Abstract--Economists²' productivity over their careers and as measured by publication in leading journals declines very sharply with age. There is no difference by age in the probability that an article submitted to a leading journal will be accepted. Rates of declining productivity are no greater among the very top publishers than among others, and the probability of acceptance is increasingly related to the author's quality rather than the author's age.

It is well known that productivity declines with age in a wide range of activities. Lehman (1953) suggests an early peak in productivity in a variety of scientific and artistic³ endeavors, and Diamond (1986) documents the pattern for several scholarly pursuits. Levin and Stephan (1992) provide clear evidence that this decline exists even after careful attempts to account for individual and cohort differences. Fair (1994) finds declines in physical ability among elite⁴ runners, as does Lydall (1968,pp. 113 passim) in physical abilities of the population generally. In this study we examine productivity declines in our own field. The main new results arise from our use of two different types of information, the equivalent of household and establishment data, to study the stone field over essentially⁵ the same period of time. Section I discusses the general results on aging and productivity, whereas section II presents evidence of the importance of heterogeneity⁶.
I. Declining Productivity with Age

Using the American Economic Association (AEA) Directory of Members, we identified tenured economics faculty⁸ at 17 top research institutions and obtained the years of their Ph.D. degrees.[1] With the citation⁹ index of the Journal of Economic Literature we replicated¹⁰ portions of the curricala vitae of each of the 208 economists currently in the economics departments of those institutions who received Ph.D. degrees between 1959 and 1983.[2]

To measure productivity we construct three indexes, combining papers published in refereed¹¹ journals. Prior research suggests that, at least in terms of salary determination, the returns from nonreferred publications are quite low Sauer (1988), so that we ignore such publications in calculating these measures. I1 weights an article by the journal where it appears based on citations¹² to that journal, using values generated by Laband and Piette (1994). This index distinguishes strongly among journals. For example, the Journal of Political Economy has a weight of 59.1, whereas Economic Inquiry¹³ has a weight of 7.9. In constructing I1 we use the weights associated with the decade in which the articles were published. I2 distinguishes somewhat less among journals by assigning all articles in the nine "core" journals identified by Laband and Piette a value of 1, whereas all other journals are valued at 0.5.[3] Finally, I3 gives all papers a weight of 1. Coauthored articles were given half credit, consistent with Sauer's (1988) findings on the economic returns to coauthorship.[4]

We measure the change in productivity over the life cycle by the percentage change in the number of publications from 9-10 years past the Ph.D. to the periods 14-15 years and then 19-20 years after. For most of the elite economists the base period is equivalent (accounting for publication lags) to the time of tenure⁷, when one might expect that incentives¹⁴ to produce are at a peak. Using two-year publication records at each point reduces the effects of noise in the performance measures. One might argue that still other scientific life-cycle mileposts (e.g., attaining¹⁵ a full professorship) should be accounted for too (and to some extent the 14-15-year point does this). But our main purpose is simply to provide detailed¹⁶ evidence on the relationship to age, and our data are not sufficient to infer the impact of every possible milepost.

Table 1 contains data on productivity loss by Ph.D. vintage measured by each of the three indexes. If we consider I1 and I2, the two indexes that take journal quality into account, the decline appears to be quite substantial. Between years 9-10 and 14-15 elite economists as a group lose 29 to 32% of their output. From years 9-10 to 19-20 they lose 54 to 60%. In other words, productivity losses are on the order of 5 % per year from the time of peak productivity. However, the losses do not appear to accelerate over these 10 years of the economists' work lives. The loss from year 10 to year 20 is approximately twice that from year 10 to year 15.

Another way to study the age-productivity relationship is to examine journals rather than individuals. The first row in each pair of years in table 2 shows the ages of authors of full-length refereed articles in several leading journals (American Economic Review, Journal of Political Economy, and Quarterly Journal of Economics).[5] The median age of authors in the 1980s and 1990s was 36. Scholars over age 50 when their studies are published are a minute fraction of all authors in these journals. Creative economics at the highest levels is mainly for the young. That is as true in the 1990s as it was in the 1960s, although the age distribution of authors does seem to have shifted slightly rightward in the late 1970s.#p#分页标题#e#

The second row in each pair in table 2 shows the age distributions of random¹⁷ samples of the membership of the American Economic Association in years near those for which the authors' ages were tabulated¹⁸.[6] The distributions are heavily concentrated between 36 and 50. Decadal variations reflect rapid expansion of American universities in the middle and late 1960s, stagnation¹⁹ in the 1970s and much of the 1980s, and a possible fragmentation of the profession in the 1980s as specialized²⁰ associations expanded. A substantial percentage of AEA members is over age 50 implying that older economists are greatly underrepresented among authors in major journals relative to their presence among those who view themselves as part of the economics profession.[7]

Among the several groups of physical scientists analyzed²¹ by Levin and Stephan (1992) the decline of productivity (high-quality publishing) with age was very pronounced. McDowell's (1982) small samples of scholars in a variety of disciplines suggest less rapid declines in productivity with age (in publications unweighted by quality), with the sharpest declines and earliest peaks in the "hard" sciences, and later peaks among English professors and historians. The evidence from our two very different types of samples of economists and economics publishing that account for the quality of publications suggests that, for whatever reason, economics is at least as much a "young person's game" as are the physical sciences.
II. Heterogeneity in Declining Productivity

The evidence in section I documents the decline in productivity at the sample means. Information on the age-productivity relationship at the extremes of the sample is interesting in its own right and might help shed some light on the possible causes of the apparent decline in productivity with age. The simplest test compares productivity losses among the top early performers with that of the entire sample of economists at elite institutions. Among the top 10% of early producers the mean values of I1, I2, and I3 at year 20 were 64, 50, and 22%, respectively. These means are quite close to those listed for the entire sample in table 1. Thus on average early promise seems to be sustained in this sample. Of the 12 top researchers on whom we have 20 years of data, five were still among the top dozen producers at year 20.

