A tradable employment quota

Metin Akyol∗, Michael Neugart,† and Stefan Pichler‡

April 2014

Abstract

Discrimination of women in the labor market requires appropriate

policy interventions. A�rmative action policies typically advocate the

introduction of an employment quota uniformly applied to all �rms. In

a heterogeneous labor market such a policy may yield avoidable welfare

losses. We propose a tradable employment quota showing its e�ects on

wages, employment and welfare in a labor market with search frictions

and taste discrimination. A tradable employment quota occurs to be

a viable alternative yielding superior labor market outcomes.

Keywords: tradable employment quota, agent-based model, a�rma-

tive action policies, taste discrimination, labor market, search and

matching

JEL-Classi�cation: J71, J78, C63

∗Technical University of Darmstadt, Department of Law and Economics, Marktplatz15, D-64283 Darmstadt, Germany, e-mail: akyol@vwl.tu-darmstadt.de†Technical University of Darmstadt, Department of Law and Economics, Marktplatz

15, D-64283 Darmstadt, Germany, e-mail: neugart@vwl.tu-darmstadt.de‡ETH Zurich, KOF Swiss Economic Institute, Weinbergstrasse 35, 8092 Zurich,

Switzerland e-mail: pichler@kof.ethz.ch

1

1 Introduction

A�rmative action policies very often take the form of employment quotas.Norway introduced a quota in 2003, and France, Iceland, and Spain havemandatory boardroom gender quotas forcing �rms to have boards with 40%women by the years 2017, 2013, and 2015, respectively. Only recently, theEuropean Parliament passed a proposal by the European Commission tobreak the glass ceiling. According to this envisaged bill, European �rms haveto appoint female directors in order to make supervisory boards two-�fthsfemale by 2020.1

As it is very likely that a uniform employment quota imposes larger ad-justment costs on some �rms than on others the question arises whether thegoal of paving the way for more female employment can be achieved at lowercosts. In particular, as the size of women's labor supply is heterogeneousacross occupations, sectors, and regions, some of the �rms forced to ful�ll a�xed quota will �nd it more di�cult to hire women who match the vacanciesthan others. A more �exible instrument is called for that does not compro-mise on the overall goal of achieving a certain share of female employment.Such an instrument should allow �rms to fall short of the quota if costs ofcompliance would become unreasonable, while allowing others to gain fromemploying relatively more women.

In this article we propose and analyze the labor market e�ects of a trad-able employment quota. Borrowing from the experience with environmentalregulation policies to combat excessive carbon dioxide emissions, we suggestto implement a mechanism that e�ciently achieves a �xed share of womenworking in relation to men. The idea is to issue permits to �rms that givethem the right to employ men and make these permits tradable. With suchan a�rmative action policy �rms would only be allowed to employ men up toa number that matches the stock of permits that they hold. As a particular�rm would want to employ an additional man it would only be able to doso by purchasing an additional employment right. Firms being in excess ofpermits because they �nd it more pro�table to employ a woman than to holdone of the permits will want to sell this right. Trading of permits betweenthose �rms that want to buy and those �rms willing to sell would yield amarket price of a permit re�ecting the pro�tability of employing an addi-tional man. While the overall supply of permits of an issuing body woulddetermine the share of female employment in the economy, single �rms couldadjust more �exibly and still comply.

On the backdrop of the recent policy initiatives to install board quotas for

1See the European Commission Database on Women and Men in Decision Making.

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women, Table 1 assembles shares of female board memberships. With 16%the U.S. and the 27 (by 2007) EU member states fare equally in terms offemale representation on �rm boards. Japan, as another major industrializedcountry, has only 1% women on �rm boards. A more closer look into singleEuropean countries reveals a large dispersion of female representation. In thethree countries with the largest representation almost every third member isfemale, a share which, however, still falls short of Norway where a quota wasintroduced by 2003 already, forcing �rms to comply by 2008. In the Europeancountries that do worst not even every tenth position is held by a woman.Interestingly, the countries doing relatively well in terms of female boardmembership hardly have women leading the board or being a CEO. Datafor Germany allows for a closer look into the within country distributionof female representation. Again, we �nd a large variance between �rms.Among the companies listed in the DAX (the major German stock marketindex), seven women serve on the board of Henkel which is composed of 16members, while no woman is serving on the board of Fresenius (a medicalcare company).

The introduction of a female board quota in Norway constituted a natu-ral experiment that allowed for an analysis of �rm reactions and their conse-quences more closely. At the time the law was introduced only 9% of womenwere on the boards of Norwegian �rms. A legislated quota of 40% imposeda major change on the composition of Norwegian �rm boards. Ahern andDittmar (2012) use the pre-quota female representation across �rms as aninstrument for the changes of boards that followed the quota. For the daysaround the announcement of the law they �nd that stock returns fell by 3.52%for those �rms with no female representation compared to �rms that had atleast one woman on the board. For the longer term, they estimate a declinein Tobin's Q of 12.4% as a response to a 10% forced increase in women repre-sentation on the boards. Overall they conclude that the constraint imposedhad a large negative impact on �rm value driven by the reorganizations ofthe boards. Drawing on the same policy change, Bohren and Staubo (2013)�nd that half of the �rms that would have been a�ected by the gender quotachose to exit into another organizational form, thus avoiding exposition tothe law. Also this piece of evidence suggests, at least indirectly, substan-tial costs of compliance that possibly could be diminished with a system oftradable permits to employ men.

