a theory of dual labor markets with application to industrial policy, discrimination and keynesian...

7/29/2019 A Theory of Dual Labor Markets With Application to Industrial Policy, Discrimination and Keynesian Unemployment

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A Theory of Dual Labor Marketswith Application to IndustrialPolicy, Discrimination, andKeynesian Unemployment

Jeremy I. Bulow, Stanford University and

National B~ireau ofEconomic Research

Lawrence H. Summers, Harvard University andNational Bureau ofEconomic Research

This paper develops a model of dual labor markets based onemployers need to motivate workers. In order to elicit effort fromtheir workers, employers may find it optimal to pay more than the

going wage. This changes fundamentally the character of labor

markets. The model is applied to a wide range of labor marketphenomena. It provides a coherent framework for understandingthe claims of industrial policy advocates. It also can provide thebasis for a theory of occupational segregation and discriminationthat will not be eroded by market forces. Finally, the model providesthe basis for a theory of involuntary unemployment.

Many economists take the position that competitive markets will tend

to make efficient microeconomic decisions about the composition ofnational output and the means by which it is produced but thatmacroeconomic problems of unemployment will remain. An alternative

We have benefited from comments provided by James Medoff, James Poterba,Andrei Shleifer, Carl Shapiro, Richard Startz, and Joseph Stiglitz. The researchreported here is part of the NBERs research programs in Labor Studies,Economic Fluctuations, and Taxation. Any opinions expressed are those of theauthors and not those of the National Bureau ofEconomic Research.

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Theory of Dual Labor Markets 377

view is that unemployment and periods of recession are just the most

obvious manifestations ofmarket imperfections that pervasively distortthe allocation ofresources. Market failures that can lead to unemployment

are also likely to distort microeconomic aspects ofperformance badly.

The existence of unemployment and the implied failure of the labor

market to clear can result only from the failure ofwages to adjust tothe point at which the supply and demand for labor are equated. Absent

minimum wage laws or other institutional impediments, the failure offirms to reduce wages in the face of unemployment must mean that for

some reason it is unprofitable for them to do so. A number of possible

reasons why firms might find it unprofitable to reduce wages even whenthey face an excess supply of labor have been provided in the context

of the burgeoning efficiency wage literature.1 This paper explores some

of the microeconomic implications ofefficiency wage models. Dualismin the labor market, discrimination, and industrial policies are analyzed.

We also show how efficiency wage models can help to make sense ofthe concept ofinvoluntary unemployment in an economy in which some

types of jobs are always available to unemployed workers.

We focus on the implications of one deviation from the standardcompetitive modelthe inability of firms to measure perfectly the

amount of effort their workers are putting forth. Firms may elicit more

effort from their workers by monitoring them more closely or by raisingtheir wages, so the cost to workers of being replaced is increased.2 A

worker who is paid only his opportunity cost has little incentive toperform well since losing his job would not be costly. It is the deviation

of workers wages from their opportunity costs that gives rise to ourmodels imperfectly competitive features. As we discuss below, formu-

Excellent surveys of the efficiency wage literature may be found in Stiglitz(1984) and Yellen (1984). The informal discussion in these surveys anticipates anumber of the points developed in this paper. Our formal analysis builds onthat ofShapiro and Stiglitz (1984). Firms may find it costly to lower wages forreasons other than those stressed by authors writing in the efficiency wagetradition. For example, firms paying low wages may be more likely to beunionized, or the act of renegotiating wage rates may be costly. In the sense thatthey explain why lowering wages is costly, these ideas are efficiency wagetheories as well.

2 The idea that firms need to elicit effort from workers can give rise to a labor

market with imperfectly competitive features h~s recently been explored in Calvo(1979), Gintis and Ishikawa (1984), Shapiro and Stiglitz (1984), and Bowles(1985). A particularly clear statement of the role of noncompetitive wages ineliciting effort may be found in Becker and Stigler (1974). The idea dates backat least to Adam Smiths observation that the wages oflabor are the encourage-ment of labor which like every other human quality improves in proportion tothe encouragement it receives: Where wages are high accordingly we shall alwaysfind the workmen more active, diligent and expeditious than when they are(Smith 1937, p . 81).


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378 Bulow/Summers

lations in which firms pay their workers more than the going wage inan effort to reduce turnover or to attract high-quality workers parallel

ours in many respects.The potential importance of the linkages between the level of wages

and worker productivity that form the basis of our analysis is well

illustrated by one of the most dramatic chapters in the history ofAmerican industrial relations. This episode also serves to highlight theimportance of the effort-elicitation problem as an explanation for non-

market clearing wages. In 1914, the Ford Motor Company introducedthe $5.00 day for industrial workers. At the time prevailing wages at

Ford and other companies were between $2.00 and $3.00 a day.Immediately following the announcement, more than 10,000 people

gathered butside the Ford plant gates looking for jobs. Ford declaredthat the motive for the wage increase was profit sharing and efficiency

engineering. ,~ A contemporary engineering study of production at Ford,

Arnold and Faurote (1915), described the results of Fords innovation:

The Ford high wage does away with all of the inertia and living forceresistance. . . . The workingmen are absolutely docile, and it is safe tosay that since the last day of 1913, every single day has seen major

reductions in Ford shops labor costs (Arnold and Faurote 1915, p. 331).Alan Nevins, in his history ofthe early Ford Motor Company, concluded

that Ford and his associates freely declared on many occasions that the

high wage policy had turned out to be good business. By this theymeant that it had improved the discipline of the workers, given them amore loyal interest in the institution, and raised their personal efficiency.

Once the Ford factory, like others had been called The House ofCorrection; now itwas temporarily called The House ofGood Feeling

(Nevins 1954, p. 549).The only available quantitative estimate of the effects of Fords high

wage policy appears to be the calculation by Fords chief of labor

relations, John Lee (1916), that productivity increased by 510/0 in 1914

following the introduction of the high wage policy. One estimate, Levin(1927), suggests that the high wage policy halved absenteeism. And

Nevins (1954, p. 567) reports that discharges for cause declined very

sharply because of the instant and unquestioning obedience of meneager not to lose their five dollar day.

The increases in productivity appear to be attributable almost entirelyto increases in worker effort. After reviewing the Ford archives, Nevinsconcluded that suggestions that management was actuated by a desire

to get the pick of Detroit mechanics and by anxiety to end a high

turnover rate are demonstrably false and misleading. . . . The massproduction methods of the Ford plant made it unnecessary to search for

Quoted in Nevins (1954, p. 538).


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Theory ofDual Labor Markets 379

picked mechanics. . . . the turnover problem had been practically solved

before the five dollar wage was adopted. The theory [that managementwas trying to avert the threat ofunionization] is not supported by real

evidence. The union had shot its feeble bolt long before the wage

decision (Nevins 1954, pp. 551 54).The contemporary importance ofvariations in effort and the costs of

monitoring them may be conveyed in a number ofways. A large fraction

of the U.S. labor force is involved in supervision rather than the directproduction of goods and services, and the maintenance ofworker morale

is a major priority for most firms. Productivity varies widely across timeand space in ways that are difficult to account for except in terms of

differences in effort broadly defined.4 A Department of Health, Education,

and Welfare taskforce on Work in America (U.S. Department ofHealth,Education, and Welfare 1973, p. 27) concluded, after reviewing hundreds

of studies of individual plants, that lowering business costs by reducing

absenteeism, tardiness, turnover, labor disputes, sabotage, and poorquality can increase productivity by up to 400/o.

This paper is organized as follows. Section I develops a basic model

of a dual labor market paralleling the Shapiro-Stiglitz analysis ofunemployment. It shows how equally productive workers can in equi-

librium be allocated arbitrarily between a primary and a secondary sector

of the economy. These sectors parallel institutional descriptions of thedual labor market such as that of Doeringer and Piore (1971). Theprimary sector is characterized by high wages and responsible career

jobs, while the secondary sector has menial jobs, low wages, and no jobladders. Although workers in the secondary sector envy those in the

primary sector and are equally productive, there is no equilibratingmarket force that can erode wage differentials. The model also explains

why firms are extremely conscious of their relative standing in settingwages and how firms paying different wages can coexist in market

equilibrium.

