ) i m

, l ^B (w B ) = (1 + m)σ

N h

λF _d ^B (w B ) + (1 − λ)F _n ^B (w B ) i m

.

For example, in the rst equation,

(1+m)(1−σ)

N

^{is the mass of A workers applying}

at a partiular rm, and the expression

[.] ^m

^{is the share of these appliants whose}

remaining

m

^{oers are allnot larger than}

w A

^.

1.3 Laissezfaire equilibrium

Sinerms' payos are separable inthe twoemployment types, stageII wage om-

petition an be solved separately for A and B workers.

Eah A worker sends at least two appliations and thus gets several wage oers

from equally produtive rms. Therefore, rms bid up wage oers to the workers'

marginalprodut. The unique equilibriumwage oerdistributionis the degenerate

distributionthat has allmass onentrated at

w _A = p

^(Bertrandequilibrium).

12

11

For simpliity,alldistribution funtions inthese expressionsareontinuous. Wheneverthere

are mass points, the employment terms must be altered aording to stage III randomization

betweenequaloers.

12

Itistrivialthattheompetitivewageisanequilibrium. UniquenessfollowsfromLemma2(ii)

ofBurdettandJudd(1983).

Clearly,thewage oerdistributionfuntionforBworkers diersfromthe oneforA

workers, sinesomermsderiveadisutilitytastewhenemployingB workers. While

disutility rms bid wage oers up to their eetive marginal produt

p − d

^{, the}

full wage oer distribution does not degenerate at that value. Nondisutility rms

realize that some of their B appliants obtain all other oers from disutility rms

at

w = p − d

^{while other B appliants obtain oers from} nondisutility rms that an protably hire this worker at higher wages. Hene nondisutility rms fae a

tradeo between low wage osts and higher reruitment rates whih gives rise to

wage dispersion, as in the stati model of Burdett and Judd (1983), or in dynami

models with searhonthejob likeBurdett and Mortensen (1998).

Sinethe wageoerdistribution

F _d ^B

degeneratesat

p − d

^{, thelowerboundof distri-}

bution

F _n ^B

^{must beequal to}

p − d

^{: no} nondisutilityrm willattrat any worker by oering

w < p − d

^{; and if the lower bound of the support of}

F _n ^B

^{was at}

w > p − d

^,

the rm oering

w

^{would hire the same number of B workers at lowerost atwage}

oer

w − ε > p − d

^{. On the other hand, no} nondisutility rm will exatly oer

p − d

^{sine it an attrat share}

λ ^m /(1 + m)

^{of all B appliantsat this wage (share}

mλ ^m /(1 + m)

^{of them willgo toa disutility rm oering the same wage and share}

1 − λ ^m

^{go to a} nondisutility rm oering a higher wage), whilst it hires at least share

λ ^m

^{of all B appliants atany slightlylarger wage. In other words, the payo}

funtion of nondisutility rms jumps upwards at

w = p − d

^{. Using standard argu-}

ments, one an also show that the distributionof wage oers of nondisutilityrms

annothave mass points and must be stritly inreasing. Hene the support of

F _n ^B

isa onneted, halfopen interval

(p − d, w ^B ]

^.

Tondtheequilibriumdistribution,wemakeuse oftheindiereneonditionwhih

statesthatany wage

w ∈ (p − d, w ^B ]

^{yieldsthe sameexpeted payo asawage oer}

arbitrarilylose to, but above

p − d

^:

(p − w)l ^B (w) = (p − w) (1 + m)σ

N h

λ + (1 − λ)F _n ^B (w) i m

= [p − (p − d)] (1 + m)σ N λ ^m .

Solving yields the unique equilibrium wage oer distribution of nondisutility rms

for B workers:

F _n ^B (w) = λ 1 − λ

h d p − w

1/m

− 1 i

,

whih has upper bound

w B = p − dλ ^m

^{. Hene, the market wage oer} distribution for B workers is

F ^B (w) = (1 − λ)F _n ^B (w) + λF _d ^B (w) =







0 , w < p − d , λ d

p − w 1/m

, w ∈ [p − d, p − dλ ^m ]

(1.1)

Proposition1.1: Under laissezfaire, theuniqueequilibriumwageoerdistribution

for A workers degenerates at

w = p

^{. The wage oer} distribution for B workers is nondegenerate with support

[p − d, p − dλ ^m ]

^{and umulative} distribution (1.1). All B workers earn lower wages than A workers. A disutility rm obtains zero payo

and positive prot

σdλ ^m /N

^{, and a} nondisutility rm earns prot

(1 + m)σdλ ^m /N

^.

Every nondisutility rm employs more B workers than any disutility rm.

