Human capital accumulation

Human capital is the sum of knowledge, experience and skills accumulated throughout a career [11]. In academia, human capital should be related to career progression, which is measured through degrees such as a PhD or a tenured professorship. Yet apart from such signs of certified knowledge, on-the-job training also exists, as publishing brings experience that presumably helps the early career academic to publish more in the future.

This entails an endogeneity problem, as research productivity is not merely an output of past research, but also an input for future productivity. That past success lays the foundation for future success is known as the “Matthew Effect” [12], which the theory of “cumulative advantage” has conceptualized [7, for a review of the literature, see 8]. The opposite of this is the “sacred spark” hypothesis, which argues for innate differences between academics in talent, drive and creativity. This latter hypothesis contradicts the theory of cumulative advantage by suggesting that differences in productivity exist regardless of prior experience [7]. While the theory of cumulative advantage thus suggests that research output can be explained by a researcher’s accumulated publication experience, the sacred spark hypothesis instead suggests that some researchers have higher rates of research output, even with the same prior experience.

Confounder: Gender

Crucially, women are said to accumulate human capital in academia more gradually than men. The starting point for this observation is that women are generally found to produce fewer publications than their male counterparts [2, 5, 13, 14], which is also the case in psychology [5, 10, 15]. This may be due to a gendered cumulative advantage in psychology [9]. Notably, scholars [16] argue that “women scientists publish fewer papers than men because women are less likely than men to have the personal characteristics, structural positions, and facilitating resources that are conducive to publication.” This suggests that women suffer from a cumulative disadvantage. For example, women may start their careers with PhDs from less prestigious institutions [3], which may have little impact on their early productivity. Yet their lower-prestige PhDs may subsequently hinder women from accessing higher quality postdoc institutions, which then hinders later publications, so that small initial disadvantages accumulate to large productivity differences over whole careers [17]. Another prominent explanation for why women accumulate success more slowly is childrearing [4, 10, 18, 19], as parental obligations may decrease the productivity of women more than of men [though cf. critically, 5; for an overview, see 18].

Early research has suggested that cumulative falling behind due to childrearing and other gendered factors may explain 60% of the gender productivity gap, while 40% of the differences in career progression cannot be explained using prior resource endowments [20]. However, the cross-sectional data used so far by research in this area cannot explain whether differences persist irrespective of prior experience or whether lower initial endowments accumulate to large differences over time [5]. Another problem is that some research does not argue that academics become more productive with successive career steps, but rather that productivity eventually declines, even suggesting the opposite of a process of cumulative advantage [2, 5, 21].

While some, therefore, argue that prior productivity predicts current productivity [22], it is unclear not only whether this is actually the case, but also whether the female productivity gap can be ascribed to cumulatively falling behind, as the theory of cumulative advantage suggests. Another problem is that the few existing studies come from STEM disciplines, leaving unclear whether a mechanism of cumulative advantage explains productivity of academic psychologists [23]. We will, therefore, examine the sacred spark versus cumulative advantage hypothesis by analyzing first to what degree earlier publications and endowments explain later productivity (which would confirm the cumulative advantage hypothesis), and then to what degree current productivity exists irrespective of past endowments (which would confirm the sacred spark hypothesis). To understand whether women fall behind cumulatively, we test whether women publish less than men before and after holding prior experience constant. However, this must take account of further confounding variables that can be seen as affecting research productivity, notably a researcher’s institutional environment and research funding.

Confounder: Institutional environment

High-status universities grant psychologists better access to resources, such as training, peers and mentors. This makes institutional environment an important confounder in how well a researcher can translate her human capital into research output. Germany’s so-called “Excellence Initiative” has bestowed the title “university of excellence” on some universities that claim to support researchers for maximum productivity [24]. Whether this is true remains unclear, however, as no studies show whether “universities of excellence” actually foster more productive researchers [25]. If they do, then “universities of excellence” would be an important mechanism behind cumulative advantage, making those researchers more productive who—presumably—were in the first place chosen for their higher productivity. It is also possible however, that while more productive researcher may be more likely to gain access to these institutions, being at these institutions might not in itself increase their publication rate, which would suggest that no cumulative advantage arises from membership of these institutions as such.

Yet while some studies suggest that more prestigious departments do indeed make scholars more productive [26], others are skeptical [2]. While some [27] argue for a strong link between an institution’s publication output and research expenditure, this leaves the question unanswered whether the same individual becomes more productive after visiting a better-endowed institution or whether these institutions attract those who are more productive in the first place—i.e. rather than making them more productive [28, 29].

