text:
## Abstract

We show that academics with experience in government jobs generate spillovers for their early-career colleagues. Our template is the National Science Foundation rotation program in which the agency employs academics, called rotators, on loan from their university. Within two years after the rotator's return, fresh assistant professors in her department increase their research resources materially and are more likely to win small and medium-size grants compared to academics in three control groups. Consistent with evidence that the mechanism is mentoring from the rotator, the results suggest that access to individuals with insights gained outside academia propels scientific careers.

## I. Introduction

To study the impact of temporary employment in government, we explore the link between research fund acquisition of early-career scientists and exposure of these scientists to rotators—academics who are seconded to the National Science Foundation (NSF) for typically two years before they return to their respective academic institutions. During their tenure at the NSF, rotators, formally designated as program directors, organize and run the peer review process from the beginning to the end while often exercising decision-making power. They become insiders at the NSF as they gain insight into the process of funding decisions, possess tacit knowledge on potential funding directions and agency priorities, and ultimately gain the ability to discern a promising proposal.

We ask three questions. First, do rotators influence the funding records of their early-career colleagues (and if so, what is the mechanism)? Second, for how long does the effect last? Third, what type of change do rotators bring about: a go-big (larger grants) approach or a go-safe approach (small and medium-size grants)?

We find evidence that rotators act as mentors. They leverage their insider knowledge to communicate to their early-career colleagues what to write in a proposal, how to write a it, and where to send it. As a result, rotators have a causal impact on the funding acquisition records of new hires landing their first faculty position in their department. We find that newly hired assistant professors in departments with a returning rotator raise approximately $200,000 more, nearly half of the average first-time grant acquired from the NSF, than similar academics in similar departments without a rotator (research question 1). The effect decays with time (research question 2): we observe significant changes in resource acquisition within two years after the return of the rotator from the NSF and a decline afterward. Rotators promote a go-safe approach (research question 3): the probability of winning small and medium-size (but not large) grants is significantly higher for academics who interact with a rotator when compared to similar others. Our work makes three main contributions. First, we add to the scarce literature on academic mentoring, which has shown that institutionalized forms of mentorship such as postdoctoral fellowships matter (Heggeness et al., 2018; Blau et al., 2010; Jacob & Lefgren, 2011). We demonstrate that informal, likely less-resource-demanding and more widely accessible forms of mentoring exemplified by the relationship between rotators and early career scientists pay off too. Second, we contribute to the literature on research fund acquisition, which has not zoomed in on early-career scientists by switching the focus to them (Feinberg & Price, 2004; Arora & Gambardella, 2005; Li, 2017). This is an important change because assessing how early-career scientists can gain access to resources is a first-order concern (Alberts et al., 2014) and allows us to better understand the sources of individual long-term productivity and scientific progress overall (Alberts et al., 2014; Rosenbloom et al., 2015; Oyer, 2006; Petersen et al., 2011; Bol, de Vaan, & van de Rijt, 2018; Lerchenmueller & Sorenson, 2018). Third, our work pushes the emerging literature on the effects of experience outside academia using the rotation program as its template to new directions. Kolympiris, Hoenen, and Klein (2019) used a different data set to set up a two-period difference-in-differences estimation to establish that rotators can serve as effective knowledge conduits for same-department peers who are similar in terms of research topic and tenure to the rotator. Here, we break new ground by bringing to light three novel insights. First, by comparing our results with the findings of Kolympiris et al. (2019), we discover that spillovers from access to superior human capital gained because of experience outside academia are not uniform across colleagues. Rotators have an effect on junior scientists, those for whom getting grants is most important, which is considerably larger than their effect on senior scientists. This finding is relevant because it reveals that access to insights gained inside and outside academia share commonalities and have differences. The main similarity is that not everyone gains equally from access to high human capital. Aligned with Waldinger (2010, 2012, 2016), who demonstrated that access to high human capital from experience within academia matters for junior scientists, has no effect for department peers, and has a moderate effect for attracting new hires, we discover that rotators benefit their early-career colleagues substantially more than they benefit their senior colleagues. The main difference is that only access to high human capital from insights outside academia translates to gain from same-department colleagues: in contrast to Waldinger (2012) and Borjas and Doran (2012), who found no and negative effects for same-department peers, respectively, we document positive effects for same-department peers. Second, our novel focus on the long-run or year-to-year effects of knowledge transfer from rotators allows us to unravel, for the first time, the sort of knowledge that is required in order to generate changes in resource acquisition. We find that recent insights gained via short tenure at continuously evolving funding organizations such as the NSF are more effective than general intuition about grant allocation. This finding has implications, among others, for the academic labor market as it advises candidates which job offer and when to accept. Third, the focus on the types of grants that rotators push their junior colleagues to pursue offers a fresh understanding of what established, knowledgeable academics recognize as the best way forward for scientists