Changes' in Unemployment and Wage Inequality: an Alternative

American Economic Association

Changes in Unemployment and Wage Inequality: An Alternative Theory and Some Evidence Author(s): Daron Acemoglu Source: The American Economic Review, Vol. 89, No. 5 (Dec., 1999), pp. 1259-1278 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/117057 Accessed: 05/03/2009 16:44

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http://www.jstor.org Changes 'inUnemployment and Wage Inequality: An AlternativeTheory and Some Evidence

By DARON ACEMOGLU*

I present a model wherefirms decide what types of jobs to create and then search for suitable workers. Whenthere are few skilled workers and the skilled-unskilled productivitygap is small, firms create a single type of job and recruit all workers. An increase in theproportion of skilled workersor skill-biasedtechnical change can create a qualitative change in the composition of jobs, increasing the demandfor skills, wage inequality,and unemployment.I provide some evidence that there has been a change in the compositionof jobs in the United States during the past two decades. (JEL E24, J31, J64)

Between 1979 and 1987, the average weekly the ages of 25 and 64 with less than four years wages of college graduates with one to five of high school stood at 4 percent.For those with years of experience increased by 30 percent high-school and college degrees, the same num- relative to the average weekly earningsof com- bers were 2.4 percentand 1.1 percent.Averaged parablehigh-school graduates(John Bound and between 1992 and 1994, the unemployment George Johnson, 1992; Lawrence F. Katz and rates for these three groups were respectively Kevin M. Murphy, 1992). Within-group(resid- 13.9 percent,6 percent,and 3.2 percent,approx- ual) wage inequality may have startedincreas- imately three times higher than the rates during ing earlier: after controlling for education and the 1970's (Statistical Abstracts of the United experience, the differentialbetween the nineti- States, 1995 Table 662).1 eth and the tenth percentile wages stood at 118 This paper offers a theory in which these percentin 1988 comparedto 92 percentin 1970 labor-marketdevelopments may be caused by a (ChinhuiJuhn et al., 1993). The rise in inequal- qualitative change in the composition of jobs. ity over this period was not only due to wage Namely, in responseto changes in the skill level increases for high-paid workers.Real wages of of the labor force or technology, "middling" high-school graduateswith one to five years of jobs open both to skilled and unskilled workers experience,for example, fell by 20 percentfrom may be replaced by high-quality (capital) jobs 1979 to 1987 (Katz and Murphy, 1992 Table I). designed for the skilled and low-wage jobs tar- Meanwhile, the unemploymentrates of all ed- geted at the unskilled. This change in the com- ucation groupshave also increased.In 1970, the position of jobs leads to higher skilled wages, unemploymentrate for civilian males between lower unskilled wages, and higher unemployment rates for both skilled and unskilled workers. To the extent that skills are positively but * Departmeintof Economics, MassachusettsInstitute of imperfectly correlated with education, these Technology, 50 Memorial Drive, Cambridge,MA 02142. I am grateful to three anonymous referees, and to Joshua changes imply higher returnsto education, in- Angrist,Brian Bell, Peter Diamond,Michael Kremer,Frank creased residual inequality, and higher unem- Levy, Steve Pischke, Jim Robinson, Robert Shimer, Jaume ployment rates for all education groups. Ventura,and various seminarparticipants for comments and The firstpossible drivingforce for the change useful suggestions. I also thank MatthewBarmack for help in the composition of jobs is an increase in the with the Panel Study of Income Dynamics data, Francesco Caselli for Figure 3, and David Autor for extracts from the decennial censuses. Maciej Dudek, JonathanDworak, John Johnson, and John Romalis provided excellent research 1 See also Murphy and Robert H. Topel (1987) and assistance. Finally, I gratefully acknowledge financial sup- Stephen Nickell and Brian Bell (1995). The unemployment port from National Science Foundation Grant No. SBR- rates have decreasedrecently due to sustained high growth 9602116 and World Economic Laboratoryat MIT. of the U.S. economy but are not at their 1970 levels. 1259 1260 THE ERICANECONOMIC REVIEW DECEMBER1999 proportionof skilled workersin the labor force. these jobs would not be as productive when Accordingto the standardapproach, an increase employing unskilled workers.As a result, when in the relative supply of skills depressesthe skill thereare few availableskilled workersand there premiumand reduces inequality.In contrast,in is a small gap between their productivity and this m-odelwhen the supply of skills reaches a that of the unsklled, the economy will be in a critical theshold, it becomes more profitableto pooling equilibrium where firtns create "mid- createjobs designed for sklled workers,and the dling" jobs, do relatively little screening, and composition of jobs undergoes a qualitative hire most applicants.Because in a pooling equi- change, altering the structureof wages and un- librium both skilled and unskilled workers are employment.2In other words, an increase in the employed in the same jobs with the same supply of skills can create more than its own amount of physical capital, unskilled workers demand and increase inequality. The second are employed at higher physical to human cap- possible driving force is an exogenous increase ital ratios than the skilled, and wage differen- in the relative demand for skilled workers, tials are compressed.Also, because firmsrecruit which may be due to skll-biased technical most applicants,unemployment is low. change or increased internationaltrade. In this The alternative to pooling is a seprating case, the change in the composition of jobs equilibrinumin which firms create separatejobs emphasized in t'fis paper is a novel economic for skilled and unskilledworkers, and searchfor mechanismfor a familiar shock, enabling us to the appropriate candidates. Jobs for skilled explain the fall in the wages of low-paid work- workers are of a higher quality in a separating ers and the increase in unemploymentfor both than in a pooling equilibrium,while unskilled skilled amd unskilled workers, which are not jobs are of higher quality in a pooling equilib- features readily explained by existing theories. rium. As a result, in a separatingequilibrium There are two crucial ingredientsin this pa- skilled workers eam more, and the unskilled per. The first is the presence of serch frictions, less, than in a pooling allocation. Furthermore, which makes it costly for firs to find suitable since skilled workers produce only with high- workers. John M. Baron et al. (1985), among capital firms and the unskilled work only with others, document the costs of recruiting work- low-capital firms, the unemploymentrates for ers. These problems appearto be more serious both types of workers are higher. Startingfrom when firms attempt to select skilled workers, a pooling equilibrium, an increase in the pro- especially given the imperfect corelation be- portion of skilled workers and/or skill-biased tween education and skills. Similarly, the evi- technical-change can push the economy to a dence in Topel and Michael P. Ward (1992) separatingequilibrium, changing the composi- indicates that it takes a long time for young tion of jobs, reducingunskilled wages, and rais- workersto find suitablejobs. Irhesecond ingre- ing skilled wages and unemploymentrates for dient is that firms have to choose what type of both groups. job to open before meeting a worker. This also Both possible drivingforces of this theoryare appearsplausible since in practice a firm which empirically plausible. Many studies argue that has opened a service job cannot easily change it the past two decades witnessed rapid skill- to a manufacturing job, nor can a firm easily biased technical change (e.g., Eli Berman et al. downgradeits technology. 1994; David H. Autor et al. 1998). This period These two ingredients imply that the skill was also characterizedby an unusually rapid composition of the labor force affects the types increasein the supply of skills. For example, the of jobs that firms want to create. When the ratio of college graduatesto noncollege gradu- supply of skills is limited, it is not profitableto ates in the labor force increased by over 54 create jobs specially designed for the skilled, percent between 1970 and 1980. Finally, there because it is difficultto find sklled workersand is some evidence suggesting that there was a change in the composition of jobs in the United States between the 1970's and the 1990's, con- 2 Katz and Murphy (1992) show that in the short run a higher supply of skilled workersreduces the skill premium. sistent with a shift from a pooling to a separat- The forces I emphasize instead operate over a longer time ing equilibrium.In particular,high-wage fims frame as capital and job composition adjust. are more selective in theirhiring than they were VOL.89 NO. 5 ACEMOGLU:CHANGES IN UNEMPLOYMENTAND WAGEINEQUALITY 1261 two decades ago, the distributionof physical driving force in Kremer and Maskin's paper, capital to labor ratios across industrieshas be- whereasthere is a large increasein the supply of come more unequal,workers appear to be better skills, which is one of the driving forces in this matchedto theirjobs, the distributionof on-the- paper.Finally, in more recent work (Acemoglu, job training across education groups has be- 1998), I extend the approachin this paper and come more unequal, and some of the jobs in point out anotherreason why an increase in the industries and occupations that typically pay supply of skilled workersmay increase inequal- close to the median of the wage distribution ity: when technical change is endogenous, an have been replaced by jobs from the more ex- increase in the supply of skills increases the treme parts of the quality distributionof jobs. market size for skill-complementarytechnolo- These patterns are consistent with the theory gies and may induce skill-bias technicalchange. outlined above and suggest that changes in the The plan of the paper is as follows. Section I composition of jobs may be an importantcom- uses a static model to expose the main ideas. ponent of the changes in the structureof wages Section II considers a dynamic and more stan- and unemployment. dard framework which confirms the main in- This paperbuilds on the search and matching sights that follow from the static model, and models of Peter A. Diamond (1982), Dale T. generates a number of new results. Section III Mortensen (1982), and ChristopherA. Pissar- provides some evidence of a change in the com- ides (1987). In contrast to those and as in Mi- position of jobs in the United States. Section IV chael Sattinger (1995), Kenneth Burdett and concludes. Melvyn Coles (1997), and RobertJ. Shimer and Lones A. Smith (1998), workers and firms are L. A Static Model ex ante heterogeneous. The approach in this paper, however, constitutes an improvement In this section, I startwith the simplest model over these studies because the heterogeneityof of endogenous job composition. Firms choose firms is not assumed exogenous but is derived what type of jobs to open and then search for from their investment decisions. In this respect workers. I show that there exist two types of the model has a similarityto Acemoglu (1996a), equilibria with different structuresof jobs and Steven J. Davis (1996), and Acemoglu and wages: pooling and separating.In the pooling Shimer (1998), who also analyze models with equilibrium, firms open "middling"jobs and ex ante investments. However, these papers do recruit all workers. In the separating equilib- not discuss the changes in the composition of rium, firms create jobs designed for high-skill jobs, and do not allow for two-sided heteroge- workers. I show that changes in the relative neity. My paper is also related to the growing supply of skills and/orin technology can switch literatureon the causes of wage inequality, in- the economy from a pooling to a separating cluding Michael Kremer and Eric Maskin equilibrium, transforming the structure of (1997). They consider a model of assignrnent wages and unemployment. where workers of different skill levels form teams. If the distributionof skills is sufficiently A. Preferences, Technology,and the disperse, a further increase in the variance of WalrasianAllocation skills may induce high-skill workersto produce with other high-skill workers and increase in- There is a mass 1 of risk-neutralworkers and equality. Their approach is therefore comple- a mass 1 of risk-neutraland profit-maximizing mentary to, but different from, this paper. In firms. The economy lasts for one period, and particular, in their model there are no firms contains workersin two educationgroups, high (independent from workers), so there is no and low (e.g., high-school and college gradu- change in the composition of jobs and in the ates). There is no perfect overlap between edu- recruitmentpractices of firms, which are at the cation and skills, however, so both groups heart of my paper. There is also no unemploy- contain skilled and unskilled workers. Natu- ment (hence no change in unemployment).Fur- rally, high-educationworkers are more likely to thermore, in the data there is basically no be skilled. I denote the overall fraction of increase in the variance of skills, which is the skilled workersby 4, and normalizethe human 1262 THEAMERICAN ECONOMIC REVIEW DECEMBER1999 capital of unskilled workers to h = 1 and the randomly.Random matching implies that high- humancapital of skilled workersto h = 7 > 1. and low-capacity firms are equally likely to Production takes place in one firm-one meet skilled workers.4I also assume that each worker pairs. A worker with human capital h firm meets one worker and vice versa. Once and a firm with capacity k produce: they meet, the worker-firmpair have to decide whether to produce together. In the dynamic (1) y(h, k) = k`h . version of the model, if the workerand the firm do not agree, they continue to search for a new The timing of events is as follows. First, each partner, whereas here, because the economy firm has to choose its capacity ("physical capi- lasts only for one period, the firm produces no tal"), k, irreversibly. This choice captures the output, and the worker receives zero income. type of job the firm has designed and the line of Recall that at the wage-determinationstage, the business it has chosen, and is assumed to be firm has already sunk the cost of capital, ck. costless.3 At this point, the firm does not know Therefore,if the firnmand the workeragree, they the type of the worker it will recruit.Next, the will share the total outputy(h, k). I assume that firm matches with a worker, finds out his type, the worker obtains a fraction ,Bof this amount, and decides whether to shut down or continue. and the firm obtains the remainder. Hence, If it continues, it installs the required equip- wages conditionaloin the capacity choice of the ment and incurs a cost ck. Finally, wages are firm are: WH(k) [ k1 a7a and wL(k) =-- determined. fk'-'. To simplify the algebra,I also normal- The Walrasian allocation of this economy ize c (1--I ,). correspondsto the case where at the wage de- The expected value of a firm choosing capac- terminationstage, firms and workerscan switch ity k can be written as: partnersat no cost, and workers receive their full marginal product. In a Walrasian equilib- (2) V(k, X8H XL) rium, a fraction 1 - ( of firms choose kL ac-l/a and the remaining 4 fraction choose -xH(1 -- 0)[k' -a,a k] kH- a 1c-l/l where a = (1 - a)l'/'. The Walrasianmechanism allocates skilled workers + (1 - p)XL(1 -- ,)[kl-a -] to high-capacity firms and maximizes output. Since workers receive their full marginalprod- where xi is the equilibriumprobability that the uct, skilled wages are wH = y(71, kH) - ckH = firmproduces with a workerof typej= L or H, aa'r/[(l - a)c-a)/a], and unskilled wages conditionalon matchingwith this worker.Since L are wL y(1, kL) - ckL = aa/[( -- a fraction 0 of workers are skilled and there is a)c(-a)/a ], so the skill premium is equal to random matching, the firm produces with a WH/WL - skilled worker with probability qxH, and obtains (1 - ,B)y(q, k) -- ck = (1 - B. Equilibriumwith Costly Search P)[kl-ay`a - k]. The second part of (2) is explained similarly. Note that when the firm Considera tradingenvironment with frictions decides not to producewith the worker,i.e., x- and without the Walrasianauctioneer to medi- 0, it does not incur the cost of capital, ck. ate trade. Firms and workers come together In this static economy, workers are passive: they accept any match that comes along (since the alternativeis to obtain zero). Therefore,an equilibriumis simply a distributionof capacity 3 An alternative interpretationis that there are many different types of firms, indexed by the variable k. In choices representedby the function F(k) over equilibrium,only the types that will make the highest profits will enter. Also note that the main results hold if the fimi incurs some cost clk when choosing its capacity, and also 4 Random matching is plausible in this context. Since incurs the production costs ck, but the analysis becomes educationand skills are imperfectlycorrelated, firms cannot more complicated. If c = 0 so that all costs are incurred easily target skilled workers, and targetingthe highly edu- before matching, the static model would not work, but the cated workerswill not be as profitablesince many of those dynamic model would give similar results. are unskilled. VOL.89 NO. S ACEMOGLU:CHANGES IN UNEMPLOYMENTAND WAGEINEQUALITY 1263