Section II shows that our dual labor market model provides a formalframework that can justify the arguments of American industrial policy

advocates that the high wage/high value added sectors of an economyshould be subsidized and protected from foreign competition. Unlike

most ofthe arguments in the industrial policy debate, ours explains why

workers and not just imperfectly competitive firms might benefit fromindustrial policies. These theoretical arguments do not of course mean

that actual industrial policies would be desirable given the political andpractical problems attending their implementation.

Section III discusses theories of wage discriminationthe observation

~Nelson (1981) surveys evidence suggesting that standard variables leave agreat deal of productivity variation unexplained.


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380 Bulow/Summers

that workers wages are affected by their demographic status as well asby their productivity. Unlike standard theories of discrimination, the

model presented here explains why discrimination endures in spite ofmarket forces tending to eliminate it. Our theory of discrimination also

provides an explanation for the empirical observation that disadvantagedgroups receive equal pay for equal work but do unequal work. Our

theory implies that affirmative action policies that subsidize desirable

jobs for members of disadvantaged groups are likely to raise totalwelfare.

Section IV extends the model to provide a theory of involuntary

unemployment. We argue that it is a natural consequence ofthe rationing

of primary-sector jobs for incentive reasons. By postulating that theprimary sector does not hire workers who are employed but only those

who are out ofwork, we are able to show that involuntary unemployment

with Keynesian features will result. The model also provides the basisfor theories ofthe cyclical upgrading of secondary workers, the absenceof work-sharing arrangements, and real business cycles.

Section V concludes the paper by suggesting directions for furthertheoretical and empirical research.

I. A Theory ofDual Labor Markets

Doeringer and Piore (1971) have described the American economy ashaving a dual labor market. Jobs fall into either the primary or the

secondary sector. Jobs in the primary sector are good jobs characterized

by high wages, job security, substantial responsibility, and ladders whereinternal promotion is possible. Jobs in the secondary sector are charac-terized by low wages and casual attachments between workers and firms

and are menial. Workers in the secondary sector envy those in the

primary sector, who have both better jobs and higher wages. A typical

example ofa primary-sector employer is a large manufacturing establish-ment, while small service firms such as fast food outlets typify the

secondary sector.

As Doeringer and Piore and others have documented, these descriptions

accurately capture many aspects of the labor market. Yet they raise anobvious question. If workers in the secondary sector envy those in the

primary sector, why are not wages in the primary sector bid down? Thelogic of competitive economics denies the possibility of equally skilled

workers receiving different wages in different jobs. The model in thissection provides an explanation for the existence of dual labor markets.

The central idea is that primary-sector firms may find it advantageousto pay more than the going wage because it helps them in eliciting

effort from their workers. By interpreting the secondary sector in the


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model presented below as home production, it can also be viewed as a

theory of involuntary unemployment.

Our formulation ofa model ofdual labor markets very closely parallelsthe model of involuntary unemployment developed by Shapiro and

Stiglitz (1984). The only minor difference is that we assume constant

returns to labor in production and less than completely elastic productdemand, whereas they assume diminishing returns in the production of

primary-sector output and no secondary sector. Developing an efficiencywage analysis of unemployment in terms ofa dual labor market suggests

a number of important areas ofapplication that we explore in subsequent

sections ofthe paper.5

The Model

We assume that the economy is comprised ofN identical infinitely

lived agents. Each can supply 1 unit of labor and produce ~ units of

output in either sector of the economy. Consumers maximize lifetimewelfare, which is given by

U f U(x1, x2as)e~~vt)dv, (1)

where x, is the number ofunits of sector i output consumed in period t,ris the discount rate, and s is an indicator variable equaling zero when

the worker works and one when he shirks. Thus it is assumed that onlytwo levels of worker effort are possible. Shirking workers are assumed

to produce no output. Note that we have assumed that shirking and

consuming extra units of x 2 are perfect substitutes. This assumptionsimplifies the analytic treatment considerably without altering any ofthe substantive conclusions. Note that in equilibrium no workers shirk.

6

We further assume that preferences are homothetic and normalize

so that U(O, 0) = 0. Risk neutrality is also assumed. It follows that

U(Xxi, 2 ~ .x2 ) = XU(x1, x2). Note also that our assumptions imply that all

consumers will consume the economys two goods in the same proportion.We assume that consumers can neither borrow nor lend. As we discuss

below, this assumption restricts workers from posting bonds against the

possibility of their shirking.

~In Sec . IV, we provide an alternative theory of involuntary unemploymentto that ofShapiro and Stiglitz. Our theory is perhaps more realistic in recognizingthat some kinds ofjobs are always available.

6 We follow tradition and label workers who are insufficiently motivated bythe wages they receive as shirkers. The word has pejorative connotations thatare not intended. We mean only to postulate that workers are over some rangehappier working less than more hard.


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382 Bulow/Summers

We normalize the price of secondary-sector output, x2, to be unity.Using the homotheticity ofthe utility function and production assump-

tions noted above, we can write

Pi =f(~) =f(~) =f(N~ E1) g(E1) g


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bility ofbeing dismissed if a worker shirks and the loss in lifetime utilityfrom being dismissed. The values of P1/1 and P1/2 may be calculated

from the recursive equations

fr ~+ (q + d 1 ) (~v2 ~)J ~~(T+q+dOt~~

and

r = + 2\(DIIPV2~ (q ~ij ~)S ~ (5)Equation (4) holds that the present value of the surplus from a primary-sector job is the sum of the discounted surplus from the current job andthe present value of the future surplus if in the secondary sectordiscounted to reflect the time until the secondary sector will next be

entered. Since workers in the secondary sector get a wage z ~3 , equation

(5) is simply the present value of the future surplus if in the primarysector discounted to reflect the time until the primary sector is nextentered. In forming equation (5) we have made use of the steady stateassumption that the flow of workers into and out of the primary

sector is equal, so that the flow rate out of the secondary sector is(E

1 /E2 ) (q + d1).

Solving equations (3 ) (5 ) yields the no shirk condition on primary-sector wages:

7

ar + a(d1 + q)N

d2d~ (d2d1)(NE1)~ (6 )

Equation (6) has several plausible implications. As the utility from

shirking, a, increases, firms must pay more to induce their workers not

to shirk. As the probability of successfully detecting a shirker, d2 ,declines, firms must also pay higher wages. Likewise, if the rate of

turnover among nonshirkers, d 1 + q, increases, firms must pay higherwages. This is because the value ofmaintaining a job is reduced if future

Another way to derive (6) is to note that the difference in present value ofaprimary- and secondary-sector job, PV, P1/2, equals (w 1 w)/{r + d 1 + q+ [E1(d1+ q)/(N E 1 )]} . This is the incremental wage from being in a primary-sector job, w1 w, discounted by the interest rate, the chance that a primary-sector worker will drop into the secondary sector, d 1 + q, and the chance that asecondary-sector worker will find employment in the primary sector, E 1 (d 1 + q)/(N E 1 ) .


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384 B u low/Summers

turnover is more likely. The greater the number of primary-sector jobs,E1, the higher wages must be to maintain the opportunity cost oflosing

a job because the time a worker must spend waiting to return to the

primary sector if fired is reduced. Finally, increases in r raise requiredwages because they reduce the present value ofthe loss from being fired.Notice that equation (6) implies that, in equilibrium, primary-sector

wages will exceed wages in the secondary sector even though all workers

are identical. Workers in the secondary sector will envy those in theprimary sector, but it will not be possible for them to bid for primary-sector jobs by being willing to accept lower wages. For if they acceptedlower wages, they would have an incentive to shirk. Hence firms will

not offer lower wages.

The model here implies that firms will be extremely conscious ofrelative wages. Primary-sector firms need to observe wages offered in

the secondary sector in order to ensure that their wages are set highenough so that their workers have no incentive to shirk. In standardcompetitive models, firms need only observe their own labor supplycurves and have no need to learn about either wage or employment

levels at other firms. Indeed, one ofthe major arguments for competitivemarkets as an allocation mechanism is that they reduce the costs ofinformation acquisition because each agent can act knowing only the

prices it faces.In fact, firms are extremely concerned with assessing where they stand

in the wage distribution. The HandbookofWage and SalaryAdministration(Rock 1984) notes that salary surveys are indispensable to an effective

compensation program.. . . The establishment of sound compensationpolicies depends on an accurate assessment ofan organizations place inthe salary marketplace. It goes on to give an idea of the volume of

survey information available by noting that there are almost 10 0 availablesurveys on the compensation of accounting clerks, almost 50 surveyswith salary data on the Chicago metropolitan area, and nine surveyswith specific data on salary for accounting clerks in Chicago (Rock1984, p. 323).

