Paula E. Stephan
Economics of Science
7. The Market for Scientists
Science emerged from World War II with enhanced respect. Its successes had shortened the war and led to reduced fatalities of American troops. There was also a growing appreciation for the important role science could play in stimulating economic growth and employment in peacetime. In a report prepared at the invitation of the White House, Vannevar Bush (1945) argued that science provided an endless frontier and should be more heavily supported by the government. One response to Bush’s report was the formation of the National Science Foundation in 1950.
This groundswell of support for science, heightened in the 1950s by the threat of Soviet scientific and technological superiority, underscored the need to understand the workings of scientific labor markets. Stellar talent was drawn to this question. First, David Blank and George Stigler (1957) published a book on the demand and supply of scientific personnel; then Arrow and William Capron (1959) wrote an article concerning dynamic shortages in scientific labor markets. Both studies set the stage for work to come.
A. A Description of Scientific Labor Markets
The majority of doctoral scientists in the United States are employed in institutions of higher education and in business and industry. A distinct minority work at FFRDCs, the government, and
29. Our knowledge of scientists working in industry comes largely from a number of excellent case studies. These include Alfonso Gambardella’s (1995) study of the pharmaceutical industry, Hounshell and Smith’s (1988) study of Du Pont, Willard Mueller’s discussion of Du Pont (1962), Nelson’s study of the development of the transistor (1962), and Robert Sobel’s study of RCA (1986).
nonprofit institutions. Over time, the sectoral composition has shifted substantially as industry has employed proportionately more scientists and academe proportionately fewer. This is shown in Table 2 [HHC: not included].
Funding for research and development in the United States comes primarily from the federal government and business and industry. The government’s rationale for supporting scientific research rests on several principles: the importance of research and development to defense; the need to subsidize the production of the public good knowledge; the desire to win what Harry Johnson (1972) calls the “Scientific Olympics”; and the importance of science to economic growth. Business and industry’s rationale relates to the desire to innovate. In addition to R&D considerations, the demand for scientists is influenced by the demand for post-secondary education.
The elements underlying the demand for scientists are far from stable, as indicated by Table 3 [HHC: not included], which gives R&D expenditure data and undergraduate enrollment data for the past 30 years. We see that the proportion of GDP spent on R&D (Column 1) grew in the early 1960s and then declined continuously until 1978. It then began a steady increase, almost reaching 1960s proportions in the mid-1980s. Since that time, the propor-
tion has again declined. These changes are driven in large part by decisions made at the federal level (Column 2). The growing importance of source of R&D funding however, has softened the government swings in recent years. The table also indicates the enormous growth that occurred in the number of bachelor degrees conferred in science and engineering in the 1960s (Column 4), followed by no growth in the 1970s and minimum to no growth in the 1980s. The supply of new doctorates in science is also summarized in Table 3 and is expressed as the ratio of Ph.D.s granted to U.S. citizens and permanent residents to the U.S. population aged 25-34. We see that the proportion in the 25-34 age category receiving a Ph.D. in both the physical (Column 5) and life sciences (Column 6) increased throughout the
1960s, declined in the 1970s, and was fairly stable in the 1980s. We also see that growth was slightly higher in the life sciences and the decline more extreme in the physical sciences.
One other labor market indicator is given in Table 3: the percentage of new Ph.D.s who have definite commitments for employment on for postdoctoral positions whose commitment is for employment. Note that in recent years the proportion with an employment commitment has declined by about 25 percent in the physical sciences (Column 7) and by over 35 percent in the life sciences (Column 8). Stated differently, for approximately 50 percent of new Ph.D.s in the physical sciences a definite commitment now means taking a postdoctoral appointment upon receipt of the Ph.D., while for almost two-thirds of those in the life sciences the first position is as a postdoctorate. Although the postdoc process provides the recipient time to accumulate publications that signal future “grant worthiness,” the dramatic increase in the number of persons with these positions (as well as the increase in the number of persons holding more than one postdoctora1 position) is generally seen as an indication of the softness of the market.
B. Studies of the Supply and Demand for New Entrants to Science
A number of studies have examined the market for new entrants to science. Larry Leslie and Ronald Oaxaca (1993) do an excellent job of surveying this literature and summarizing the major findings, as does Ehrenberg (1991, 1992).  The market variables that are usually found to affect the supply of enrollees (or the number of graduates) in field j are salary in field j, salary in an alternative occupation such as law or business, and (for men) the draft deferment policy. These variables almost always have the expected signs and are highly significant. The magnitude of the implied elasticities, however, varies considerably across studies, even when field is held constant (Ehrenberg 1992). Another market variable often included in predicting supply is some measure of concurrent, past, or future supply. Other things being equal, enrollments are positively associated with present cohort size. Various lag structures are used in estimating these models and it is common to assume some form of adaptive (or rational) expectations. Supply variables generally ignored by these studies (primarily because of a reliance on aggregated data) include type of support available while in school, debt level upon graduation from college, and average time to degree.
Demand equations prove more difficult to specify, partly because we know so little about the behavior of universities and governments (David Stapleton 1989). There is, however, convincing evidence that demand relates to R&D expenditures and that these expenditures in turn affect supply decisions. In a series of equations, for example, Richard Freeman (1975) finds degrees at the B.S., M.S., and Ph.D. level in physics for the period 1950 to 1972 to be significantly related to R&D expenditures. The propensity of recent doctorates to work increasingly for industry is in part a response to higher relative salaries in industry (Ehrenberg 1991). It also undoubtedly relates to the type of academic jobs available. Most students enter graduate school with the expectation of eventually working in the academic sector and these preferences are reinforced while in school. The academic jobs they want, however, are not at four-
30. Most studies focus on long-run adjustments. A few, however, examine the short-run responsiveness of the market by also focusing on the movements of trained personnel between fields and sectors (Blank and Stigler 1957).
year institutions, but at research institutions where they can have their own lab. When jobs are scarce in this top sector (as they have been for a number of years), industry becomes substantially more appealing.
