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SHERWIN ROSEN September 29, 1 938-March 1 7, 2001 BY EDWARD P. LAZEAR SHERWIN ROSEN WAS ONE of the great appliecl microeconomic theorists of recent clecacles. His life was clevotec! to un- clerstancling how diverse people, products, en cl technolo- gies couIcl be brought together en cl allocatecl appropriately. As an example of the kinc! of analyses that Rosen pioneered, consider the many varieties of automobiles that are pro- clucecI. Some are higher quality than others, some are small, some are large, some fast, some slow, some are beautiful, en cl others are comfortable. People have different prefer- ences with respect to these attributes. A larger person might prefer a larger car. A ciarecleviT might like a faster one. How does the right car get to the right person? The obvious answer is that the market ensures that cars are available and consumers, through free choice, purchase the car they want. But at what price? How are the prices of the various attributes set so as to equate supply with clemancI, not just for some homogeneous commodity like wheat but also for some complex goocl like an automobile? Most economists would probably classify Rosen as among the twentieth century's finest labor economists because much of his work focused on labor markets. In labor markets, too, diversity is key. Workers have different skills en cl tastes 177

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178 B I O G RA P H I C A L EMOIRS for job attributes (like hours flexibility, cianger, Tocation) en cl jobs have different requirements en cl abilities to ac- commociate worker preferences. How clo wages get set to ensure that workers en c! jobs are pairec! appropriately? Much of Rosen's work centered on labor allocation en cl wage cle- termination in the context of heterogeneous workers en cl jobs. Sherwin was born to Nell en cl foe Rosen in Chicago in 1938. His mother was Canaclian en cl his father was from Illinois. His parents met on a kosher ciairy farm in Quebec, Canada. Sherwin's father, foe, en cl his Uncle Harry jointly owned a hardware store en cl Sherwin spent a goocl bit of his chiTc~hooc! playing in that store. Despite this on-thejob training Sherwin was hopeless at performing any kind of repair work. Sherwin was very close to his brother, Eciclie, who slier! when he en c! Sherwin were both only in their 30s. Sherwin spoke often of his father, describing him as a bit of a character who hacl an eye for women en cl a slight wiTc! streak. Sherwin inherited! part of that from his ciacI. Sherwin lovecl fast cars en cl enjoyocl an occasional journey to the track to bet on a horse or two. He clescribecl these field! trips as eclucational, of course, as he attempter! to unclerstancl at the purely intellectual level the system of pari-mutuel betting. Sherwin attenclec! Purclue University en c! stucliec! engi- neering. This served him well as an economist. In our joint work he wouIcl put me to shame when it came to integrat- ing-by-parts en c! teaser! the rest of us mercilessly for our ineptitude at differentiating complex integrals. But Sherwin was not cut out to be an engineer en cl cleciclecl to attend graduate school in economics at the University of Chicago. At first there was concern that he clicl not have the touch for economics either. He failecl the general exam known as "the core" and was advised by Milton Friedman to drop out

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SHERWIN ROSEN 179 of economics to pursue another cliscipline. Perhaps, sug- gestecl Milton, he might make a better accountant. Even Milton Friedman errs occasionally, en cl fortunately Sherwin clic! not follow his acivice. He perseveres! en c! eventually received his Ph.D., studying uncler one of the great teach- ers in labor economics, H. Gregg Lewis. The most important event of Sherwin's unclergracluate career consisted of a trip back to RoselancI, Illinois, where he met a girl namecl Sharon Girsburg from the north sicle of Chicago. Sharon wouic! become Sherwin's wife of 40 years. Sharon is herself a remarkable person, having both charm en cl strength. Sherwin's tendency to experience occasional moot! changes was regulates! by Sharon's love en c! consis- tency. Sharon en cl Sherwin hacl two daughters, Jennifer en cl Aciria. Jennifer still lives in Chicago en cl Aciria, now a teacher in Berkeley, California, has just provided a grandchild ap- propriately namecl Leonardo Sherwin. Sherwin was a truly sophisticated person. He hacl a creep unclerstancling of music, art, en c! literature. He was an intellectual in the best sense of the word, curious about everything en cl able to enjoy the finer things that the worIcl hac! to offer. He hac! many hobbies. He was an avic! golfer from childhood, he played jazz piano and enjoyed a good meal en cl fine wine. SHERWIN THE TEACHER Sherwin was my most important teacher. In many re- spects he was a superb teacher, but his classes were often tough slecicling. Sherwin was a clear speaker, but harcIly an impassioned orator. The truth is, he was sometimes hard to follow. What set Sherwin apart as a teacher (anc! also as a scholar) was the depth of his unclerstancling. Because he unclerstoocl things at a level creeper than most economists, what he taught was sometimes less than transparent. But