some supportIt, and two acceptance functions the pooling equilibrium because each worker xH(k) and xL(k) such that for all k' E If, (k', meets a firm and they always agree. In the xH(k ), xL (k )) E arg maxk, XHXL V(k, xH, XL). separating equilibrium, firms create separate jobs for skilled workers and turn down the un- PROPOSITION 1: If skilled, and skilled workerseam more than they did in the pooling equilibrium, because firms targeting the skilled choose a larger capacity, < (3) i.e., kH > kp, and so wH i -(3a[4,q + (1- Id))](la)/7,a/(1 - a) < wsep - P3a/(1 - then, there is a unique equilibrium which is a). In contrast,in a separatingequilibrium, the pooling. All firms choose: earnings and employment of the unskilled collapse. k= a[4rr' + (1 - )]11t, Figure 1 draws equation (3) in the space of the fraction of the skilled in the labor force, 4), i.e., ( = {kp}, and xH(kp) = xL(kP) 1. If and the relative productivityof skilled workers, - rj > [(1 - -/( 40)]1/, there is a unique ,q. It is a downward-slopingcurve because a equilibrium which is separating. All firms pooling equilibriumrequires both 4 and q to be choose capacity kH = arq, i.e., X = {kH}, relatively small. Changes in these two variables xH(k) = 1, and xL(k) = 0. give the main comparativestatic results of the paper. An increase in the proportionof skilled PROOF: workers, (A,may be driven by an improvement An equilibrium (k', xH(k'), xL(k')) maxi- in the educationalattainment of the labor force, mizes (2). The first-ordercondition of (2) with or by changes in the curriculumof high schools respect to k for given xL and xH is: (1 - and colleges increasing the fraction of skilled 3)[4xH((1 - a)ka a - 1) + (1 workers in the two education groups. An in- - XH 0)X%(( - a)k-a 1)] 0. When crease in rqis equivalent to skill-biased techni- xL = 1, this solves for kp in the text, and yields cal change because it increases the productivity a maximal value of VP V(kp, xH 1, x of capital when combined with skilled workers 1) = (1 - 1)aa[04,a + (1 - 4)]1Ia/(1 but does not affect the productivity of capital a). Alternatively,for xH = 1 and xL = 0, the used with unskilled workers.S It can also be first-ordercondition solves for kH aq and viewed as an increase in the relative price of yields VH V(kH,xH 1 x= , 0) (1 - goods produced by skilled workers resulting 3)aao4q/(I - a). Next note that V(k, xH < 1, from opening to internationaltrade. xL 1) < VP, and V(k, xH < 1, x 0) < To focus on the most interestingcomparative VH. Now, comparing VP and VH gives condi- statics, I consider an economy in the pooling tion (3). Finally, when (3) holds, V(k, xH C 1, equilibrium and analyze the impact of an in- xL < 1) < VPand when (3) does not hold, V(k, crease in 4 and r. ?H' 1, xL< 1) < VH, so either the pooling or the separating allocation is the unique (1) As long as we are inside Region I (pooling equilibrium. equilibrium)in Figure 1, an increase in (A has no effect on wage inequality, which The firsttype of equilibriumis called pooling remains at wH/wL = q'. If 4 continues to because firms choose the same amountof level increase, eventually the economy switches of capacity (capital) and "pool" across the two from Region I to Region II, where the equi- types of workers. In this equilibrium,unskilled librium is separating.The switch creates a workers have higher physical to human capital ratios than skilled workers (kp versus kpI). This differential in physical to human capital ' To see this, consider the aggregateproduction function: = /P ratios compresses the wage differentialto WHI Y K- a[NP + 4NHPI where Ni is the numberof type i workers, and p > 0. An increase in ; is skill-biased wL = = which is 3y(Qq,kP)1/3y(1, kp) 77a, technical change. In the current model, since each firm lower than the wage differential in the Walra- employs either a skilled or an unskilled worker, an increase sian allocation,r. There is no unemploymentin in ; is equivalent to an increase in r. 1264 THEAMERICAN ECONOMIC REVIEW DECEMBER1999

