good jobs versus bad jobs - mit economics

Good Jobs versus Bad Jobs

Daron Acemoglu, Massachusetts Institute of Technology

This article develops a model of noncompetitive labor markets inwhich high-wage (good) and low-wage (bad) jobs coexist. Minimumwages and unemployment benefits shift the composition of employ-ment toward high-wage jobs. Because the composition of jobs in thelaissez-faire equilibrium is inefficiently biased toward low-wagejobs, these labor market regulations increase average labor produc-tivity and may improve welfare.

I. Introduction

The current debate on labor market regulations focuses on their effectson the level of employment. This article argues that these measures mayhave a first-order impact on the composition of employment as well as thenumber of jobs. I show that in a standard model of the labor market,unemployment insurance and minimum wages induce firms to createmore high-wage jobs, increase average labor productivity, and may im-prove welfare. Similar points have been made informally. Unions, forexample, often support minimum wages and other regulations, arguingthat they will improve the quality of jobs (see, e.g., Harrison and Blue-

This is the theory part of a previous study entitled “Good Jobs versus Bad Jobs:Theory and Some Evidence.” I thank Josh Angrist, Olivier Blanchard, RicardoCaballero, Peter Diamond, David Genesove, Jonathan Gruber, Alan Krueger,Steve Pischke, Jaume Ventura, and seminar participants at the European Univer-sity Institute in Florence, the Centre for Economic Policy Research RisingInequalities Conference, the National Bureau of Economic Research SummerInstitute, Massachusetts Institute of Technology, Princeton, and SUNY Albanyfor useful comments and suggestions. Financial support from the World Eco-nomic Laboratory at the Massachusetts Institute of Technology and NationalScience Foundation grant SBR-9602116 are gratefully acknowledged.

[ Journal of Labor Economics, 2001, vol. 19, no. 1]© 2001 by The University of Chicago. All rights reserved.0734-306X/2001/1901-0001$02.50

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stone 1988). This article demonstrates that some of these claims, perhapsin a less extreme form, follow from standard economic models.

I develop a simple extension of the standard search model of Diamond(1982), Mortensen (1982), and Pissarides (1990) with two different typesof jobs. In the model economy, wage differentials for homogeneousworkers emerge because different types of jobs have different creation(capital) costs.1 Search frictions break the link between marginal productand wages, and they introduce rent-sharing between firms and workers.Although in many search models, an appropriate division of bargainingpower can internalize the pecuniary externalities from rent-sharing (e.g.,Hosios 1990a; Pissarides 1990), in the unregulated (laissez-faire) equilib-rium of this economy, the composition of jobs is always inefficientlybiased toward low-wage jobs. The reason for this inefficiency is a form of“hold-up.” A firm with a capital-intensive job, which has already sunk itsmore expensive investment, is forced to bargain to a higher wage andcreates a greater positive (pecuniary) externality on workers. Since firmsdo not internalize this effect, they open too few high-wage and too manylow-wage jobs. The more novel results of this framework concern theimpact of labor market regulations on the composition of jobs, laborproductivity, and welfare. With higher unemployment benefits, waitingfor high-wage jobs is less costly, so some workers who would haveotherwise accepted low-wage jobs wait for high-wage (good) jobs.2 Thischange in search behavior induces more good jobs to be created. There isalso an indirect—general equilibrium—effect: as more good jobs are created,the value of being unemployed increases because workers anticipate a higherprobability of getting a high-wage job and they become even less willing toaccept bad jobs. The minimum wage has the same overall effect but workssomewhat differently. A binding minimum wage increases the wage that badjobs have to pay, which makes them less profitable and improves the com-position of jobs. Both minimum wages and unemployment insurance in-crease labor productivity because they shift employment toward more cap-

1 In the data, there are large and stable wage differentials among observationallyidentical workers in different industries and occupations (see Krueger and Sum-mers 1987, 1988). Workers who change industry appear to receive the wagedifferential between their previous and new job (Krueger and Summers 1988;Gibbons and Katz 1992), and high-wage jobs have lower quit rates (Krueger andSummers 1988) and longer worker queues (Holzer, Katz, and Krueger 1991). Asin this model, high-wage industries and jobs are on average more capital intensive(Dickens and Katz 1987).

2 I refer to high-wage jobs as “good,” especially since in equilibrium there willbe too few of these jobs. This does not imply that it is always welfare improvingto have more high-wage jobs.

2 Acemoglu

ital-intensive good jobs. Since there are too few good jobs in the laissez-faireequilibrium, these labor market regulations may even improve welfare.

The general equilibrium effects can also lead to multiple equilibria withdifferent compositions of jobs. In one equilibrium, there are many goodjobs, so the outside option of workers is high and bad jobs can onlyemploy them by paying relatively high wages. This makes bad jobsunprofitable. In the other equilibrium, there are many bad jobs, so theoutside option of workers is low. The resulting low wages encourageentry and increase labor market tightness and vacancy duration. Becausegood jobs have larger upfront investments, a tighter labor market hurtsthem more and encourages the creation of bad jobs.