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80 B I O G RA P H I C A L EMOIRS eventually the student fell in love with both the substance en cl style of what he saicI. He macle it clear that the superfi- cial unclerstancling of a topic that we hacl was simply insuffi- cient. He unclerstooc! issues at so many different levels en c! wouIcl think about the same problem literally for years, each paper tackling another layer of it. For this reason his classes conic! be daunting to the unwashec! ~racluate student. My early impressions of Sherwin as a teacher were not only from the class that he taught when I was a graduate student at Harvard. Sherwin was then a 34-year-oic! visiting Professor teaching labor economics. Perhans eaualIv im- -o ~ --r r red lo lo portent was our interaction In the ~;h~cago-style seminar at Harvarc! that was attenclec! by Chicago expatriates like Zvi Griliches en cl by Chicago wannabes like myself. Sherwin attenclecl that seminar. I was constantly amazed by his in- sight. Sherwin wouic! appear to be thinking about some- thing else much of the time, cirawing elaborate cloocIles on the clay's paper, en cl staring out the Winslow. He literally seemec! out of it, almost ignoring the talk that was taking place. Then, in a somewhat clumsy manner, he would blurt out a one-sentence comment that would completely change the nature of the talk. Sherwin wouic! see right through the problem and cut to the key point, or more often, key flaw in the speaker's logic. The point was never cleliverecl in an aggressive or belligerent way. Sherwin never trier! to Took goocl at the speaker's expense. He just unclerstoocl the is- sue at a level far creeper than that contemplatecl by the speaker en c! macle it clear to all. As a teacher, that was his style throughout his career, en cl many in this audience have benefited from his insights. Sherwin began his teaching en c! research career at the University of Rochester in 1964, where he remained until 1977. He was a dominant figure in the economics clepart- ment because of his ability to Took deeply into so many 1 1 ~ . ~ . . ~ 1- 1-

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SHERWIN ROSEN 181 issues. He macle many friencis there, the closest of which was Stanley Engerman, en cl they remained friends until Sherwin's cleath. Much of Sherwin's early important research was clone at Rochester, inclucling the classic paper on he- clonic prices. Aciclitionally, Sherwin influenced a number of Rochester students who are now themselves fine economists. But Sherwin was not really home until he returnee! to the University of Chicago in 1977. The University of Chi- cago is unique. It epitomizes intellectual activity. Those of us who have spent significant parts of our careers at Chi- cago view it as the center of the universe. Despite Sherwin's happiness with the University of Rochester en cl despite his many good, productive years there, he conic! not resist the sirens that beckoned him to return to Chicago. It was for him the pinnacle, en cl he came home. Chicago defines the term "tough love," en c! like the rest of us, Sherwin enjoyed! a number of "romantic" experiences in the Chicago work- shops, where his work, although acimirecI, was taken apart piece by piece. An c! this macle him better. Sherwin en cl I workocl closely together en cl we were each other's most frequent coauthor. But Sherwin also en- joyoc! the personal en c! intellectual company of a number of Chicago greats, most notably Gary Becker en cl Bob Lucas. Both influenced Sherwin. It is impossible to overstate the significance of the workshop that he ran jointly with Gary for many years, not only on his own work but also on that of the rest of us who participated. Sherwin had a number of offers to move elsewhere during his career, but Chicago was his soul. He spent sum- mers en cl occasional winter months at the Hoover Institu- tion at Stanford, but was unwilling to leave the Chicago department even for the beauty en cl climate of the San Francisco Bay area. His Chicago students en cl colleagues