q, relative productivity 16 14 12 Region II 10 \ Separating 8 X Equilibrium 16 Region I . Pooling 4 Equilibrium 2

_ fraction skilled 0.e2 0n4 O0e6 0.o8 1

FIGURE 1. POOLING AND SEPARATING EQUILIBRIA IN THE STATIC MODEL FOR a 0.4 AS A FUNCTION OF THE FRACTION OF SKILLED WORKERS, 4, AND THE RELATIVE PRODUCTIVITY OF SKILLED WORKERS, X7

qualitative change in the structure of the will increase. Finally, since there is no perfect labor market: middling jobs open to both overlap between education and skills and high- types of workers are replaced by high- educationworkers are more likely to be skilled, capacityjobs designed for skilled workers, when the economy switches from a pooling to a skilled wages increase, and unskilled em- separatingequilibrium, both residual wage in- ployment and wages collapse. equality and returnsto education increase as a (2) An increase in -q always increases wage result of the equilibriumswitch.6 inequality. As long as we stay in Region I, however, unskilled wages also increase C. An Alternative Theoryof U.S. with -q. In contrast, when the change takes Labor-MarketChanges the economy from Region I to Region II, once again skilled wages jump up, ampli- In the light of the comparativestatic results, fying the direct impact of iq on wH, and the developmentsin the U.S. labor marketsdur- unskilled employment and wages collapse. ing the late 1970's and the 1980's can be given a differentinterpretation. Recall that neitherthe Increases in 4 and q raise unskilled wages existing skill-biased technical change stories when the economy remainsin Region I, because nor others that have been advancedreadily pre- they increase kp, the level of capital that the