A number of studies are related to this work. First, as noted above,I build on the search models of Diamond (1982), Mortensen (1982),and Pissarides (1990). However, in contrast with these contributions,I analyze a search model with an endogenous distribution of jobs (seealso Davis 1995; and Acemoglu 1996, 1997, 1999), and I emphasize thedistortions in the composition of jobs arising from a version of the“holdup problem” (Grout 1984). Pissarides (1994) also analyzes aneconomy with heterogeneous jobs, but his focus is the modelling ofon-the-job-search in the standard search setup. None of these papersdiscusses the impact of labor market regulation on the composition ofjobs, which is the main focus of this article. Diamond (1981), Acemo-glu and Shimer (1999a), and Marimon and Zilibotti (1999) also con-sider models in which unemployment benefits may improve welfare,but for reasons different from those we consider here. The influentialpaper by Burdett and Mortensen (1989) demonstrates that minimumwages may increase employment, while Lang (1987) shows that whenthere is signaling in the labor market, a minimum wage law maydiscourage low-ability workers from imitating high-ability workersand increase welfare. Most closely related to the current study’sperspective are previous multisector labor market models with fric-tions. Bulow and Summers (1986) construct a two-sector efficiencywage model. Davidson, Martin, and Matusz (1987, 1988) and Hosios(1990b) construct two-sector search models where the equilibriummay be inefficient due to standard search inefficiencies, which isdifferent from the hold-up inefficiency explored in this article. Noneof these studies (except in part Acemoglu and Shimer 1999a) shares theresult that minimum wages and unemployment insurance improve thecomposition of jobs, since this feature crucially relies on search and onthe heterogeneity of jobs.

The remainder of this article is organized as follows. Section II analyzesthe basic model. It determines the equilibrium composition of jobs and

Good Jobs versus Bad Jobs 3

exposes the link between labor market regulation and the mix of jobs.Section III considers some extensions.

II. The Basic Model

A. Technology and Preferences

Labor and capital are used to produce two nonstorable intermediategoods that are then sold in a competitive market and immediately trans-formed into the final consumption good. Preferences of all agents aredefined over the final consumption good alone. Throughout the article, Iwill normalize the price of the final good to 1. There is a continuum ofidentical workers with measure normalized to 1. All workers are infi-nitely lived and risk neutral.3 They derive utility from the consumption ofthe unique final good and maximize the present discounted value of theirutility. Time is continuous, and the discount rate of workers is equal to r.On the other side of the market, there is a larger continuum of firms thatare also risk neutral, with discount rate r.

The technology of production for the final good is

Y 5 ~aYbr 1 ~1 2 a!Yg

r!1/r, (1)

where Yg is the aggregate production of the first input, Yb is the aggregateproduction of the second input, and r , 1. The elasticity of substitutionbetween Yg and Yb is 1/(1 2 r), and a parameterizes the relative impor-tance of Yb. The reason for the use of the subscripts g and b will becomeclear shortly. This formulation captures the idea that there is some needfor diversity in overall consumption-production, and it is also equivalentto assuming that equation (1) is the utility function defined over the twogoods.

Since the two intermediate goods are sold in competitive markets, theirprices are

pb 5 aYbr21Y12r, (2)

pg 5 ~1 2 a!Ygr21Y12r. (3)

The technology of production for the inputs is Leontieff. When matchedwith a firm with the necessary equipment (capital kb or kg), a worker

3 The assumption that workers are risk neutral obviously leaves out the mostimportant role of unemployment insurance, but it also helps to highlight that theimpact of unemployment benefits on job composition is distinct from theirinsurance role. See Acemoglu and Shimer (1999a) for a model of search and riskaversion.

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produces one unit of the respective good.4 The equipment required toproduce the first input costs kg, while the cost of equipment for thesecond input is kb. Throughout this article, I assume that kg . kb.

Before we move to the search economy, it is useful to consider theperfectly competitive benchmark. Since kg . kb, in equilibrium, we willhave pg . pb. But firms hire workers at the common wage, w, irrespectiveof their sector. Thus, there will be neither wage differences nor bad norgood jobs. Also, since the first welfare theorem applies to this economy,the composition of output will be optimal.

B. Search: The Main Idea

Before presenting the detailed analysis, I will heuristically describe themain result. As soon as we enter the world of search, there will be somerent sharing. This implies that a worker who produces a higher-valuedoutput will receive a higher wage. As noted above, because kg . kb, theinput that costs more to produce will command a higher price; thus, inequilibrium, pg . pb. Rent-sharing, then, leads to equilibrium wagedifferentials across identical workers. That is, wg . wb. Hence, the terms“good job” and “bad job.” Next, it is intuitive that since, as comparedwith the economy with competitive labor markets, good jobs have higherrelative labor costs, their relative production will be less than optimal. Inother words, the proportion of good (high-wage) jobs will be too low ascompared with what a social planner would choose. The rest of thissection will formally analyze the search economy and establish theseclaims. It will then demonstrate that higher minimum wages and moregenerous unemployment benefits will improve the composition of jobsand possibly improve welfare.