C. Forecasting Scientific Labor Markets
Although models of scientific labor markets have been somewhat successful in providing insight into factors affecting demand and supply, reliable forecasts of scientific labor markets do not exist, partly because of the unavailability of reliable predictions of exogenous variables. While this problem is endemic to forecasting in general, the ups and downs of federal funding make forecasts of scientific labor markets particularly unreliable.
The failure of researchers to successfully forecast labor market conditions in science (for anything except the very near future) has been well documented by Leslie and Oaxaca (1993). Their work should be required reading for anyone who is tempted to enter this arena. Stapleton (1989) also chronicles the issues involved, which, in addition to the problem of forecasting federal R&D, include inadequate data, a poor understanding of the behavior of educational institutions, and poor estimates of undergraduate enrollments and degrees conferred. To this list must be added the failure to come up with consistent estimates of elasticities (Ehrenbeng 1991). Despite these problems, forecasts of scientific labor markets are somewhat common, in part because they are mandated by Congress, supposedly in an effort to keep the U.S. competitive. In the recent past, forecasters predicted an impending “shortage” of scientists.  While some of this was wishful thinking on the part of science advocates in the United States, it also stemmed from the assumption that scientists would retire and be replaced on a one-to-one basis. Such has not been the case, in part because changes in the law permitted retirements to be deferred; in part because tight budgets have limited the number of replacements hired at universities.
8. Life-cycle Models
Ever since the path-breaking work of Gary Becker (1962) and Theodore Schultz (1963), economists have focused attention on the question of how behavior varies over the life cycle in occupations where human capital plays an important role. The models developed predict that, due to the finiteness of life, investment behavior declines (eventually) over time.  This decline may be hastened if the production of human capital is non-neutral, meaning that time is more productive in the market than in the production of human capital. These models typically incorporate a depreciation rate for human capital that produces a peaked profile. In the presence of depreciation, earnings also peak, although at a later time than the human capital profile.
Several authors have adapted the human capital framework to develop life-cycle models of scientists or academics. Like their first cousins, these models are driven by the finiteness of life and investigate the implications this has for the allocation of time to research over the life cycle. The models differ in the assumptions they make concerning the objective function of the scientist but reach somewhat similar conclusions. In its simplest form the objective is the maximization of
31. This was not the first time that a shortage was discussed. Talk of shortages in the early 1950s led Blank and Stigler to examine alternative meanings of the term (1957, pp. 22-24). At other times the concern has been that an “oversupply” exists.
32. Sociologists generally use age as a proxy for experience (Zuckerman and Merton 1973) while economists, though interested in experience, focus on the idea that age is a measure of time left in the career, or more generally, in life.
income, itself a function of prestige capital (Diamond 1984). In a more complex form, the objective is the maximization of a utility function that includes income as well as research output (Levin and Stephan 1991).  The latter is included given the strong anecdotal evidence that puzzle solving is part of the reward to science.  The implications of these models are that the stock of prestige capital peaks during the career and then declines and that the publishing profile declines over the life cycle. The addition of puzzle solving to the objective function produces the result that research activity is greater at any time, the greater is the satisfaction derived from puzzle solving; it also produces the strong suggestion that the research profile is flatter, the larger is the satisfaction derived from puzzle solving.
The implications of the human capital models for science have been investigated in a number of empirical studies. The dependent variable is generally earnings on publishing activity. In a few instances researchers have adapted the human capital model to study the acceptance of new ideas. The rationale behind the latter studies is that scientists as they age become increasingly vested in their own ideas and hence more and more resistant to alternative theories. In the discussion that follows we summarize these empirical studies, organizing our discussion around the three variables most frequently studied.
A. Empirical Studies of Research Activity 
The research productivity of scientists over the life cycle has received minimal attention from economists, although there have been numerous studies by psychologists and sociologists (e.g., Alan Bayer and Jeffrey Dutton 1977; Stephen Cole 1979; Harvey Lehman 1953; and Zuckerman 1977). The only studies by economists that examine the publishing activity of scientists in a life-cycle context are those by Diamond (1986b), Weiss and Lillard (1982), and Levin and Stephan (1991).
Several classes of problems present themselves in studying research productivity in a life-cycle context. These include measurement, the confounding of aging effects with cohort effects, and the availability of an appropriate database.
Publication counts are generally used as a proxy for research activity. This is justified on the grounds of the high acceptance rates - often in excess of 70 percent (Lowell Hargens 1988) - that exist among scientific journals. The question of attribution in the case of joint authorship is sometimes addressed by prorating article counts among coauthors, despite the work by Raymond Sauen (1988) that indicates that co-authors receive more credit for work than such a device would suggest. Article quality is often proxied by weighting article counts by some type of citation measure.
Because scientists of different ages come from different cohorts, aging effects are confounded with cohort effects in cross-sectional studies. One type of cohort effect is associated with change in the knowledge base of the scientist’s field. If, for example, there is a secular
33. The objective function can also include fame as an end in itself, not only as a means for generating income. Levy (1988) uses such a model to investigate what happens when the rewards to a field change and fame becomes rewarded more handsomely in the market. He does not, however, draw implications for life-cycle behavior.
34. This way of dealing with the puzzle issue is not completely satisfactory because it assumes that it is the product of discovery that enters the utility function, not the input of time in discovery. Yet, it is the process of discovery that is often reported as giving enjoyment to scientists.
35. Parts A and B of the discussion draw on joint work with Levin (Levin and Stephan 1991; Stephan and Levin 1992).
progression of knowledge (to paraphrase Jacob Mincer 1974, p. 21), the latest educated should be the best educated and hence the most productive, other things being equal. Another factor that affects research productivity and varies by cohort is access to the resources that affect research. Finally, in addition to differences in the rate that knowledge becomes obsolete and differences in opportunities that greet different cohorts over time, cohorts may vary in the level of ability on motivation they bring to the fields or specialty areas they enter.