unskilled work with (Acemoglu, 1996a). Yet 6 both hurt There is another reason why residual inequality and changes unskilled workers when the returns to education may increase together in this setting. economy switches from pooling to separating Consider an extension of the basic model with a more equilibrium.Therefore, the impact of the supply general matching technology where skilled workers are of skills and technical change on unskilled more likely to meet high-capitalfirms. A previous version workers is nonmonotonic.In interpretingthese of the paper,Acemoglu (1996b), demonstratedthat the main results of the paper continue to hold, but there is an equi- results, it is also worth bearing in mind that in librium distributionof capital. Some workers will draw a the dynamic model, similar results will be ob- high wage from the distributionof jobs open to them, and tained, but the separatingequilibrium will also therewill be a distributionof wages for workersof the same involve low capital jobs designed for the un- skill level due to pure luck. In a separatingequilibrium, the skilled. As a when the distributionof capital choices is more disperse than in a result, economy switches pooling equilibrium, so there is more wage dispersion from a pooling to a separatingequilibrium, the among identical workers and greater residual wage unemploymentrates for both types of workers inequality. VOL.89 NO. 5 ACEMOGLU:CHANGES IN UNEMPLOYMENTAND WAGEINEQUALITY 1265 dict: (i) the fall in unskilled wages; (ii) the possibilities remain unchanged, an increase in increase in the unemploymentrates of all work- the proportionof skilled workerscan switch the ers; (iii) a change in the compositionof jobs. As economy from a pooling to a separatingequi- pointed out in the introduction, the first two librium and increase inequality. features have accompaniedthe recent increase in wage inequality,and Section III will provide II. A DynamicModel detailed evidence that there has been a change in the composition of jobs. I now describe a dynamic version of the First, suppose that, as many believe, the past environment of Section I which confirms the 25 years have been characterizedby skill-biased main insights obtained from the static model. technical change, raising '1. The increase in '1 When the economy switches from a pooling to can move the economy from a pooling to a a separatingequilibrium, there will now be low- separatingequilibrium. This creates a qualita- capital jobs targetedat the unskilled as well as tive change in the compositionof jobs, reducing the high-capital jobs designed for the skilled, unskilled wages and increasingwage inequality and the unemploymentrate of skilled workers and unemployment. As noted above, an in- will also increase. crease in the prices of skill-intensivegoods due to international trade would have the same A. Technology,Preferences, and the effects. WalrasianAllocation A more novel explanationfor the U.S. labor- market trends also emerges from this simple Consider a continuous time economy popu- model. The supply of skilled workers in the lated by a mass 1 of infinitely lived risk-neutral U.S. labor marketincreased sharply during the agents, discountingthe futureat the rate r. Once 1970's.7 A simple relative supply-demandap- again, a fraction 4 of these agents are skilled, proach would predict a decline in the relative with human capital h = 7q > 1, and the re- wages of skilled workers in response to this maining 1 - are unskilled with h = 1. increase. In the data, however, the large in- On the other side of the market, there is a crease in the supply of skills during the 1970's larger mass of risk-neutralfirms, also discount- is followed by a rise in the skill premium.In my ing the future at the same rate r. Each firm can model, when skilled workers become more employ at most one worker and is in one of abundant,firms find it profitableto design jobs three states: inactive, unfilled vacancy, and for them rather than pool across the two skill filled job. Inactive firms obtain a payoff of 0, groups. This transformsthe structureof the la- and can rent a site to open a vacancy. There are bor market, increasing returns to education, 0 2 1 sites and the flow rental price of a site is residual inequality, and unemployment.There- ry. The equilibriumrental price y will be de- fore, in contrast to the conventional approach, termined in equilibrium. Unfilled vacancies my theory predicts that even if technological meet an unemployed worker at the instantaneous rate q, and unemployed workers meet a vacancy at the rate p; p and q are assumed 7 See, for example, Autor et al. (1998), who show that exogenous, and p, q < oo so that decentralized while the employmentshare of college graduatesgrew by 6 percentage points between 1950 and 1970, it increased tradingtakes time. much faster, by 11.6 percentagepoints, from 1970 to 1990. At every instant, some of the existing firms This increase in skills was also at least partly exogenous, exit and new firms rent their sites. Immediately ratherthan a simple responseto anticipatedhigher retums to upon renting a site, and before meeting a skills in the future,driven by (i) the Vietnam-eradraft laws worker, each firm has to a and which exempted males enrolled in college from military design job service and induced many more young males to stay in choose its capacity (capital), k. As in the static college in orderto avoid the draft(see LawrenceM. Baskir model, this (irreversible)capacity choice cap- and William Strauss, 1978); (ii) the increased govemment tures the type of job created and its quality, and financial aid for college over this period (e.g., Michael S. the firm incurs no costs until matching. New McPherson and Morton Owen Schapiro, 1991). The large cohort sizes of the baby-boom generation interacted with and old unfilled vacancies search for workers, these high college-enrollmentrates and also contributedto and upon meeting a worker, they decide the large increase in the supply of skills. whether to employ the worker and whether to 1266 THEAMERICAN ECONOMIC REVIEW DECEMBER1999 buy the necessary equipment at the cost Ck. skilled by A. This will in general differ from (A This capital cost is incurredonly once, but if the because the two types of workers may have worker leaves the relation, the equipment be- differentjob finding rates. Then: comes obsolete. Finally, the workerand the firm negotiate the wage rate. At the wage determi- (4) rV(k) = q LAxH(JH(k) -Ck - V(k)) nation stage, the cost of capital is alreadysunk. If the firm and the worker reach an agreement, ? (1 - A)XL(jL(k) Ck - V(k))]e they produce flow rate of outputgiven by (1) in the previous section; otherwise,they continueto Intuitively, V(k) is the asset value of a vacancy search for new partners.The capital equipment with capacity k [more formally, this should be of each firm breaks down at the instantaneous V(k, xH, XL) but I suppressthe latterarguments rate s, and in this event, the firm exits the to simplify the exposition]. This vacancy re- market, the worker becomes unemployed, and ceives no revenue in its currentstate but meets the productionsite is rented to a new firm. a worker at the flow rate q. Random matching Before characterizing the equilibrium with implies that with probability A, the worker is costly search, it is instructive to look once skilled, and the pair decide to produce together again at the Walrasian allocation where trade with probabilityxH. In this case, the firmnrelin- takes place at full market-clearing prices an- quishes the value of its current state, V(k), nounced by the auctioneer at time 0. In this incurs the cost of capital, Ck, and obtains allocation, a fraction 1 - 4 of active firms JH(k), the value of a firn with capacity k, choose kL = a[(r + s)C]K-1 and produce producingwith a skilled worker. Alternatively, with unskilled workers, while the remaining it meets an unskilled worker at the flow rate 4 fraction choose kH= a_77[(r + s)CKL-/ q(l - A), agrees to produce with him with and produce with skilled workers, where a probability xX, and obtains JL(k) - Ck - (1 - a)1/a. The equilibrium rental price of V(k). sites will be y = 0, because there are more With a similar logic, the asset values for a firms than workers. Workers, on the other matched firm are: hand, receive their full marginal product, which in this case is the flow rate of output, (5) rJj(k) = kl-ah - w'(k) - s(J'(k) - y(h, k), minus the discounted cost of capital. That is, wH = (kH)lI-otr - (r + s)CkH, wherej = H, L. Recall that the capital equip- wL = (kL)I-a - (r + s)CkL, The wage ment breaksdown at the flow rate s, and in this differential between skilled and unskilled case, the firm exits the marketand stops paying workers is therefore exactly equal to the skill the rental price of the site, hence the term 'y in differential: WH/WL = -q. Notice also that the last expression. I denote the distributionof there is a high degree of "separation"as there capacity choices among vacancies by F(k) and are different jobs for skilled and unskilled its support by Xf. The asset values for unem- workers, because high-capacity firms have a ployed workers are: higher willingness to pay for skilled workers and employ them in equilibrium (see Sat- tinger, 1993). (6) rU1 p xi(k)(W'(k) - Uj)dF(k), B. Equilibriumwith Costly Search for j = H, L, where W'(k) is the value of a I now turnto the analysis of the search econ- worker of type j employed by a firm with ca- omy where matching is random, so that firms pacity k, and xJ(k) is the probability that a with different capacities have the same likeli- worker of type j and a firm with capacity k hood of meeting skilled workers. Throughout agree to produce together.Intuitively, a worker the paper, I limit the analysis to steady states receives nothing when unemployed, but at the and only write the Bellman equationsthat apply flow rate p, he meets a vacancy with capacity in steady state. I also denote the fraction of randomly drawn from the distribution F(k). workers in the unemployment pool who are Also, the values for employed workers are: VOL. 89 NO. 5 ACEMOGLU: CHANGES IN UNEMPLOYMENTAND WAGEINEQUALIT 1267

(7) rW'(k) = w'(k) - s(Wi(k) - U'). V(k), Ji(k), Ui, and Wi(k) satisfy (4), (5), (6), and (7) for j = H, L, wages are given by (8), and the following conditions hold: Because trading is a costly process, matched pairs have a quasi-rentto be shared. I assume 1. (Optimal capacity decision): for all k E XK, that wages are determinedby bargaining with k E arg maxk V(k'). alternatingoffers.8 Namely, if r[UJ + V(k)] > 2. (Free entry): for all k E Xf, V(k) = y. kl-hj, then workerj and a firm with capacity 3. (Optimalagreement): for all k E XK,(xL(k), k would break up the relation. Otherwise, the xH(k)) E arg max V(k). wage is: 4. (Steady-stateaccounting): uH, uL, and A satisfy (9) and (10). (8) wJ(k) = max (rUj; In a steady-stateequilibrium, firms make opti- min {13k1-ahj;kl-ahj -rV(k)}), mal capacity choices, the rentalmarket for production sites clears (free-entry),and agreement where ,Bis the bargainingpower of the worker. decisions are optimal. The next proposition es- In words, this wage rule states that the worker tablishes that an equilibriumexists, and gives and the firm divide the flow returnof the match, some details about capacity choices and accep- k1 h7, with shares J and 1 -, unless the tance decisions. To simplify the expressions, I returnto one of the partiesis less than what they normalize C (1 - ,B)/(r + s). could obtainby not agreeing.The cost of capital investment does not feature in this wage rule PROPOSITION2: A steady-state equilibrium because it is already sunk, and the outside op- exists. In any equilibrium, the support of the tion of the firm is rV(k), because in case of a capacity distributionamong vacancies, X, has disagreement,it will look for a new worker,and at most three elements, kL, kp, and kH aq, its capital will become obsolete. and we have: xL(kL) = 1, xH(kL) 0, Finally, from steady-state accounting, we xL(kP) 1, xH(kP) = 1, xL(kH) = 0, and have: xH(kH) 1.

s The proof of this propositionis given in Ap- (9) uJ pendix A, which is available upon request. In there are at most three different s + p j xi(k)dF(k) equilibrium, levels of capacity, and one of these, kH, is equal to an, and is chosen by firms which only produce with skilled workers. kL maximizes (4) 4UH when xH = 0 and xL = 1, and is chosen by (10) A H =uuH + (1 - )U firms which only produce with unskilled workers. Finally, kp, the capacity choice of firms where =-H, L, uJ is the unemploymentrate of producing with both types of workers, maxi- workersof typej, and A is the fractionof skilled mizes (4) atxH xL = 1. workers in the unemploymentpool. A steady-state search equilibriumis a tuple C. Pooling and SeparatingEquilibria (F(k), XK,xL(k), xH(k), A, UH, UL, y) such that I denote the fractionof vacancies with capacities kL, kP, and kH by AL, gp, and pLH. A 8 See Ariel Rubinstein (1982) and Avner Shaked and pooling steady-stateequilibrium is an allocation John Sutton (1984). The resulting sharing rule is different where up- = 1, so that all firms create middling from Nash bargainingnormally used in search models, but jobs with capacity kp and recruit all workers may be argued to have somewhat better microfoundations. they meet. In this equilibrium, uH = UL and The main reason why I use it here is that it simplifies the = algebra, without affecting the main results. See Acemoglu A q5.Because all jobs have the same capacity, (1996a) for a derivation of this wage rule in a search workers' outside options do not bind (firms' equilibrium. outside options never bind-see Appendix A, 1268 THEAMERICAN ECONOMIC REVIEW DECEMBER1999