In ontrast toa perfetly ompetitivelabor market, adisriminatory taste of some

rms together with searh fritions aets the shape of the wage oer distributions

whih exhibits both betweengroup and withingroup (group B only) wage disper-

sion. Notehowever thatallwage dispersion disappears inthe limit

d → 0

^{. Another}

ompetitive limit obtains when

m → ∞

^{. Although the wageoer} distribution is stillnondegenerateinthe limit(ithas mass pointsat

p − d

^andat

p

^{),the earnings}

distributionisnot: all

B

^{workersare employedat}nondisutilityrmsatwage

w = p

^.

AsinBeker's model,segregation eliminatesany wage dierentialsinaompetitive

labormarket.

1.4 Equal pay with strit armative ation

Supposenowthegovernmentimposesanequalpaylawthatprohibitswagedieren-

tialsin idential oupations withinthe same rm. Suppose furthermore that there

is a perfetly enforeable equal employment opportunity law whih stipulates that

eah rm must employ at least as many B workers in relation to its A workers as

orresponds to the relative population share. Alternatively, the law regulates that

theBA ratioofnewhiresisnot lowerthanthisratiointhe rm'sappliationpool.

But this seond requirement is idential to the rst in the random searh environ-

ment of this model. In any ase,the legislationpresribes that the ratio between B

and A employment inany rm may not fall short of

σ/(1 − σ)

^.13

Underthispoliyregime,eahrmanoeronlyonewagetoboth typesofworkers

anditannotrejetanyBappliantwheneverithiresallitsAappliants. Formally,

the seond stage of our model is alteredas follows.

Stage IIEvery rmdeidesa ommonwage

w

^{for allitsworkers. Itmay oerthis}

wagetoasmany appliantsasitwants,buttheratiobetweenB andAworkersmay

not fall short of

σ/(1 − σ)

^.

Clearly, a nondisutility rm hires all appliants at any wage

w < p

^{. If a disutility}

rm hires

ℓ

^{workers at wage}

w

^{, its payo is}

(p − σd − w)ℓ

^{sine fration}

σ

^{of its}

workers must beof type B. Hene, a disutility rm deidesto hire allappliantsat

any wage

w < p − σd

^{, but it is unwilling to hire any workerat a wage}

w > p − σd

^.

Put dierently,

p − σd

^{isthe marginalpayo ofanadditionalworker foradisutility}

rm in this poliy regime. We assume that disutility rms hire all appliants at

wage

w = p − σd

^{,although they are indierentbetween alllegal hiringstrategies at}

this wage.

Similar to the laissezfaire ase, there is again perfet wage ompetition between

disutility rms who bid their wage oers up to their eetive marginal produt

p − σd

^{. On the other hand, the wage oer} distribution of nondisutility rms does notdegenerate. Thepositiveprobabilitythatanappliantgets allotheroers from

disutilityrmsat

p−σd

^{givesthesermssomemarketpower,sothattheyrandomize}

wages froma ommondistribution whose lower bound isat

p − σd

^.

In the mixedstrategy equilibrium, nondisutility rms are indierent between any

wage

w

^{inthe support ofthe wage oer}distribution anda wage arbitrarilylose to the lower bound

p − σd

^:

(p−w)[l ^A (w)+l ^B (w)] = (p−w) 1 + m N

h λ+(1−λ)F _n (w) i m

= [p−(p−σd)]1 + m N λ ^m .

13

Amoregeneralpoliywouldbetherequirementthateahrmrespetstheonstraint

ℓ ^B /ℓ ^A ≥ γσ/(1 −σ)

^withsome

γ ∈ [0, 1]

^{measuringthestrengthofarmativeation. Thissetiononsiders}

theextreme

γ = 1

^{,whilstthenextsetionfousesontheabseneofarmativeationwhere}

γ = 0

^.

Solving yieldsthe equilibriumwage oerdistribution of nondisutility rms:

F n (w) = λ 1 − λ

h σd p − w

1/m

− 1 i ,

whoseupperboundis

p− dσλ ^m

^{. Themarketwage oer}distribution,i.e.the fration of all rms paying

w

^{or less to both types of workers, is}

F (w) = λF d (w) + (1 − λ)F n (w)

^,

F (w) =







0 , w < p − dσ , λ

p σd − w 1/m

, w ∈ [p − dσ, p − dσλ ^m ] .

(1.2)

Comparison with (1.1) shows that the wageoer distribution rstorder stohas-

tially dominates the distribution for B workers under laissez faire. Therefore, the

mean wage for B workers ishigher while the mean wage for A workers is lowerun-

der the poliy. Obviously, the wage dierential between the dierent demographi

groupsistotallyeliminated. Perhapssurprisingly,protsforallrmsareunhanged

relativeto laissezfaire.