The presence of cohort effects dictates a research design that uses a pooled cross section time series data base. Such databases are not only costly to create; issues of confidentiality can limit access to the ones that do exist. Diamond uses a database he assembled for mathematicians at Berkeley; Levin and Stephan develop a database by matching records from the National Research Council’s biennial 1973-1979 Survey of Doctorate Recipients (SDR) with publishing information from the Science Citation Index. Weiss and Lillard use a sample of Israeli scientists.
Levin and Stephan analyze six areas of science. They find that, with the exception of particle physicists employed in Ph.D.-granting departments, life-cycle effects are present in the fully specified model that controls for fixed effects such as motivation and ability.  For the fields of solid-state physics, atomic and molecular physics, and geophysics the evidence suggests that publishing activity initially increases but declines somewhere in mid-career. For particle physicists at FFRDCs, as well as for geologists, the profile decreases throughout the career. The absence of life-cycle effects for particle physicists at Ph.D.-granting institutions is not totally unexpected. Abstract theorists working on unification are often depicted as involved in a “religious quest,” handed them by Albert Einstein, or, as is commonly stated in the literature, the “search for the Holy Grail.”
Diamond finds that the publishing activity of Berkeley mathematicians declines slightly with age. Weiss and Lilland use a pooled model to estimate the growth rate of publications for 1,000 Israeli scientists. They find that the average annual number of publications tends to increase in the early phase of the academic careen and then decline. They also find that, along with the mean, the variance of publications increases markedly over the first ten to 12 years of the academic career.
The results of these (as well as other) studies should not, however, be used to conclude that the human capital model provides a satisfactory explanation of life-cycle research activity. Despite the fact that some indication of an age-publishing relationship is found, the amount of variation explained is usually small. Diamond, for example, reports R-squares of .09 or less for his research productivity equations; Aloysius Siow (1994) reports R-squares between .05 and .08. The low explanatory power of these models suggests, at a minimum, that other important factors, often ignored by economists, are at play in affecting productivity.
B. Empirical Studies of the Acceptance of New Ideas
The notion that older scientists are slow to adopt new ideas and may actually impede the progress of science by blocking innovative work of younger scientists has been articulated by several scientists and is consistent with a human capital
36. Vintage variables cannot be included in a fixed-effects model because the vintage variable is invariant over time for an individual. Equations were also estimated that included vintage variables but excluded the fixed effects.
model that age determines how vested a scientist is in a particular idea. The concept is often referred to as Planck’s Principle, because Max Planck stated in his autobiography that
a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. (1949, pp. 33-34)
Planck’s Principle has been tested by several researchers. The focus of two of these studies is the plate-tectonic revolution that occurred in the mid-to-late 1960s (Stewart 1986; Peter Messeni 1988). Two others look at the acceptance of Darwin’s ideas on evolution in the nineteenth century (Hull, Peter Tessner, and Diamond 1978; Hull 1988). The results of these studies suggest that the effect of an additional year lowers the probability of acceptance by only a tiny percentage. The general conclusion is that “Age matters, but it does not matter much” (Diamond 1980, p. 841). A recent study by Levin, Stephan, and Walker (1995) commenced with the goal of seeing whether this outcome was caused by the failure of previous researchers to control for censoring. Their results concerning the acceptance of Darwin’s ideas indicate that the age effects obtained after controlling for censoring are statistically insignificant at conventional levels. They conclude that, at least for the theory of evolution, age is a poor predictor of acceptance.
C. Empirical Studies of Earnings Functions
Estimates of earnings functions constitute the bread and butter of labor economics; thus an essay of this length can hope to scratch only the surface of this literature, even when we restrict the analysis to estimates of the earnings functions of scientists and ignore the issue of the role of gender in the reward structure. In an effort to further focus discussion, here we examine only earnings equations that use pooled databases and hence make an effort to disentangle experience effects from cohort (or time-period) effects.
Five studies nicely fit this bill. Four focus on scientists in the United States (Diamond 1986b; John Laitner and Stafford 1995; Lillard and Weiss 1979; and Weiss and Lilland 1978). One studies scientists in England and Australia (John Creedy 1988). The five all find that the earnings profile is concave from below, peaking (at the very earliest) in late career.  This finding is fairly robust with regard to specification, estimation technique, and database. Of particular interest is the finding by Laitner and Stafford (1995) that the profile remains concave from below even when the earnings measure is expanded to include “other earnings.” The parameter estimates of experience (when the dependent variable is the natural log of real earnings) are generally between .05 and .06; those for experience squared somewhere between - .0008 and - .0005. The R-squares (when the statistical techniques employed permit their computation) are quite respectable, being in the neighborhood of .50.
Clearly the earnings of scientists are related to experience or age. It would be imprudent, however, to suggest that these robust results with regard to age/experience confer infallibility on the human capital model in terms of an explanation of earnings. First, a number of other theories (e.g., principal agent/bonding/antishirking models; efficiency wage models; and rank-order tournament models) predict a positive relation-
37. A related question not addressed here is why in cross-sectional data Michael Ransom (1993) finds a negative seniority wage premium for faculty members but not for the population in general or for other highly skilled occupations.
ship between age/experience and earnings. Second, the driving force of the human capital model is the finiteness of life. Yet early in the career the present value of an investment declines only modestly with age, unless the discount factor is quite large. It is only toward middle age that the finiteness of life takes on substantial economic significance. 
D. Does the Human Capital Model Come Up Short?
While it is an overstatement to say that across the board the human capital model comes up short when applied to scientists, it is fair to say that it does not come up king. Especially with regard to publishing activity and the acceptance of new ideas, the empirical results (even when sophisticated estimating strategies are employed) fail to convince, at least this observer, that the human capital approach provides the cornerstone on which we should model the behavior of scientists. Neither does the human capital model provide a ready explanation of why the publishing activity of a cohort becomes increasingly unequal over time.