which is available upon request), so the wage and A is no longer equal to 4. Also, observe rule (8) becomes w(h, k) = Pk-ha. The that since there is only one type of job open to maxiization of (4) yields kp a[(l - q4)+ each worker, outside options are once again n)al I/a, and so V(kp) = q(l - 8)aa[(l - nonbinding along the equilibrium Math,so (8) - 4))+ 4),a]1/al[(l a)r(r + s + q)] = y. becomes wJ(k) -k1Pk ahj, For A > O to be The condition for the steady-state equilibrium equilibrium, the expected values of opening to take this form is that there should be no vacancies with capacity kH and with capacity profitabledeviation, especially by a firm choos- kL have to be equal, that is, V(kH) = V(kL) ing kH and employing only skilled workers. y. Using equations (4) and (5) for j H, L, Therefore, we need V(kH) < y [and also this implies: Aq/(r + s + qA) (1 - V(kL) < y which is automatically satisfied]. A)/(r + s + q(l - A)), which solves SubstitutingxH = 1, xL = 0, A = (), and kH uniquely for A*(qT),and together with (10), a,q in (4) and (5), we obtain V(kH) = )(l - determines pH. Now we can see that a sepa- f3)aaTg/[(l - a)(r + s)(r + qo)] + q4)sy/ rating equilibrium with pL > 0 will exist if: [(r + s)(r + qo)]. Simple algebra gives the V(kl) ? y= qAk*(q)(l - 3)aaq/1[(l - condition for a pooling equilibriumas: a)r(r + s + qA*(Qq))], where V(kp) is the XL maximized value of (4) when =XH e1 (11) This inequality is likely to hold when both 'r + + 1/a (1-+)(r0 s q)a and 4 are relatively low, thus defining another nc(r +s+q q)(c-+ (r +s + qO)"O downward-sloping curve in Figure 2. Finally, for 4 and ' sufficiently high, in Region V, This parallels (3) from the previous section there exist separating equilibria in which and is drawn in Figure 2. Intuitively, a pool- AL = 0, SO that no jobs are opened for ing equilibrium requires that firms find it unskilled workers. profitable to employ skilled and unskilled In the separating equilibrium: (i) skilled workers in the same type of job, a strategy workers work with higher capital, but physi- which will be profitable when the productiv- cal to human capital ratios are equalized; (ii) ity differential between the two types of la- there is no wage compression: wHIwL - bor, -, is small. Also, the strategy of choosing 3(kH)1-ana/p(k )l -- 'Ti, and so there is a higher capacity and searching for skilled more wage inequality in the separating equi- workers, the main alternative to pooling, will librium than in the pooling equilibrium. be less profitable when the fraction of skilled While skilled workers obtain higher wages in workers, 4, is small. Hence (11) traces a the separating equilibrium, i.e., wp> W1001P downward-sloping curve. the unskilled receive less, i.e., W'epL< Three importantfeatures of the pooling equi- This is because in the separating equilibrium, libriumare: (i) thereis only one type of job with firms targeting the unskilled choose kL < kP9 capacity, kp, which employs both skilled and so the unskilled work at lower capital firms unskilled workers. Therefore, as noted in Sec- and earn less; (iii) the unemployment rates for tion I, skilled workers are employed at a lower both groups are higher than in the pooling capacity to human capital ratio than unskilled equilibrium, because high-capital firms do not workers (kpl/r versus kp); (ii) as a result of the accept unskilled workers, and the skilled pre- first observation, wage differentials are com- fer to wait for jobs designed for them. pressed-wHIWL = f(kp)1 -anal/P(kP)1-a = Separatingand pooling equilibriaare not the r1 is less than -q, the wage differential in the only possibilities. There can also be "mxed p , H> frictionless model; (iii) since all firms are the equilibria"with p 0, where some firms same and accept all workers, both groups have choose kP and pool, while others choose kH and the same unemployment rate, uH - UL only accept skilled workers.In this equilibrium, > Up,001 - S(P + S) O. there is higher unskilled unemployment than As in the static model, anotherpossibility is upOo1,but since all firms accept skilled workers, a separating equilibrium. Firms create jobs skilled unemployment is still equal to upoo,. with capacity kH for skilled workers and kL Unskilled wages are lower in the mixed equi- for the unskilled. In this equilibrium, lip = 0, librium than in the pooling equilibriumbecause VOL 89 NO. S ACEMOGLU:CHANGES IN UNEMPLOYMENTAND WAGEINEQUALITY 1269

ri, relative productivity 3.5 lzL_Re ionIlI [ Iutiple 3 Eqilibria Region V Separating 2.5 Region II Equilibrium Separating = EquilibriumiL=0 2 L>0

1.51.5 - s4Re ion IV ix ~~~~~~~~~Equilibrium 1 RegionI Pooling 0.5 Equilibrium

- i 0. fractionskilled 0.2 0.4 0.6 0.8

FIGURE 2. POOLING AND SEPARATING EQUILIBRIA IN THE DYNAMIC MODEL FOR a = 0.4, p 5, q = 5, r = 0.05, AND , = 0.5 AS A FUNCTION OF THE FRACTION OF SKILLED WORKERS, 4, AND THE RELATIVE PRODUCTIVITY OF SKILLED WORKERS, 73

A < 4, so kp is now less than a[(l - )) + from Section I are that unskilled employment ,q1a]1/, and wage inequalityis higherbecause and wages do not collapse completely and the some of the high-skill workersare employed in unemployment rate for skilled workers also high-capital jobs designed for them, earning increases. wep = 3arl/(l - a). Finally, there are multiple eqLuilibriain the partof the parameterspace II. Some Evidence denoted as Region III in Figure 2. The intuition for the multiplicity is that when there are sepa- The theoretical analysis established that a rate jobs for skilled workers, their outside op- change in the composition of jobs could be tion may be high enough that a firm which responsiblefor the U.S. labor-markettrends tak- deviates to a lower capital, kp, will have to pay ing place since the late 1970's. I now offer a the outside option of skilled workers. This re- variety of evidence suggesting that there was a duces profits from deviation and ensures a sep- change in the composition of jobs. Most indi- arating equilibrium. In contrast, when other vidual pieces of evidence are open to alternative firms also choose kp, the outside options of interpretations,and the changes may have been skilled workers do not bind, and choosing kp is caused by technology, the increase in the supply more profitablethan targetingonly the skilled, of skills, or otherfactors. Nevertheless, together and this makes the pooling allocation an this evidence paints a pictureconsistent with the equilibrium. approachin this paper, and suggests that the The main comparativestatic resultsfrom Fig- changingcomposition of jobs may be an impor- ure 2 are similar to those from Figure 1. An tant component of the changes in the structure increase in q always raises wage inequality,and of wages. may take us from a pooling to a separating equilibrium.An increase in the supply of skills A. ChangingRecruitmnent Practices of Firms as capturedby a rise in 4 can also switch the economy to a separatingequilibrium, perhaps The first piece of evidence is that there has via Regions III and IV, reducing unskilled been a change in the recruitmentpractices of wages, and increasingskilled wages and unem- firns. In my model, the pooling equilibriumis a ployment for both groups.The main differences situation where firms recruit all applicants. In 1270 THE AMERICANECONOMIC REVIEW DECEMBER1999