These conclusions are confirmed when we examine the entire sample. For each index Ij, j = 1, 2, 3, we estimate b0 and b1 in

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Table 3 reports the parameter²² estimates. For all three indexes productivity in year 20 is positively²³ and significantly related to productivity in year 10. There is also substantial productivity loss. The joint²⁴ hypothesis that b0 = 1 and b1 = 0 (i.e., no productivity loss) is rejected (F-statistics of 134, 152, and 39, respectively). Productivity loss is least severe in I3, which weights all journals equally, regardless of quality.

If productivity losses were less among economists with high early productivity (high Ij,10), b1 would be negative. In fact, for two of the three indexes the estimated b1 is effectively zero. We cannot reject the hypothesis of a linear relationship between late and early productivity. Only for I3 does it appear that productivity loss is higher for top early producers, and even here the effect is quite small. An economist¹ in the top 10% of this sample at year 10 loses only an additional 0.5 (unweighted) paper compared to an average researcher in this sample at year 10. The very top producers in this elite sample keep on producing high-quality research, but at a slower rate. Those who were not at the top early in their careers slow down as rapidly as the top people, but their slowdown leads them to publish increasingly in lower quality outlets²⁵.

Another way of examining heterogeneity is to look at how authors of different quality free in the publication process conditional²⁶ on their efforts. We obtained data on a random sample of initial submissions²⁸ to a major general journal during a four-month period in 1991. (Some of the data were initially²⁹ supplied by the journal's office for use in Hamermesh (1994).) Refereeing³⁰ at this journal is double-blind, so that the chance that referees³¹ (though possibly not the editors) were affected³² by authors' reputations is reduced. The ages of the authors of these 313 papers are measured as of 1993 to account for the probable two-year average lag between the submission²⁷ of a paper and its publication.

The simple fact in these additional data is that acceptance rates at this journal are remarkably³³ constant by author's age. The probabilities of an article being accepted are 0.122, 0.114, and 0.123 in the three age groups 50, respectively.[8] On average there is no decline with age in the acceptance rate of papers submitted to this journal.[9] Probits on the acceptance of a submission that also included variables indicating whether the author was a member of the AEA, was in a top 20 department (as listed in Blank, 1991), was resident in North America, or was female, and the author's prior citation record yield an identical conclusion. The declining presence of older authors in top economics journals does not occur because older authors who keep submitting papers suffer higher rejection³⁴ rates.#p#分页标题#e#

The probits included interaction terms between indicator³⁵ variables for age and the extent of citations. (Low-cited economists were defined as those with fewer than 10 citations per year, well-cited with at least 10.) As figure 1 clearly shows, acceptance rates for each age group differ sharply by citation status. Comparing authors age 36-50 to those over 50, it is quite clear that the degree of heterogeneity increases with age. This appears to be less true in comparing the oldest to the youngest group, but that inference is due mainly to a very small sample. (Only six authors under age 36, the future superstars of the profession, were well cited.) The general tenor³⁶ of the combined results from this sample is that the profession signals to less able scholars that their work no longer meets the profession's highest standards, and most of them respond by reducing their submissions to the highest quality journals.
III. Conclusions

We have followed the careers of economists and measured the demographic characteristics of publishers in leading journals. The evidence seems quite clear that publishing diminishes with age, especially publishing in leading journals, at rates as rapid as in the physical sciences. Indeed, remarkably few older people publish successfully in the scholarly outlets on which the profession places the highest value. As economists age, those who were the most productive early in their careers are among the few "survivors³⁷" still contributing to scholarship through the leading scholarly outlets.

Whether this relationship is due to natural declines in capacity or decreased incentives to produce is extremely difficult to discern. Unlike athletes, where it is likely that pure physical deterioration³⁸ causes the reduction in productivity with age, among scholars even the fairly subtle facts that we have uncovered can be marshaled as support for each of these competing hypotheses. Without direct observation on how scholars' use of time changes as they age, we are unlikely to be able to distinguish between explanations of the declining ageproductivity relationship in science.
REFERENCES

Berger, Mark, and Frank Scott, "Changes in U.S. and Southern Economics Deparment Rankings over Time," Growth and Change 21 (Summer 1990), 21-31.

Blank, Rebecca, "The Effects of Double-Blind versus³⁹ Single-Blind Reviewing," American Economic Review 81 (Dec. 1991), 10411067.

Diamond, Arthur, "The Life-Cycle Research Productivity of Mathemati cians and Scientists," Journal of Gerontology 41 (1986), 520-525.