The failure of the human capital model to deliver is undoubtedly related to the fact that the production of scientific knowledge is far more complex than the human capital model assumes and that these complexities have a great deal to say about patterns that evolve over the life cycle. Human capital models also come up short in their failure to recognize the importance that priority plays in the objective function of scientists, or to fully incorporate puzzle solving as an argument in the objective function. In the discussion that follows, we focus on the complexities of the production function and discuss what they mean for the modeling process.
9. The Production of Scientific Knowledge 
Any new idea - a new conceptualization of an existing problem, a new methodology, or the investigation of a new area - cannot be fully mastered, developed into the stage of a tentatively acceptable hypothesis, and possibly exposed to some empirical tests without a large expenditure of time, intelligence, and research resources.
So Stigler described the “production function” for knowledge in his 1982 Nobel lecture (1983, p. 536). Here we explore these components in more detail, arguing that as economists we have focused most of our attention on the attributes that the individual contributes directly to the process, ignoring the importance of research resources.
A. Time and Cognitive Inputs
Although it is popular to characterize scientists as having instant insight, studies suggest science takes time. Investigators often portray productive scientists - and eminent scientists especially - as strongly motivated, with the “stamina’ or the capacity to work hard and persist in the pursuit of long-range goals” (Mary Frank Fox 1983, p. 287). A strength of the human capital models described above is their explicit recognition of the role time plays in discovery. These models also recognize the importance of intelligence or, more broadly speaking, cognitive inputs.
Several dimensions of cognitive resources are associated with discovery. One aspect of this is ability. It is generally believed that a high level of intelli-
38. It is interesting to note that studies by psychologists suggest that it is only in the late forties that individuals begin to measure time in terms of years left to live instead of years since birth (Bernice Neugarten 1968).
39. Section A draws on joint work with Levin (Stephan and Levin 1992).
gence is required to do science, and several studies have documented that, as a group, scientists have above average IQ’s.  There is also a general consensus that certain people are particularly good at doing science and that a handful are superb. Another dimension of cognitive inputs is the knowledge base the scientist(s) working on a project possess. This knowledge is used not only to solve a problem but to choose the problem and the sequence in which the problem is addressed.
The importance knowledge plays in discovery leads to several observations. First, it intensifies the race, because the public nature of knowledge means that multiple investigators have access to the knowledge needed to solve a problem. Second, knowledge can either be embodied in the scientist(s) working on the research or disembodied, but available in the literature. Different types of research rely more heavily on one than the other. The nuclear physicist Leo Sziland, who left physics to work in biology, once told the biologist Sydney Brenner that he could never have a comfortable bath after he left physics. “When he was a physicist he could lie in the bath and think for hours, but in biology he was always having to get up to look up another fact” (Lewis Wolpent and Allison Richards 1988, p. 107).
Third, the knowledge base of a scientist can become obsolete if the scientist fails to keep up with changes occurring in the discipline. On the other hand, the presence of fads in science (particularly in areas such as particle physics) means that the latest educated are not always the best educated (Stephan and Levin 1992). Vintage may matter in science, but not always in the way that Mincer’s “secular progression of knowledge” would lead us to believe (Mincer 1974, p. 21).
Fourth, there is anecdotal evidence that “too” much knowledge can be a bad thing in discovery in the sense that it “encumbers” the researcher. There is the suggestion, for example, that exceptional research may at times be done by the young because the young “know” less than their elders and hence are less encumbered in their choice of problems and in the way they approach a question. 
Finally, the cognitive resources brought to bear on a problem can be enhanced by assembling a research team, or at a minimum engaging in a collaborative arrangement with another investigator.  Because of spiraling specialization and an increased emphasis on equipment that requires unique skills, teams have become increasingly important in science. Andy Bannett, Richard Ault, and David Kaserman (1988) suggest two other factors leading persons to seek coauthors. One is the desire to minimize risk by diversifying one’s research portfolio through collaboration; the other is the increased opportunity cost of time. An additional factor is quality. The literature on scientific productivity suggests that scientists who collaborate with each other are more productive, often-
40. Lindsey Harmon (1961, p. 169) reports that Ph.D. physicists have an average IQ in the neighborhood of 140. Catherine Cox, using biographical techniques to estimate the intelligence of eminent scientists, reports IQ guesstimates of 205 for Leibnitz, 185 for Galileo, and 175 for Kepler. Anne Roe (1953, p. 155) summarizes Cox’s findings.
41. There is a literature suggesting that individuals coming from the margin – “outsiders” if you will - make greater contributions to science than those firmly entrenched in the system (Thomas Gieryn and Richard Hirsch 1983). Stephan and Levin (1992) argue that this is one reason why exceptional contributions are more likely to be made by younger persons. In studying Nobel laureates, they conclude that although it does not take extraordinary youth to do prize-winning work, the odds decrease markedly by mid-career.
42. Although teamwork and collaboration are used interchangeably here, Donald Beaver (1984) suggests that teamwork is a step beyond collaboration.
times producing “better” science, than are individual investigators. 
One indication of the trend toward collaboration in modern science is given in Table 4 [HHC – not included]. Panel A reports the mean number of authors per authored source item in the Science Citation Index. We see that in the short span of 15 years the mean number has increased by one, a factor of almost 40 percent. Not surprisingly, coauthorship patterns vary by field and organizational setting. This can be seen from Panel B of Table 4, which gives the average number of collabora-
43. Frank Andrews (1979) and S. M. Lawani (1986) discuss the relationship among quantity, quality, and collaboration in science. Other considerations are that collaborative work is more likely to be based upon funded research and more likely to be experimental rather than theoretical (Mary Frank Fox 1991).
tors on articles written by respondents to the Survey of Doctorate Recipients in four broad fields over the period 1972-1981. The large number of coauthors on articles written by physicists working at FFRDCs reflects the fact that time on the large particle accelerators must be shared and the setting up of experiments at accelerators involves more specialized skills than any single individual can possibly command. Indeed, there are stories in physics that it is possible, on an experimental article, for the author list to be longer than the article!