C. The Technology of Search

Firms and workers come together via a matching technology M(u, v)where u is the unemployment rate, and v is the vacancy rate (the numberof vacancies). The underlying assumption here is that search is undirected;thus both types of vacancies have the same probability of meeting work-ers, and it is the total number of vacancies that enters the matchingfunction. Section IIB allows for directed search, whereby workers decidefor which type of job to apply. The function M(u, v) is twice differen-tiable and increasing in its arguments, and it exhibits constant returns toscale. This enables me to write the flow rate of match for a vacancy asM(u, v)/v 5 q(u ), where q[ is a differentiable decreasing function, and

4 Since utility is linear, whether we think of kb and kg as capital costs or not isimmaterial. The assumption that one worker and equipment ki produce one unitof the corresponding intermediate good is a convenient normalization.


u 5 v/u is the tightness of the labor market. It also immediately followsfrom the constant returns to scale assumption that the flow rate of matchfor an unemployed worker is M(u, v)/u 5 uq(u ) (see Pissarides 1990).In general, q(u ), uq(u ) , `; thus it takes time for workers and firms tofind suitable production partners. I also make the standard Inada-typeassumptions on M(u, v), which ensure that uq(u ) is increasing in u andthat limu3` q(u ) 5 0, limu30 q(u ) 5 `, limu3` q(u )u 5 0, and limu30q(u )u 5 `.

All jobs end at the exogenous flow rate s, and in this case, the firmbecomes an unfilled vacancy and the worker becomes unemployed. Fi-nally, there is free entry into both good-job and bad-job vacancies;therefore, both types of vacancies should expect zero net profits.

I denote the flow return from unemployment by z, which will bethought as the level of unemployment benefit financed by lump-sumtaxation.5 I assume that wages are determined by asymmetric Nashbargaining, where the worker has bargaining power b (see Pissarides1990). Nash bargaining per se is not essential, though rent sharing iscrucial for the results.

Firms can choose either one of two types of vacancies: (i) a vacancy foran intermediate good 1—a good job or (ii) a vacancy for an intermediategood 2—a bad job. Therefore, before opening a vacancy, a firm has todecide which input it will produce, and at this point, it will have to buythe equipment that costs either kb or kg. The important aspect is thatthese creation costs are incurred before the firm meets its employees. Thisis a reasonable assumption, since, in practice, k corresponds to the costsof machinery, which are sector and occupation specific.

D. The Basic Bellman Equations

I will solve the model via a series of Bellman equations. I denote thediscounted value of a vacancy by JV, of a filled job by JF, of beingunemployed by JU, and of being employed by JE. I will use subscripts band g to denote good and bad jobs. I also denote the proportion ofbad-job vacancies among all vacancies by f. Then, in steady state,

rJU 5 z 1 uq~u !@fJbE 1 ~1 2 f!Jg

E 2 JU#. (4)

5 Naturally, unemployment insurance and assistance in the real world do nottake this simple form (see, e.g., Atkinson and Micklewright 1991). First, benefitsdepend on past employment history and earnings (see Sec. IIIC on this); second,unemployment benefits typically expire after a while; and third, there are addi-tional eligibility requirements. Including these complications will not change themain qualitative implications of the analysis (see Mortensen 1977 for a detailedpartial equilibrium analysis of the impact of unemployment insurance on searchdecisions).

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Since this type of equation is rather standard (e.g., Pissarides 1990), I willonly give a brief explanation. Being unemployed is similar to holding anasset. This asset pays a dividend of z, the unemployment benefit, and ithas a probability uq(u )f of being transformed into a bad job, in whichcase the worker obtains Jb

E, the asset value of being employed in a bad job,and loses JU. It also has a probability uq(u )(1 2 f) of being transformedinto a good job, yielding a capital gain Jg

E 2 JU (out of steady state, JU hasto be added to the right-hand side to capture future changes in the valueof unemployment). Observe that this equation is written under theimplicit assumption that workers will not turn down jobs, which I willdiscuss further below (see n. 6). The steady-state discounted present valueof employment can be written as

rJiE 5 wi 1 s~ JU 2 Ji

E!, (5)

for i 5 b, g. Equation (5) has an intuition similar to that of equation (4).Similarly, when matched, both vacancies produce one unit of their

goods, so

rJiF 5 pi 2 wi 1 s~ Ji

V 2 JiF !, (6)

rJiV 5 q~u !~ Ji

F 2 JiV!, (7)

for i 5 b, g, where I have ignored the possibility of voluntary jobdestruction, which will never take place in a steady state.

Since workers and firms are risk neutral and have the same discountrate, Nash bargaining implies that wb and wg will be chosen so that

~1 2 b!~ JbE 2 JU! 5 b~ Jb

F 2 JbV!,

(8)~1 2 b!~ Jg

E 2 JU! 5 b~ JgF 2 Jg

V!.

Note that an important feature is already incorporated in these expres-sions: workers cannot pay to be employed in high-wage jobs; due tosearch frictions, at the moment a worker finds a job, there is bilateralmonopoly, and this leads to rent sharing over the surplus of the match.