at their formative stages of their career. This finding has broad implications for the direction of science and what it means for mentoring to promote the go-safe option. For our identification strategy, we compare the funding records of new hires landing their first faculty post in departments with and without a rotator—the former belonging to our treatment group and the rest belonging to our control group(s). The major empirical challenge in this exercise is that superior human capital is not distributed randomly. Instead, endogenous sorting places individuals with high human capital next to each other (Kim, Morse, and Zingales, 2009; Waldinger, 2016). Within our framework, this would imply that the colleagues of rotators are more equipped than others in raising research funds. To circumvent this sorting issue, we exploit two features of the rotation program and carefully construct three control groups. The first feature is that the (timing of) entry into rotation is independent of the needs of the colleagues to raise funds. Academics become rotators because they want to learn more about the NSF, not because they recognize emerging colleagues who need advice. The second feature is that the return to the home institution is also exogenous to the needs of colleagues to raise funds. The rotation duties have a fixed end date. As a result, rotators do not return to their institutions because (or when) their colleagues need help. These two features of the program suggest that the allocation of early-stage academics to the treatment and control group is largely exogenous to their choice of employer. However, three different sources of endogeneity may still allocate individuals to treatment and control groups nonrandomly, which would constitute a threat to identification. We discuss these sources and focus on how we address them next. First, initial job placement can be endogenous to job candidates' choice to accept an offer from a department with a rotator because of the rotator's presence in that department and the associated expectation of mentoring how to raise research funds. Along the same lines, labor market conditions differ across years and can have a strong impact on which job candidate lands where. We tackle these issues by exploiting time variation: we construct our first data set including new hires joining the same department at different points in time when labor market conditions vary, the focal colleague had or not left for the NSF, and had or not the rotation experience. Second, if the academic labor market works efficiently, then the best candidates will land in the best positions and the lesser candidates will land in lesser positions (Cole & Cole, 1973). If this holds true, then success in raising funds may be explained by this matching process with rotators belonging to the better departments. Similarly, difficult-to-capture heterogeneity among PhD holders may also explain initial job placements. We tackle these issues by crafting a second data set comprising PhD holders (some landing a job in a department with a rotator and others acquiring a job in a department without a rotator), who had the same PhD advisor, worked in the same science field, and graduated in about the same year (Kahn & MacGarvie, 2016). Given that advisor standing and graduating institution are the prime determinants of initial job placements (Miller, Click, & Cardinal, 2005; Terviö, 2011), it is expected that, as shown in tables 2 and 3, new hires from the same advisor land their first faculty post in departments whose main difference is the presence of a rotator as they are generally of comparable status, academic productivity, and research fund acquisition records. Importantly, because the selection into advisors is not random (Waldinger, 2010) and PhD training is largely standardized within doctoral programs (hence, both the selection and treatment are nearly identical), these new hires are also similar to each other at the time of their first academic appointment in terms of age, gender, academic productivity, and other similar qualities. Third, university-wide policies, tenure-track incentives, grant-writing support, and other university-specific factors may boost incentives to become a rotator, shape the types of emerging scientists who decide to join a given university, and ultimately explain the increase in grant acquisition rates. This may lead to erroneous conclusions about the impact of rotators if they are disproportionally employed at institutions that are more successful in research funding acquisitions than in others. We tackle this issue by constructing our third data set. This data set holds university-wide factors constant and allows the comparison of funding records of new hires who joined the same university at approximately the same time but in different, yet comparable, departments having one main difference: some have a rotator as a faculty member and some do not. Despite the careful construction of the data sets to match new hires in the treatment and control departments, remaining differences in training, ambitions, and career goals, among others, may still exist. We include several control variables in the analysis to account for such factors. Further, we perform a battery of exercises that reinforce the stability of our estimates and allow us to pinpoint with precision the mechanism driving the estimates. ## II. The Rotation Program at the NSF and How Rotators Can Induce Changes in Grant Acquisition The NSF has an annual budget that exceeds$7.5 billion and funds approximately 12,000 proposals out of 40,000 submissions annually in all nonmedical scientific fields. These proposals support more than 360,000 scientists, teachers, and students employed at close to 2,000 institutions (National Science Foundation, 2017). The agency is structured hierarchically; its seven directorates, corresponding to different scientific fields, are split into divisions that are subdivided into programs. The program directors (PDs) are subject matter experts who run each program. They put together the review panels, communicate ex ante and ex post with submitters of funded and rejected proposals, review proposals even from programs and directorates outside their own, make grant allocation decisions, participate in panels outside their programs, and provide inputs to central strategic planning not only within their program but also across programs and directorates (Li & Marrongelle, 2013). Overall, PDs are an integral part of the NSF and are key to shaping the direction of science.