Equation (6 ) also provides an additional explanation to standardhuman capital arguments for the existence of enduring attachments

between workers and firms, one that does not rely on the productivity-enhancing effects ofexperience. Reductions in the exogenous separation

rate, q, reduce the wage that primary-sector firms pay in order to ensurethat workers will not shirk. Firms therefore will have an incentive tominimize this separation rate. At a minimum this means that they willnot replace workers not determined to be shirking. Firms also have anincentive to give laid-off workers first priority for new jobs and toprovide alternative jobs within the firm for poorly matched workers.


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Theory ofDua l Labor Markets 385

Equation (6) provides one relation between primary-sector employmentand wages. A second relation is necessary to characterize the market

equilibrium. This relation (7) results from the requirement that workers

in the primary sector are paid their marginal product. It holds that

p1w = ~3f(~) = (7)

The determination of equilibrium by the intersection of the productmarket equilibrium condition and the no shirk condition is depicted infigure 1. It is apparent that, in competitive equilibrium, identical workerswill be paid different wages. We defer until the next section an analysisof the efficiency properties of this equilibrium. It is clear, however, thatthe composition of output will be affected by factors such as the

probability of detecting shirking workers, the interest rate, and the util-ity workers get from shirking. In equilibrium of course no shirkingwill occur.

The analysis so far has assumed that the only sanction available tofirms when workers are suspected of shirking is dismissal. One can

W a g e s

Employment

FIG. I .The determination of equilibrium


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386 Bulow/Summers

imagine firms developing various other means for inducing workers not

to shirk. For example, workers in primary-sector jobs might be asked

to post bonds that would be forfeited in the event they were detected

shirking. Since the probability of detection is less than one, these bondswould have to exceed the value ofthe output forgone because ofworkershirking. As Shapiro and Stiglitz (1984) note, bonds ofthis type are not

observed in practice for two reasons.8 First, workers simply do not havethe requisite liquidity to post bonds.9 Second, and probably moreimportant, third-party verification of detected shirking is impossible.

Firms would have an incentive to label workers as shirkers falsely in

order to collect their bond. Even if firms did not do this there wouldremain the problem of determining in which employment separations

the bond should be forfeited.The same mechanisms that might eliminate the payment ofnoncom-

petitivewages

couldalso

obviate theneed to

havemore than tokenmonitoring of workers. The fact that we observe more than token

monitoring suggests that there are factors that limit the use of these

mechanisms. While these factors can be overcome by sophisticatedcontracts in simple models, these contracts become inadequate when the

environment is complicated by introducing problems of risk aversionand adverse selection. Most real-world contracts are simpler than those

suggested by sophisticated incentive theories, and so it seems plausible

to study the properties ofenvironments in which sophisticated contractsdo not eliminate the need to pay noncompetitive wages.

While we do not observe the posting of bonds in the actual economy,

a number of the features of actual primary-sector firms may performsome of the same economic functions that bonding might perform. Inparticular, these firms are characterized by job ladders and rising age-

wage profiles, while similar phenomena are not observed in the secondarysector. As emphasized by Lazear (1981), a rising age-wage profile can

maintain the present value of a job as a workers years to normal

retirement diminish. As Medoff and Abraham (1981) have argued, it isdifficult to ascribe rising age-wage and tenure profiles to rising produc-

~Contracts with bonds sufficiently large to deter shirking would requiredamage payments far in excess of the actual damages firms could prove. It isnot likely that they would be enforceable because of the general refusal ofcourtsto enforce liquidated damages provisions in contracts. Moreover, the lawinterferes with bonding by refusing to allow pension arrangements in whichworkers accumulate substantial unvested pension assets.

~Note that as long as some assets are illiquid, so that a worker who is forcedto forfeit a ll h is liquid assets can subsist, requirements that workers post all theirliquid assets as bonds will be insufficient to ensure that workers do not shirk.The simple fact is that more than 800/o of the working population has only tokenfinancial assets.


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tivity. Rising age-wage profiles are of course subject to the same sort of

incentive problems as bonds, with one important addition. Rising age-

wage profiles, unlike posted bonds, will encourage workers to stay with

firms even when they have higher productivity opportunities elsewhere.

As long as firms cannot fully solve the effort elicitation problem withrising age-wage profiles, wage differentials will persist.

It is noteworthy that job ladders appear in parts of the economy

where individual performance is difficult to disentangle but not in partswhere it is easily monitored. Thus John Dunlop (19.85) writes, Capital

intensive production methods as in electric power generation, refineries

and basic steel tend to be associated with . . . lengthy promotion ladders

and elongated pyramids, while more labor intensive operations as inlight assembly, grocery stores and sewing have few promotion laddersand flat pyramids. As Doeringer and Piore (1971) emphasize, promotion

opportunities predominate in high- rather than low-wage sectors.

Intraindustry Wage Differentials

The analysis presented so far provides an explanation for interindustryand interoccupation wage differences even for equally skilled workers.

This analysis is clearly relevant to empirical observations such as theoften-emphasized finding that wages in U.S. manufacturing exceed those

in service jobs, even after controlling for many measures of workerquality. It is also relevant to the dualism that is said to characterize the

labor market. Yet a second type ofanomaly in the wage structure alsostands out. There appear to be substantial, persistent differences in wageswithin industries. Large literatures document the correlation of wage

rates with unionism (e.g., Freeman and Medoff1984) and firm size (e.g.,

Brown and Medoff 1984), and there is substantial idiosyncratic varianceas well. The analysis of these wage differentials poses a difficult issue.Leaving aside the question of why firms choose to pay different wages,

how do high-wage firms remain viable in the marketplace? The question

is a critical one. For typical firms the wage bill is four times profits. If

a firm paid even bob above the going wage, its profits would be reducedby 400/o

In part, we believe the answer lies in the monopolistically competitive

character of product markets as described in Weitzman (1984). But a

simple extension of the model can provide a further part of theexplanation. Imagine, as in parts of Shapiro and Stiglitz (1984), that the

probability of detecting a shirking worker in the primary sector is notgiven exogenously but depends on the expenditure of resources. These

resources are consumed according to a function ~k(d2),where k > 0.Then primary-sector firms will solve the problem

mm: w + ~k(d2), (8)


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388 Bulow/Summers

subject to the no shirk condition, to produce output most efficiently. Itis immediately apparent from the first-order conditions for the solution

of (8) that first-order changes in the wages of a single firm will have noeffect on labor costs.0 This is dramatically different from the standard

model in which wage changes translate directly into cost changes. itfollows that discrete changes in wages will give rise to much less thanproportional changes in labor costs. This helps to explain how high-wage firms endure. From the perspective of this model, the observationthat firms in the same industry pay different wages is no more mysterious

than the observation that their factor proportions differ. Wage premiums

in this model contribute directly to productivity, just as do standard

factors ofproduction.Indeed the minimization problem, (8), provides an explanation for the

union productivity effect discussed by Freeman and Medoff (1984). When

wages are increased, firms are able to conserve on resources devoted to

monitoring workers, and so total productivity is enhanced. As predictedby this line ofargument, Brown and Medoff(1978) report some evidence

suggesting that the ratio of nonproduction to production workers is

lower in the unionized than the nonunionized sector.

Equation (8) also provides a basis for a theory of the firm-size effect.Large firms enjoy economies of scale and are able to get reduced prices

from suppliers but because of their size have less favorable 4(d2 )

functions. They therefore substitute high wages for supervision. These

ideas comport well with a number of Brown and Medoffs (1984)empirical findings: (a ) quit rates are lower in large and unionized

establishments, (b ) large employers have more pronounced job laddersand steeper age-wage profiles than do smaller firms, and (c ) the wagedifferential between large and small firms decreases with skill level. It is

greatest at the bottom ofthe hierarchy, where differences in monitoring

technologies are likely to be greatest.The result that changes in wages will give rise to much less than

proportional changes in labor costs is much more general than ourmodel. It will obtain in any model in which firms choose wages and

attain an interior solution. This can occur if turnover or labor qualityconsiderations affect the choice ofwages as well as if high wages serve

an incentive function. Note, however, that theories in which wage

differentials arise as a result of legal impediments to changing wages,costs of wage adjustment, or union threat effects cannot explain intra-

industry wage differentials ofthe kind discussed in this section.

