Age and the Impact of Innovations
Average impact falls but the hits keep coming
Like the rest of New Things Under the Sun, this article will be updated as the state of the academic literature evolves; you can read the latest version here.
No podcast today, as I am sick and can’t talk without coughing: maybe later. Also, there is more to say about age and innovation, so stay tuned!
Scientists are getting older.
Below is the share of employed US PhD scientists and engineers in three different age ranges: early career (under 40), mid-career (ages 40-55), and late career (ages 55-75). The figure covers the 26 years from 1993-2019.
Over this period, the share of mid-career scientists fell from about half to just under 40%. Most (but not all) of that decline has been offset by an increase in the share of late career scientists. And within the late career group, the share older than 65 has more than doubled to 27% over this time period.1
This trend is consistent across fields. Cui, Wu, and Evans (2022) look at more than one million scientists with fairly successful academic careers - they publish at least 10 articles over a span of at least 20 years. Cui and coauthors compute the share of these successful scientists who have been actively publishing for more than twenty years. Across all fields, it’s up significantly since 1980 (though, consistent with the previous figure, this trend may have peaked around 2015).
Alternatively, we can get some idea about the age of people doing active research by looking at the distribution of grants. At the NIH, the share of young principal investigators on R01 grants has dropped from a peak of 18% in 1983 to about 3% by 2010, while the share older than 65 has risen from almost nothing to above 6%.
This data ends in 2010, but the trend towards increasing age at receiving the first NIH grant has continued through 2020.
Is this a problem? What’s the relationship between age and innovation?
Aging and Average Quality
This is a big literature, but I’m going to focus on a few papers that use lots of data to get at the experience of more typical scientists and inventors, rather than the experience of the most elite (see Jones, Reedy and Weinberg 2014 for a good overview of an older literature that focuses primarily on elite scientists).
Yu et al. (2022) look at about 7mn biomedical research articles published between 1980 and 2009. Yu and coauthors do not know the age of the authors of the scientists who write these articles, but as a proxy they look at the time elapsed since their first publication. They then look at how various qualities of a scientific article change as a scientist gets older.
First up, data related to the citations ultimately received by a paper. On the left, we have the relationship between the career age of the first and last authors, and the total number of citations received by a paper.2 On the right, the same thing, but expressed as a measure of the diversity of the fields that cite a paper - the lower the number, the more the citations received are concentrated in a small number of fields. In each case, Yu and coauthors separately estimate the impact of the age of the first and last author.3 Note also, these are the effects that remain after controlling for a variety of other factors. In particular, the charts control for the typical qualities of a given author (i.e., they include author fixed effects). See the web appendix for more on this issue. Also, they’re statistical estimates, so they have error bars, which I’ve omitted, but which do not change the overall trends.
The story is a straight-forward one. Pick any author at random, and on average the papers they publish earlier in their career, whether as first author or last author, will be more highly cited and cited by a more diverse group of fields, than a paper they publish later in their career.
In the figure below, Cui, Wu, and Evans (2022) provide some complementary data that goes beyond the life sciences, focusing their attention on scientists with successful careers lasting at least twenty years and once again proxying scientist age by the time elapsed since their first paper was published. They compute a measure of how disruptive a paper is, based on how often a paper is cited on it’s own, versus in conjunction with the papers it cites. The intuition of this disruption measure is that when a paper is disruptive, it renders older work obsolete and hence older work is no longer cited by future scientists working in the same area. By this measure, as scientists age their papers get less and less disruptive (also and separately, papers are becoming less and less disruptive over time, as discussed more here).4
Last up, we can even extend these findings to inventors. Kaltenberg, Jaffe, and Lachman (2021) study the correlation between age and various patent-related measures for a set of 1.5mn inventors who were granted patents between 1976 and 2018. To estimate the age of inventors, Kaltenberg and coauthors scrape various directory websites that include birthday information for people with similar names as patentees, who also live in the same city as a patentee lists. They then compute the relationship between an inventor’s estimated age and and some version of each of the metrics discussed above. Once again, these results pertain to what remains after we adjust for other factors (including inventor fixed effects, discussed below).
On the left, we have total citations received by a patent. In the middle, a measure of the diversity of the technologies citing a paper (lower means citations come from a narrower set of technologies). And on the right, our measure of how disruptive a paper is, using the same measure as Cui, Wu, and Evans. It’s a by-now familiar story: as inventors age, the impact of their patented inventions (as measured by citations in various ways), goes down.