A similar problem arises when trying to measure the effect of international mobility on research productivity. International mobility may enhance one’s career prospects due to network expansion or exposition to new and stimulating environments. Yet international mobility may itself be endogenous to research productivity, as more productive academics may have better access to high-status institutions abroad [30]. This is one reason why the effect of international experience on productivity is unclear: some studies reject such an effect [31], while others suggest one [30]. To disentangle the effect of international experience on productivity, one needs to first measure the relationship between research output and prior research experience, and then test whether this relationship holds after controlling for experience in different institutional environments, disentangling whether international experience acts as a confounder that increases a researcher’s output beyond what would be expected given her prior publication trajectory.

Confounder: Research funding

Another confounder on the link between earlier and later research productivity is research funding, which can be a resource to increase research output beyond what would be expected based on a researcher’s prior publication trajectory. Yet whether research funding actually increases research output is debated [5], with some suggesting substantial effects [32], and others rejecting this [28]. Therefore, even studies that do find effects ask for a replication of their findings in different scientific disciplines with longitudinal data [32]. This again needs to address reverse causality, as funding may not only result in, but also result from prior publications [33]. It is therefore important to first test whether some psychologists acquire more funding in the first place, and then test whether such funding explains current research productivity beyond what would be expected given prior research productivity [34].

Variables

Tables A1–A4 in the S1 Appendix show descriptive information on all used variables, separately for men and women at each of four possible career stages (pre-PhD, postdoc, untenured professor, tenured professor). Our dependent variable is a psychologist’s count of annual publications in peer-reviewed journals listed in the Social Science (SSCI) or Science Citation Index Expanded (SCIE). Studies of psychology have shown that such journal articles are the most relevant measure of productivity in academic psychology, leading to tenured professorships like no other measure of scientific productivity [35]; SSCI/SCIE articles are also highly correlated to other types of productivity, further making it reasonable to assume that they are a good indicator of general research productivity [2, 36]. We adjust journal articles for co-authorship, using the weighting factor 2/(# of authors+1). This way, a co-authored publication counts as 0.67 of an individual publication, a publication with three authors counts as 0.5, etc. We also calculated co-author adjusted publications by the formula (1/# of authors) as done by others [37, 38]; but our results are robust to this (see Table A5 Model 2, compared to Table A5 Model 1 in the S1 Appendix) and even to counting each publication as single-authored regardless of the number of co-authors (see Table A5 column 3 compared to column 1 in the S1 Appendix). We also weighted each SSCI/SCIE article by the journal’s impact factor, which did not substantially change our results either (cf. Table A5 Model 4 compared to Model 1 in the S1 Appendix), suggesting that our dependent variable of publishing peer reviewed articles is robust to the prestige of different journals.

Not all academics show their entire publication list. Senior academics in particular tend to report their top publications only. We account for this missing data by tagging researchers with “selected publication” lists through a corresponding dummy. Incomplete publications lists are fairly equally distributed across gender (around 5% of women and 9% of men, see Table A7 in the S1 Appendix), so we do not assume that our results are biased by gender-specific reporting. To adjust our models for varying labor market conditions, we use dummy variables for cohorts, based on when individuals had their first publication. To adjust for prior productivity, we control for six types of accumulated prior research output (each variable is adjusted for co-authors as described above): the number of 1) prior SSCI/SCIE journal articles, 2) monographs, 3) book chapters. 4) non-SSCI/SCIE journal articles, 5) edited volumes, 6) other literature (gray literature such as reports, working papers, literature reviews). While other researchers [39] have used a combined productivity metric, we adjust for each type of prior productivity separately. We add the constant of 1 and then log all publications as well as other continuous variables to account for diminishing returns, since e.g. publishing a sixth article increases research output by 20% compared to the fifth, while publishing a second article increases research output by 100% compared to the first article.

A female dummy accounts for gender. Dummy variables also account for the following career stages: 1) pre-doc (no PhD yet), 2) post-doc (PhD, but no Habilitation—which is a post-doctoral thesis in the German academic system—or assistant professorship), 3) assistant professor (Habilitation or assistant professorship but no tenured professorship), 4) tenured professorship (W2/W3, which are rofessorial salary grades in German academic system). Further splitting up the category of tenured professorship into the categories W2 and W3 made little sense, as differences between types of tenured professorships are typically minor. We separately measure career steps at a “university of excellence”; we measure international experience through a doctoral degree from an institution obtained outside Germany and through the number of months spent abroad, assuming five months for a semester and ten months for an academic year if websites did not list exact months. Research funding is measured through a researcher’s grants from Germany’s largest funding agency DFG (accessed through https://gepris.dfg.de/).