B. Research Resources
The production of knowledge also requires research resources. In the social sciences this generally translates into a personal computer, access to a database and one on two graduate research assistants. For physical scientists the resource requirements are considerably more extensive, involving access to substantial equipment, and the assistance of numerous graduate students and postdocs. In the life sciences research also requires access to subjects (both of the human and nonhuman variety) as well as access to certain strains. It is common practice in these disciplines to reward with coauthorship colleagues who share such access. Thus the authorship counts of Table 4 do not necessarily reflect the actual size of the team involved in any one undertaking.
An appreciation of the magnitude of equipment employed in academic research can be obtained by studying the triennial reports issued by NSF on characteristics of science/engineering equipment in academic settings. The most recent survey (National Science Foundation 1991b) describes the 1988-89 stock of movable science/engineering equipment in the $10,000 to $999,999 price range at the nation’s research-performing colleges, universities and medical schools. It estimates that the aggregate purchase price of the equipment was about $3.25 billion dollars, expended in the majority of instances during the previous five years. The results of this survey are summarized in Table 5 [HHC – not included] The table provides information on incidence of equipment as well as mean price. We see, for example, that the mean price of an electron microscope was $119,600; the mean price of an NMR was $146,000. And these averages may be biased toward teaching equipment. Sophisticated NMRs and mass spectrometers can easily cost in excess of one million dollars and hence are excluded from the study. Other types of equipment are also excluded because of cost. Accelerators and telescopes, for example, often easily cost in excess of $10 million and are usually shared across institutions. 
The importance of graduate students and postdocs to the research process is harder to document, but case studies of productive scientists lead to the conclusion that, in most fields, they are a necessary component of research. It is common practice, for example, for a chemist to have three to four graduate students and one to two postdocs working in the lab.
The overwhelming importance of resources to the research process in science means that in many fields access to resources is a necessary condition for do-
44. It is important to note that technology is a source of much of the instrumentation used in science, a fact often ignored by those who argue that science is the engine of technology and thus a necessary condition for technological change. This is a common theme of Rosenberg (1982, 1994) and was masterfully articulated by Price (1986, p. 247) in one of his last public lectures: “If you did not know about the technological opportunities that created the new science, you would understandably think that it all happened by people putting on some sort of new thinking cap... The changes of paradigm that accompany great and revolutionary changes may sometimes be caused by inspired thought, but much more commonly they seem due to the application of technology to science.”
HHC: Table 5 not displayed
ing research. It is not enough just to decide to do research, as human capital models assume. At universities, equipment is provided by the dean only in the first years of the career and usually only for equipment at the low end of the cost scale. Thereafter, it, and the stipends that graduate students and postdocs receive, become the responsibility of the scientist. Scientists whose work requires access to “big” machines off campus must also submit grants to procure time (e.g., beam time) at the research facility. This means that for a variety of fields funding becomes a necessary condition for doing research, at least research that is initiated and conceived of by the scientist. Scientists working in these fields take on many of the characteristics of entrepreneurs. As graduate students and postdocs they must work hard to establish their “credit-worthiness” through the research they do in other people’s labs. If successful in this endeavor, and if a position exists, they will subsequently be provided with a lab at a research university. They then have several years to leverage this capital into funding. If they succeed, they face the onerous job of continually seeking support for their lab; if they fail, the probability is low that they will be offered “startup” capital by another university.
C. An Alternative Approach to the Study of Scientists
This leads one to wonder if we should not use our talents as economists to develop a different approach to the study of scientists that stresses the importance of resources in the process of discovery rather than the importance of the finiteness of life. A key component of such an approach would be the recognition that past success is extremely important in determining funding and hence future success. These models could draw inspiration from empirical work done in the field of industrial organization that examines the entrance of new firms and their survival over time.  A common finding of this work is that, while entry may be fairly easy, survival is not and depends upon reaching a critical size within a certain time frame. An analogy exists in science, particularly if we think of entry as occurring in graduate school. The majority of entrants survive this phase and a large number continue to the postdoctoral phase. Getting “startup” capital from a dean (or other nonprofit entity) is far harder, and a significant number of scientists never become independent researchers. For those who do, the crucial issue then becomes whether this capital can be used to attain (in a specified period of time) the reputation required to attract resources in the form of grants. The process is made more difficult because funding constraints and priorities, which are exogenous to the scientist, change over time. Such a model, we suspect, does a far better job of fitting the data than the human capital models, which treat current effort (and hence outcome) as a function of years remaining in the career, not as a function of past success and the attainment of a critical mass. This approach, we might add, is consistent with an increased variance in the research productivity of a cohort over time, at least in the early years when scientists fail to get permanent jobs in the research sector. Obviously the approach draws heavily on the concept of cumulative advantage or more gener-
45. Early studies linked firm size positively to the likelihood of survival. Later studies explicitly linked the startup of new firms and their survival and growth to underlying technological regimes. Audretsch (1995) summarizes this literature. The analogy between scientists and firms is not limited to the concept of critical mass. It also relates to learning. As entrepreneurs gain experience in the market they discover whether they have “the right stuff.” They also learn whether they can adapt to market conditions and strategies employed by rival firms. Scientists, too, learn as their careers unfold.
ally the concept of path dependence articulated by Brian Arthur (1990).
To sum up, a reasonable case can be made that economists need to rethink the way we study the careers of scientists. A parsimonious model, with strong explanatory power, would portray scientists as having the objective of directing their own labs or research agendas. Given the importance of resources to research and the role past success plays in getting these resources, this means that scientists must continue to do research if they want to keep their place in the funding queue.
10. Funding Regimes
The conventional wisdom holds that because of problems related to appropriability, public goods are underproduced if left to the private sector. Although priority goes a long way toward solving the appropriability problem in science, this ingenious form of compensation does not insure that efficient outcomes will be forthcoming. In addition to problems caused by uncertainty and indivisibilities, as well as other efficiency concerns raised in Section 5, there is the problem that scientific research requires access to substantial resources. Unless priority can be translated into resources, it cannot come close to generating a socially optimal amount of research. Research must still be subsidized, by either the government or philanthropic institutions. 