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82 B I O G RA P H I C A L EMOIRS en c! Chicago's intellectual atmosphere were simply too much a part of him. Since his cleath, so many of his students have talkocl about Sherwin in much the same way. He was as kinc! as any man I have ever known. Although sometimes gruff, Sherwin spent much of his life ensuring the well-being of his stu- clents en c! junior colleagues. He was generous with his in- sights. He shared them with others, especially his junior colleagues, en cl so many of us profitecl as a result. SHERWIN THE SCHOLAR Although Rosen's impact on his students was profound, one can only affect a few through direct classroom contact. By far his greatest impact was through his written work, of which there was much. Rosen publishecl about 80 papers in scholarly journals, en c! many have become classics. Prob- ably his best-known paper is "Heclonic Prices en cl Implicit Markets" (1974~. This paper forms the basis for understanding diversity how the market solves the problem of matching buyers and sellers along many different dimensions of quality. Two examples help clarify the issues: one from the labor market en c! one from product markets. A product market example has aIreacly been mentioned en cl it involves the pricing of attributes of quality. To make things simple, think about automobiles as hav- ing one dimension of quality, namely horsepower. (This is consistent with Sherwin's love of speecI. ~ Inclivicluals have preferences over horsepower, en c! it may be that other things equal, most prefer more horsepower to less. Now, incliviclu- als might be willing to pay more for higher levels of horse- power, but the relationship neec! not be linear. In fact, one might expect it to be concave, it is worth more to increase the horsepower from 50 to 100 than it is increase it from 350 to 400. But the Problem is that it is costly to produce

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SHERWIN ROSEN 183 cars that cleliver more power, especially in a package that is small enough en cl light enough to be practical. There is an analogous relation on the producer sicle that matches that of the consumer. Producers can supply more output to con- sumers but only at increased cost. Furthermore, the increased cost relationship is probably not linear en cl is likely to be convex. It costs more to increase horsepower from 350 to 400 than it floes to increase it from 50 to 100. Which level of horsepower is proviclecl en cl at what price? The Rosen analysis shower! that if all consumers hac! the same preferences en cl all producers hacl the same cost tech- nology, there wouIcl be one en cl only one type of car pro- clucec! en c! its price wouic! be cleterminec! uniquely. Of course, this is the extreme case. In the real worIcl both sicles of the market wouIcl be characterized by heterogeneity, en cl again the Rosen analysis explainer! uncler which circumstances an investigator couIcl infer either preferences or cost technol- ogy. If consumers were iclentical, but firms clifferecl in their ability to provicle increasing horsepower at increaser! costs, then there wouIcl be many varieties of cars proclucecl en cl the price wouIcl rise with horsepower in a concave fashion. The concave function that relater! price to horsepower wouic! be an exact representation of consumer preferences. That is, it wouIcl tell us how much consumers were willing to pay for aciclitional horsepower at every level of horsepower. For example, if the price of a car with 100 horsepower were priced at $15,000 and an identical car with 150 horsepower were priced at $~S,000, this would imply that every con- sumer (since they are iclentical) viewocl 50 aciclitional horses as being worth $3,000. The converse is also true. If consumers differed in their preferences, but producers were identical in their ability to produce horsepower at increasing cost, then the market relation of price to horsepower would trace out the producers'

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84 B I O G RA P H I C A L EMOIRS cost relation. For example, if the price of a car with 150 horse power were $~S,000 en cl the price of one with 200 horsepower were $25,000, then this wouIcl imply that the extra 50 horses cost $7,000 to produce. If, as is typical, both sicles of the market are heteroge- neous, then the market prices provide neither the prefer- ences nor costs of any given producer. This is because sort- ing occurs en cl the market facilitates this sorting. Those producers who produce cars with 150 horsepower at $~S,000 conic! not increase horsepower to 200 at a cost of $25,000. Although there is some firm that couIcl provide that higher level of power at that price, the firm that chooses to pro- cluce the Tower horsepower car is the one that has a com- parative advantage at low horsepower en cl a comparative clisacivantage at high horsepower. Analogously, the person who buys the 150-horsepower car at a cost of $~S,000 wouic! not be willing to pay an extra $7,000 for 50 more horse- power. IncleecI, that is why he chose the low-cost, low-horse- power car in the first place. Conversely, the individual who buys the $25,000 car with 200 horsepower wouIcl not settle for a 150-horsepower car at $~S,000. She preferred the high- horsepower car at a cost of $25,000 to the Tow-horsepower car at a cost of $~S,000. This revealecl preference is gener- atecl by the market mechanism that Rosen iclentifiecI. The point is even more profound! in the labor market context. To put it simply, when choosing a job, money isn't everything. People care about other aspects of the job and Rosen shower! us how to analyze en c! unclerstanc! the tradeoffs. Again, to make it simple, suppose that jobs clifferecl in only one dimension flexibility of hours. Some people (e.g., mothers of small children) prefer lobs that offer a great deal of flexibility c antly lower wages to nave sucn coos. utners te.g., o~-year- oic! men) might be less interested! in flexible hours. Although ---I a----- ~~ ---- ~ a--~- and might he willing to accent si~nifi- -1-- - a ~ ~ ~ A_ . ~ ~ ~ A --a