Data from our email survey allows us to measure whether researchers have children. We separate this information by gender, to account for motherhood and fatherhood separately. These variables thus have time-varying coefficients that take the value of 1 when a psychologist’s first child is born. The status “children unknown” accounts for non-response by gender. We conducted a complete-record analysis, using only information from those survey-participants who responded to our question about children. The results for this group are virtually the same as in our main specification, suggesting that lack of information on children does not systematically bias our results (see Table A5 Model 5 compared to Model 1 in the S1 Appendix).

All analyses were done using Stata. The following sections first describe the correlates of research output and then present the results of random-effect (RE) models, which—as a first step—explicitly do not control for prior publications. These regressions are therefore still descriptive in the sense that they show how career trajectories differ among psychologists. We then use RE regressions that do control for prior research output, thus showing who is more productive than others, irrespective of past productivity. As these models adjust for prior productivity, while the previous models did not, the difference between these and the prior RE models shows whether the productivity of researchers is mainly explained by their past publishing experience (supporting the theory of cumulative advantage) or whether some researchers are more productive than others irrespective of their past productivity (supporting the sacred spark hypothesis). Because theories of academic success argue that women have more difficulty accumulating publications than men, we introduce gender as our first variable to explain publications. Concordant with what the literature deems important as mentioned above, we then test whether effects of gender on publications are confounded by access to advanced career stages and international experience, as well as access to better universities. We then test whether effects are confounded by research funding.

Finally, we use fixed-effects regressions (FE) that control for prior productivity, to show what accounts for differences within a career. Fixed effects regressions derive their name from holding all time-invariant differences between individuals constant (fixed) by calculating how each individual diverges from her person-specific mean value, e.g. on publications, awards etc. at each point in time. Thus, FE regressions show how research careers progress within an individual, rather than showing how researchers differ from each other (e.g. how men and women differ), as RE regressions do. As they hold known time-varying and even unknown time-invarying confounders constant, or “fixed” within individuals, FE regressions cannot account for unknown time-varying confounders such as biological age (to the degree that it is not already accounted for by career stages), or for time-varying caring responsibilities (to the degree that these are not accounted for by gender and parental status), or for personal characteristics such as time-varying career orientation. However, using FE regressions does allow us to show who publishes more than his or her prior publication trajectory would lead one to expect, and how this is influenced by access to higher career stages and institutions as well as by research funding.

Controlling for six different types of prior publications, we can control for past achievements to explain current productivity net of past productivity more comprehensively than is typically the case. This addresses the problem that academic performance and motherhood confound each other, as it measures how motherhood impacts performance before, but, crucially, also after controlling for prior performance, thus measuring the effect of motherhood before and after accounting for productivity-based selection into motherhood. Generally, we can account for reciprocal causality in this way, as we a) measure the effect of e.g. mobility and grants on later performance while not adjusting for controls, and then measure the same relationship while we do adjust for prior performance. In addition, we use stepwise regressions that follow our theoretical model in introducing first what cannot conceivably come later, e.g. publications can be related to gender, but gender cannot result from publications.

Finally, we use an Oaxaca-Blinder decomposition that shows 1) the extent to which publications are related to gender, 2) whether men publish more because they have more of whatever explains higher productivity or 3) because men publish more because whatever explains higher productivity has a stronger effect on their publications than on those of women. In the following, we begin our analysis descriptively.

Random-effects models

The RE models presented below show what explains research productivity, first before (Table 1) and then after (Table 2) controlling for prior productivity. Table 1 shows who publishes more than others, testing the sacred spark hypothesis that some researchers are innately more productive, while the contrast to Table 2 tests the cumulative advantage hypothesis, which posits that those who publish more do so because they have accumulated more publication experience.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Random-effects models with annual SSCI/SCIE publications, without controlling for prior publications.

https://doi.org/10.1371/journal.pone.0317673.t001

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Random-effects models with annual SSCI/SCIE publications, controlling for prior publications.

https://doi.org/10.1371/journal.pone.0317673.t002

Since we are interested in whether the slower accumulation of experience explains why women publish less than men do, we measure differences in numbers of publications both before and after controlling for prior productivity. To understand how this is mediated by access to advanced career stages, institutions and research funding, we successively introduce these controls, measuring how the female coefficient changes after doing so, which will show how much less women publish if these influences are held constant.