As there is free entry on the firm side, it should not be possible for anadditional vacancy to open and make expected net profits. Hence

JiV 5 ki . (9)

Finally, the steady-state unemployment rate is given by equating flowsout of unemployment to the number of destroyed jobs. Thus


u 5s

s 1 uq~u !. (10)

E. Characterization of Steady-State Equilibria

A steady-state equilibrium is defined as a proportion of f of bad jobs;tightness of the labor market u; value functions Jb

V, JbF, Jb

E, JgV, Jg

F, JgE, and

JU; prices for the two goods, pb and pg, such that equations (2), (3), (4),(5), (6), (7), (8), and (9) for both i 5 b and g are satisfied. The steady-stateunemployment rate is then given by equation (10).6 In steady state, bothtypes of vacancies meet workers at the same rate, and in equilibriumworkers accept both types of jobs; therefore Yb 5 (1 2 u)f, and Yg 5 (12 u)(1 2 f). Then, from equation (3), the prices of the two inputs canbe written as

pg 5 ~1 2 a!~1 2 f!r21@afr 1 ~1 2 a!~1 2 f!r#12r

r ,(11)

pb 5 afr21@afr 1 ~1 2 a!~1 2 f!r#12r

r .

Using equations (5), (6), (8), and (9), simple algebra gives

wi 5 b~ pi 2 rki! 1 ~1 2 b!rJU (12)

as the wage equation. Intuitively, the surplus that the firm gets is equal tothe value of output, which is pi minus the flow cost of the equipment, rki.The worker gets a share b of this, plus (1 2 b) times his outside option,rJU. Using equations (6) and (7), the zero-profit condition, equation (9),can be rewritten as

q~u !~1 2 b!~ pb 2 rJU!

r 1 s 1 ~1 2 b!q~u !5 rkb, (13)

q~u !~1 2 b!~ pg 2 rJU!

r 1 s 1 ~1 2 b!q~u !5 rkg. (14)

A firm buys equipment that costs ki, which remains idle for a while dueto search frictions (i.e., because q(u ) , `). This cost is larger for firmsthat buy more expensive equipment and open good jobs. They need to

6 One might wonder at this point whether a different type of equilibrium, withJU 5 Jb

E and workers accepting bad jobs with probability z , 1, could exist. Theanswer is no. From eq. (8), this would imply Jb

V 5 JbF, but in this case, firms could

never recover their upfront investment costs.

8 Acemoglu

recover these costs in the form of higher net flow profits, that is, pg 2 rkg. pb 2 rkb. From rent sharing, this immediately implies that wg . wb.More specifically, combining equations (12), (13), and (14), we get

wg 2 wb 5~r 1 s!~rkg 2 rkb!

q~u !. 0. (15)

Therefore, wage differences are related to the differences in capital costsand also to the average duration of a vacancy. In particular, whenq(u ) 3 `, the equilibrium converges to the Walrasian limit point andboth wg and wb converge to rJU, so wage differences disappear. Thereason for this is that in this limit point, capital investments never remainidle; thus good jobs do not need to make higher net flow profits. Also,with equal creation costs, that is, with kb 5 kg, wage differentialsdisappear again.

Finally, equation (4) gives the value of an unemployed worker as

rJU 5 G~u, f! ;~r 1 s! z 1 buq~u !@f~ pb 2 rkb! 1 ~1 2 f!~ pg 2 rkg!#

r 1 s 1 buq~u !.

(16)

It can easily be verified that G( z , z ) is continuous, strictly increasing inu, and strictly decreasing in f. Intuitively, as the tightness of the labormarket, u, increases, workers find jobs faster; thus rJU is higher. Also asf decreases, the greater fraction of good jobs among vacancies increasesthe value of being unemployed, since wg . wb (i.e., Jg

V . JbE). The

dependence of rJU on f is the general equilibrium effect mentioned in theintroduction: as the composition of jobs changes, the option value ofbeing unemployed also changes.

A steady-state equilibrium is characterized by the intersection of twoloci: the bad-job locus equation (13) and the good-job locus equation (14)(both evaluated with eqq. (11) and (16) substituted in). Figure 1 drawsthese two loci in the u-f plane. Locus (14), along which a firm that opensa good-job vacancy makes zero-profits, is upward sloping: a higher valueof f increases the left-hand side of equation 14; thus u needs to change toincrease the right-hand side (and to reduce the left-hand side throughG(u, f)). Intuitively, an increase in f implies a higher pg (from eq. [11]).So, to ensure zero profits, u needs to increase to raise the duration ofvacancies. In contrast, locus (13) cannot be shown to be decreasingeverywhere. Intuitively, an increase in f reduces pb, and thus it requiresa fall in u to equilibrate the market, but the general equilibrium effectthrough JU (i.e., that a fall in f reduces JU) counteracts this and maydominate. This issue is discussed further in the next subsection.


Here, I start with the case in which r # 0, so that good jobs and badjobs are gross complements. In this case, it is straightforward to see thatas f tends to 1, equation (13) gives u3 `, whereas equation (14) impliesu3 0. Thus, the bad-job locus is above the good-job locus. The oppositeis the case as f goes to 0. Then, by the continuity of the two functions,they must intersect at least once in the range f [ (0, 1). The followingproposition summarizes these results.

PROPOSITION 1. Suppose that r # 0. Then, a steady state equilibriumwith f [ (0, 1) always exists and is characterized by equations (11), (12),(13), (14), and (16). In equilibrium, for all kg . kb, we have pg . pb, andwg . wb.

When r . 0, an equilibrium continues to exist, but it does not need tobe interior, so one of equation (13) and (14) may not hold. A particularexample of this is discussed in the next subsection.