In order to study whether a tradable emplyoment quota is a feasible a�r-mative action policy and what labor market e�ects would possibly unfold webuild an agent-based simulation model of the labor market and the market

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Table 1: Women on boards

Country Members of board Board chairs [%] CEOs [%]Ave. share [%] Min [%] Max [%]

USA (a) 16Japan 1EU-27 16 3 2Finland 29 4 0Latvia 28 13 3Sweden 26 0 4...Germany 18 0 (b) 44 (b) 3 0...Portugal 7 0 0Hungary 7 0 0

quad Malta 4 0 5Norway (c) 39

Data source: European Commision Database on women and men in decision making for

2012 if not otherwise stated. (a) European Commission: Women on boards - Factsheet 2,

Gender equality in member states; (b) Der Spiegel 48/2013, p.74; (c) Ahern and Dittmar

(2012, p.143).

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for permits. We study a labor market with a set of �rms being allocated tomultiple sectors. A fraction of the �rms is characterized by taste discrimina-tion against women as proposed by Becker (1957). The remaining fractionof �rms is indi�erent between men and women. Workers have sector speci�cskills meaning that their productivity does not fully unfold if they work in asector that requires di�erent skills than the ones embodied. Firms post va-cancies to which workers apply and are matched. In this framework we studythe e�ects of a tradable as opposed to a non-tradable employment quota onwelfare and various other labor market indicators. Our main �nding is thata tradable employment quota fares better in a heterogeneous labor marketwere �rms are facing sectorally di�erentiated levels of female labor supply.

We use an agent-based model to analyze whether a permit solution mayactually work and what labor market e�ects potentially emerge. Evaluat-ing labor market policies using agent-based models has been suggested byFreeman (1998) already some time ago. Generally speaking an agent-basedapproach suits well for analyzing problems characterized by interacting het-erogeneous agents. Moreover, agent-based modeling allows for a relativelydetailed implementation of institutional arrangements. As we build a modelwith a sectoral structure hosting workers of di�erent skill types to be em-ployed by �rms that may discriminate against women and, furthermore, willaugment the labor market with a permit trading system, the agent-basedapproach seems to suit well for our purposes. Our approach may also be sub-sumed under what Roth (2002, p.1341) called �design economics� where heargues that computational techniques should be seen as complementarity toother tools applied to studying and designing markets, namely game-theory.One of the earliest attempts to analyze the e�ects of labor market institu-tions in an agent-based model can be found in Bergmann (1990). Othersfollowed, with Tesfatsion (2001) working on wage setting or Neugart (2008)looking into training policies. Those and other contributions are surveyed inNeugart and Richiardi (2014).

Building a computational model we touch upon various strands of theliterature. Our theoretical explanation of men and women being treateddi�erently draws on taste discrimination (Becker, 1957). The alternativeexplanation is statistical discrimination (Arrow, 1973; Phelps, 1972). Em-pirical work long evolved separately along these two explanations (Guryanand Charles, 2013). Only in recent years e�orts have been made to test tastebased explanations of discrimination against explanations pointing at sta-tistical discrimination (See, e.g., Altonji and Pierret, 2001; Knowles et al.,2001). The jury still seems to be out and we do not make an attempt toresolve the issue here. There is also no particular reason, why we chose amodel of taste discrimation. At this point, all that we need is some sort of

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discriminatory behavior as a starting point to analyze the two a�rmativeaction policies in comparison.

Welch (1976) was probably among the �rst dealing with a�rmative actionpolicies from a theoretical point of view. Equal employment opportunitiesas one proliferation of a�rmative action policies have been studied in theframework of a search and matching model of the labor market by Kaas andLu (2010). They �nd that if an imperfectly monitored equal employmentopportunity legislation is combined with an equal pay obligation inequalityincreases.2 Contrary to them we do not look into a �xed quota but a tradableone.

While tradable permits have gained widespread attention in the area ofenvironmental policies3, there is little to no application in the area of la-bor market policies.4 This contribution may be seen as a �rst step into theanalysis of such kind of a�rmative action policies. Our starting point is aheterogenous labor market where lack of appropriate skills in certain seg-ments may cause considerable adjustment costs following the introductionof a uniform quota. Thus, once more, it underscores the importance of abetter understanding of the reasons why women do not make it into certain(and well paid) segments of the labor market such as top-level managementpositions (Bertrand et al., 2010).

In the following Section 2 we lay out our model and introduce the readerto the two a�rmative action policies we are going to compare. After havingdescribed the parametrization and the simulation set-up in Section 3, we dis-cuss labor market outcomes in a baseline speci�cation of our model withoutpolicies in Section 4. The main purpose of this Section is to reveal the proper-ties of our simulation model and put these into relation to the �ndings of theexisting literature on labor market models with taste discrimination. Section5 studies the e�ects of a tradable employment quota in comparison with anon-tradable quota on welfare and other labor market indicators and reportson the results of various robustness tests. In the last section we conclude andpoint towards desirable extensions of the current work.

2Other contributions looking into the labor market consequences of equal pay legislationare Bowlus and Eckstein (2002); Coate and Loury (1993); Kaas (2009). Further searchand matching models with taste discrimination but without policy analyses can be foundin Black (1995); Lang et al. (2005); Rosen (2003).