Many European countries fund scientists indirectly by supporting the research institutes where they work. This practice is less common in the United States, especially for scientists working in academe. Instead, U.S. scientists are responsible for raising their own funds through the submission of proposals to funding agencies. This raises the question of whether knowledge advances more rapidly under the peer-review grants system or under the “institute” approach. The issue, to the best of our knowledge, has been ignored by the economics profession. It is, therefore, hoped that the ad hoc discussion that follows will stimulate research on this important topic.
The benefits of the institute approach are several: it insures that scientists can follow a research agenda (with an uncertain outcome) over a substantial period of time, it exempts scientists from devoting long hours to seeking resources and it minimizes administrative expenditures. These benefits are not trivial.
The costs of the institute approach are also substantial. Foremost is the question of the research agenda. In many institutes the agenda is set by the director, and younger scientists are constrained from following leads they consider promising. The guarantee of resources also encourages shirking; consequently, alternative methods of monitoring must be found. The institute approach also enhances stratification in science and hence the possible waste of human resources. Most appointments are made early in the career. If the scientist does not succeed in getting an institute appointment (and tenure in the job), the scientist will have minimal access to resources in that country for the rest of the career. One effect of this is that it encourages migration.
The grants system also has its benefits. At the top of the list is peer review, which promotes quality and the sharing of information. The system also encourages scientists to remain productive throughout the life cycle, because scientists who wish to have a lab must remain productive. To the extent that success in the grants system is not completely determined by past success, the system provides some opportunity for last year’s
46. Callon (1994) proposes that public support of science is needed to ensure that multiple lines of inquiry remain open.
losers to become this year’s winners. The system also encourages entrepreneurship among scientists and makes them somewhat disposed to explore the possibility of technology transfer (Stephan and Levin 1996). It also provides younger persons the opportunity to establish independent research agendas.
Just as some of the benefits of the grants system are costs of the institute system, so, too, some of the benefits of the institute approach are costs of the grants system. Grant applications divert scientists from spending time doing science. A funded chemist in the U.S. can easily spend 300 hours per year writing proposals. While some of this effort undoubtedly generates knowledge, much of it is of a “bean counting” nature and adds little of social value. The grants system also encourages scientists to choose sure(r) bet short term projects that in the longer run may have lower social value. The system also implicitly encourages scientists to misrepresent their work or the effort required to generate certain outcomes. It is typical, for example, for scientists to apply for work that is almost completed (yet not acknowledge that it has been performed) and to use some of the proceeds of funding to support “unfundable” work that is dearer to their hearts. 
11. Science, Productivity, and the New Growth Economics
The foremost reason economists have for studying science is the link between science and economic growth. That such a relationship exists has long been part of the conventional wisdom, articulated first by Adam Smith ( 1982, p. 113). Technology, an intermediate step between science and growth, has been the subject of extensive study by economists. More generally, the whole issue of the research and development strategies of companies has occupied a significant proportion of the profession during the past 50 or so years.
It is one thing to argue that science affects economic growth or to establish that a relationship exists between R&D activity and profitability. It is another to establish the extent that scientific knowledge spills over within and between sectors of the economy and the lags that are involved in the spillover process. To date, three distinct lines of inquiry have been followed to examine these relationships. One inquires into the relationship between published knowledge and growth. Another samples innovations with the goal of determining the scientific antecedents of the innovation and the time lags involved. A third examines how the innovative activity of firms relates to research activities of universities (and other firms). The studies suggest that spillover effects are present and that the lags between scientific research and its market impact are not inconsequential.
James Adams (1990) uses the published-knowledge line of inquiry to examine the relationship between research and growth in 18 manufacturing industries between the years 1953 and 1980. The study is ambitious; for example, Adams measures the stock of knowledge available in a field at a particular date by counting publications in the field over a long period of time, usually beginning before 1930. He creates industry “knowledge stocks” by weighting these counts by the number of scientists employed by
47. 1t is not accidental that the two systems are found in countries which have different attitudes toward education and social mobility. The institute approach is a logical outcome of a culture that places heavy ‘emphasis on screening. The grants system, on the other hand, is a logical extension of a culture that values (at least publicly) the opportunity of a second chance and places less emphasis on screening. Ultimately, of course, the results of research in both systems are judged by the international scientific community, irrespective of how the research was funded.
field in each of the industries being studied. He then relates productivity growth in 18 industries over a 28-year period to stocks of “own knowledge” and stocks of knowledge that have flowed from other industries. Adams finds both knowledge stocks to be major contributors to the growth of productivity. He also finds that the lags are long: in the case of own knowledge, on the order of 20 years; in the case of knowledge coming from other industries, on the order of 30 years.
A different way to study the relationship between research and innovation is to seek the scientific and technological roots of certain innovations. A 1968 study prepared for the National Science Foundation by the IIT Research Institute does precisely this, tracing the key scientific events that led to five major innovations (magnetic ferrites, video tape recorders, the oral contraceptive pill, electron microscopes, and matrix isolation). Of particular significance is the finding that in all five cases non-mission scientific research  played a key role and that the number of non-mission events peaked significantly between the 20th and 30th year prior to an innovation. The study also finds that a disproportionate amount of the non-mission research (76 percent, to be precise) was performed at universities and colleges.
A somewhat related approach to the question focuses on firms, instead of specific products, in an effort to ascertain the role that university research plays in product development. Mansfield (1991) uses such a technique. He surveys 76 firms in seven manufacturing industries to ascertain the proportion of the firm’s new products and processes commercialized in the period 1975-85 that could not have been developed (without substantial delay) in the absence of academic research carried out within 15 years of the first introduction of the innovation. He finds that 11 percent of the new products and 9 percent of the new processes introduced in these industries could not have been developed (without substantial delay) in the absence of recent academic research. Using sales data for these products and processes, he estimates a mean time lag of about seven years. He also uses these data to estimate “social” rates of return of the magnitude of 28 percent. In a follow-up study, Mansfield (1995) finds that academic researchers with ties to the firms report that their academic research problems frequently or predominantly are developed out of their industrial consulting and that this consulting also influences the nature of work they propose for government-funded research.