Most PDs are permanent NSF employees. However, since the passage of the Intergovernmental Personnel Act in 1970, roughly one out of three PDs are academics who are posted at the NSF temporarily (Mervis, 2016). These academics, called rotators, infuse the agency with new viewpoints as they move to the NSF headquarters. The rotators, on loan from their university, work full time for the NSF for up to four years (most commonly two) and effectively stall their academic duties during their tenure at the NSF. From 2004 to 2014 alone, 800 rotators from around 400 academic institutions served at the NSF. Rotators are subject to strict restrictions during and even after their tenure at the NSF to avoid any conflicts of interest or favoritism (e.g., they cannot submit proposals or evaluate proposals of previous collaborators).

As revealed during a handful of discussions with former rotators, the main reason academics enter the program is a desire to acquire an in-depth understanding about the NSF and to generally contribute to the field of science.1 These drivers explain why we do not identify specific trends among rotators; besides the fact that they were generally successful in winning grants from the agency in the past, they are employed at universities of varying size, status, and location. Additionally, they vary in terms of scholarly productivity, leadership activities, and methodological approaches in their research, among others. The fact that the decision of rotators to join the rotation program is exogenous to the need of colleagues for help in raising funds alleviates concerns of endogeneity; these endogeneity concerns arise from the former's potential entry into the NSF as a deliberate response to the latter's need for mentoring to raise funds.

During their tenure at the NSF, rotators become insiders at the agency; they evaluate numerous proposals, observe others performing similar tasks, and gain hands-on knowledge of the largely unobserved factors that shape panel decision making (Bagues, Sylos-Labini, & Zinovyeva, 2017); they also become aware of what the NSF prioritizes and the areas where the demand for promising proposals exceeds the supply. We expect these unique insights to enable rotators to recognize a competitive proposal. In turn, because knowledge sharing is stronger among individuals of the same group (department, in our application) (Hargreaves Heap & Zizzo, 2009), this insider knowledge can spill over to rotators' colleagues and create an advantage for them in that they gain knowledge that their counterparts lack. In fact, evidence on the effects of rotators on later-stage academics without previous NSF grants supports this expectation (Kolympiris et al., 2019).

For early-career scientists, having access to an insider can be instrumental as rotators can act as informal mentors. Evidence on formal forms of mentoring (e.g., postdoctoral fellowships) suggests that it pays off (Blau et al., 2010; Heggeness et al., 2018; Jacob & Lefgren, 2011) and indeed fundraising comes up regularly in academic mentoring (Feldman et al., 2010). Specifically, rotators can mentor their early-career colleagues on three main fronts in securing grants. First, rotators can direct colleagues to research areas the NSF prioritizes that are otherwise difficult to detect. In other words, they can provide suggestions on what the agency is eager to fund. Second, because grant writing is typically not the focus of doctoral training, rotators can fill the gap and assist their colleagues in presenting ideas effectively and generally crafting proposals in ways that communicate their research insights in an appealing manner. The sheer number of proposals that the NSF receives makes communication and framing vital to allowing external reviews and, subsequently, to panel members to appreciate the merits of a given proposal in a better manner. Third, rotators can address the main obstacle concerned with the initiation of the proposal: idea generation (Custer, Loepp, & Martin, 2000). Since rotators possess tacit knowledge on research themes that are more likely to receive funding, they can guide their early-career colleagues on research questions they can pursue. Indeed, as we explain in section VI, we find evidence that rotators influence the direction of research for their early-stage colleagues.