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SHERWIN ROSEN 185 they wouic! accept somewhat Tower wages to obtain flexibility, the amount they wouIcl be willing to give up to obtain flex- ible hours is not as large as the amount mothers of small children would give up. On the employer sicle, it is costly to provicle flexible hours, but more costly to some types of firms than to oth- ers. For example, firms that can accommodate telecommuters, like bill-tracking operations, can offer flexible hours with less harm to production than those running assembly lines. Factories will prefer to pay relatively high wages en c! re- quire rigid work scheclules, whereas bill-tracking firms pre- fer to pay lower wages en cl allow flexible hours. The market will sort accorclingly so that we shouic! see few mothers of small chilciren on assembly lines en cl few 54-year-oIcl men who prefer high wages working for bill trackers. The wage mechanism establisher! by the market incluces people to self-sort. Furthermore, the Rosen approach allows a conceptu- ally appropriate way to value nonmonetary amenities of a job. If firms that offer flexible hours pay $100 per clay less than those that require rigicl scheclules, we can say that the market value of flexibility is $100, that the marginal worker values flexibility at $100 en cl the cost to the marginal firm of offering flexibility is $100. Thus, we have founcl a mon- etary equivalent for nonmonetary attributes. All of this is possible in a world of heterogeneity. An extension of valuing attributes allowocl Rosen to conceptualize en c! estimate the value of a life. This approach is still usecl tociay both in academics en cl in litigation that involves damages for wrongful death. The idea is to exam- ine different earnings in risky en c! less risky occupations. If an occupation that has a slightly higher probability of death also carries with it a 10-percent higher salary, then that 10- percent aciclitional salary must compensate for the higher

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86 B I O G RA P H I C A L EMOIRS probability of death. By using estimates from real wage and hazard ciata it is possible to estimate how much one's heirs wouIcl have to inherit to compensate for one's own life. Many researchers have user! this approach, with some mocli- fications, in the health economics context to determine the cost effectiveness of various meclical treatments. The Rosen work on heclonics is probably his most im- portant contribution, but there are many others as well. Sherwin en cl my collaboration in the late 1970s resultecl in a literature caller! "tournament theory." Our paper "Rank- Orcler Tournaments as Optimum Labor Contracts" (1981) was followocl by Sherwin's paper "Prizes en cl Incentives in Elimination Tournaments" (1986~. Tournament theory ex- plains wage dynamics in hierarchies. How large a raise shouIcl inclivicluals receive when they are promoted from director to vice-presiclent? There are a number of puzzles en c! basic questions that can be answered by using tournament theory. For example, why clo salaries jump so ciramatically when an incliviclual is promoter! from vice-presiclent to chief execu- tive officer? If he wouIcl work for $500,000 per year as a vice-presiclent, wouIcl he really turn clown the CEO job at $800,000? Is it necessary to pay him $2 million, and if so, what function floes it serve the firm? Why are earnings skewocl so that the promotion from assistant vice-presiclent to vice- presiclent carries a Tower raise than the promotion from vice-presiclent to president? The basic iclea behind tournament theory is that a firm's internal labor market can be thought of in the metaphor of, say, a tennis tournament. There are three main points. First, in the tournament all prizes are fixecl in advance en c! baser! on relative performance. The player who wins the championship does so not because he is good all players in the tournament are excellent but because he is better on that given clay than his rival. The statement is relative.

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SHERWIN ROSEN 187 In firms the person who receives the promotion is generally the one who is regarclecl as the best of all the choices. Furthermore, to a first approximation, when he is promoted, he receives the salary that goes with the job, not the one that matches his ability. Second, the larger is the spreacl between the winner's en c! Toser's prizes, the more effort that goes into the con- test. Players work harcler in a winner-take-all contest than in one where the prize money is split evenly between win- ner en c! loser. In the firm the larger the difference in salary between the president en cl vice-presiclent, the more effort the vice-presiclents will put into their jobs so that they can win the presidency. The presiclent's salary serves as a moti- vator for the vice-presiclents as much or more than it floes for the president. Third, the spreac! can be too large. If the difference in prize money is too great, effort is too high and individuals will not voluntarily join the firm. Recruitment en cl reten- tion clifficulties place limits on the size of the spreac! en c! create equilibrium where a unique, optimal salary structure is cleterminecI. The theory helps explain why there is a larger spreac! in earnings between the top en cl bottom in new industries than in oIcl ones. Think about playing tennis in a hurri- cane. Players wouic! tent! to give up because their effort would have little impact on the probability of winning. Simi- larly, when luck is an important component of the inclus- trial environment, the managers tent! to give up as well because their effort has little impact on the probability of being promoted. To counter this tendency, the spread be- tween the prize of the winner en c! prize of the loser must be increased, which results in a larger difference in earn- ings. New industries are riskier, they have more luck associ- atec! with the production process. To counter this, new