Since we have centered all coefficients on 1, the constant of .58 of Table 1 in Model 1 indicates that during an average year, male researchers with full publication records who belong to the post-2009 cohort publish 58% of what is typical for psychologists in our sample. The “selected publications” coefficient in Model 1 shows that psychologists who only publicize some of their publications have 17% fewer codable publications, which likely means that the dummy variable captures the 17% of publications that these researchers do not show. Importantly, the first variable of Model 1, the female dummy, indicates (before controlling for career steps and other predictors) that female psychologists publish 34% less annually than men do. This is therefore the largely descriptive difference in productivity between men and women that other variables such as accumulated publication experience may explain in the following.

Model 2 adds career stages, measured as pre-doc-, post-doc-, untenured and tenured professor, as well as experience in “universities of excellence” and abroad. Including these factors lowers the productivity gap of women from 34% to 31%. One reason why women publish less than men do is thus that they are less likely to reach advanced career stages, where—as the results show—academics tend to publish more. Notably, post-docs publish 46% more, assistant professors 84% more and tenured professors even 131% more SSCI/SCIE articles annually than psychologists without a PhD. Those who have spent more (log) months outside Germany publish 13% more. Table A6 in the S1 Appendix shows regression models with non-logged coefficients, to illustrate what these results mean in terms of a one-unit increase, indicating that psychologists publish 1% more articles for each month they have spent abroad. Those who have a doctoral degree from abroad do not publish significantly more or less than those who have a domestic doctoral degree. Psychologists with a degree from a university of excellence publish 11% more than psychologists from other universities.

Model 3 includes research funding, indicating that psychologists with more (log) grants are 66% more productive. Including research grants does not substantially alter the effects of other variables, however, except that it decreases the effect of being a tenured professor. This implies that tenured professors partially publish more because they have acquired more grant money. However, being a woman, having more international experience, or being in a high-status university is unaffected by controlling for research grants.

Model 4 additionally accounts for parental status. It indicates that mothers publish 22% less than childless women, while fathers are not significantly less productive than childless men. Interestingly however, controlling for parental status hardly affects the negative female term, indicating that even though mothers publish significantly less than childless women, this does not explain why childless women publish less. The children non-respondence control is non-significant for women, but significant for men. Finally, Models 5 and 6 calculate separate effects for men and women, suggesting that women profit more from an international doctoral degree and from having been at a “university of excellence.”

Table 2 replicates Table 1, but includes past research output in all models. As in Table 1, the coefficients therefore still show differences relative to an average annual research output in psychology, but they now adjust for a psychologist’s prior productivity. The models of Table 2 thus show whether variables increase publications because they themselves are related to prior publications or because they make researchers more productive than their prior publication trajectory would lead one to expect.

Model 1 of Table 2 indicates that the number of past (log) SSCI/SCIE publications determines current publications very significantly (t-value of 28) and substantially: academics who published more SSCI/SCIE papers in the past publish 81% more currently, and thus almost twice as much as what is typical for psychology in a given year. The non-logged result of Table A7 in the S1 Appendix shows that for each additional article published in the past, psychologists publish 6% to 8% more articles currently, depending on what is held constant. Those who were highly productive in publishing peer reviewed journal articles in the past are, therefore, also highly productive in the present. However, all other types of prior publication productivity are only insignificantly related to current journal publications. Table 2 Model 1 also shows that female psychologists publish 17% less, even with the same accumulated publication experience. Comparing this to the 34% of Model 1 in Table 1 (which does not account for publication experience), indicates that a process of cumulative disadvantage explains half of the lower female productivity: women publish less than men due to having accumulated less experience in publishing. In contrast, about half of the lower female productivity seems due to women being less productive independently of their past experience.

Model 2 of Table 2 also suggests that post-docs, assistant professors and tenured professors respectively publish 19%, 31% and 23% less than would be expected from an average output trajectory in psychology. Comparing this to the stronger effects of career stages in Table 1 indicates that psychologists publish more at later career stages because they have more experience with publications during these later career stages, rather than because they have reached higher career stages per se. The apparent positive effect of career stages on publications therefore seems to be largely epiphenomenal of the experience in publishing that comes with later career stages. Model 2 of Table 2 also shows that irrespective of their publication experience, those who have spent more months abroad publish more, while those with a foreign PhD publish less than a typical publication trajectory would suggest. Also, those who have their degree from a high-status university publish 12% more than would be expected based on their career stages and prior publication trajectories.