## III. Data Sources and Empirical Approach

### A. The Treatment Group

To construct the data sets that trace, over time, the NSF grant acquisition record of new hires in departments with and without a rotator, we collect and merge new data from multiple sources. We accessed the list of 240 academics who ended their tenure as rotators at the NSF under the Intergovernmental Personnel Act (IPA) from between 2009 and 2011 via a Freedom of Information (FOI) request directed to the NSF.2 Following existing work relying on online data retrieval for academics (Terviö, 2011; Amir & Knauff, 2008; Kim et al., 2009), we visited current and archived university websites from https://archive.org/ and combined this search with the career information retrieved from the Men and Women of Science database to identify faculty members who, as their first faculty position, were hired as assistant professors before, after, and during the year of the rotator's return to the department. We were able to build comprehensive and detailed career histories for eighty rotators. Subsequently, we examined the professional history of more than 3,200 seasoned and early-stage academics belonging to these eighty departments with a rotator; of these 3,200 academics, we identified 210 academics with a comprehensive career history, who as their first faculty post joined 64 departments with a rotator between five years before and two years after the rotator returned from the NSF.3 The 210 academics in the 64 departments with a rotator comprise the treatment group, and the indicators of a treatment effect by a rotator (discussed below) assume positive values as they all overlap with the rotator for at least one year after the rotator's return from the NSF.

We identify three cohorts within the 210 academics in the treatment group: (a) 55 academics who joined when (or shortly after) the rotator returned from the NSF, (b) 68 academics who joined when the rotator was at the NSF, and (c) 87 academics who joined within two to five years before the rotator had left for the NSF. The formulation of three cohorts helps us to surmount endogeneity and sample selection concerns. It helps us with endogeneity because from these cohorts, we can eliminate nearly with absolute certainty the possibility that the new hires chose to join the department expecting to learn from a returning rotator for cohort c: the academics who joined the department before the given scientist left for the NSF. With regard to sample selection, the rotation experience may correlate with an increased ability to select job candidates with higher chances of attracting research grants. If this was true and if rotators participated in selection committees, then the treatment groups would have been populated with new hires who were better equipped to win grants. However, the issue cannot hold for cohort b—academics who joined when the returning rotator was at the NSF—and it is less likely to hold for cohort a—academics who joined at the time of the rotator's return from the NSF. Essentially, these two cohorts allow us to address the potential for sample selection at hand.4

### B. The First Control Group

The first control group allows us to hold department effects fixed and is composed of 25 academics belonging to 14 departments; these academics joined a department with a rotator, but their tenure at the department did not overlap with the tenure of the rotator. The absence of overlap may be either because these academics left the respective departments before the rotator returned from the NSF or, in a few cases, because the rotator moved to a new university at the end of her tenure at the NSF.5

### D. The Third Control Group

The third control group accounts for university-specific initiatives that can promote entry into administrative roles outside the university, grant funding sessions, and tenure track criteria that can explain differences in raising funds across different institutions. Retrieving data from university websites and the Men and Women of Science database, we populate the third control group with academics who started their first faculty position as assistant professors at the rotator's university but in a different yet comparable department the same year, two years before, and two years after the rotator returned from the NSF. We find similar departments by employing the following criteria. First, the department must belong to the same larger division or school as the department with a rotator. For instance, when the department of the rotator is an engineering department, we limit the search to other departments in the school of engineering. Second, the control department must be in an intellectual space that is adjacent to the department with a rotator. Adhering to the previous criterion, when the treatment department is industrial engineering, we choose the department of civil engineering within the school of engineering and not, for instance, the department of chemical engineering. Typically, the title of the department serves as a sufficient tool to identify similar departments. When it is not, we choose departments whose faculty members publish in the same journals as the faculty members of the rotator departments. Third, we select a comparable department that hired an assistant professor during the time frame of our study. These selection criteria yielded 60 academics from 18 departments of the same university that had departments with rotators who were hired into their first position anytime between two years before and two years after the focal academic joined the focal department.6

Subsequent to the finalization of the list of names belonging to the treatment and the three control groups, we extracted data from the above-mentioned sources, the bibliographic database SCOPUS, and the NSF grant retrieval website to build a full career history for the focal academics. Leveraging on the career history of the academics, we construct variables that describe the NSF acquisition records, tenure at the institution, research productivity, and annual academic position, among others. Online appendix table 1 provides an elaborate description of the sources of data and the associated variables.