F. Multiple Equilibria

Since locus (13) can be upward sloping over some range, more than oneintersection, and hence multiple equilibria, are possible. Locus (13) ismore likely to be upward sloping when relative prices change little as aresult of a change in the composition of jobs. Therefore, to illustrate thepossibility of multiple equilibria, I consider the extreme case where r 5 1,so that goods g and b are perfect substitutes and there are no relative price

FIG. 1.—Equilibrium determination

10 Acemoglu

effects. Furthermore, I assume that 1 2 2a . r(kg 2 kb). In the absenceof this assumption, good jobs are not productive enough, and they willnever exist in equilibrium.

The absence of substitution between good jobs and bad jobs immedi-ately implies that pg 5 1 2 a . pb 5 a. The equilibrium can then becharacterized diagrammatically. To do this, totally differentiate equations(13) and (14), with pg 5 1 2 a, and pb 5 a, which gives

du

dfU

i

5

2]G~u, f!

]f

]G~u, f!

]u2 kiF ~r 1 s!~1 2 b!q9~u !

~1 2 b!q~u !2 GF]G~u, f!

]u G . 0, (17)

where i 5 b is the zero-profit condition for bad jobs (eq. 13), and i 5 gis the zero-profit condition for good jobs (eq. 14). The derivative inequation (17) is positive, irrespective of whether it is for good jobs or badjobs, because rJU 5 G(u, f) is decreasing in f and increasing in u, whileq9(u ) , 0. Since kb , kg, this equation also immediately implies thatlocus (13) is steeper than locus (14). So locus (13) has to intersect locus(14) from below, if at all, in which case there will be three equilibria, asshown in figure 2.7 The first is a “mixed strategy” equilibrium at the pointwhere the two curves intersect. The other two equilibria are more inter-esting. When f 5 0, we have ug . ub, so that it is more profitable to opena good job (see fig. 2).8 Hence, there is an equilibrium in which all firmsopen good jobs. It is not profitable for firms to open a bad job, becausewhen f 5 0, workers receive high wages and have attractive outsideoptions; so a firm that opens a bad job will be forced to pay a relativelyhigh wage, making a deviation to a bad job unprofitable. In contrast, at f5 1, we have u9g , u9b, so it is an equilibrium for all firms to open badjobs. Intuitively, when all firms open bad jobs, the outside option ofworkers is low, so firms bargain to low wages, making entry relativelyprofitable. In equilibrium, u has to be high to ensure zero profits. But atight labor market (a high u) hurts good jobs relatively more since theyhave to make larger upfront investments. The multiplicity of equilibria inthis model illustrates the strength of the general equilibrium forces that

7 Alternatively, the two curves may never intersect. In this case, if ub . ug andu9b . u9g, then the unique equilibrium is one with bad jobs only, or if ub , ug andu9b , u9g, there will only be good jobs.

8 Firms that open good jobs make zero profits at u 5 ug, while firms thatopen bad jobs make zero profit at u 5 ub. Since ug . ub, good jobs are moreprofitable than bad jobs.


operate through the impact of job composition on the overall level ofwages.

G. Welfare

To analyze the welfare properties of equilibrium, I look at the totalsteady-state surplus of the economy, defined as total output minus totalcosts, that is, the net output of the economy. This measure is what anagent would care about before entering the economy (as is the conventionin these models; see Hosios 1990a; Pissarides 1990). Total surplus (insteady state) can be written as

TS 5 ~1 2 u!@f~ pb 2 rkb! 1 ~1 2 f!~ pg 2 rkg!#

2 uu@frkb 1 ~1 2 f!rkg#. (18)

Total surplus is equal to total flow of net output, which consists of thenumber of workers in good jobs [(1 2 f)(1 2 u)] times their net output( pg minus the flow cost of capital rkg), plus the number of workers in badjobs [f(1 2 u)] times their net product ( pb 2 rkb), minus the flow costsof job creation for good and bad vacancies (respectively, uu(1 2 f)rkgand uufrkb).

It is straightforward to locate the set of allocations that maximize total

FIG. 2.—Multiple equilibria

12 Acemoglu

social surplus. This set would be the solution to the maximization ofequation (18) subject to equation (10). Inspecting the first-order condi-tions of this problem, it can be seen that decentralized equilibria will notin general belong to this set; thus a social planner can improve over theequilibrium allocation. The results regarding the socially optimal amountof job creation are standard (Hosios 1990a; Pissarides 1990): if b is toohigh, that is b . h(u) (where h(u) is elasticity of the matching function,q(u )), then there will be too little job creation; if b , h(u), there will betoo much. Since this article is concerned with the composition of jobs, Iwill not discuss these issues in detail. Instead, I will show that regardlessof the value of u, the equilibrium value of f is always too high; that is,there are too many bad jobs relative to the number of good jobs. To provethis claim, it is sufficient to consider the derivative of TS with respect tof at z 5 0 (note that the constraint, eq. [10], does not depend on f):

dTSdf

5 ~1 2 u! z Fd~fpb 1 ~1 2 f! pg!

df G 2 @~1 2 u 1 uu ! z ~rkb 2 rkg!#.