10 The argument here is similar to but different from that of Akerlof and

Yellen (1984). They ef~nphasize that inertia may not be very costly for firms. Ourpoint is that a variety of compensation-monitoring strategies will be aboutequally attractive to firms. This will make it easier for unions to extractconcessions from firms, e.g.


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Wage Dynamics

In addition to contributing to an explanation ofstatic wage differentials,the model presented here can contribute to the explanation of aspects

of the dynamics ofwage differentials that are otherwise puzzling. In anumber ofhigh-wage industries, in the United States and Europe, notablysteel, wage differentials increased substantially at the same time that themarket conditions facing the industry deteriorated dramatically. In the

United States, for example, steel wages rose by 35O/~ relative to those in

all manufacturing between 1970 and 1980. No standard competitive orbargaining theory would predict a dramatic increase in relative wages in

the face of declining product demand.1 One would expect reductions

in labor demand to lead to both lower employment and lower wages.

The actual outcome is suggested by the model presented here. Anincrease in the probability that the employer will initiate a separation

will necessitate the granting of a wage increase in order to ensure thatthe no shirk condition (6) is satisfied. Mathematically, a layoffprobability

would serve the same function in (6) as a higher quit rate. Thus failing

firms will find themselves forced to raise wages creating the prospect ofdynamic instability. This may also partially explain why firms tend to

give relatively little notice before plant closings.12 The amplification of

adverse demand shocks hitting an industry appears to be a feature on~y

of efficiency wage models based on the effort elicitation problem andnot ofalternative models ofwage rigidity.

Summary

The analysis in this section suggests that, in any economy in whichfirms cannot monitor workers perfectly, they will pursue policies that

will cause workers to value their jobs. A necessary consequence of

workers being led to value their jobs is wage differentials unrelated to

skill differentials. The contribution of this factor to wage inequality isdifficult to gauge. But some evidence suggests that arbitrary wage

differentials not linked to differences in skill may be of substantialimportance. Studies consistently find that differences in genes, parental

upbringing, years of schooling, and IQ all taken together can explain

Lawrence and Lawrence (1985) discuss an endgame explanation for thisphenomenon. Their explanation depends critically on union bargaining strategies,while their empirical work suggests that it occurs about equally frequently inthe union and the nonunion sectors. This suggests the possible relevance of theexplanation presented below.

20n many occasions struggling firms do extract wage reductions from theirworkers. But the packages frequently include other elements operating directlyon the no shirk condition. These may include job guarantees or profit-sharingplans that give workers an incentive to monitor each other.


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390 Bulow/Summers

only a very small part of the inequality in wages.3 As Jencks (1972) and

Thurow (1976) argue, this suggests the possible importance of luck inwage determination. The formulation presented here shows how luck

can affect wages in a competitive market.

A labor market in which there are pervasive wage inequalities unrelatedto productivity differentials is profoundly different from a competitivelabor market. In the next section we explore the normative propertiesofour model.

II. Trade and Industrial Policies

The previous section provided a model that was consistent with the

existence of both large interindustry and intraindustry wage differentialsthat are not readily explicable in terms of differences in labor quality.The standard competitive analysis of industrial subsidies and tradepolicies presumes the absence of these differentials. It is natural to askhow this analysis must be modified in the presence of endogenouslygenerated wage differentials. While we focus on the effects of subsidieswithin the model presented in the previous section, it should be clearthat similar results could be obtained in alternative efficiency wagemodels.

American industrial policy advocates such as Robert Reich and LesterThurow take the position that nations should try to focus economicpolicies on encouraging high value added sectors. These sectors, it isargued, provide good high-wage jobs, in contrast to the low-wage

jobs found in other sectors of the economy. Industrial policy advocates

credit much ofthe economic success ofJapan over the last 20 years totheir successful encouragement of high value added production. Theyare alarmed by what they se e as the deindustrialization of America andthe consequent loss of high value added employment. While sophisticatedindustrial policy advocates recognize the economic truth that a nationmust have a comparative advantage in something, they find little solacein this. In George Meanys picturesque phrase, You cannot have a

successful economy built on everyone doing everyone elses laundry.From the perspective of standard neoclassical economic theory the

claims of industrial policy advocates are difficult to understand. Com-petition equalizes the marginal productivities of all equivalent workers.

There is no such thing as a good or a bad industry. Domestic industrialsubsidies distort the composition ofeconomic activity without redeemingbenefit. Foreign subsidies should be welcomed by domestic consumers.

~ Results presented in Taubman (1977) estimate that the expected absolutedifference in earnings between identical twins is about two-thirds as great asbetween randomly chosen members of the population. Jencks (1972) reportssimilar results for a host ofother variables, including schooling and IQ.


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Theory ofDual Labor Markets 3 91

These conclusions rest on the assumption that competition equalizes

wages across sectors. We shall see that the claims of industrial policyadvocates become explicable in the context of a model like ours withendogenously generated wage differentials.

It is apparent from figure 2 that, as noted by Shapiro and Stiglitz(1984), a laissez-faire economy will not reach a first-best outcome in amodel like ours. The deadweight loss relative to the first best is equalto the shaded area in the figure. A subsidy to primary-sector production,which had the effect of shifting the product market clearing (PMC)locus to the right, would increase total economic welfare. Indeed, asubsidy large enough to shift the PMC locus out sufficiently to causeprimary-sector employment to rise to X would achieve the same Pareto-optimal outcome that would be achieved under laissez-faire if there wasno effort elicitation problem. Note that an equivalent outcome could be

attained by subsidizing primary-sector workers and thereby shifting theno shirk condition (NSC) outward.

A more subtle question is whether a subsidy to primary-sectoremployment that was financed by a lump sum tax would represent aPareto improvement. Workers in the secondary sector would be taxedto subsidize workers in the primary sector who were already better off

W a g e s

Employment

E 2

FIG. 2.Subsidies and economic efficiency


17/39

392 Bulow/Summers

than they were. Nonetheless, it turns out that such a subsidy wouldrepresent a Pareto improvement. This may be seen as follows. The NSCimplies that

dPV1 dPV2 _

d s ds 0, (9)

where s is the rate of subsidy. A change in the subsidy rate must havean equal effect on the present value of lifetime welfare for workers inboth the secondary and the primary sector. Equating the present value

of the gain in economic welfare from a change in the subsidy with thesum of the present value gains for workers currently in the primary andsecondary sectors, we have

w,z~3dE, dPV1 dPV2 dE

r -~=E1 d s +E2 d s +(PV,PV2)-~-

1, (10)

where we have used the fact that d E , / d s d E 2 / d s . Since we know

that (w, z ~3 ) /r > P1/, PV

2 starting at a zero subsidy rate, it followsthat dPV,/ds = dPV2/ds > 0. A small subsidy will represent a Paretoimprovement. It is not difficult to show, however, that a subsidy large

enough to increase employment to its socially optimal level wouldreduce the present value oflifetime welfare for workers in the secondarysector. At the utilitarian optimum an increased subsidy to primary-sectorworkers has a second-order effect on social welfare, but the transfer

effect is first order; thus secondary-sector workers must lose.

4

In some respects these results parallel standard results, surveyed inBhagwati and Srinivasan (1983), suggesting that, if wages are artificiallyhigh in some part of an economy, it is desirable to provide a wage

subsidy to counteract the distortion. There are three important differences.First, the wage differentials considered here are not arbitrarily fixed asin standard models but instead are determined endogenously and depend

on the relative sizes of the two sectors. Increases in the subsidy raise

1 4 These results have implications for the effects ofother labor market policies.

A proportional or progressive income tax reduces the utility gain from holdinga primary- rather than a secondary-sector job, thus shifting the NSC to the left

and reducing economic welfare. Note that this effect is first order, unlike thesecond-order welfare costs normally associated with labor income taxes. Thedifference arises because of the preexisting distortions present in our model.Similarly, policies directed at compressing wage differentials will, in a modellike this one, have unfortunate consequences. If primary-sector workers cannotbe bonded to work hard by high wages, the market equilibrium will ofnecessityinvolve a large threat of being confined to the secondary sector. This in turnrequires an expansion in the secondary sector at the expense of the primarysector.