3See Schmalensee and Stavins (2013) for the U.S. experience or for the European Uniontrading system: http://ec.europa.eu/clima/policies/ets/index_en.htm.

4Winker (2000) sketches the idea of how collective wage agreements could be mademore �exible using tradable permits and Fernandez-Huertas Moraga and Rapoport (2011)apply tradable permits to immigration policies. Casella (1999) proposes a permit tradingsystem as an alternative to the Stability and Growth Pact regulations on de�cit rules.

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2 The model

2.1 A general description

Our model consists of a labor market hosting heterogeneous �rms and work-ers, and a permit market. The labor market has a sectoral structure. Firmssitting in a particular sector have distinct skill needs. Workers are equippedwith di�erent sector speci�c skills. A worker's productivity unfolds fully ifshe is employed in a sector that matches her skills. Workers employed by�rms in other sectors lose part of their productivity. Labor demand for each�rm is �xed. Vacancies are posted and workers apply. A �xed share of �rmsdiscriminates against women. Due to taste discrimination these �rms willonly employ women instead of men if wages of the former are su�cientlylow. Firms send wage o�ers to the workers with highest pro�tability. Work-ers accept the best o�er they get conditional on the wage being above theirreservation wage.

We consider two a�rmative action policies. Under a non-tradable em-ployment quota every �rm is allowed to only employ a share of men that doesnot exceed the quota. Alternatively, we implement a tradable quota issuingpermits that give a �rm the right to employ a man. The permit market ismodeled as a central market maker to whom each individual �rm submitsits individual supply and demand schedule of permits. The central marketmaker aggregates these bids and asks up, and determines the market clearingprice at which the permits are reallocated.

2.2 Labor market environment

We consider a partial labor market where �rms' labor demand is derived fromaggregate product demand. Firms reside in S sectors. Workers are equippedwith sector speci�c skills. A worker employed at a �rm in a sector withher speci�c skills unfolds full productivity A. Worker speci�c productivitydeclines as she is employed in a more distant sector. Sectors are allocatedon a Salop circle, i.e., a worker's productivity with speci�c skills in sector k,working in sector s follows

pk,s =

{A− a · |k − s| if |k − s| ≤ S/2A− a · (S − |k − s|) else,

(1)

with 0 < a < 1, k = 1, ..., K, and s = 1, ..., S. As there are as many skilltypes as sectors we have K = S. Full productivity A is su�ciently large sothat a worker's productivity never becomes negative.

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2.3 Agents

2.3.1 Workers

The �xed total labor supply of size I can be decomposed into of a fraction(1 − σ) of male workers and a fraction σ of female workers. A worker i hasan individual reservation wage wri that is drawn from a uniform distributionwith support [0, A].

Workers send out m > 1 applications preferably to �rms which valuetheir sector speci�c skills. Unobservable characteristics orthogonal to theirskill endowment make some sectors more attractive to a speci�c worker thanothers implying that a worker has also preferences over non-wage job char-acteristics. Thus, she may send an application to a �rm in a sector whichdoes not value her speci�c skills most. More formally, we recur to a discretechoice speci�cation postulating that workers with speci�c skills in sector ksend out an application to a �rm in sector s̃ with probability

Probk,s̃ =eλpk,s̃∑s e

λpk,s, (2)

where λ ≥ 0 drives the intensity of choice and the denominator sums up theexponentials of worker speci�c productivities in all sectors, respectively.

Workers accept job o�ers with attached wage o�ers above their reservationwage wri . If a worker receives more than one job o�er, she chooses the jobo�er with the highest wage.

2.3.2 Firms

Each sector is populated with N �rms. Each �rm j's, with j = 1, ...J , labordemand l is �xed. Within each sectors there is a share µ > 0 of discriminating�rms. A discriminating �rm has a dis-utility from hiring a female workerwhich is modeled with a discrimination coe�cient d as suggested by Becker(1957). The �rm j residing in sector s has payo�s calculated as the sum ofpro�ts, which are productivities net of wage, minus discrimination costs overall workers nj:

πj,s =∑nj

(pk,s − dg − wj,k,g,s), (3)

where g = M,F is the gender of the worker. For discrimination costs onehas dM = dF = 0 for a non-discriminating �rm and dF > 0 for a �rm thatdiscriminates against an employed a woman.

Firms set male and female wages to maximize payo�s. Job o�ers are sentout including the worker speci�c wage o�ers. Then, the �rm may face two

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distinct situations: a) the �rm is able to �ll all the vacancies as no workerwho received a job o�er declined it, b) some workers who received a job o�erdeclined it. Firms are facing a trade-o� such that higher wage o�ers increasethe likelihood that a vacancy can be �lled and becomes productive. Higherwage o�ers, however, increase the wage bill and depress pro�ts. Firms learngiven their past experience on payo�s made and wage o�ers made how to bestplace themselves on this trade-o�. To this end, each �rm runs regressionsof payo�s per job o�er on the wage o�ers of the past τ iterations. For apositively estimated slope coe�cient β̂, a �rm j that resides in sector s willadjust the wage o�er wo for a worker coming from sector k and of genderg upwards by a �rm speci�c parameter �j in iteration t with respect to theprevious iteration t−1. For a negatively estimated slope coe�cient the wageis adjusted downwards:

woj,k,g,s,t =

woj,k,g,s,t−1 + �j if β̂j,k,g,s,t > 0,

woj,k,g,s,t−1 − �j if β̂j,k,g,s,t < 0,woj,k,g,s,t−1 else.