contrast, in the separating equilibrium, firms their relatively high-qualityjobs. Moreover, in with high capacity only accept the skilled. line with the theory in this paper, not all em- Therefore, we should observe more screening ployers are following this hiring strategy.Mur- and "selectiveness" on the part of firms. Al- nane and Levy discuss the case of another though human resource practitionerswhom I company, Sports Plus, which employs assem- talked with agree that there is more screening blers. It pays between $5.50 and $7.00 per hour, now than20 years ago, there are relatively little offers little training, and basically hires every data to back this up. The increasedspending by applicantwithout any screening. companieson theirown humanresource depart- The results of Peter Cappelli and Steffanie ments and human resource consulting firms is Wilk (1997) are also of interest in this context. consistent this view, but does not prove it. They employ a new data set of 2,945 establish- The most suggestive evidence comes from ments to analyze the determinantsof hiring case studies. Richard J. Murnane and Frank practices and intensity of screening of produc- Levy (1996) reporttheir interviews with human tion workers. Of most interest for this paper's resourcepersonnel at a numberof companies.A focus, they look at how average wages of pro- manager at Ford Motor company in 1967 de- duction workers, average education of produc- scribes their hiring strategy as follows: "If we tion workers, the reported level of skill had a vacancy, we would look outside in the requirementsof jobs, and the fraction of work- plant waiting room to see if there were any ers using computers covary with hiring prac- warm bodies standing there. If someone was tices. They find that each of these four variables there and they looked physically OK and has a statisticallysignificant and robustpositive weren't an obvious alcoholic, they were hired" effect on selection intensity, and the component (p. 19). Ford at the time was a high-wage em- of screening that increases most in response to ployer, and its lack of screening can be inter- these variables is selection on education and preted as a pooling strategy: it realized that ability (as opposed to experience or recommen- some of the workers would be less productive, dation). Therefore,firms using more computers but it still chose to recruitthem because it was and more skills, which are also the ones offering not profitable to search and wait for more higher-wage jobs, spend more resources on skilled workers. In contrast,similar companies screening in order to find workersthat have the in the late 1980's appearto use a very different required level of education and are generally recruitmentstrategy. Murnane and Levy discuss "6skilled."These results are cross-sectional and the cases of Honda of America, Diamond Star cannot be directly extrapolatedto changes from Motors, and NorthwesternMutual Life. These the 1970's to the 1990's. Nonetheless, com- are high-wage employers, with somewhat bined with the case study evidence, they suggest higher real wages than Ford in the 1960's, and that the widespread increase in computer use the first two are in the same industry as Ford. (Autoret al., 1998) and rising skill requirements All threecompanies spend substantialresources (Cappelli, 1996; Murnaneand Levy, 1996) are on recruitmentand hire only a fraction of those likely to have been associated with increased who apply. The first two use formal cognitive screening. tests, including mathematics,aptitude, and En- glish tests, as well as a series of lengthy inter- B. Changes in MismatchBetween views. The third company employs more Jobs and Workers intensive interviews but no formal tests. The interviewprocess in all threecompanies is quite In a pooling equilibriumhigh- and low-skill costly as it involves a large number of fellow workers are employed in the same jobs using employees and managers,but they view this as the same quality equipment.Therefore, skilled a worthwhile activity. Although there may be workers, employed at the physical to human different interpretationsfor these trends (e.g., capital ratio kp/h, are "overskilled"for their the increasedimportance of team production),a job, while the unskilled,working at the physical plausible interpretationis that firms are no to humancapital ratio kp, are "underskilled."In longer happy to "pool" across different skills, contrast,in a separatingequilibrium, both types and they want to hire only high-skill workersfor of workers are employed at the physical to VOL.89 NO. 5 ACEMOGLU:CHANGES IN UNEMPLOYMENTAND WAGEINEQUALITY 1271 human capital ratio a where kp > a > kplI1. that Sicherman'sfindings hold in each year, and So, workers are better matched to their jobs in the coefficients in these cross-sectional regres- separatingequilibrium than in pooling equilib- sions, except the returnto schooling, are quite rium.The forces I discuss may be less important similar, suggesting that there has not been a for education than for other dimensions of majorchange in the interpretationof these ques- skills, because schooling is observable,making tions by the respondents.The key results for my the search for educatedworkers relatively easy. hypothesis are reportedin Table 1. The sample Nevertheless, in a world of costly search and includes male heads of households between the imperfectcorrelation between skills and educa- ages 18 and 60, who are currentlyin employ- tion, there will be educationalmismatch in the ment or temporarilylaid off, excluding the self- labor market,and more so in a pooling equilib- employed. No other sample restrictions are rium. Therefore,the approachin this paperpre- applied. The first part of Table 1 reports the dicts less over- and undereducationduring the numberand fraction of workers who have their 1980's than in the 1970's. last grade completed within the bracket of re- There is a large literatureon overeducationin quired education (exact), those who have more the labor market.The most interestingand care- education than requiredfor their jobs (overed- ful paperin this literatureis by Nachum Sicher- ucated), and those with less education than re- man (1991), who studies data from the Panel quired (undereducated) for each year. The Study of Income Dynamics (PSID) in response columns (4) to (6) give the mean years of over- to the question:"How much formaleducation is education for each group, with standarddevia- requiredto get a job like yours?"He constructs tions in parentheses.Recall that overeducation over- and undereducationvariables by subtract- is definedas actualminus requirededucation, so ing the response to this question from actual a negative number means that requirededuca- education. He finds that workers who reportto tion for that group exceeds actual education. be overeducated for their job earn less than Finally, the last two rows give the varianceand others with the same amount of education,but average absolute deviation of the overeducation more thanworkers with less educationdoing the variable. same job. This is reversed for undereducated The results in Table 1 show that both the workers. Moreover, overeducated workers amount and variance of overeducation have switch to higher-wage jobs more quickly than decreased. The proportion of workers who others, suggesting that they are truly overedu- have exactly the required education for their cated for their jobs, ratherthan less skilled in job has increased from less than 43 percent in some other dimensionunobserved to the econo- 1976 to over 46 percent in 1985. This increase metrican.These findingsare consistentwith this is significant at 1 percent. Also, the average paper's predictions: on average, overeducated number of years of schooling that an overed- workers are those working with lower physical ucated worker has beyond what is required to human capital ratios; they earn less than for his job has declined from 1976 to 1985, workerswith the same education,but more than which also suggests that workers are better others with lower education working with the matched to their jobs in 1985 than during the same amount of physical capital. 1970's. The changes from 1976 to 1978 are The question on required education in the PSID is asked in 1976, 1978, and 1985. Sicher- man pools the three years. Here I repeat this in 1985, actual schooling was only available in the individ- exercise separatelyfor each year to see whether ual files, for consistency, the education variable from the the amount of over- and undereducation(mis- individual files has been used for 1976 and 1978 as well. Using the education variablefrom the family files for 1976 match) has changed from mid-1970's to and 19778 does not change any of the results for these years. 1980's.9 First, results not reportedhere confirm In all the calculations,the following values were substituted for the requirededucation variable:4 when the bracketwas 0-5, 8 for the bracket6-8, 10 when the bracketwas 9-11, and 14 when the bracket was 13-15. These are the values 9 The requirededucation variable is bracketed,with the used by Sicherman (1991) and using the means of the following brackets:0 -5, 6-8, 9-11, 12, 13-15, 16, 17. The relevantbrackets (e.g., 2.5 instead of 4) increases the mag- actual schooling variable is last grade completed. Because nitude of the changes from 1976 to 1985. 1272 THEAMERICAN ECONOMIC REVIEW DECEMBER1999

TABLE 1-CHANGES IN MISMATCH FROM 1976-1985

Panel A Panel B Number of observations Average overeducation (1) (2) (3) (4) (5) (6) Year 1976 1978 1985 1976 1978 1985 Overeducated 978 1,028 1,149 4.78 4.83 3.50 [0.40] [0.38] [0.39] (2.81) (2.83) (3.13) Exact 1,045 1,174 1,350 -0.05 -0.03 0.00 [0.43] [0.43] [0.46] (0.42) (0.37) (0.27) Undereducated 426 517 438 -2.38 -2.42 -2.71 [0.18] [0.19] [0.15] (1.58) (1.63) (1.51) Total 2,447 2,719 2,937 1.47 1.35 0.966 (3.40) (3.42) (3.02) Variance of overeducation 11.6 11.7 9.1 Absolute deviation of overeducation 2.3 2.3 1.8