18/39


wage differentials but are nonetheless desirable. Second, the distortion

considered here is not a result of union power or other institutional

forces. Unlike these cases, there is no cause for concern that subsidizingthe high-wage sector will lead to greater distortion. Third, our model

permits us to assess separately the effects of a subsidy on the lifetimewelfare of workers in the primary and secondary sectors because the

flow between sectors is explicitly modeled.The analysis so far has concentrated on the case of a closed economy.

In the case ofan open economy, the differences between our formulation

and the standard competitive one become much more dramatic. This is

illustrated heuristically in figure 315 Imagine that the domestic economyis small and takes prices as given on world markets. Figure 3 illustratesa situation in which the world price of the primary-sector good, pless than the domestic price. This may occur for any ofthe conventional

natural reasons why foreigners might have a comparative advantagein the primary sector ifforeign workers are less prone to shirk, ifforeigngovernments subsidize the primary sector, or if foreign firms have foundbetter contracting devices for inducing workers not to shirk. Each of

these possibilities has some relevance to the current U.S. policy debate.The region ABDE represents the welfare loss to the economy due toreductions in rents caused by the reduction in primary-sector employment.

The triangular area ABCrepresents the gain from free trade, as the priceofimported goods is reduced. It is apparent that, as long as the domesticprimary sector is nearly competitive, allowing free trade will reduce

national economic welfare. The lost rents as primary-sector employment

contracts from OFto OG represent a greater loss than the second-ordergain to consumers from allowing free trade.

There is a simple intuition for this result. The gains to consumersfrom allowing free trade are of second order in the change in the relativeprice of primary-sector output. On the other hand, the gains in primary-sector employment from restricting trade represent a first-order welfare

gain because of the wage differentials between the two sectors.

We can show this result formally by recognizing that in a free tradeenvironment the no shirk condition (4) must still be met but that productmarket clearing is now given by

where f r ~ is the world relative price ofthe primary good. Other conditions

for equilibrium include the trade balance equation

15 The graphical analysis is only heuristic because of its use of consumers

surplus as a welfare measure and its neglect of the income effects of policychanges on the demand for primary-sector output.


19/39

3 94 Bulow/Summers

W age s

0

Loss from Gain fromtrade t rade

FIG. 3.International competition and welfare

ppi3E1 + ~(N E 1 ) fi1x1 + ~2, (12)

where x, is domestic consumption of good i, and

~i (13)

which is a result ofour assumption of homothetic tastes.With the system of equations (6) and (1 1)(13) we can solve for E 1 as

a function of p ~ to explore the effect of world prices on primary-sector

employment and welfare. The result is

d E 1

dW ( w 1 ~) ~- ( z ~ E 1 x1), (14)r

where Wis the sum of the equivalent variations associated with a changein Pi.

Employment


20/39


The intuitive explanation of (14) is that a reduction in world prices

has two effects. The first term on the right side of (14) arises because

primary-sector size is constrained by a combination of the NSC andworld prices; a lower p ~ reduces primary-sector employment, causing awelfare loss. In a competitive model in which wages were equalized,

this term would not arise. The second term reflects the welfare gainfrom the lower foreign prices. It is equal to net imports, (x i ~3E1)times the price drop. It is clear that, if the world price is below butsufficiently close to the autarky price so that net imports are small, theloss of primary jobs and their attached rents implies that welfare is

reduced by free trade. Furthermore, analysis that is substantively identicalto that of (9) and (10) shows that, if world primary-sector prices are

below but sufficiently close to autarky prices, then free trade is Pareto

inferior for domestic workers; the gain to secondary workers in lowerprimary-sector prices is outweighed by the reduced opportunities for

primary-sector employment. It is also possible to demonstrate thatprotection can represent a Pareto improvement in a Harris-Todaro-type

model like that presented in Section IV in which workers queue forprimary-sector jobs.

A second conclusion with clear implications for industrial policy

debates follows from comparing a and b in figure 4. The welfare gainsper dollar of revenue cost from a subsidy to the primary sector aregreater in an open economy that would have had an autarky price less

than or equal to the free trade price than they would be in a closedeconomy. This is because the demand for primary-sector output is

perfectly elastic in the case of a small open economy. Therefore, for any

subsidy per primary-sector employee more people will switch to theprimary sector, and marginal worker shifts will provide as much of anincome gain as inframarginal movements. Subsidies in a closed economyrun into diminishing returns. As primary-sector output expands, it comes

to be valued less and less. In the open economy, when primary-sector

output can be exported, there is no similar factor limiting the gains fromsubsidizing primary-sector output.

6

An equally important implication of our model, which can be seenfrom (14), is that nations should subsidize winnersprimary-sectorproducts that have a comparative advantage. The greater the world price

ofprimary-sector output, the greater the gain from increasing primary-sector employment, w, & There is little advantage to be had fromsubsidizing primary-sector employment if the world price of primary-

sector output is close to the secondary-sector wage, i ~ 3 . In that case,

16 This proposition and the one in the next paragraph may be verified by

calculating dE,/ds explicitly from eqq. (6) and (7) for the closed economy and(6) and ( 11 ) for the open economy.


21/39

/

W age s

W ag es

Employmen t

b ) free tradeFIG. 4.The effects of subsidies. a, Autarky. b, Free trade

P M C N SC

/

//

*7,A,

-7

7,

Emp loyment

a ) autarky


22/39


there is little loss from letting workers export secondary-sector output

and purchasing the primary-sector good from abroad. Where the worldprice is high and the home economy has a substantial comparative

advantage, a subsidy yields the maximum benefit.

The model presented here captures many of the prominent themes in

the industrial policy debate. There are good jobs and bad jobs even inequilibrium. Good jobs have higher wages and higher average productivity.Value added per worker is higher in these jobs. Protecting sectors with

good jobs can raise total economic welfare. International competitiveness

raises the stakes and increases the payoff to primary-sector subsidies.Note also that the model suggests an explicit criterion for picking

industries to support. Industries in which wages are high after controlling

for differences in workers human capital and for working conditionsshould be subsidized. Previous models endeavoring to illuminate the

industrial policy debatehave

focused onthe strategic

interactions ofimperfectly competitive firms. Policies in some circumstances will help

local oligopolistic firms at the expense of foreign oligopolistic firms.These models seem less relevant to the debate than does our model,

which focuses on the effects of industrial policies on the number of

good jobs available for workers.7

In models with competitive labor markets, public interferences in freetrade through protection or export subsidies are undesirable. Yet govern-ments regularly engage in these practices. The model presented herepresents a rationale for these actions. Obviously, an analysis of this kindtaken alone cannot justify any particular industrial policy. It does,however, provide a basis for thinking about many of the issues raisedby the industrial policy debate.

III. Discrimination in the Dual Labor Market

The persistence of discrimination in competitive markets has been

difficult for economic theory to explain. As originally noted by Becker

(1957) and emphasized by Arrow (1973), one would expect discriminationto be eliminated by competition. Firms that did not discriminate would

have lower costs than firms that did and would therefore grow, tendingto eliminate discrimination. With perfect capital markets, capital wouldbe put to its most profitable use by ending up in the hands of

~The formal model that we have presented here does not include capital as afactor of production. Adding capital as a factor does not change the conclusions

reached so far but does lead to another conclusion. Traditional competitivemodels suggest that it is in the national interest to allow capital to seek thehighest return available either at home or abroad. Once wage differentials areconsidered, this conclusion is no longer valid. Keeping capital at home, and inthe primary sector, may raise welfare by increasing rents created by primary-sector jobs.