Proposition 1.2: Under the equalpay poliy with strit armative ation, the

equilibrium wage oer distribution has support

[p − σd, p − σdλ ^m ]

^{and umulative}

distribution (1.2) whih stohastially dominates wage oers for B workers under

laissezfaire. Mean wagesfor Aand B workersare equalized. Disutilityrmsobtain

zero payo and positive prot

σdλ ^m /N

^{, and} nondisutility rms earn prot

(1 + m)σdλ ^m /N

^{, the same as under laissezfaire.}

1.5 Equal pay without armative ation

When ombined with strit armative ation, equalpay legislation sueeds in

eliminatingwage dierenes between worker groups. However, suh an ideal result

obtains onlyif the employers are not allowed to disriminate in hiring by rejeting

less attrative job appliants. That is, equal opportunity of employment must be

perfetlyenfored. As wehaveargued inthe introdution,there are several reasons

why thismaynotbethe ase. Wethusexplorethesituationwhereequalpaypoliy

workseetivelywhilehiringdisriminationannotbeprohibited. Thekeyquestion

is whether the poliyis stilleetive in lowering wage inequality and raising wages

for B workers. We nowhave

Stage IIEvery rmdeidesa ommonwage

w

^{for allitsworkers. Itmay oerthis}

wage to asmany appliantsas it wants.

In this alternative poliy senario, a disutility rm deides to hire all appliants

at any wage oer

w < p − d

^{but it rejets all B appliants at any wage oer}

w >

p−d

^. Consequently,theequilibriumoutomeofProposition1.2annotbesustained anymore. Partiularly, at their equilibrium wage oer

p − σd

^{, all disutility rms}

would rejet as many B appliants as possible. This also implies that there must

be hiring disrimination in equilibrium, i.e. some disutility rms must oer wages

w > p − d

^{and rejet B workers. For ifthis wasnot the ase, hiring behaviorwould}

be the same as in the previous setion; ere wage ompetition would set in again

so that, at some point, all rms will oer wages above

p − d

^{whih, in turn, must}

induedisutility rms torejet B appliants.

SinesomeB appliationsget rejeted,allrmsgainmarketpowerandare inlined

to hange their pay poliy; antiipating that some workers do not obtain another

oer,they are able toattrat atleast a few B workers by merely oering the reser-

vation wage. Indeed, in stark ontrast to our previous results, the lower bound of

the wage oer distributionis now atzero.

Beause the possibility ofhiring disriminationaets B workers only,laborsupply

of B workers to any rm is generally less elasti than labor supply of A workers.

For this reason, a nondisutility rm oers a lower wage than a disutility rm who

oers

w > p − d

^{and attempts to hire only A workers whose labor supply is more}

elasti. Indeed, it turns out that the highest wages are oered by disutility rms

that hire only A workers. Sometimes, however, afration of disutility rms donot

rejet B workers and oers wages whih are even lower than the wages oered by

nondisutility rms. This is intuitively easy to explain: the marginal payo of an

additionalworker islargeratanondisutilityrmthan atadisutilityrm thathires

all workers. These results an be formally stated in the following Lemma whih is

proven inthe Appendix.

Lemma 1.1: Let

F = λF d + (1 − λ)F n

^{be the} equilibrium distribution of wage oers. Then

F

^{isstritly inreasingand ontinuous (thatis, there are no holes and}

no mass points) and the lower bound of the support is at the workers' reservation

wage of zero. Moreover, for any

w n

^{in the support of}

F n

^and

w _d ⁱ

^,

i = 1, 2

^{, in the}

support of

F d

^{suh that}

w ¹ _d ≤ p − d < w _d ²

^{, it holds that}

w _d ¹ ≤ w n ≤ w _d ²

^.

From this Lemma follows that equilibrium an be desribed as follows. There are

wage thresholds

0 ≤ w ₀ ≤ p − d < w ₁ < w < p

^{and anumber}

µ ∈ [0, 1)

^{suh that:}

1. Fration

µ

^{of disutility rms make low wage oers, drawn from} distribution

F _d ^l

^{with support}

[0, w ₀ ]

^{. These rms hire all appliants.}

2. Nondisutility rms draw wage oers from distribution

F n

^{whih has support}

[w ₀ , w ₁ ]

^{,and they hire allappliants.}

3. Fration

1−µ

^{ofdisutilityrmsmakehighwageoers, drawnfrom}distribution

F _d ^h

^{with support}

[w ₁ , w]

^{. These rmshire onlyA appliants.}

In the Appendix (proof of Proposition 1.3) we haraterize the equilibrium wage

oer distribution. For given

µ

^{, one an derive}

F

^{and the ritial wage thresholds}

frombottomtotop, usingstandardindiereneonditions. Atthe end,the fration

µ

^{ispinneddowntoensurethatdisutilityrmsareindierentbetweenoeringwages}

inthe loweror inthe upper wage range. We nd that

µ

^{ispositiveif, and only if,}

d < d ^∗ ≡ pσ

σ + (1 − σ)(1 − λ) ^m .