(19)

For the composition of jobs to be efficient at the laissez-faire equilibrium,equation (19) needs to equal zero when evaluated in the equilibriumcharacterized above. Some simple algebra (details are available on request)using equations (10), (11), (13), and (14) to substitute out u, and ki gives:

dTSdf

Udec.eq.

5uq~u !

s 1 uq~u !z F1 1

~s 1 q~u !!~1 2 b!

r 1 s 1 ~1 2 b!q~u !G z ~ pb 2 pg! , 0.

This expression is always negative, regardless of the value of u; so startingfrom laissez-faire equilibrium, a reduction in f will increase social sur-plus. Therefore:

PROPOSITION 2. Let fs(u ) be the value of f that the social plannerwould choose at labor market tightness u, and let f*(u) be the laissez-faireequilibrium with z 5 0; then f*(u ) . fs(u ) for all u. That is, in thelaissez-faire equilibrium, the proportion of bad jobs is too high.

The intuition is simple; in a decentralized equilibrium, it is always thecase that wg . wb. Yet, firms do not take into account the higher utilitythey provide to workers by creating a good job rather than a bad job;hence, there is an uninternalized positive externality, which leads to anexcessively high fraction of bad jobs in equilibrium. Search and rentsharing are crucial for this result. Search ensures that firms have to sharethe ex post rents with the workers and that they cannot induce compe-tition among workers to bid down wages. Firms would ideally like tocontract with their workers on the wage rate before they make the


investment decision, but search also implies that the firms do not knowwho these workers will be, and thus cannot contract with them at the timeof investment (Acemoglu 1996).

H. The Impact of Minimum Wages and Unemployment Benefits

As is usual in models with potential multiple equilibria, only thecomparative statics of “extremal” equilibria are of interest. Therefore, Iassume in this subsection that the economy is in an equilibrium wherelocus (14) cuts locus (13) from below.9 Now consider an increase in z,which corresponds to the unemployment insurance system becomingmore generous. Both the bad-job locus (eq. [13]) and the good-job locus(eq. [14]) will shift down (to the dotted curves in fig. 1). Hence, u willdefinitely fall. It is also straightforward to verify that (13) will shift bymore; therefore, f is unambiguously reduced.10 Intuitively, with f un-changed, relative prices and hence wages will be unchanged, but then withthe higher unemployment benefits, workers would prefer to wait forgood jobs rather than accept bad jobs. This increases wb and reduces f(the fraction of bad jobs). Furthermore, a more generous unemploymentbenefit not only increases the fraction of good jobs, but it may alsoincrease the total number of good jobs. Totally differentiating equations(13) and (14), we obtain that the total number of good jobs will increaseif and only if

wg 2 wb . S 1h~u !

2 1Du~1 2 f!Sd~ pg 2 pb!

df D ,

where h(u) is the elasticity of q(u ). This inequality is likely to be satisfiedwhen the two inputs are highly substitutable, that is, when r is close to 1,when wage differences are large, when h(u) is close to 1, or whenunemployment is low to start with. Thus, only increases in unemploy-ment benefits that start from moderate levels increase the number of goodjobs.

The impact on welfare depends on how large the effect on u is relativeto the effect on f. We can see this by totally differentiating equation (18)after substituting for u. This gives a relationship between u and f, drawnas the dashed line in figure 1, along which total surplus is constant. Shifts

9 It is straightforward to extend the analysis to show that in the case where thereare multiple equilibria, labor market regulations make the equilibrium with moregood jobs more likely.

10 To see this formally, totally differentiate eqq. (13) and (14) with respect to u,f, and z, and write A(du df)9 5 bdz, where A is a 2 3 2 matrix and b 5 (1 1)9.It is straightforward to see that in a “stable” equilibrium determinant A . 0 anda11 2 a21 5 q9(u )(r 1 s)(rkg 2 rkb)/q(u )2 , 0, which gives df/dz , 0.

14 Acemoglu

of this curve toward the northeast give a higher surplus. When this curveis steeper than locus (14), a higher z can improve welfare, and this is thecase drawn in figure 1. For example, if b is very low to start with, thenunemployment will be too low relative to the social optimum (see Hosios1990a; Pissarides 1990); in this case, an increase in z will unambiguouslyincrease total welfare.11

More generally, regardless of whether total surplus increases, a moregenerous unemployment benefit raises average labor productivity, fpb1 (1 2 f) pg, which is unambiguously decreasing in f. Therefore, whenunemployment benefits increase, the composition of jobs shifts towardmore capital-intensive good jobs and labor productivity increases.

A minimum wage has a similar effect on job composition. Consider aminimum wage wI such that wb , wI , wg, so the wage is only bindingfor bad jobs. The equation for Jb

F now becomes JbF 5 ( pb 2 wI 1 skb)/(r

1 s). Then, equation (13) changes to

q~u !pb 2 wI

r 1 s 1 q~u !5 rkb. (20)

Since at a given u, the left-hand side of equation (20) is less than that ofequation (13), the impact of a higher minimum wage is to shift thebad-job locus, curve (13) in figure 1, down. The good-job locus is stillgiven by equation (14), but now, combining equations (4) and (5), wehave

rJU 5 G~u, f! ;~r 1 s! z 1 buq~u !@fwI 1 ~1 2 f!~ pg 2 rkg!#

r 1 s 1 uq~u !@1 2 ~1 2 b!~1 2 f!#.