Knowledge spillovers can also be studied by examining the relationship between some measure of innovative activity of firms and the research expenditures of universities. This line of inquiry ignores the lag structure, but focuses instead on the extent that such spillovers exist and are geographically bounded. The rationale for expecting them to be bounded is that tacit knowledge is difficult to communicate in writing, but instead is facilitated though face to face communication. The approach is not restricted to examining the relationship between innovation and university research, but often includes a measure of private R&D expenditure in the geographic area to determine the extent that spillovers occur within the private sector. Sometimes the measure of innovative activity used is counts of patents (Adam Jaffe 1989); sometimes it is counts of innovations (Zoltan Acs, Audretsch, and Maryann Feldman 1992). In either case, measured at the geographic-industry
48. The study defined non-mission research to be research “motivated by the search for knowledge and scientific understanding without special regard for its application” (p. ix).
level, innovative activity is found to relate to the expenditure variables of university units in the geographic area doing research in scientific disciplines that relate to the industry as well as to the R&D expenditures of other firms in the same geographic area. There is some indication that these spillovers, particularly those coming from universities, are more important for small firms than for large firms (Acs, Audretsch, and Feldman 1994). 
Despite the crudeness of the measures and the problems inherent in the various approaches,  these studies go a long way toward demonstrating that the spillovers between scientific research and innovation are substantial, as are the lags. We cannot, however, leave the growth story here. Recent work suggests that knowledge spillovers are a major source of long-term growth and that these spillovers are set in motion by endogenous forces. The story goes something like this: In an effort to seek rents, firms engage in R&D. Public aspects of this R&D then spill over to other firms, thereby creating increasing returns to scale and long-term growth (Paul Romer 1994). The work of Jacob Schmookler (1966) and Scherer (1982), which demonstrates the responsiveness of R&D to demand factors, is consistent with this concept of endogenous growth. So is the work of Jaffe (1989) and Acs, Audretsch, and Feldman (1992), which suggests that firms appropriate the R&D of other firms. Empirical work summarized above also implies that scientific research conducted in the academic sector of the economy spills over to firms.
Does this mean that research in the academic sector is an important component of the new growth economics? The answer depends upon the extent that scientific research in the academic sector is endogenous.  If it is not, spillovers from universities to firms are important, but not as a component of the new growth economics. Five aspects of science that we have developed in this essay lead us to argue that an endogenous element of academic research exists. First, profit-seeking companies support academic research, and this support is growing. Second, the problems that academic scientists address often come from ideas developed through consulting relationships with industry. Third, markets direct, if not completely drive, technology, and technology affects science (Rosenberg 1982 and Price 1986).  For example, instrumentation, which often comes from technology, has proved to be extremely important in ushering in new scientific discoveries. Fourth, government supports much of university research, and the level of support available clearly relates to the overall well-being of the economy. Finally, there is evi-
49. The actual mechanism by which spillovers occur has not been studied. Without a trail linking the knowledge-producing center with the firm using the knowledge, it is difficult to know if this type of knowledge transfer is indeed geographically bounded. The Mansfield (1995) and Audretsch and Stephan (1996) studies represent first steps in this direction. Future work should also focus on the role mobility within the industrial sector plays in facilitating spillovers. Scientists sometimes become mobile, joining other firms or starting their own firms in order to appropriate the value of their human capital.
50. David, David Mowery, and Edward Steinmueller (1992) offer a good critique. They emphasize the limitations inherent in cost-benefit approaches for evaluating the contribution of basic research and propose an alternative information-theoretic approach for identifying the economic benefits. They also note the importance of non-findings as well as findings in guiding applied research and development.
51. It goes without saying that the science performed in companies is endogenous and spills over to other companies. A good portion of this essay has been devoted to demonstrating that profit-seeking companies hire scientists, direct them to do basic research, and often allow (encourage) them to share their research findings with others.
52. This counter thesis of “technology push” is also important. That is, in many cases the invention of a new technology leads to new demands.
dence that relative salaries and vacancy rates affect the quantity and quality of those choosing careers in a field. “Hot fields” like biotechnology have attracted a disproportionate number of people in recent years when the rewards (at least for a few) have been extraordinary. The impact on academic research has been substantial. 
One could even argue that university researchers have become too responsive to economic incentives for the good of science, or for the long-term good of the economy (Stephan and Levin 1996). A common theme is that a host of factors are leading university-based scientists in certain fields increasingly to “privatize” knowledge, trading what could be thought of as reputational rights for proprietary rights and the financial rewards attached to these rights.
Among the factors encouraging increased secrecy is a change in the law that enables universities, nonprofit institutions, and small firms to own patents resulting from sponsored research, an entrepreneurship spirit that grantsmanship fosters, and a time collapse in fields such as the life sciences that dramatically shortens the lag between basic discovery and application (Gambardella 1995). While the move to “privatize” can do much to foster knowledge spillovers, basic science is also affected by the process. Privatization keeps knowledge from being available in a codified form (Dasgupta and David 1994) and by-passes the peer-review system that helps to monitor quality and produce consensus in science.
This essay suggests several areas of inquiry in which economists have added significantly to an understanding of science and the role that science plays in the economy. Some of these draw heavily on observations made by sociologists of science and demonstrate the continued need to approach the study of science from an interdisciplinary perspective.
First, we have begun to quantify the relationship between science and economic growth, both in terms of payoff and lag structure. We have also achieved a better understanding of how science relates to growth, as a result of two threads of research coming together. One demonstrates that firms benefit from knowledge spillovers. The other suggests that knowledge spillovers are the source of growth and that these spillovers are endogenous. Although the authors of the new growth economics focus on the role that the R&D activities of firms play in this spillover process (both as creator of spillovers and recipient of spillovers), a good case can be made that research in the nonprofit sector spills over and has endogenous elements that are set in motion by profit-seeking behavior.