When the disutilityparameter is larger than

d ^∗

^{,no disutilityrm oers lowwages,}

in whih ase

µ = 0

^and

w ₀ = 0

^{. On the other hand, it always holds that}

µ < 1

^;

there must be some disutility rms rejeting B appliants, as has been explained

above.

Figure1.1 showsthewageoerdensityinanumerialexamplewhere

p = 1

^,

d = .1

^,

σ = λ = .5

^and

m = 1

^{. Here the ritial wage thresholds are}

w ₀ ≈ .897

^,

w ₁ = .95

and

w ≈ .953

^{. Fration}

1 − µ ≈ 10.5%

^{ofdisutilityrmsset highwages}

w ∈ [w ₁ , w]

^,

rejeting B workers. Hene, in this example, the hane that a B worker ends up

withouta joboer is merely

(λ(1 − µ)) ² ≈ 0.27%

^.

Figure 1.1: The equilibrium wageoer density for parameters

p = 1

^,

d = .1

^,

λ = σ = .5

^,

m = 1

^{. About 89.5% of disutility rms oer wages}

w ∈ [0, .897]

^{and 10.5%}

of them oerwages

w ∈ [.95, .953]

^{,rejeting B workers.}

Relativetotheoutomesunderlaissezfaireandunderstritenforementofpayand

hiringequality,wage dispersionis muhlarger inthis poliyregime. In the absene

of hiring disrimination, no rm is willing to oer wages below

w = p − d

^(under

laissezfaire)orbelow

w = p − σd

^{(underequalpay witharmativeation). Witha}

reasonablysmall disutility tasteparameter, wage dispersionis smallsine allwages

are lose to marginal produt. Without enforement of hiring equality, however,

there are always rms who oer muh lower wages and the support of the wage

oer distribution is larger, ertainly so when

d ≤ p/2

^{.14 Not only the support of}

14

Nevertheless,inthelimit

d → 0

^thewageoerdistributiononvergestotheDiradistribution at

w = p

^{. Although the support of}

F

^{is still the full interval}

[0, w]

^with

w → p

^{, the standard}

wageoerdistributionsbeomeslarger,thestandarddeviationofearningsinreases

under the poliy, aswedemonstrate numeriallyin the next setion.

Although overall wage dispersion inreases, it is analytially intratable to answer

what happens to the mean wages of workers in the two groups and to the wage

gap between A and B workers, although it is obvious that a positive wage gap

must remain. The next setion sheds lighton these questions with afew numerial

examples. Sine both typesof rms gain market power and hene lowertheir wage

oersunderthepoliy,payosofallrmsarealways higherthanunderlaissezfaire.

And obviously, total welfare is somewhat lower sine some B workers do not nd

employment.

Proposition1.3: Under theequalpay poliy withoutarmative ation,a fration

1 − µ > 0

^{of disutility rms rejets all B workers and oers wages in someinterval}

[w ₁ , w]

^{. Provided that}

d < d ^∗

^{, there is also a positive fration}

µ

^{of disutility rms}

oering wages

w ∈ [0, w ₀ ]

^{who employ all workers.} Nondisutility rms oer wages in the range

[w ₀ , w ₁ ]

^where

w ₀ > 0

ⁱ

d < d ^∗

^{. Provided that}

d ≤ p/2

^{, the support of}

the wageoer distributionis largerthan underlaissez faire or under equal pay with

equal opportunity of employment. Payos of all rms are higher than under laissez

faire.

1.6 Mean wages and the wage gap

In this setion we analyze numerially whether the equal pay poliy is eetive in

lowering wage inequality and raising wages for B workers. We also examine how

the eetiveness of poliy depends on the relative shares of minority workers and

of disutility rms and on the degree of ompetition, as measured by

m

^{. If poliy}

would magnify wage inequality between dierent demographi groups or redue

wagesforBworkersunderertainonditions,poliymakersshouldbemoreautious

toimplement it.

Inallnumerialexamples,wenormalizeworkers'produtivityto

p = 1

^andwehoose

deviationbeomesarbitrarilysmallin thislimit.