Since wI . wb, both curves shift down in figure 1, but, as in the case ofunemployment benefits, curve (13) shifts down by more, so both f andu fall. Again, the rise in minimum wages can increase the number, not justthe proportion, of good jobs and total welfare. Moreover, for the samedecline in u, an increase in minimum wages reduces f more than does anincrease in z; therefore, minimum wages appear to be more powerful inshifting the composition of employment away from bad jobs towardgood jobs. Overall:

PROPOSITION 3. Both the introduction of a minimum wage wI and anincrease in unemployment benefit z decrease u and f. Therefore, they

11 Namely, dTS/dz 5 [(]TS/]f)/(df)/dz)] 1 [(]TS/]u )(du/dz)]. The firstterm is positive, and if b is sufficiently low that ]TS/]u , 0, then the second termwill be positive too, and an increase in z will unambiguously increase net output.


improve the composition of jobs and average labor productivity, but theyincrease unemployment. The impact on overall surplus is ambiguous.

This section only reported the response of the steady state to changesin policy. Transitory dynamics are more involved but do not change thebasic predictions. Essentially, in response to an increase in z (or a bindingminimum wage, wI ), the economy stops creating bad jobs for a while andcreates only good jobs. Therefore, the short-run impact of the policychanges will be quite large. Overall, in finite time, the right fraction ofgood jobs and bad jobs is achieved, but the unemployment rate adjustsmore slowly. As a full analysis of transitory dynamics requires consid-erably more notation, the details are left out.

III. Extensions

A. Endogenous Search Effort

In the above analysis, although higher unemployment benefits andminimum wages improve the composition of jobs and potentially welfare,they always increase unemployment. However, this not a general result.If we also include a margin of choice on the worker side, this result nolonger holds. In this subsection, I briefly outline the simplest way ofmodelling this by introducing search effort (see, e.g., Pissarides 1990).

I assume that the matching function is given as M(eu, v), where e is theaverage search effort of unemployed workers. Similar equations can nowbe written, but u needs to be defined as u 5 v/eu. Throughout thissection, I will only consider symmetric steady-state equilibria in which allworkers use the same strategy; thus e 5 e. The probability that a workersearching at intensity e finds a job is euq(u), where u 5 v/eu. I alsoassume that the flow cost of choosing search effort e is c(e), where c[ isa strictly increasing, differentiable, and convex function. Then, the Bell-man equations for the firm are unchanged and, for the worker, onlyequation (4) changes. It is replaced by

rJU 5 z 2 c~e! 1 eu# q~u# !@fJbE 1 ~1 2 f!Jg

E 2 JU#. (21)

Also, equation (10) now becomes

u 5s

s 1 e#u# q~u# !.

Differentiating equation (21), we get the condition for e to be chosenoptimally, and evaluating this in equilibrium, that is, where e 5 e, weobtain

u# q~u# !@fJbE 1 ~1 2 f!Jg

E 2 JU# 5 c9~e# !.

16 Acemoglu

As before, for given e, an increase in the minimum wage will reduce u,but with endogenous search effort, it will also increase e (as long as itincreases Jb

E). Therefore, the overall impact on u is ambiguous: if thechange in e is large enough, unemployment may fall because the increasein wages caused by the minimum wage legislation encourages all workersto search more. This model with variable search effort therefore offers analternative and complementary explanation to Burdett and Mortensen’s(1989) model for why, in the instances studied by Card and Krueger(1995), higher minimum wages did not reduce employment of affectedworkers and may have even increased it slightly.

The analysis of an increase in unemployment benefit is similar. How-ever, the impact of unemployment benefits on employment is now morenegative. This is because, in contrast to an increase in minimum wage,which tends to encourage search, a higher level of z creates a standardmoral hazard effect and discourages search effort.

B. Directed Search

In practice, workers do have some information about which sectors payhigher wages. Therefore, a model of directed search where workers decidefor which type of job to apply describes the functioning of the labormarket better. This subsection briefly discusses the extension of themodel to include directed search.

Suppose that workers can apply to the good-job sector or to thebad-job sector. The number of bad-job matches is given by M(ub, vb) andthat for good jobs is given by M(ug, vg), where ui is the number ofunemployed workers applying to i-type jobs and vi is the number ofi-type vacancies.12 The assumption that both sectors have exactly thesame matching function is for simplicity and highlights that differences inthe technology of matching are not the source of the results. SinceM( z , z ) exhibits constant returns to scale, the flow rate of a match fora worker applying to sector i is uiq(ui), and the flow rate of a match fora type i-vacancy is q(ui). The steady-state value of an unemployedworker applying to sector i is

rJiU 5 z 1 uiq~ui!@ Ji

E 2 JiU#. (22)

For there to be both types of jobs, we require that rJU 5 rJbU 5 rJg

U. Theother Bellman equations, (5), (6), and (7); the wage equation (8); and thezero-profit condition (9) are the same as above. Now, we have to deter-mine ub and ug separately, and the aggregate production of bad and good

12 See Acemoglu and Shimer (1999b, 2000) for a detailed analysis of directedsearch with wage posting.


intermediate goods are Yb 5 (1 2 ub)l and Yg 5 (1 2 ug)(1 2 l),where l is the fraction of workers applying to the bad-job sector. Theprice equation (11) is also modified accordingly.