23/39

3 9 8 Bulow/Summers

nondiscriminatory entrepreneurs. While enduring discrimination can berationalized by pointing to the tastes of customers, this explanationseems implausibl.e in many settings in which discrimination is thought

to occur. Nor is discrimination easily explained by pointing to workers

tastes since firms composed only of minority-group members wouldhave lower costs than other firms. Some evidence (Blau 1984) suggeststhat men working in heavily female establishments actually receive lower

wages ceteris paribus.8Beyond their difficulties in explaining the persistence ofdiscrimination,

existing theories have a difficult time accommodating the phenomenonof occupational segregation. Studies of discrimination, particularly sex

discrimination, find that much of the discrimination takes the form of

equal pay for equal work but unequal work (e.g., Lloyd and Niemi

1979). Doeringer and Piore (1971), in their discussion of the dual labormarket, emphasize that members of disadvantaged groups are confined

to the secondary sector. Even granting the existence ofwage differentialsarising from employer discrimination, it is hard to see why occupational

segregation should result.The dual labor market model developed here has as its central element

wage differentials that are unrelated to productivity differentials. It isnatural to suspect therefore that it can provide the basis for a theory of

discrimination. Indeed Yellen (1984) suggests that, in an environment

like the one considered here, employers can costlessly discriminate since

there is excess demand for primary-sector jobs. This is not correct. Ifthe equilibrium allocation of workers in different groups who areotherwise identical differs, firms can lower the wage offered to disadvan-

taged workers without fear that they will shirk. As noted in Section I,an increase in the fraction of workers confined to the secondary sector

reduces the wage that must be paid to satisfy the no shirk condition.

Competition will eliminate discrimination as firms hire labor as inexpen-sively as possible. Our model thus cannot explain discrimination ifit isassumed that there are no differences at all among members ofdifferent

groups.

However, our dual labor market model can rationalize discriminationif it is assumed that there are group differences that are unrelated toproductivity. After showing how these differences can lead to occupational

Phelps (1972) and others have suggested theories ofstatistical discrimination.A s emphasized by Aigner and Cain (1977), these models have the disquietingimplication that the difference in average wages between groups exactly equalsdifferences in productivity. Alternatively discrimination can perhaps arise fromdifferential measurement ability for different groups, as in Lundberg and Startz(1983). Stiglitz (1973) anticipates the line of argument developed here by notingthat the efficiency wages for different groups ofworkers may differ.


24/39


segregation and wage discrimination, we investigate the welfare effects

of antidiscrimination policies.

Turnover and Discrimination

A major characteristic of groups thought to be disadvantaged in thelabor market is that they have a very high separation rate. For example,

Poterba and Summers (1984) estimate that the rate of labor force

withdrawal is about 1% per year for males aged 2559 but about 19%per year for women in the same age bracket.9 Data in Marston (1976)

suggest large age and race differences in separation probabilities as well.

These differences have provided the basis for theories of occupationaldiscrimination that are based on considerations of human capital accu-mulation, as, for example, in Mincer (1974). Here we present an

alternative explanation of how higher separation rates can lead to group

differences in wages. In our formulation experience has no effect onproductivity. Unlike human capitalbased explanations for wage inequal-ity, our model suggests that antidiscrimination policies may well increase

economic efficiency.

Taking account ofthe fact that there are two identifiable groups in

the population, the basic equilibrium conditions require that workers be

paid their marginal products and that both men and women in theprimary sector be induced not to shirk. Thus equilibrium is characterizedby the conditions

= ~g(E,m + Etf~ = WPi(Eim + EiA, (15)

a r a r ( d , + qm)Nm (16)+ d, (d

2 di)E2m

a ,- ar(d, + qf)Nf(wI~z~3)=d +

2 d 1 (d2d,)E2f (17)

where the subscripts m andfare used to denote males and females, forconcreteness in the discussion. Note that competition ensures thatprimary-sector men and women receive the same wages. However,

comparing equations (16) and (17), it is clear that a higher proportion

19 Some empirical studies suggest that turnover rates do not differ across groups

after controlling for job characteristics. These findings are not inconsistent withthe analysis presented here. If, as implied by our model, high turnover workersare assigned by the market to certain types of jobs, then controlling for jobcharacteristics is inappropriate. Moreover, our analysis depends on workersexpected horizon in the labor force, not on the current job. Here the differencesbetween groups are especially pronounced.


25/39

400 Bulow/Summers

of women will be confined to the secondary sector if qfis greater than

qm. Since women have a shorter horizon in primary-sector jobs, theymust receive a greater inducement if they are not to shirk. With equal

wages, this can occur only if secondary-sector women have a smallerchance of moving to the primary sector than do secondary-sector men.

These points are illustrated in figure 5. As long as the NSC for women

lies above the NSC for men, there will be partial occupational segregation.Figure 5 suggests an alternative theory ofoccupational discrimination.

Ifgroups differ in the utility they get from being in the secondary sector,

which may be taken to include home production, occupational segregation

will result. The model captures a commonly observed aspect of firm

behavior. Firms prefer to give jobs to workers who really need themthan to workers who gain less surplus from holding them.

It is consistent with the observation emphasized by Blau (1984) that

marriage raises the wages of men but reduces or has no effect on theearnings of women. Marriage reduces males probability of employment

separation but increases females separation probabilities. It is alsoplausible that marriage raises the cost to men of losing a desirable job

NS Cm+f

W age s I

N m +N

N f

Em

Employment

H

Ef N m Em+Ef

FIG. 5.Discrimination in the dual labor market


26/39


but reduces the costs to women for reasons relating to the analysis ofBecker (1985). The differential effects of marriage on men and women

mitigate against theories ofdiscrimination based on employer prejudice.The welfare effects of antidiscrimination policies in this model are

considered below. Before turning to this analysis it should be noted thatour framework suggests a number of other theories of discrimination.One such theory might be based on the differential ability of different

groups to enter into efl~cient labor contracts in the primary sector.

Population groups that are liquidity constrained and therefore unable to

accept low starting wages and rising age-wage profiles will not be ableto get primary-sector jobs. The wage they must be paid in order to get

them not to shirk may well exceed the going primary-sector wage. For

example, historically, some workers may not have been able to affordapprenticeships.

An argument paralleling theories of statistical discrimination mightrun as follows. Employers cannot predict workers productivity accurately.

Therefore they make use of a workers demographic status in assessinglikely productivity. In a perfect labor market, workers in disadvantaged

groups could be offered primary-sector jobs at low wages, reflectingtheir low expected productivity, and given a chance to prove themselves.

In the environment considered here, there would be no 1ncenti~e for afirm to make such an offer since at low wages all workers would shirk.

Antidiscrimination Policies

It is clear from the discussion in the preceding section that a policyof subsidizing employment in the primary sector would continue to bedesirable with two classes of workers. A more interesting questioninvolves a policy of subsidizing the primary-sector employment ofdisadvantaged workers and taxing the primary-sector employment of

advantaged workers in a balanced-budget manner. Equivalently, what

are the normative properties of policies that require that disadvantagedworkers and advantaged workers be hired in some fixed proportions inthe primary sector? We examine these questions in the context of themodel presented above, in which discrimination arises from differencesin separation probabilities, and then consider other possible sources of

discrimination.We consider the effects of a tax at rate t on male employment in the

primary sector used to finance a subsidy to womens employment. It

follows that the subsidy to womens employment is at rate (E,M/E,F)t.In order to show that at least a small tax is desirable, we proceed as

follows. Since men and women have the same utility function, a taxincrease will be desirable if d(EIM + E1~)/dt> 0.

Substituting equation (15) into (16) and (17) and introducing the tax


27/39

402 Bulow/Summers

into the latter two equations allows us to differentiate implicitly (16)and (17) to find d(EIM + EIF)/dt. After some tedious algebra this yields

d(EIM+ElF

dt

ar 1 [(d1qm)NMEIM_ ( d , + qj)NjEif] _ t(EIM+Elf

d 1 Elf L(NM ElM)2 (NfElf)2 j E~ f

A l+

(18)

Att=0

( d

1 + qM)NM_

( d 1 + q f ) N fNMElM NfElf

So

c L r I ( d ~ + qM)NM V ElM NfEIjI-.

d(EIM+Elf) _ d2d1 Elf NMElM LP4MLIM

c it I A ! >0.

(19)

Equation (19) is clearly positive because the ratio of male primary-

sector participation, EIM/(NM

ElM), exceeds the ratio of femaleprimary-sector participation at a tax rate of zero. Its implication is that

a small subsidy to women will increase welfare.