(The figures are for the patents of solo inventors, but the same trend is there for the average age of a team of inventors)
So in all three studies, we see similar effects: the typical paper/patent of an older scientist or inventor gets fewer citations and the citations it does get come from a smaller range of fields, and are increasingly likely to come bundled with citations to older work. And the magnitudes involved here are quite large. In Yu et al. (2022), the papers published when you begin a career earn 50-65% more citations than those published at the end of a career. The effects are even larger for the citations received by patentees.
The Hits Keep Coming
This seems like pretty depressing news for active scientists and inventors: the average paper/patent gets less and less impactful with time. But in fact, this story is misleading, at least for scientists. Something quite surprising is going on under the surface.
Liu et al. (2018) study about 20,000 scientists and compute the probability, over a career, that for any given paper, their personal most highly cited paper lies in the future. The results of the previous section suggest this probability should fall pretty rapidly. At each career stage, your average citations are lower, and it would be natural to assume the best work you can produce will also tend to be lower impact, on average, than it was in earlier career stages.
But this is not what Liu and coauthors find! Instead, they find that any paper written, at any stage in your career, has about an equal probability of being your top cited paper!
The following figure illustrates their result. Each dot shows the probability that either the top cited paper (blue), second-most cited paper (green), or third-most cited paper (red) lies in the future, as you advance through your career (note it’s actually citations received within 10 years, and normalized by typical citations in your field/year). The vertical axis is this percent. The horizontal one is the stage in your career, measured as the fraction of all papers you will ever publish, that have been published so far.
This number can only go down, because that’s how time works (there can’t be a 50% chance your best work is in the future today, and a 60% chance it’s in the future tomorrow). But the figure shows it goes down in a very surprising way. Assuming each paper you publish has the same probability of being your career best, then when you are 25% of the way through your publishing career, there is a 25% chance your best work is behind you and a 75% chance it’s ahead of you. By the time you are 50% of the way through your publishing career, the probability the best is yet to come will have fallen to 50%. And so on. And that is precisely what the figure appears to show!
What’s going on? Well, Yu and coauthors show that the number of publications in a career is not constant. Through the first 20-25 years of a career, the number of publications a scientist attaches their name to seems to rise before falling sharply. Since the average is falling over this period, but the probability of a top cited paper is roughly constant, it must be that the variance is rising (the best get better, the worse get worse), in such a way that the net effect is a falling average.
And Yu and coauthors present evidence that is the case. In the figure below, we track the average number of citations that go to hit papers in two different ways. In dark blue, we simply have the additional citations to the top cited paper by career stage. Note, unlike average citations, it does not fall steadily to zero: instead, it actually rises slightly (slightly) for the first 20 years!
In the light blue, Yu and coauthors do something interesting. They count how many papers the scientist published in their first 5 years; let’s say it is four papers. Then, for each of the next 5-year career stages, they find the four most highly cited papers (or however many the scientist managed to publish in the first 5 years) and plot the average number of extra citations received to this subset. This group does not fall steadily to zero either! Scientists put out just as many good papers through the middle of their career as they did when they were young; they just also put out a bunch of extra stuff that has low impact.
But there’s still some bad news.
First, Yu and coauthors still find a sharp fall off in both productivity and citations to top papers after 25 years of career experience. For a scientist who first published at the age of 25, that’s 50 years old. And as we saw at the beginning of this post, the share of scientists who fall into this “late career” demographic have been on the rise.
Second, it’s not clear if these trends apply at all to patented inventions. Kaltenberg, Jaffe, and Lachman find that among inventors, the annual number of patents peaks at a young age, around age 30, and then falls off steadily through the rest of the lifecycle.
More broadly, we only really have this data for the number of citations to papers; I am quite curious if something similar is going on with the disruption scores, or the diversity of impact. That would be quite interesting, because I think we also have a bunch of evidence that the nature of innovation changes as scientists age, and that might not show up in citation counts.
Thanks for reading! As always, if you want to chat about this post or innovation in generally, let’s grab a virtual coffee. Send me an email at matt.clancy@openphilanthropy.org and we’ll put something in the calendar.
Why are scientists getting older? The main story is just the demographics of the US labor force, but declining rates of retirement among older faculty is also a significant factor. See Blau and Weinberg (2017) for more discussion.
For more on the use of citations to evaluate ideas, see Do Academic Citations Measure the Impact of Ideas?
These authorship positions signify important information in biomedicine. Typically the first author is junior and designs/executes the experiment, analyzes the data, and writes the manuscript; the last author tends to be the principal investigator of the lab where the first author works and supervises/guides the whole process.
Does the index actually map to our ideas of what a disruptive paper is? It’s a new measure and its properties are still under investigation, but Wu, Wang, and Evans (2019) tried to validate it by identifying sets of papers that we have independent reasons to believe are likely to be more or less disruptive than each other. See this discussion in Science is getting harder for a brief overview.