(4)

The �rm speci�c adjustment parameter �j is drawn from a uniform distribu-tion with bounds [�, �]. Wage o�ers are adjusted if they are within bounds[0, A].

2.4 Policies

2.4.1 An employment quota

We consider an a�rmative action policy where every single �rm has to employat least σ̄nj women. In order to comply with the quota �rms rank applicantsby gender and payo�s. Again, the �rm will send binding o�ers to the bestworkers taking into account the quota. As it turns out that after the hiringprocess expired the �rm cannot comply, the �rm withdraws its previous o�ersto male workers up to the point where the quota is ful�lled.

2.4.2 A market for a tradable employment quota

Alternatively, we simulate a market with permits for employing men. Inthis case, a �rm is only allowed to employ as many men as it holds permitsfor employing male workers. There is a �xed number for permits C for thewhole economy. Initially every �rm gets an equal share of the total number ofpermits. These permits can be sold and bought at a central clearing agency.For the clearing agency, we consider a central market maker who collects

9

ask and bid prices, determines the market clearing price in every period andreallocates the permits between the buying and selling �rms.

A single �rm's o�er curve for permits is constructed in the following way.All unused permits are o�ered at reservation price zero. The o�er of thatsingle �rm increases by one more permit at a price equal to the payo� of theleast pro�table male worker. The second least pro�table worker determinesthe price of yet an additional permit. As we move to even more pro�tableworkers the full schedule of the o�er curve for that particular �rm is derived.Turning to the demand side the central market maker looks into a single �rmthat will ask for as many permits as there are more men employed than the�rm holds permits currently. Permits are used to employ the most pro�tablemale workers in the �rm. The bid price for the �rst additional permit is thepayo� of the most pro�table male worker for whom the �rm does not yethave a permit. The bid price for the second additional permit is the payo�of the second most pro�table male worker for whom the �rm does not yethave a permit, and so on.

Aggregating up the single �rms' supply and demand schedules the marketmarker constructs the aggregate supply and demand curves for the employ-ment permits. She determines the market clearing price and reallocates thepermits from those �rms willing to sell at the going price to those willing topurchase permits at the going price. Firms that did not buy the requirednumber of permits to employ all the men whom they made an o�er have torevoke from actually employing these men.

2.5 Sequencing

The pseudocode outlined in Algorithm 1 gives the timing of the variousactions. A particular iteration starts with each �rm j posting l vacancies.Workers apply to �rms with a positive number of vacancies, with each workersending out m applications. Firms evaluate how high their wage o�er shouldbe to best optimize on the trade-o� of actually attracting workers and notletting the wage bill increase by too much. Firms make binding job o�ersobeying the non-tradable employment quota including the wage they arewilling to pay to the most pro�table applicants. Workers choose the job withthe best wage o�er conditional on it being above their individual speci�creservation wage. Firms that were not able to hire enough women to ful�llthe quota withdraw their o�ers to male workers.

For the case where we are looking into an economy with a tradable em-ployment quota �rms observe how many workers they are able to attract andcompare their stock of permits with the number of male workers willing towork for them. Each �rm draws its individual supply and demand schedule

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for the permits. The market maker aggregates these up and determines themarket clearing price at which the permits are reallocated between �rms.Firms not able to purchase the required number of permits for all the menwho wanted to work for them withdraw their o�ers to the least pro�tablemen.

Finally, the �rms produce and observe their payo�s. At the end of eachiteration all workers are dismissed and the cycle restarts.

3 Simulation set-up

3.1 Parametrization

In order to be able to compare the results from our simulation model with theoutcomes form already existing analytical models we, �rst, set-up a simpli-�ed version with one sector only. Then we extend this model to �ve sectors.For the multi-sector version we simulate two policy scenarios with two dif-ferent labor markets. First we look into an a�rmative action policy whichprescribes every single �rm to employ at least 30% women. Then, we in-troduce a tradable employment quota. To this end 100 permits are equallydistributed among the �rms initially which then can be traded at a central-ized clearing agency. The two labor markets within which the two policies aresimulated di�er with respect to the distribution of women across sectors. Inone scenario women are equally distributed across sectors, in the other theyare unequally distributed across sectors (while keeping the overall supply ofwomen constant.)

There are 1,000 workers in the economy. Depending on whether we sim-ulate a single- or a multi-sector model, sectors are populated with 100 or 20�rms, respectively. A �rm posts 10 vacancies. Half of the �rm populationdiscriminates against women. The wage adjustment parameter τ = 10 im-plies that �rms learn over the past 10 iterations. They adjust wages fromone iteration to the other between 2.5% and 10% of the maximum possibleworker productivity. Table 2 summarizes all these parameters.

Each iteration t as described in the Pseudocode is replicated for T = 1, 010times. This we call a single run. Every treatment consists of 100 runs. Forour analysis of the simulation outcome we record the average of the last10 observations of every run. Thus, we have 100 observations for everytreatment.