However, we can also calculate whether an optimal policy wouldproduce a large enough subsidy to drive the female primary-sector

participation rate up to the male level. At the point at which ElM/NM

=EIf/Nfwe find

ar Nf t(EIM+Eif

d(EIM+EIf) _ ~ E~f . (20)

dt

A lBecause qf> qm, expression (20) must be negative. Thus starting with tpositive to the point at which the sectoral composition of employmentis the same for men and women, a reduction in the subsidy to the hiringofwomen will raise welfare. A policy intermediate between the laissez-faire outcome and the elimination of apparent discrimination is optimalin the sense of maximizing the sum ofutilities.


28/39

Theory ofDual Labor Markets 40 3

These results may be justified intuitively. It is clear from figure 5 that

in the absence of any subsidy the NSC for women is less steep than the

NSC for men. Hence a policy oftaxing each man in the primary sector$1.00 and subsidizing each woman in the primary sector by $EIM/EIF

will be a net revenue raiser and will increase total employment.20 If norevenues were raised but all the proceeds were used to subsidize theemployment of women, the employment gains would be even greater.

On the other hand, if the share of men and women in the primarysector is equalized, equations (16) and (17) imply that the NSC is flatterfor men than for women. This is because a small increase in wages raises

the present value of a job by more for men than for women because of

their longer horizon. In this case, reducing the tax on men and the

subsidy to women raises total employment.It should be clear that equivalent results hold for affirmative action

policies. Each possible choice of t is equivalent to a policy mandating

that a specific proportion of women be hired in the primary sector. Ifpolicy is carried on through such quotas, the wages ofwomen will riseabove average primary-sector wages, and male wages will fall. A quotapolicy that reduces male wages by t0/o relative to average primary-sector

wages is exactly equivalent to a t% tax on male employment withrevenues used to finance subsidies to primary-sector women.

An alternative policy that might be labeled comparable worth wouldartificially compress the wage differential between the primary and thesecondary sectors. This would be disastrous for both men and women.

With a compressed wage differential between the two sectors, the noshirk condition would require reduced primary-sector employment of

both men and women.These results pertain to a model in which apparent discrimination

results from differences in turnover probabilities across groups. We have

also considered the case in which discrimination results from one group

getting more utility from a secondary-sector job than the other. In thiscase, the effect of a subsidy on total welfare, even starting at t = 0, 15ambiguous. This is because a subsidyin addition to raising totalemployment, which increases welfarecauses the substitution of womenfor men in primary-sector jobs. This reduces welfare under the maintainedassumption that women value primary-sector jobs less than men do. Wehave not yet considered the welfare effects of affirmative action policies

in situations in which discrimination results from group differences in

20 There is a general principle here. If it is desirable to subsidize primary-

sector employment, bang for the buck may be maximized by subsidizingminority-group members since less money will flow to those who would havehad primary-sectorjobs anyway. This principle will hold regardless of the reasonfor the wage differential. Alternative efficiency wage models will not necessarilyimply that affirmative action programs necessarily raise total welfare.


29/39

404 Bul ow/Summers

the ability to post bonds or is statistical. We suspect that it will be easyto construct examples in which it will be welfare enhancing.

Although primary-sector jobs are rationed in our model, we have so

far assumed that no rent-seeking behavior takes place. In a sense

therefore the allocation of workers to the primary sector is arbitrary. Inthe remainder of the paper, we relax this assumption and provide atheory ofunemployment.

IV. Unemployment in a Dual Labor Market

Most economists accept the idea of involuntary unemployment. Some

workers who would like to work at the going wage are unable to findwork. Yet, as many critics have pointed out, the concept of involuntary

unemployment involves an essential ambiguity. What is meant by the

going wage? The option of self-employment is always open to the

unemployed. Andeven

intimes

ofstagnation,

somejobs are available.

We propose here a formulation that resolves these ambiguities. This is

done by assuming that primary-sector employers hire workers only

directly from the pool of unemployed workers. This generates waitunemployment as workers queue for primary-sector jobs. This unem-

ployment is involuntary in the sense that workers just like the unemployed

hold primary-sector jobs at a wage that the unemployed would bepleased to accept. It is voluntary in the sense that some jobs are available.

Note that this view of unemployment requires that there be noncom-petitive wage differentials between sectors.2

The assumption that workers must queue for primary-sector jobs maybe justified both theoretically and empirically. Imagine that workersdiffer in either their turnover probabilities or their tastes for primary-sector work and that these differences are not observable to firms. Then

workers with lower turnover probabilities or stronger tastes for primary-

sector work will opt for unemployment, while others opt to remain inthe secondary sector. Primary-sector firms will then be justified in hiring

only the unemployed because they will require lower wages to ensurethat they do not shirk than will other workers. As an empirical matter

workers who lose primary-sector jobs appear to be very unlikely toaccept stopgap jobs in the secondary sector and to maintain highreservation wages (Clark and Summers 1979). Only rarely do secondary

workers leave their jobs to become unemployed and seek primary-sectorwork. This is exactly what signaling considerations would lead one toexpect.

21 Stiglitz (1982) discusses some models of less-developed economies in which

the primary sector is taken to be the urban sector and pays an efficiency wage,in which unemployment arises because workers cannot simultaneously searchfor work in urban areas and work in rural areas.


30/39

Theory ofDua l Labor Markets 40 5

Imposing the requirement that workers must be unemployed beforethey can accept primary-sector employment, we have the equilibrium

conditions

=~5pi(~-~), (21)

( P 1)zi3(d2 d1a d,qr (22)

and

(d,+q)E, (p,1)~ (23)

NE,E2 d,+q+r

recalling from before that the utility from being unemployed (having noincome) has been normalized to zero.

These equilibrium conditions are easily interpreted by recognizingthat, in equilibrium, secondary-sector workers must be indifferent to

becoming unemployed and unemployed workers must be indifferent to

accepting secondary-sector jobs. Equation (21) simply determines therelative price of primary-sector output. Note that we can no longer

write it as g(E,) because now some workers are unemployed. Equation(22) holds that the utility gain from shirking in the primary sector must

equal the present value of holding a job in the primary sector. This ismost easily reckoned by considering the alternative ofbeing permanently

confined to the secondary sector. Equation (23) holds that the differencein instantaneous utility between holding a secondary-sector job andremaining unemployed equals the instantaneous probability of obtaining

a primary-sector job times the present value of such a job. Thisformulation differs somewhat from that of Harris and Todaro (1970),who assume that workers must be indifferent between secondary-sector

employment and locating in the primary sector with proportionalchances ofbeing employed and unemployed.

The determination of equilibrium is depicted in figure 6. Note thatequilibrium requires both that the PMC and the NSC cross and thatsecondary-sector workers be indifferent to being unemployed. Theunemployment in figure 6 correspoxads to Keynesian unemploymentin three senses. First, it is involuntary, as workers are queuing forprimary-sector jobs and are identical to primary-sector job holders but

cannot bid down wages and get primary-sector jobs. It is voluntary onlyin the sense that all unemployment is voluntarysome undesirable jobs

are available.Second, relative to the first best, the level of unemployment is too

high and the level of primary-sector employment is too low. As we


31/39

40 6 Bulow/Summers

Wi

W a g e s

Em p 1 oym ent

FIG. 6.The determination of equilibrium unemployment

discuss more formally below, subsidies to employment or taxes on

unemployment will increase welfare.

Third, if productivity varies, unemployment, wages, and aggregateconsumption will a ll move procyclically as long as product demand isnot too elastic and/or the primary sector is not too small. Thisproposition may be examined by substituting (21) into ( 22) and (23) andimplicitly differentiating the latter two equations with respect to & We

find:

(p1-1)N1d ~ 3 N E 1 E 2 J

Ifp ~ * c x c (consumers have very inelastic relative demands for thetwo goods), then E 1 and E 2 both rise proportionately and N E 1 falls. But ifp ~ * 0 so that relative prices will not change much, theprimary sector will expand in response to a positive productivity shock,while constant relative prices will imply the same ratio of (N B 1 E2) /E1 as before the shock and thus increase unemployment.

I II

N-E1-E2~U E 2 N


32/39


If the primary sector already dominates the economy (E1 /E2 large),then an increase in w will, by its reduction in the primary-sector

unemployment rate, raise total employment. If, however, the economy

is dominated by the secondary sector, the principle effect of a shockwill be to move workers into the primary sector, where the unemploymentrate is higher.