Model 3 adds research funding to the model. Researchers with more funding publish 29% more than otherwise similar researchers. Yet excluding their prior publication record, funded scientists were in any case almost 66% more productive (Model 3 in Table 1); there thus remains a net positive effect of research funding on current publications, but most of the effect of funding on publications can be explained through the publication experience that comes with research funding. The inclusion of grants in the model hardly alters the effects of other variables. Model 4 adds parent status. As this is the full covariate model, Fig 4 visualizes its relevant coefficients.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Visualized effects of Model 4 in Table 2.

https://doi.org/10.1371/journal.pone.0317673.g004

Holding all other factors constant, women publish 21% less than men, while mothers publish 27% and fathers 19% less than an average publication trajectory would lead one to expect. Research funding and having been at a university of excellence predict current productivity less than prior productivity does, making prior productivity by far the strongest and most significant indicator of current productivity. Model 4 in Table 2 also shows that all variables together explain 66% of productivity differences between and 18% of productivity-variation within the careers of psychologists.

Models 5 and 6 calculate the full Model 4 separately for women and men. Comparing the effect sizes of Model 5 and 6 does not suggest that male and female productivity is influenced by starkly different variables, except that male productivity declines more with career stages.

Fixed-effects models

Table 3 displays fixed-effects models to explain annual SSCI/SCIE publications, controlling for prior accumulated (log) publications. Coefficients thus indicate under what conditions a psychologist publishes more or less than her or his own typical publication trajectory would lead one to expect, allowing for the most causal interpretation of what influences productivity within a career. Note that this within-career analysis is also a disadvantage of FE models, as these cannot include a female effect or any other time-invariant variable; they only display effects of changes over time within a career, rather than any “between-researcher” effect.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 3. Fixed-effects models with yearly SSCI/SCIE publications, controlling for prior publications.

https://doi.org/10.1371/journal.pone.0317673.t003

Model 1 of Table 3 indicates that prior SSCI/SCIE articles predict current SSCI/SCIE very significantly. That the effect is lower than in the prior RE Model 1 of Table 2 (.55 vs. .81) suggests that the random effect models partially draw their explanatory power from a between- or population-effect. In other words, the effect of 0.81 partially indicates why some researchers publish more than others, while the effect of 0.55 only indicates that the same psychologist publishes more than she or he does after having accumulated more publication experience.

Model 2 of Table 3 indicates that psychologists do not publish above their own normal publication rate if (or when) they are a post-doc, assistant professor, or tenured professor. This again implies that reaching higher career stages has no influence on productivity per se. Instead, publications at these career stages merely follow the individual’s pre-established productivity trajectory. However, having spent more (log) months abroad increases research output by 4% above a researcher’s prior trajectory. In contrast, spending time at high-status universities does not increase an academic’s output above her or his average trajectory. That the effect was positive in the random-effects model suggests that high-status universities have more productive researchers, but going there does not make the same individual more productive.

Model 3 in Table 3 implies that psychologists publish 44% above their individually typical productivity with each log increase in DFG-funded projects. The random-effects models showed a weaker effect, indicating that grants are not simply awarded to more productive academics, but rather that they make the same psychologist more productive than she or he would otherwise have been without funding. This is the opposite of the effect of high-status universities, which attract more productive psychologists, but do not make the same individual more productive.

Model 4 of Table 3 suggests that becoming a mother significantly decreases publication rates, while becoming a father does not. Comparing this to the random-effects models of Table 2 suggests that both mothers and fathers are less productive than childless researchers (holding other influences constant), yet only the productivity of a mother declines below the publication trajectory she had before having children, while a typical father does not publish less after having children.

The last two models estimate the fixed-effects regressions separately for males and females. The results again suggest that when male psychologists have children, they publish only insignificantly less; yet when women have children, they do publish significantly less than they did before. Note also that that the effect of research funding on the publications of men is twice as high as on the publications of women, meaning that men turn the same research funding into more measurable productivity. As is the case with the other statistical relationships, we do not know the causal mechanism behind it.

Sensitivity tests