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88 B I O G RA P H I C A L EMOIRS industries rewarc! winners in a bigger way than clo oic! industries, which results in a large difference between the top en cl bottom wages in the firm. The mathematics of the tournament theory is perhaps the earliest application of game theory to the labor market. Rosen was a pioneer in bringing new formal techniques to a field! that was previously institutional. Always interested in why wages take the form that they clo in the real worm, Rosen often revisited the topic of earnings skew. The most important paper on this topic was probably "The Economics of Superstars" (1981~. This was a truly remarkable paper because it provided a simple and convincing explanation for the existence of a highly skewer! income distribution. Rosen's analysis explainecl why there were a few very high earners in each occupation en cl which occupations were most likely to have a skewer! earnings clis- tribution. His argument reliecl on economies of scale, best illustratecl by the example of performers. Suppose that there are two or three great tenors in the worm. Among them are clearly Luciano Pavarotti en cl Placiclo Domingo. Suppose further that most opera fans rank Pavarotti above Domingo (although many aficionados might reverse the ranking). Even if the difference between the two were minuscule, Pavarotti could end up with earnings many times that of Domingo. The reason is that there are tremendous economies of scale in the recording business. Pavarotti can, with the same ef- fort, produce one CD of Tosca or 100 million CDs of Tosca. As a result, if most view Pavarotti as better, then he will sell many more CDs than Domingo en cl his earnings will be many times higher, despite his talent being only trivially greater. The theory implies that occupations that are subject to the greatest economies of scale will be the most skewocI. Furthermore, over time, as technology allows greater econo-

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SHERWIN ROSEN 189 mies of scale (e.g., the invention of the phonograph en c! raclio), earnings of workers in those occupations will be- come more skewocI. Chief executive officers leverage their talent by com- bining it with capital en cl other labor. A variant on the superstars theory helps us unclerstancl why CEOs of large firms earn more than CEOs of small firms. They are essen- tially combining their talents with other factors of procluc- tion to make greater use of the given amount of talent, which can be spreac! over a larger unit. Just as Pavarotti can entertain many simultaneously, the CEO of a firm that has $] billion in assets can make the same amount of talent more productive than the one who presides over a firm with only $] million in assets. Sherwin was a major contributor to the theory of hier- archies en c! relater! this to the relation of earnings to firm size just clescribecI. In a couple of papers, inclucling "Au- thority, Control, en cl the Distribution of Earnings" (1982), Rosen determined how individuals with various talents would sort among firms of different sizes en cl levels. This is the question of whether it is better to be a big fish in a small ponc! or a small fish in a larger one. Again relying on his deep understanding of diversity and equilibrium, Rosen af- firmecl that the marginal incliviclual must be indifferent be- tween being a level-two incliviclual in a large firm or a level- one incliviclual in a small firm. This iclea, couplecl with some assumptions about unclerlying technology en cl talents, not only provides a rich theory of wages within a hierarchy but also has implications for the size distribution of firms en cl the number of hierarchical levels that each has. Rosen examiner! so many different areas in labor eco- nomics that it is impossible to discuss all of them. But it is important to feature the work that he clicl with Robert Willis on sorting in labor markets. A problem that plagued labor

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90 B I O G RA P H I C A L EMOIRS economists for many years (and still does to some extent) is whether the positive relation of earnings to education is causal or simply indicates that more able people go to school. While few doubt that some is causal, the question of bias in statistical estimates remains. In "Education and Self-Selec- tion" (1979) Willis and Rosen were able to shed light on this question. Through a very clever technique that relied on revealed preference in a sorting context, they found that not only were those who went on to college better at doing college jobs, but those who did not were better in an absolute sense at high school lobs. Thus. those who not ~ ~ ~ ~ . ~ ,. ,' ~ college degrees did so tor two reasons. First, they were good at jobs that required a college degree. Second, they were bad at jobs that required only a high school diploma. This meant that the biases in estimates of the return to investing in education were unlikely to be biased very much, which is the prevailing view after 30 years of statistical estimation. Rosen worked in a large number of other areas, in- ~ . eluding labor market segmentation, discrimination, agricul- tural economics, housing, occupational choice, risk, and product market pricing. His contributions were profound and will have lasting impact on the profession. SHERWIN THE MAN Despite Sherwin's many accomplishments he was an overwhelmingly modest person. His own view of his accom- plishments was far less favorable than that held by his col- leagues, students, and the economics profession at large. Sherwin loved to laugh and had a wonderful sense of hu- mor. I remember Sherwin once talking admiringly about one of his colleagues. He described him as a "real man" and said that the expression, although not politically cor- rect in these times, captured the essence of the individual. More than anyone I have known, Sherwin was a real man.