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Algorithm 1 Pseudocode of model implementationcreate sectors

create workers

create �rms

for t = 0 to T iterations dofor all �rms j = 1 to J do

post vacancies

end for

for all workers i = 1 to I dosend m applications

end for

for all �rms j = 1 to J doadjust wage o�er given past experience

end for

if economy has tradable employment quota then

for all �rms j = 1 to J dosend job o�ers

end for

else

for all �rms j = 1 to J dosend job o�ers to male and female applicants obeying employment quota

end for

end if

for all workers i = 1 to I doif wage o�er above reservations wage then

accept best wage o�er

else

decline

end if

end for

if economy has tradable employment quota then

for all �rms j = 1 to J dodraft supply and demand schedules for permits

end for

central market maker aggregates supply and demand schedules

central market maker determines market clearing price

central market maker reallocates permits

end if

for all �rms j = 1 to J doif a�rmative action policy is not ful�lled then

�rm withdraws o�ers to excess male workers

end if

produce

dismiss all workers

end for

end for

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Table 2: Parameter choices

Parameters

Number of workers M = 1000Number of applications per worker m = 10Intensity of choice λ = 2Number of �rms per sector

One sector model N = 100Five sector model N = 20

Vacancies per �rm l = 10Share of female workers σ = 0.5Share of discriminating �rms µ = 0.5Discrimination coe�cient dM = 0, dF = 0.5Full productivity A = 2Sectoral productivity decline a = 0.5Quota σ̄ = 0.4Number of permits C = 100Learning period τ = 10Wage adjustment � = [0.05, 0.2]

3.2 Di�erence-in-di�erence approach

A simple comparison of a tradable with a non-tradable quota would yield�awed results with respect to their labor market e�ects. Only if it was possi-ble to issue the number of permits which exactly matches the restrictions that�rms are facing from a uniformly applied quota the two policies would becomparable. However, as overall employment and the structure of employ-ment by gender are endogenous, this particular number of permits whichmakes the policies comparable cannot be determined in advance.

As a solution we apply a di�erence-in-di�erence approach to analyze thepolicy e�ects in comparison. The procedure will be to compare the dif-ference of the variables of interest arising from a non-tradable employmentquota comparing an equal with and un-equal distribution of female laborsupply across sectors, with the di�erence between the same variables undera tradable employment quota. Denote with v the labor market variable ofinterest, with ntq the policy of a non-tradable employment quota, with tq thetradable employment quota, and with eqFemDis whether female workers areequally or unequally (UneqFemDis) distributed across sectors. Then, the

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policy e�ect T writes:

T = (v(ntq,eqFemDis)−v(ntq,UneqFemDis))−(v(tq,eqFemDis)−v(tq,UneqFemDis)) (5)

4 Baseline scenarios without policy

4.1 One sector set-up

We start o� with the one-sector version of our model without policy interven-tion comparing labor markets with and without discriminating �rms. Thesimulation results are shown using box plots drawing on the 100 observationsfor each treatment as explained in the simulation set-up.

Figure 1 (a) shows the employment rates when there are no discriminating�rms and, alternatively, when every second �rm discriminates against women.Overall employment rates and employment rates by gender are equal for thenon-discriminating scenario as it should be. Allowing for discriminating �rmsreduces overall employment with respect to the reference scenario where weonly have non-disutility �rms. The decrease in overall employment is drivenby a sharp decline in female employment which, moreover, falls short of maleemployment. Turning to wages, see panel (b), reveals that female workersare paid less than male workers as we allow for disutility �rms.

Both, the employment and the wage e�ects, can be explained by the in-crease in the relative demand for male workers as discriminating �rms areintroduced. These �rms have a distaste for female workers making compe-tition for male workers �ercer. Consequently, male workers' wages increaseand female wages decline. Although there is upward pressure on male wages,on average these wages are only slightly higher than in the non-disutility casebecause those men with relatively high reservation wages will enter the labormarket now. By the same token, female employment is driven down as somewomen will withdraw from the labor market as the going wages have fallenbelow their reservation wage.

Disentangling the employment e�ects when we have 50% discriminating�rms into the employment ratios for those �rms that discriminate and thosethat do not discriminate yields Figure 1 (c). The discriminating �rms haveoverall lower employment than the non-discriminating �rms because they hireless women than men and the gender employment gap is larger at discrimi-natory �rms than at non-discriminatory �rms. Due to taste discriminationwomen earn lower wages at discriminatory �rms than men. But there is alsoa small gender wage di�erential at non-discriminating �rms as these �rmsface a relatively larger female supply.

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Overall these simulations are in line with the �ndings of the existing lit-erature on taste discrimination in search models of the labor market. As inKaas (2009) and Kaas and Lu (2010) the simpli�ed version of our simula-tion model generates employment segregation. The non-discriminating �rmsemploy more women than men and the discriminating �rms employ sub-stantially more men. Comparable to Bowlus and Eckstein (2002) wages forwomen are lower than those for men. Moreover, we can relate to the searchand matching model with heterogeneous reservation wages by Burdett andMortensen (1998) who argue for the emergence of a wage dispersion in suchframeworks. The wage dispersion generated by our model is exempli�ed inFigure 8 panels (a) to (d). We plot the wages paid by gender and by �rmtype for a single run at iteration 1,000 for all workers employed. There is nosingle market wage, neither by gender nor by the type of �rm.