Notes: All data from Panel Study of Income Dynamics. Sample includes male heads of households in employment,between the ages of 18 and 60. Overeducationis defined as actual education minus requirededucation. The last two rows give the varianceand average absolute deviation of overeducationin each of the three years. Proportionof the total is given in square bracketsin the first three columns and standarddeviations in parenthesesin the last three columns. insignificant at 10 percent whereas all the equilibrium,and more generally,with increased changes from either 1976 or 1978 to 1985 are screening and selection by employers. once again significant at 1 percent. Also cor- roborating this picture, the cross-sectional C. Changes in the Distributionof Jobs variance of overeducation fell from 11.6 in 1976 to 9.1 in 1985 and the average absolute In this subsection, I provide some evidence deviation fell from 2.4 to 1.8. In both cases, that "middling"jobs have been replacedby jobs this drop of over 20 percent is statistically from more extreme parts of the quality distri- significant at 1 percent. Therefore, these num- bution. The difficulty with this exercise is to bers suggest that there is less mismatch in the define and rankjobs. A reasonablefirst pass is 1980's than during the 1970's. to use industry-occupationcells to representjob An alternativeexplanation for this finding is categories, and rank them accordingto average that firmshire through"ports-of-entry," and as a wages (or average residualwages after control- result, young workersare overeducatedfor their ling for worker characteristics).Middling jobs jobs. If there are fewer young workers in 1985, would correspondto industry-occupationcells overeducation will have declined. To investi- that pay close to the median of the wage distri- gate this, I restrictedthe sample to either young bution. Having rankedjob categories, changes workers or to those with short tenure. The re- in the distribution of employment across the sults were very similar and, in fact, stronger.In cells can be analyzed to see whetherin the late particular,restricting the sample to those be- 1980's there is more weight in the cells at the tween the ages 18 and 45, I found that in 1976, tails of the quality distribution of jobs than 43 percent of workers had exactly the required earlier. This approach may underestimatethe education.This numberincreased to 47 percent change in the distributionof jobs if a substantial in 1985. Restricting the sample to those with fractionof the shift from middling to high- and less than 35 months of tenure, 39 percent of low-quality jobs took place within narrow in- workers had exactly the requiredyears of edu- dustry-occupationcells, but there is no easy cation in 1976, and this fractionhad risen to 45 way of analyzing changes in job composition percentby 1985. Therefore,it appearsthat there within these cells. is a significantdecline in educationalmismatch I use the Annual Earnings File of the Cur- between 1976 and 1985, which is consistent rent Population Survey (CPS), Outgoing Ro- with a switch from a pooling to a separating tation Group files uniform extract of the VOL.89 NO. 5 ACEMOGLU:CHANGES IN UNEMPLOYMENTAND WAGEINEQUALITY 1273

National Bureau of Economic Research, from Table 2 reportsthe cumulativepercentage of 1983 to 1993 to study the changes in the employment in the correspondingyear at the distribution of jobs (the information refers to cells with 10th, 25th, 50th, 75th, and 90th per- the previous year). I limited the sample to centile ranks.Formally, let ei, be the percentage those who are employed or temporarily out of of the (restricted)sample employmentin year t work and between the ages 18 and 60. I also and cell i. Then, for all t, V' eI it= 100 where excluded everyone who reported less than $1 N is the numberof cells (in this case N = 174). or more than $100 hour wage and all those Also recall that if i > i', then average residual who are in the agriculture, forestry, fishing, wage in cell i is higher than in i', i.e., Coi> Coi. armed forces, and public administration in- The cumulative percentage at the 25th percen- dustries. The years before 1983 cannot be tile in year t is then equal to 'N4 ei, and the used because industry and especially occupa- 75th percentile is equal to S3-N/4 ei, The num- tion classifications are noncomparable. ber 79.5 at the 75th percentile in 1993, for I constructedcells using 19 major industries example, implies that in this year, 20.5 percent (excluding public administration,arned forces, of employment is in the quarterof the job cat- forestryand agriculture)and 12 1-digit occupa- egories with the highest averageresidual wages. tion categories. I excluded the cells that con- The last column of Table 2 reports "weight at tained less than 200 workersbetween 1983 and the tails," WT, defined as the cumulative per- 1993. This gave a total of 174 cells, containing centage at the 25th percentile plus one minus over 72 percentof total employmentin the CPS. the cumulative percentage at the 75th percen- Although it is possible that workers in a given tile.10 That is, WT =1 eit + =3N/4 eit. cell are performingvery differentjobs in 1993 This measure therefore gives the total percent- than they were in 1983, this seems unlikely to age of workers employed in the top 25 percent be true for a large fraction of the 174 cells. In and bottom 25 percent cells. An increase in WT fact, average cell wages are very highly corre- implies that middling jobs have been replaced lated across years. Therefore, in terms of the by jobs that are typically either higher or lower model one can consider each cell as a separate quality. job category correspondingto a different level Table 2 shows that 35 percentof employment of k. In the model, a worker with given char- was in the top and bottom 25 percentjob cate- acteristics obtains a higher wage in a job with gories. By 1993, this number had risen to just higher k. This suggests that we can rank cells under38 percent.So, approximately2.5 percent accordingto residualwages from 1983 to 1993, more workersnow have either higher- or lower- and interpretthe higher-rankedcells as contain- quality jobs ratherthan middling jobs. In other ing higher-qualityjobs. More precisely, con- words, the fraction of employment in highest- sider the regression of real wages on four and lowest-qualityjob categories has increased education dummies, sex, race, a quartic in ex- approximatelyby 7 percent of its 1983 value. perience, and a dummy for those living in a These changes are not due to business-cycle metropolitan area, and let wji be the average variations:the years 1983-1984 were at a sim- residual in cell i and year t. Then, I calculate ilar stage of the business cycle to 1992-1993. It )i = >, it, and rank cells in ascending order is possible that even more majorchanges in job accordingto 6i (so cell ranksare the same in all composition took place before 1983, but due to years). The average correlation of Coiwith wi, is 0.95, suggesting thatthere are no majorchanges in the distribution of residual wages across 10 The cells above the 75th percentile include, among cells. Observe also that the increase in wage others, transport,mining, and communicationtechnicians; speciality occupationsin transport,business and repair ser- inequality from 1983 to 1993 does not iniply vices, construction,finance, communications,hospital, and anythingabout how the distributionof employ- mining, durable manufacturingsales occupations, and a ment across cells should have changed. For variety of executive, administrative,and managerialoccu- example, the changes in inequality could have pations. The cells below the 25th percentile include han- dlers, laborers,and a variety service occupationsin a variety taken place within cells, and the distributionof of industries,including retail trade (which includes, among employment across cells may have remained others, department and food stores, eating and drinking unchanged. places), business and repair, and social services. 1274 THE AMERICANECONOMIC REVIEW DECEMBER1999

TABLE 2-CHANGES IN THE COMPOSITION OF EMPLOYMENT, 1983-1993

Percentiles WT: weight at the tails 25th + Year 10th 25th 50th 75th 90th (1-75th) 1983 7.4 16.0 47.0 80.8 92.2 35.2 1984 7.3 15.7 46.3 80.5 91.9 35.2 1985 7.4 15.8 46.0 80.2 91.8 35.6 1986 7.3 15.9 45.8 80.1 91.7 35.8 1987 7.2 15.8 45.8 79.9 91.6 35.8 1988 7.1 15.8 45.6 79.6 91.5 36.2 1989 7.3 16.0 45.9 79.6 91.3 36.4 1990 7.2 16.2 46.2 79.5 91.4 36.7 1991 7.5 16.5 46.5 79.2 91.2 37.3 1992 7.7 17.0 46.9 79.7 91.9 37.3 1993 7.8 17.1 47.0 79.5 91.8 37.6

Notes: The numbersare the cumulativepercentage of workersemployed in the 1-digit industry, 1-digit occupationcell at the indicatedpercentile of the job distribution.The cells are rankedaccording to averageresidual wages between 1983 and 1993. Residual wages are obtainedfrom a regression of real wages on four education dummies, a quarticin experience, sex, race, and a dummy for those living in a metropolitanarea. The total numberof cells is 174, which excludes those with less than 200 observationsbetween 1983 and 1993. The last column gives a measure of the weight at the tails of the employment distribution,WT. WT is defined as the sum of the fraction of people employed at the bottom 25 percent and top 25 percent cells. All calculations are from the Outgoing Rotation Group Files of the CurrentPopulation Survey, and use CPS weights.