An equilibrium exists and, since equation (12) still applies, we have wg. wb. Worker indifference between the two sectors, rJb

U 5 rJgU, also

implies that ubq(ub) . ugq(ug), that is, that workers who apply to badjobs suffer shorter unemployment spells. This is in line with the evidencecited in the introduction that high-wage jobs attract longer queues (Hol-zer, Katz, and Krueger 1995). Labor market regulations have the sameeffects as before in this model. First, a higher level of z at given ub, ug, ub,and ug would lead to rJg

U . rJbU, which would encourage more workers

to apply to the good-job sector. To ensure the indifference condition forworkers, rJb

U 5 rJgU, pg and wg have to decline, so the production of good

g and the fraction of workers applying to the good-job sector, 1 2 l, willincrease and the price of the output of sector g will fall. Therefore, theunemployment benefit once again shifts the composition of employmenttoward high-wage jobs. Minimum wages will again work more directlyby pushing wb up, thus reducing profits from opening bad jobs andencouraging the creation of more good jobs.

Welfare implications are now more complicated, and they depend onwhether the bargaining power of workers, b, is greater than or less thanthe elasticity of the matching function, h(u) (Hosios 1990a). When b. h(u), there will be too little job creation, and the composition of jobswill be biased toward low-wage jobs. The reason why directed searchdoes not necessarily help in solving the inefficiency problem is that firmsare unable to commit to wages, which are still determined by bargainingafter matching takes place.13

C. Unemployment Benefits Conditional on Past History

The analysis so far has considered an unemployment insurance systemthat pays a constant amount z to all unemployed workers. In practice, thelevel of benefits depends on the earnings history of individual workers,often with a progressive form. This can be incorporated into the model byintroducing two levels of unemployment benefits, zg and zb, such thatworkers previously employed in a good (high-wage) job receive zg, whilethose previously employed in a bad (low-wage) job receive zb. Theanalysis becomes considerably more complicated, in part because thevalue of obtaining a certain job includes future unemployment benefitsthat the worker will receive after being employed at this job. The main

13 See Acemoglu and Shimer (1999b) for a discussion of the differences betweendirected search and wage posting. The results in Acemoglu and Shimer (1999b)also imply that when b 5 h(u), the composition of jobs would be efficient.

18 Acemoglu

results are unaffected, but we obtain the additional result that an increasein the progressivity of unemployment benefits increases the fraction oflow-wage jobs. Notice that in this setup, workers have a further reason towait for high-wage jobs, since these are associated with a higher unem-ployment benefit, zg, in the future. An increase in the progressivity of theunemployment benefit system, which corresponds to a decrease in zgrelative to zb, therefore weakens this motive and makes workers morewilling to take low-wage jobs. This encourages the creation of more badjobs.

D. Capital-Labor Substitution

The technology of production used so far is Leontieff, and each firmemploys only one worker. So there is no room for capital-labor substi-tution within firms. It is instructive to investigate whether the resultsgeneralize to the case with capital-labor substitution and diminishingreturns to labor. With diminishing returns, the exact form of bargainingbecomes important. If workers bargain as a group against the firm, forexample in the form of a union, the results so far immediately generalize.The more involved case is the one where the firm bargains individuallywith each worker. This case has been analyzed by Stole and Zwiebel(1996), who use a bargaining concept similar to the Shapley value. Astriking result of their analysis is that, when a firm bargaining with eachemployee individually faces a perfectly elastic demand curve, it will hiremore workers than would a wage-taking firm. It will do so to reduce theproductivity contribution of a marginal worker and to hold down work-ers to their outside option. In our context, suppose that a firm in the gsector has the production function kg

12glgg and a firm in the b sector has

the production function kb12hlb

h, where h . g, ensuring that the b sector ismore labor-intensive. It is straightforward that a wage-taking firm facinga wage of v would choose lg 5 g1/(12g)pg

1/(12g)v21/(12g)kg. Stole andZwiebel’s (1996) result 1 implies that a firm bargaining with its employeesindividually will instead hire lg 5 (2g)1/(12g)(1 1 g)21/(12g)

3 pg1/(12g)v21/(12g)kg . lg, and it will pay v to all of its employees.

Similar expressions apply for sector b firms; they, too, pay v to all theiremployees; so wage differentials across workers disappear.

This may suggest that the results here do not generalize to a situationwith capital-labor substitution, diminishing returns to labor, and individ-ual bargaining between firms and workers. This is not necessarily the case,however. The main difference between the situation considered by Stoleand Zwiebel (1996) and my model is that here the firm cannot costlesslyhire new workers. Instead, after a firm purchases the required equipmentand opens a vacancy, recruitment of workers will be a slow process,which is the source of all the inefficiencies and of the results in the aboveanalysis. Therefore, even if the firm finds it optimal to build up its labor


force to lg, there will be an extended period of time during which theproductivity of the marginal worker is quite high, and during this period,the firm will have to pay high wages. Although such a model is quitedifficult to solve, it seems natural that this problem would imply higherlabor costs for sector g firms than for sector b firms, which would onceagain bias the composition of jobs toward low wages.14

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