.3.3

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Average Wages Disc vs. NonDisc Firms

discriminating non-discriminatingdiscriminating female non-discriminating femalediscriminating male non-discriminating male

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Figure 1: Employment and wage e�ects for one-sector model; (a) total em-ployment rates , (b) average wages, (c) employment rates discr. vs. non-discr.�rms, (d) average wages discr. vs. non-discr. �rms by gender

15

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0 .5 1 1.5 2 Wage

(c) (d)

Figure 2: Wage distribution for baseline run at iteration 1000, seed 2: (a)female wages at discriminating �rms, (b) male wages at discriminating �rms,(c) female wages at non-discriminating �rms, and (d) male wages at non-discriminating �rms

4.2 Multiple sectors

Extending our labor market model to multiple sectors and re-running theanalysis shows the same employment and wage patterns by gender as inthe one-sector version of the model. However, employment and wages haveshifted down, see Figures 3 (a) and (b). This is due to the higher degree offrictions in a multi-sector labor market. Some workers may want to work insectors not exactly matching their skill endowment. For these workers �rmsmake lower wage o�ers given the lower productivity of these applicants. Withuniformly distributed reservation wages overall less workers will accept thejob o�ers driving down employment in this economy. A closer look into thewage and employment patterns by discriminating (�gures not shown here)yields qualitatively the same results that we already could observe for the

16

labor market with a single sectorNow we introduce an unequal distribution of sector-speci�c skills for

women holding the overall share of women supplying labor constant. Theshare of women increases as we move from one sector to the other from 0.1in steps of 0.2 so that the �fth sector hosts a share of 0.9 women. We re-run the analysis for the unequal distribution of �rms and compare it to theresults for an equal distribution of �rms. For ease of comparison Figures 4(a) and (b) include the results for an equal distribution as already shown inthe previous Figure. There occurs to be a slight decrease in overall employ-ment as we move to an unequal distribution of women across sectors, andan increase in the gender employment gap. Wages slightly decline, both formen and women. Overall, however, the wage and employment patterns donot change qualitatively and can be explained on the same grounds as al-ready done for the simpler versions of this model. The heterogeneous supplyof women across sectors will be the labor market within which we run andcompare the two a�rmative action policies.

.25

.3.3

5.4

.45

Em

ploy

men

t Rat

io

Total Employment Rates

overall femalemale

1.1

1.2

1.3

1.4

1.5

Wag

e

Average Wages

overall femalemale

(a) (b)

Figure 3: (a) Total employment rates and (b) average wages for multiplesector labor market.

17

.25

.3.3

5.4

.45

Em

ploy

men

t Rat

io

equal unequal

(by distr of females, discShare = 0.5)Total Employment Rates

overall femalemale

11.

11.

21.

31.

4W

age

equal unequal

(by distr of females, discShare = 0.5)Average Wages

overall femalemale

(a) (b)

Figure 4: (a) Total employment rates with discriminating �rms, and (b) av-erage wages with discriminating �rms, for an equal and un-equal distributionof women across sectors.

5 Policy evaluation

5.1 Results

The welfare e�ects of the two policies using the di�erence-in-di�erence ap-proach from equation (5) can be seen in Table 3. We de�ne welfare as the sumof all wages paid in the economy and all payo�s accruing to �rms. The thirdrow of Table 3 shows a decline in welfare as we move from a labor market withan equal distribution of women across sectoral skills to an un-equal distri-bution applying a non-tradable employment quota of 40.021 units.5 Welfarealso decreases for a tradable employment quota as we make the distributionof women over sectors unequal by 13.433. However, the decline is smaller sothat the comparison of the welfare losses between the two policies (26.589)speaks for a tradable employment quota as the superior policy instrument.

5These units may be interpreted in relation to total possible output in this economy.With 1,000 workers and a maximum per worker productivity of 2, the maximum of totalunits possible to produce in this economy is 2,000. Measured welfare falls short of thisupper bound due to labor market frictions leaving vacancies un�lled, the allocation ofworkers to sectors where their productivity does not fully unfold, and the discriminatorybehavior of �rms.

18

Table 3: Welfare analysis

eqFemDis UneqFemDis di�

non-tradable quota

welfare 495.450 455.428 -40.021payo�s 155.089 142.897 -12.192wage sum 340.361 312.532 -27.829empl. 0.271 0.254 -0.017empl. female 0.411 0.393 -0.019empl. male 0.130 0.115 -0.015

wages 1.257 1.232 -0.025avwagefem 1.246 1.222 -0.023avwagemale 1.291 1.263 -0.028

tradable quota

welfare 495.427 481.994 -13.433payo�s 182.613 177.433 -5.180wage sum 312.814 304.561 -8.253empl. 0.262 0.258 -0.004empl. female 0.323 0.315 -0.008empl. male 0.200 0.200 0.000

wages 1.195 1.182 -0.013avwagefem 1.246 1.227 -0.019avwagemale 1.113 1.111 -0.003

di�-in-di� p-value

welfare 26.589 0.000payo�s 7.012 0.000wage sum 19.577 0.000empl. 0.013 0.000empl. female 0.011 0.014empl. male 0.015 0.000

wages 0.012 0.048avwagefem 0.005 0.535avwagemale 0.026 0.001

What stands behind these �ndings? Let us �rst look into the functioningof the permit market. Figure 5 shows a snapshot of the supply and demandschedules that the market maker is facing at a particular iteration given thedecisions of all the �rms how many permits to sell and buy for the labor

19

market with an unequal distribution of women across sectoral skills. Thedownward sloping market demand stems from aggregating up the individual�rms' demands for permits given prices. Similarly the upward sloping supplyis the sum of permits �rms are willing to sell at given prices. As explainedearlier, the market maker chooses the price where supply and demand sched-ules cross and reallocates the permits from those willing to sell at the marketclearing price to those �rms willing to buy.