Second, economists have examined how a priority-based reward system provides incentives for scientists to behave in socially beneficial ways. In particular, it can be demonstrated that the reward of priority encourages the production and sharing of knowledge and thus goes a long way toward solving the appropriability dilemma inherent in the creation of the public good knowledge. While this line of inquiry was established by the sociologist Merton, Dasgupta and David, as well as several other economists, have done much to extend Merton’s observation that priority is a special form of
53. This is not to argue that outcome X is endogenous, but merely that the growth of knowledge has an endogenous component. At any point in time constraints clearly exist to discovery, either through the technology that is available to address the problem or because of lack of fundamental knowledge in an area necessary to the inquiry. Many of these constraints must be viewed as being exogenously determined, at least over a specific period of time (Rosenberg 1974).
property rights. Surely this is interdisciplinary fertilization at its very best!
Third, science is not only about fame; it is also about fortune. Another contribution of economists is the demonstration that many of the financial rewards in science are a consequence of priority: salary, for example, is positively related to both article and citation counts. Because the financial rewards often come in the form of consulting and royalty income, we will never know the full extent of the relationship until we have reliable data on nonsalary dimensions of the income of scientists. There is also the suggestion that reputation matters to industry. We know, for example, that some firms encourage scientists to publish. We also know that startup companies use highly cited scientists as a signal of quality to financial markets.
Fourth, economists have a reasonably good understanding of the way scientific labor markets function, although the estimates of elasticity are not as robust as one would like. Neither can we forecast market conditions with much accuracy. We should not accept responsibility for this failure, however, because much of the problem rests on the impossibility of predicting the whims of Congress.
Economists have also contributed to an appreciation of how the finiteness of life affects behavior of an investment nature. Human capital models have led to the prediction that earnings, research productivity and receptivity to new ideas of scientists will decline in late career. Much effort has been allocated to testing these models. The empirical results, especially with regard to publishing activity and the acceptance of new ideas, lead this observer of science to conclude that the human capital approach does not provide the cornerstone on which we should model the behavior of scientists. Neither does the human capital model provide a ready explanation of why the productivity of a cohort of scientists becomes increasingly unequal over time. The failure of the model is undoubtedly related to the fact that the production of scientific knowledge is far more complex than the human capital model assumes, and that these complexities have a great deal to say about patterns that evolve over the life cycle. This leads us to conclude that economists need to rethink the way we study the careers of scientists. A parsimonious model, with strong explanatory power, would portray scientists as having the objective of directing their own lab or research agenda.
There are other ways economists could contribute to a better understanding of the workings of science. Eight are mentioned here. First, economists have a comparative advantage in understanding and analyzing the role that risk and uncertainty play in science. We can, for example, explain why risk aversion on the part of funding agencies dissuades scientists who are by disposition willing to take risk from engaging in this kind of research. We have the tool kit required to understand choices as outcomes of games and the possibility of using experimental economics to better understand how outcomes depend on rewards and funding.
Second, economists can continue to contribute to a discussion of efficiency questions: Are there too many entrants in certain scientific contests or, more generally, too many scientists? A related question concerns whether science is organized in the most efficient way, particularly in the nonprofit sector. Is the demand for graduate students as research assistants and subsequently as postdocs so strong that it masks market signals concerning the long-run availability of research positions and encourages inefficient investments in human capi-
al?  Could other kinds of personnel (e.g., individuals with terminal masters degrees) substitute for graduate students and postdocs in the lab? 
Third, economists can contribute to an understanding of science by extending to the study of science approaches that have proved fruitful in the study of firms. We have already suggested, for example, that work in industrial organization that examines the entrance and survival of new firms could provide a framework for studying the careers of scientists. Another possibility is to view the production of scientists through the lens of an evolutionary model (Nelson and Winter 1982). Diversity and selection - the heart of evolutionary economics - are clearly present in the way in which scientists are trained, promoted and rewarded.
Fourth, economists can contribute to a better understanding of how the reward structure of science leads some scientists to behave in socially irresponsible ways. Issues here concern the fragmentation of knowledge that a focus on article counts encourages and the temptation to engage in fraudulent behavior.
Fifth, given the role that resources play in scientific discovery, it is important to understand more fully how scientific outcomes relate to the way governments and philanthropic organizations provide resources. Several governments abroad are currently experimenting with new approaches for planning research support, evaluating program performance, and using the results of evaluation in subsequent decisions. Research concerning the effectiveness of different approaches is clearly needed.
Sixth, as a discipline we need to pay considerably more attention to understanding the way scientific effort is organized, monitored, and rewarded in industry. We also need to study how knowledge spillovers are transmitted to industry.
Seventh, the question of how increased opportunities for entrepreneurial behavior affect the practice of science bears further exploration. When millions of dollars are at stake, for example, are journal editors less inclined to declare a winner and more inclined to declare a tie, as anecdotal evidence would suggest?
Eighth, we need to understand more fully how science relates to patterns of international trade. Although knowledge is a public good, it has exclusive aspects once it is embedded in traded goods. Work by Ralph Gomory and William Baumol (1995) and George Johnson and Stafford (1993) suggests that the lessons of David Ricardo concerning the gains to trade may fail to be realized in a world where developing countries appropriate the technological advances made by others.
In short, economists have accomplished a reasonable amount in our study of science; but other issues await investigation. It is hoped that this essay will encourage that process.
54. In its most extreme form this question asks if the current system of graduate education is fundamentally a pyramid scheme in which graduates recruit new talent in order to keep the system going.
55. The need to restructure graduate education and postdoctoral training in math and the physical sciences was the topic of a June 1995 NSF conference. The summary report (John Armstrong 1995) stresses the need to broaden graduate education and make increased use of periods of off-campus experience. A report on the graduate education of scientists and engineers issued by the National Academy of Sciences (1995) made similar recommendations with regard to providing a broader range of options to graduate students.