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SHERWIN ROSEN 191 He clicin't gloat over his many successes. More important, he never revealecl his clispleasure when things clicin't go his way. Sherwin took his lumps in silence en cl bore the pain without comment. Sherwin's recognition came late in life. His election to the National Academy of Sciences came when he was 59. I remember how thriller! he was at the news. The following year he was electecl president of the American Economics Association, which is the 25,000-member, preeminent soci- ety in economics. This, too, brought him great pleasure en cl he enjoyocl enormously organizing en cl attending the January 2001 meeting. It was at this meeting that he began to fee! some of the symptoms that were associated with the disease that took his life. He founcl out that he hacl very acivancecl cancer in February 2001. Knowing that there was not much time left, I suggested to Sherwin that we have a conference that wouIcl bring together all his friends to talk about his work. "Nah, I clon't want people to have to clo that," he repliecI. "If my work is any good, people will talk about it after I am gone." But his wife Sharon en cl I persuaclecl him that he wouIcl enjoy the conference en c! seeing everyone at least one last time. He agreed. Unfortunately Sherwin's first instinct pre- vailecl because he cliecl just one month after hearing his ~ cI~agnos~s. The memorial service helcl in Chicago in May 2001 attracted a huge crowcl from around the worIcI. Sherwin truly unclerestimatec! the feelings that others hac! for him. He was a scholar who hacl a creep unclerstancling of the world. He was teacher who inspired and nurtured his stu- clents. He was a man who was a beacon to his family en c! friends. His career was cut short while he was still writing insightful papers, but the economics profession is fortunate

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192 BIOGRAPHICAL MEMOIRS that he was so productive cluring his career. The vast en c! important literature that stems from his work is his legacy. THE AUTHOR THANKS Sharon Rosen and Michelle Rosen for their in- put into this biography.

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SHERWIN ROSEN SELECTED BIBLIOGRAPHY 1968 193 Short-run employment variation on class-I railroads in the U.S., 1947-1963. Econometrica 36 (3/4) :511-29. 1969 Trade union power, threat effects and the extent of organization. Rev. Econ. Stud. 36~1) :185-96. 1972 Learning and experience in the labor market. 7. Hum. Res. 7~3~:326- 42. 1974 Hedonic prices and implicit markets: Product differentiation in pure competition. 7. Polit. Econ. 82 ~ 1 ~ :34-55. 1975 With J. R. Antos. Discrimination in the market for public school teachers. 7. Econom. 3~2) :123-50. 1978 With M. Mussa. Monopoly and product quality. 7. Econ. Theory 18~2) :301-17. 1979 With R. J. Willis. Education and self-selection. 7. Polit. Econ. 87~5~:S7- 36. 1981 The economics of superstars. Am. Econ. Rev. 71~5~:845-58. With E. P. Lazear. Rank-order tournaments as optimum labor con- tracts. 7. Polit. Econ. 89 (5) :841-64. 1982 Authority, control, and the distribution of earnings. Bell f. Econ. 13 (2) :311-23.

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194 BIOGRAPHICAL MEMOIRS 1985 Implicit contracts: A survey. 7. Econ. Lit. 23~3~:1144-75. 1986 Prizes and incentives in elimination tournaments. Am. Econ. Rev. 76~4) :701-15. 1988 With R. H. Topel. Housing investment in the United States. 7. Polit. Econ. 96~4) :718-40. The value of changes in life expectancy. 7. Risk Uncertainty 1 (3) :285- 304. 1990 With E. P. Lazear. Male-female wage differentials in job ladders. 7. Labor Econ. 8 ~ 1 ~ :S106-23. 1997 Manufactured inequality. 7. Labor Econ. 15 (2) :189-96. 1998 With H. Li. Unraveling in matching markets. Am. Econ. Rev. 88~3~:371- 87. 1 999 Potato paradoxes. 7. Polit. Econ. 107~6~:S294-329.

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