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100 120 140

PRICE

Quantity

Demand

Supply

Figure 5: Bid-ask-diagram for permit trading market with an equal femalelabor supply across sectors at iteration 1000

The price for the permits and the traded volume as shown in Figure 5 isone observation of all the observations entering the box plots in Figures 6 (a)and (b). Here we compare the labor markets with an equal and an unequaldistribution of women showing that fewer permits are traded in the formercase. It occurs that with an unequal distribution of women the demandschedule shifts outwards as more �rms are struggling to �nd women to �llthe vacancies. But also the supply of permits goes up due to the unequaldistribution of women across sectoral skills. The share of �rms residing insectors that have a relatively large supply of women are in excess supply ofpermits and want to sell. The outward shift of the supply of permits seemsto be of the same magnitude since the permit prices hardly change (Figure6 (b)).

20

3035

4045

Qua

ntity

equal unequal

(by distr of females)Permit Trading

.45

.5.5

5.6

.65

Pric

e

equal unequal

(by distr of females)Permit Price

(a) (b)

Figure 6: (a) Permit trading, and (b) permit prices

About two thirds of the e�ect of a tradable employment quota on welfareaccrues to changes in the wage sum. This e�ect we can disentangle intoa signi�cant employment and a non-signi�cant wage e�ect (see Table 3).The drop in employment is less pronounced for the tradable quota as onemoves from an equal to an unequal distribution of women across sectors ifcompared to the non-tradable quota. Without permits a �rm wanting toproduce may be constrained by the employment quota. There is a vacancyto be �lled, and while there is no female applicant to �ll the vacancy, amale worker would be willing to accept the job o�er. However, the �rmcannot employ him because the employment quota has to be obeyed. Atradable employment quota gives �rms facing such a situation more �exibility.They may purchase a permit allowing them to employ an additional man,and they will do so as long as the additional male worker's pro�tabilitycovers the price of the permit. Thus, more vacancies can actually becomeproductive with a tradable employment quota when female (and male) laborsupply is distributed unequally as re�ected in the non-decline of the maleemployment rate for the tradable quota. The increase in the employmentrate also explains the e�ect of a tradable employment quota on payo�s asan otherwise unproductive vacancy is �lled now, without an increase in theaverage wage rate.

5.2 Extensions and robustness

Besides making female labor supply unequal across sectors, one may arguethat the share of discriminating �rms is also unequally distributed acrosssectors. One could imagine that discrimination already unfolds as youngwomen make their human capital investment decisions avoiding the acquisi-

21

tion of skills for sectors which are known to host �rms having a taste for men.In such a scenario, the share of women and the share of discriminating �rmswould be negatively correlated across sectors. A version of our simulationmodel along these lines yields qualitatively similar results, i.e. a tradableemployment quota is welfare improving.

In addition to the aforementioned extension of the simulation analysis weran a series of robustness tests involving changes of the key parameters ofour model. We were interested in whether our main result on the di�-in-di�e�ect on welfare survives. To this end we combined the two key policy pa-rameters, i.e. the number of permits issued and the quota with one of theremaining parameters, respectively. The results of this exercise are summa-rized in Figures 7, 8, and 9. In all left columns of these �gures we combinechanges in the number of permits with one of the remaining parameters.and in the right columns we combine changes in the quota with one of theremaining parameters. The grids are over three values of each parameter,thus consisting of 9 combinations of parameters. The welfare e�ects of thosenine parameter constellations are combined to a plane. The green planesshow the mean e�ect on the di�-in-di� welfare measure of 100 repetitions.Upper and lower planes constitute the con�dence interval. Figure 7 collectsall parameters related to the adjustment behavior of �rms and workers andthe number of interations of each run. Figure 8 brings together parametersrelated to heterogeneity and frictions in the labor market, and 9 assemblesall parameters on discriminatory behavior. Black dots are related to the pa-rameter constellation that underlies the results in Table 3. The upshot of allthree �gures is that the qualitative results are robust to a large set of param-eter changes. In all cases considered, welfare e�ects are signi�cantly di�erentfrom zero indicating that a system of tradable permits improves welfare.