The Cyclical Behavior ofLabor Markets

The response ofthe economy considered here to productivity shocks

corresponds well to the cyclical behavior of actual labor markets assummarized in Okun (1982). First, Okun noted that quits are procyclical,

while employer-initiated separations move countercyclically. This is

predicted by our model. Positive productivity shocks lead to quits asworkers leave the secondary sector, while negative shocks lead to jobloss as the primary sector contracts. Second, Okun observed the shrinkingof relative wage differentials at cyclical peaks. In the model consideredhere, positive productivity shocks lead to equal absolute increases inwage levels. Assuming that dismissal rates are proportional to hours onthe job (so that a nonshirking part-timer is less likely to be erroneously

caught shirking than a nonshirking full-timer) but that quit rates arerelated to calendar time on the job, the no shirk wage per unit of time

worked for a z-time employee, w~, in an economy in which all other

primary jobs are full-time is given by

r + ( d 1q)zE 1 (d 1q

NB1

z[r+diq+Ei(diq

NB1

The crucial insight is that both a full-time and a part-time worker get

the same benefit from shirking for an hour, and each is as likely to be

caught. Therefore, to prevent the part-timer from shirking the employer

must offer him a job that is equally valued (has the same present value)as a full-time job. Such a constraint necessarily implies that the part-

time employees will require higher hourly pay than the full-timeemployees to prevent shirking.An important feature of actual unemployment is that it is strongly

serially correlated. While we have not completed a full dynamic analysisofour model, it is clear that temporary productivity shocks can give rise

to serially correlated movements in unemployment. Consider, for example,

an increase in productivity that is known to be temporary. It is apparentthat primary-sector employment must move continuously after theproductivity shock is observed. If a discontinuous movement were

anticipated when productivity reverted to its normal level, the instanta-


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40 8 Bulow/Summers

neous separation rate would be arbitrarily high, and so workers would

shirkunless wages were infinite. It follows that a temporary productivity

shock would give rise to an immediate increase in primary-sector

employment followed by a slow decline. Notice that primary-sectorwages would rise more and employment less for a temporary productivityshock than for a permanent productivity shock. This is because theknowledge that the shockwas temporary would reduce workers horizons.

Structural Unemployment

While this model is able to account for a number of features ofcyclical fluctuations, it does not provide a satisfactory explanation ofthe

driving force behind fluctuations. The work of the real business cycleschool notwithstanding, we find it implausible that productivity shocksare the primary cause ofcyclical fluctuations. Aggregate demand, which

cannot be defined in a real model like ours with competitive productmarkets, seems to matter in cyclical fluctuations. We return to this issuein the concluding section of the paper. It may be more appropriate tothink of our model as providing insights into the determinants of

natural or structural~ unemployment. Indeed our model, or, alter-natively, the simpler two-sector formulation of Shapiro and Stiglitz

(1984), suggests some hypotheses about the dramatic increase in structuralunemployment observed in Europe over the last decade.

Consider first the effect of an increase in social insurance benefits.Higher benefits may be thought of as corresponding to an increase in

the utility from being unemployed along with a tax on wages. Raising

unemployment benefits increases the incentive ofsecondary-sector em-ployees to become unemployed. This effect is accentuated by the taxesnecessary to finance insurance benefits. Reduced secondary-sector output

leads to a reduced relative price for primary-sector output and lowerprimary-sector wages. This in turn causes primary-sector output tocontract, further increasing unemployment. The analysis parallels theanalysis of a negative productivity shock exactly, except for the furtherdistortions caused by the taxes necessary to finance unemploymentinsurance.

Notice that the adverse effect ofunemployment insurance on unem-ployment occurs despite the maintained assumption that it does not

affect workers search decisions and that its financing does not affect

employers decisions about layoffs. Rather its effect occurs primarilythrough firms wage-setting behavior. This model provides a possiblebasis for suspicions about the adverse effects ofsocial insurance programs

on macroeconomic performance that is consistent with the relativelymodest effects typically found in microeconomic studies.

A second implication of our analysis is that policies directed atincreasing job security may substantially increase unemployment and


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reduce primary-sector employment. Such policies may be thought of asreducing d2 , the likelihood that a shirking worker will be detected andlaid off. As we have already seen, policies directed at work sharing may

be counterproductive. If, as a result of work-sharing arrangements,primary-sector firms must raise their wages, primary-sector employment

will decrease and unemployment will rise.

Third, our model suggests that public or private policies directed at

compressing wage differentials may have deleterious effects. Equation(22), the no shirk condition, pins down the relationship between primary

and secondary sector wages that must exist if primary workers are notto shirk, as long as secondary-sector jobs are freely available. If thiswage differential is reduced, primary-sector firms will not be able tooperate because the no shirk condition cannot be satisfied.

V.Conclusions

We believe that the analysis in this paper suggests the applicability ofefficiency wage models to a wide variety ofproblems in labor economics.

They can contribute to the understanding of many phenomena that aredifficult to account for in other ways. And they have very different

normative implications than do other labor market models. Takingaccount of the effort-elicitation problem calls into question the general

proposition that private labor market arrangements are efficient. It alsocomplicates the analysis ofvarious labor market policies.

A good example is provided by minimum wage laws. Taking accountof the effort-elicitation problem introduces several new elements into

the analysis of minimum wages. First, minimum wages may interferewith efficient contracting, leading to unemployment and allocative

distortions. If minimum wage laws constrain firms so that they cannot

offer age-wage profiles that are as steep as they would like, they willhave to raise the total level of compensation in order to ensure that

workers do not shirk. Second, minimum wage laws have a potentiallybeneficial effect that could conceivably offset the distortions they create.Because they will in general create some unemployment, they raise the

cost to being laid off from the primary sector. This will permit lowerprimary-sector wages and greater primary-sector employment. Third,minimum wage laws may have a second potentially beneficial effect in

raising productivity in firms affected by the minimum. Such firms will

be able to reduce the resources that they devote to the supervision ofworkers. If as we argue below competitive equilibrium is characterizedby excessive supervision, this may enhance social welfare.

While we have focused on the implications of efficiency wage modelsin which noncompetitive wages help firms elicit effort from theirworkers, other models that rationalize noncompetitive wages would belikely to have similar implications. Subsidies to high-wage sectors would


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410 Bul ow/Summers

raise welfare. Discrimination and wait unemployment would be ob-

served, and many of the other aspects of labor markets that we have

discussed would be observed. In this sense our analysis is more generalthan the specific model presented. In future research it would be valuableto explore the normative implications of alternative models ofnoncom-petitive wages. Certain of our results, such as desirability of affirmativeaction policies and the Pareto optimality of targeted subsidies, areprobably not extremely robust; others may well be robust.

Beyond their application to various labor market issues, there are anumber of important directions for future research on models of the

effort-elicitation problem. We consider them in increasing order ofimportance. First, we and other writers have made strong assumptions

about the nature of compensation arrangements. It is theoreticallypossible that compensation arrangements can be devised that obviate the

need for firms to offer more than the going wage in order to insure thatworkers do not shirk. It would be valuable to model explicitly theimpediments to these arrangements created by the problems ofworkerliquidity, moral hazard on the part of firms, risk aversion on the part ofemployees, and inabilities offirms to make certain types ofcommitments.The observation that many workers are paid more than their opportunity

cost requires rationalization.A related question emphasized by Shapiro and Stiglitz (1984) concerns

firms choice of a supervision technology. It is easy to see that modelsof the type discussed in this paper suggest that the architecture ofeconomic organizations will be flawed. There will be too many chiefs

and too few indians. Firms will invest in supervision until the marginaleffect of a dollar spent on supervision equals the marginal effect of adollar spent on higher wages in reducing workers incentive to shirk.Extra wages benefit workers, but extra monitoring does not, so therewill be more supervision than is socially efficient. Policies that encouragefirms to give workers more responsibility and to raise their wages will

increase social welfare. Of course they may reduce the welfare of thosewith human capital that is specialized toward supervisory ability.

A second direction for future research concerns the sources of thelinkages between wages and productivity. In keeping with the work ofothers, we have emphasized the effects of increases in the wages firms

pay on the level ofeffort that they are able to elicit from their workers.The mechanism we have stressed is the role of the fear of job loss in

inducing workers not to shirk. This may not in fact be of centralimportance in wage setting. Businessmen, union leaders, and textbookson personne

a theory of dual labor markets with application to industrial policy, discrimination and keynesian...

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