changes in the occupation and industry codes, percent in 1993. I also performed the same this is much harderto study. calculations using different levels of aggrega- To investigate the sources of this finding, I tion (and once again rankingthe cells according looked at the changes for men and women sep- to residual wages). Using 1-digit industry as arately, and also analyzed the changes by edu- above but 72 occupation categories," I obtain cation group (in all cases maintainingthe same 576 cells with over 67 percent of the total CPS rankingof cells as above). For men, there is an employment. In this case, WT increases from increase of 1.5 percentage points in WT from 40.3 percent in 1983 to 42.7 percent in 1993. 36.3 percent to 37.7 percent between 1983 and This increase in WT from 1983 to 1993 is 1993. For women, the increaseis approximately approximately2 percentage points for men, 4 4 percentagepoints, from 33.7 percent to 37.5 percentage points for women, 3 percentage percent. Among education groups, the largest points for workerswith high school or less, and changes are for those with high school or less. 2 percentagepoints for college graduates.When WT for this group increases by 3 percentage I use 2-digit occupation and 2-digit industry, points, and most of this increase is at the lower there are 865 cells containingover 65 percentof tail. WTfor college graduatesincreased by over CPS employment,and WTin this case shows an 1 percentage point, mostly at the upper tail. increase from 53.2 in 1983 to 55.3 percent in Interestingly, there is no increase in WT for 1993. those with some college. Finally, to investigate longer-termchanges, I To check the robustness of the results, I re- looked at census data on 138 industries from peated the exercise by ranking cells according 1970 to 1990.12 1 do not know of any consistent to average wages (ratherthan average residual wages). The results are unchanged; WT increases from 52.2 percent in 1983 to 54.1 per- " These are an extended version of the 2-digit occupa- cent in 1993. When I exclude cells that have tions created by splitting some of the larger occupations less than 20 observations in any year (rather along the 3-digit lines (see Acemoglu, 1997). than those with less in 12 Agriculture,forestry, fishing, and public administra- only than 200 total), the tion are excluded. These are industries aggregatedconsis- number of cells is reduced to 161, and WT tently across the censuses and used in Autor et al. (1998). 1 increases from 34.5 percent in 1983 to 36.9 thank David Autor for providing me with these data. VOL.89 NO. 5 ACEMOGLU:CHANGES IN UNEMPLOYMENTAND WAGEINEQUALITY 1275

occupation codes for these years, so I only type of "training to improve skills on the analyzed the changes in the industrialcomposi- current job." The same proportion was 33 tion of employment. Ranking these 138 indus- percent for high-school graduates, 43 percent tries accordingto average wages between 1970 for those with some college, and 55 percent and 1990, WT was 43.2 percent in 1970, 42.4 for the college graduates. These numbers in- percentin 1980, and increasedto 43.9 percentin dicate that the distribution of training was 1990. To compare this increase to the results very unequal across the education groups in from the CPS data, I created cells using only 1983. But in the next eight years, it became 3-digit industries, which gave 189 cells, con- even more unequal: in 1991, 17 percent of taining 70 percentof total CPS employment.In those without high school, 35 percent of high- this case, WT increases from 50.5 percent in school graduates, 45 percent of those with 1983 to 51.8 percent in 1993. Therefore, the some college, and 63 percent of college grad- census and CPS resultsusing industriesonly are uates received such training. Although Con- similar,which is reassuring.But the changes are stantine and Neumark show that the changes also somewhat smaller than the other CPS re- in training only account for a small fraction of sults, suggestingthat a significantfraction of the the changes in wage inequality, this process is change in job composition is within industries indicative of changes in the composition of and that these latter measuresmay significantly jobs. In fact, this patternis consistent with the underestimatethe change in the distributionof view that the composition of jobs has been jobs. changing, and the more skilled (educated) Overall,these results suggest that the compo- workers have been the winners in this pro- sition of employment underwent a number of cess. changes duringthe 1980's and the early 1990's. In particular,part of the employment in job 1,. Changes in Physical Capital categories that typically pay close to the median and Labor Ratios of the wage distributionappears to have been replaced by employment in higher- and lower- Another implication of my model is that the quality jobs, which is the pattern predicted amount of physical capital workers produce by a switch from a pooling to a separating with should become more heterogeneous as equilibrium. we move from a pooling to a separating equilibrium. Recall that the dispersion of physical D. Changes in the Distribution to human capital ratios falls (due to the same of On-the-Job-Training reason that mismatch falls). But when instead of looking at human capital, we look at capital To study anotherdimension of the change in per employee, we see that in a pooling equi- the quality distributionof jobs, one can look at librium all workers are employed at capital how on-the-job-traininghas changed. Work:ers kp, while in a separating equilibrium, some who obtain trainingreceive higher wages, and use kH while others use kL < kH. Therefore, more advancedand expensive equipmentsgen- the dispersion of capital to labor (as opposed erally requiremore training.If unskilled work- to human capital) ratios should increase ers are now working with less capital and the around the same time as the switch from skilled with more, we might expect such a pooling to separating equilibrium. Francesco change to be reflected in the distribution of Caselli (1999) also constructs a theory which on-the-job-training.Since skills are unobserved, predicts the same outcome (though not the I looked at the distributionof training across other predictions discussed here). To provide education categories. evidence in favor of this pattern, Caselli cal- Jill M. Constantine and David Neumark culates measures of dispersion of the ratio of (1994) analyze data from the CPS Supple- dollar value of equipment divided by total ments of 1983 and 1991, and report the fol- employment for 450 4-digit manufacturing lowing figures for "training to improve skills industries. Caselli's Figure 3 reports the log on the current job." In 1983, 18 percent of difference between the 90th and 10th percen- those with less than high school received any tiles of the distribution of the ratio of dollar 1276 THE AMERICANECONOMIC REVIEW DECEMBER1999

0 2.7 0

~2.6- 0 Jm2.5-.0/

0.2.4

X- 0

2.2

2.1 58 61 64 67 70 73 76 79 82 85 88 91 Year

FIGURE 3. LOG DIFFERENCE OF THE 90TH AND 10TH PERCENTILES OF THE DISTRIBUTION OF THE DOLLAR VALUE OF EQUIPMENT CAPITAL TO EMPLOYMENT ACROSS 450 4-DIGIT MANUFACTURING INDUSTRIES Note: The change from 1975 to 1995 is 17.5 percent. Source: This figure is taken from Caselli (1999).

value of equipment capital to employment increased their capital-labor ratio were the across these 450 industries, which is repro- ones paying higher wages during the 1970's, duced here as Figure 3. It shows that the and they were also more likely to increase dispersion of equipment capital to labor is their average wages further and hire more fairly constant until the 1980's, and then skilled workers (nonproduction workers). starts increasing rapidly. The capital-labor ra- These findings are consistent with the view tio difference between the 90th and 10th most that beginning in the late 1970's, some jobs capital-intensive industries has increased by targeted skilled workers and became more 17.5 percent between 1975 and 1990.13 Ca- capital intensive, while industries that already selli (1999) also shows that industries which employed less skilled workers reduced capital per employee as implied by a switch from a pooling to a separating equilibrium. 13 The numbers reported in Figure 3 do not weight industries. Caselli obtains very similar results when he IV. ConcludingRemarks weights each industry with the time-average of its employment, and when he uses other measures of dispersion, such as the log variance. When he uses current This paper has offered a model of endoge- employment as weights, the 90th and 10th differential nous job composition. In the model economy, still increases by 8.4 percent between 1975 and 1990, but firms decide what types of jobs to create and the log variance shows a slight decline over this period. Changes in the fraction of high-skill workers over this period, however, make the log variance with current weights harder to interpret. For example, even when the amounts of physical capital that skilled and unskilled skilled employees in the work force will have a first-order workers use remain constant, a change in the fraction of effect on this measure. VOL.89 NO. S ACEMOGLU:CHANGES IN UNEMPLOYMENTAND WAGEINEQUALITY 1277 then search for workers. When there are rela- premium, the model can easily generate tively few skilled workers and the productivity multiple equilibria. Further, in this case, gap between the skilled and the unskilled is relatively small shocks to the cost of edu- limited, the equilibriumis pooling: firms create cation may have large effects on the supply one type of-middling-job and pool across of skills (see Acemoglu, 1998). differentskill levels. When the productivitygap (3) An importantarea of researchis to explain between the skilled and the unskilled increases the different experiences of the United or when the proportionof skilled workersin the States and Continental Europe. Germany, labor force rises, the economy may switch to a for example, has experiencedvery little in- separatingequilibrium with higher-qualityjobs crease in wage inequality and until the designed for the skilled and low-capital jobs unification,no significantchange in unem- targeted at the unskilled. This qualitative ployment (see Nickell and Bell, 1995). change in the composition of jobs reduces un- The theory in this paper suggests that skilled wages, increases the earnings of the the training system in Germany may skilled, and increases the unemploymentrates be an important factor. Because training for both types of workers. increases the human capital of less skilled Either one of two developments may have (educated) workers, a developed training triggereda switch from a pooling to a separating system may make the strategy of creating equilibrium:(i) the proportionof college grad- separatejobs for the skilled less profitable uates in the U.S. labor force increased substan- and a pooling equilibrium more likely. tially over the past 25 years; (ii) as many More generally, the impact of labor-market economists believe, new technologies or in- institutions on job comipositionis another creased internationaltrade may have increased area for furtherresearch. the marginal product of skilled workers more than thatof the unskilledduring this period. The REFERENCES resulting transformationof the composition of jobs leads to higher returnsto education,greater Acemoglu,Daron. 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