6 Conclusions

Discrimination of women (as well as other labor market groups) calls fora�rmative action policies. In an economy where women's labor supply isheterogeneous across sectors or regions, an employment quota applied uni-formly to �rms may cause avoidable costs to society. Firms located in sectorsor regions where the supply of female labor is relatively scarce may �nd itinherently di�cult to comply with an employment quota whereas �rms inother sectors where female labor supply is relatively strong will do betterin terms of �lling vacancies with female workers. Output losses may occurin sectors with relatively weak female labor supply as �rms subject to theemployment quota cannot �ll up vacancies with men even if a woman cannot

22

be found.We propose and analyze a �exible quota solution. As we argue, a tradable

employment quota gives �rms additional �exibility to hire men if female laborsupply is insu�cient. By issuing permits to �rms allowing them to hire menand making these permits tradable across �rms, �rms in shortage of womenwill not be forced to abandon output. Rather they will try to purchase apermit that allows them to hire a man up to the point where this additionalman's pro�tability covers the costs of the permit. Equally, we will have �rmsin this market that will �nd it pro�table to sell permits as they can easily�ll their vacancies with women. An advantage of a tradable permit systemis that it allows for a �exible adjustment at the �rm level without having tocompromise on the overall policy goal to achieve a certain share of femaleemployment in the labor market. The scope of female employment in theeconomy can be managed at the aggregate level by issuing or withdrawingpermits.

For analyzing the labor market e�ects of a tradable employment quotawe developed an agent-based labor market model of heterogeneous workersand several sectors, hosting �rms that may taste discriminate against women.The choice of a computational technique to analyze the policy proposal wasmotivated by our aim to show that a permit system may work in a realisticmarket context. Our simulation results suggest that a market for a tradableemployment quota may emerge, and that a more �exible policy solution isactually improving welfare.

Although we did make an e�ort to implement features of the labor andpermit market in considerable detail, we have been silent about the occu-pational or regional scope of a permit system. Given our discussion in theintroduction on the recent moves to make shares of female workers legallybinding for boards of �rms, one may at �rst think of a permit market forthat segment. In principle, however, we believe that a tradable employmentquota would also work for other groups of occupations, may it be introducednationally or for a set of countries as the European Union.

This brings us to our last point, i.e. the odds that a system of permittrading �nds political support. We try to shed light on this question by,once more, drawing analogies to the case of environmental policies. Stavins(1998) presents an insightful discussion on how the main parties involvedpro�ted from a command-and-control environmental policy and had reasonsto oppose a tradable permit system. Similar arguments may apply for a trad-able employment quota. A crispy, �xed employment quota may be easier forpoliticians to communicate to the public which matters for symbolic politics.Moreover, assuming voters have limited information, once �xed regulationsare introduced, �rms and politicians can agree upon mutually bene�cial ex-

23

emptions. The fact, that employment quotas have been introduced for asmall segment of the labor market, very often for boards of publicly listedcompanies only, may evidence such a line of reasoning. It is also reported,that environmental interest groups were hostile towards market-based instru-ments in the beginning. One could imagine, that this could also become thefate of a tradable employment quota. But opposition to a market-based in-strument may also arise for less philosophical reasons. Bureaucracies andlegislators trained in law may lose expertise, and even control as implemen-tation of the a�rmative action policy is left to largely private decisions witha permit system. Thus, there are many reasons to expect that an a�rmativeaction policy based on tradable permits will never be implemented. This isthe more pessimistic outlook. A more optimistic outlook has a glance at thetrading places for pollution rights in Chicago, Leipzig and other cities aroundthe globe.

24

0.04

0.06

WageAdjustment

50

100

150

Permits

0

10

20

30

WelfareDiD

0.04

0.06

WageAdjustment

0.30

0.35

0.40

0.45

0.50

Quota

0

10

20

30

WelfareDiD

(a) (b)

1000

1200

14001600

NumberOfTimesteps

50

100

150

Permits

0

10

20

30

WelfareDiD

1000

1200

14001600

NumberOfTimesteps

0.30

0.35

0.40

0.45

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Quota

0

10

20

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WelfareDiD

(c) (d)

5

10

1520

Learning

50

100

150

Permits

0

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30

WelfareDiD

5

10

1520

Learning

0.30

0.35

0.40

0.45

0.50

Quota

0

10

20

30

WelfareDiD

(e) (f)

Figure 7: Robustness with respect to dynamic behavior of agents

25

5

10

1520

NumberOfApplications

50

100

150

Permits

0

20

40

WelfareDiD

5

10

1520

NumberOfApplications

0.30

0.35

0.40

0.45

0.50

Quota

0

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20

30

40

WelfareDiD

(a) (b)

1

2

34

ApplicationChoice

50

100

150

Permits

0

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40

WelfareDiD

1

2

34

ApplicationChoice

0.30

0.35

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Quota

0

20

40

WelfareDiD

(c) (d)

0.300.35

0.400.45

0.50ProductivityDecline

50

100

150

Permits

0

10

20

30

WelfareDiD

0.300.35

0.400.45

0.50ProductivityDecline

0.30

0.35

0.40

0.45

0.50

Quota

0

10

20

30

WelfareDiD

(e) (f)

Figure 8: Robustness with respect to labor market frictions and heterogeneity

26

0.300.35

0.400.45

0.50DiscriminationCost

50

100

150

Permits

0

10

20

30

WelfareDiD

0.300.35

0.400.45

0.50DiscriminationCost

0.30

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0.40

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0.50

Quota

0

10

20

30

40

WelfareDiD

(a) (b)

0.30.4

0.50.6

0.7DiscriminationShare

50

100

150

Permits

0

10

20

30

WelfareDiD

0.30.4

0.50.6

0.7DiscriminationShare

0.30

0.35

0.40

0.45

0.50

Quota

0

10

20

30

WelfareDiD

(c) (d)

Figure 9: Robustness with respect to extent of discrimination

27

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