### E. Baseline Estimation Setup

We employ an ordinary least squares (OLS) estimator wherein the dependent variable is the inflation-adjusted amount of research funds raised from the NSF in a given year by a given new hire who belongs to either a treatment or a control group (to address our third research question, we build logistic models, which we explain below). These amounts reflect new grant(s), with the focal academic being the principal investigator, not continuations or extensions of existing grants.

Each observation is a person-year starting from the year the focal academic joined the given department as her first faculty post in an assistant professor position and ending up to five years after the return of the rotator to the department. On average, we track the yearly grant acquisition rate for each academic in the treatment group for 8.7 years (up to 5 of which are after the return from rotation) and for each academic in the three control groups for 7.7 years. Therefore, in line with the importance of early-career academics raising research funds early on, we follow them for the years leading to the tenure clock running out. To test whether rotators induce changes in the NSF grant acquisition record of their early-career colleagues, we include variables that take the value of 1 when the focal academic is in the department of the rotator in the same year that the rotator returned from the NSF (Treatment 0), in the first year since the rotator returned from the NSF (Treatment 1), and, in a similar fashion, until the fifth year since the rotator returned from the NSF (Treatment 5). The person-year setup and the associated Treatment 0 to 5 variables allow us to test the treatment effect of the rotators on their colleagues with precision (research question 1), and hence we can uncover the duration of the effect and its magnitude over time (research question 2).

We conduct the analysis on three data sets. Each includes the treatment group and the first, second, and third control group, respectively.

### F. Control Variables

As we demonstrate through tables 1 to 3, by and large, academics in the treatment and control groups are similar to each other and belong to similar departments. These similarities suggest that any differences in the grant acquisition records between academics in treatment and control groups ex post can be attributed to the rotator. However, additional differences may exist. Accordingly, we include several control variables in the analysis to account for such differences.

Table 1.
Selected Statistics for the Junior Academics in the Treatment and Control Groups
Treatment GroupFirst Control GroupSecond Control GroupThird Control Group
210 Academics Who Joined a Department with a Rotator and Overlapped with Her25 Academics Who Joined a Department with a Rotator but Did Not Overlap with Her104 Academics Who Joined a Department without a Rotator and Had the Same Advisor with Those in the Treatment Group60 Academics Who Joined a Department without a Rotator in the Rotator's University in a Similar Department
Previous NSF funding at the start of the faculty post ($M) 0.028 0.045 0.003 0.034 (0.115) (0.201) (0.019) (0.181) Yearly NSF funding from the start of the faculty post until the rotator's return from the NSF ($M) 0.099 0.108 0.068 0.042
(0.315) (0.238) (0.261) (0.134)
Total NSF funding in the 5 years ex post rotator return ($M) 0.831 0.543 0.418 0.409 (1.229) (0.913) (0.929) (0.584) Male 0.710 0.720 0.683 0.733 (0.455) (0.458) (0.468) (0.446) Years as a postdoc 2.181 2.320 2.308 2.650 (2.006) (1.6) (2.252) (1.83) H-index at the time of the first faculty post 2.345 3.898 1.821 3.429 (3.204) (4.26) (2.643) (3.43) Yearly non-NSF funding until first faculty post ($M) 0.006 0.002 0.004 0.002
(0.054) (0.01) (0.028) (0.013)
Years between PhD graduation and first faculty post 3.676 2.400 3.827 4.017
(2.045) (2.021) (2.545) (2.221)
First author publication before PhD graduation 0.719 0.000 0.654 0.783
(0.451) (0.000) (0.478) (0.415)
Treatment GroupFirst Control GroupSecond Control GroupThird Control Group
210 Academics Who Joined a Department with a Rotator and Overlapped with Her25 Academics Who Joined a Department with a Rotator but Did Not Overlap with Her104 Academics Who Joined a Department without a Rotator and Had the Same Advisor with Those in the Treatment Group60 Academics Who Joined a Department without a Rotator in the Rotator's University in a Similar Department
Previous NSF funding at the start of the faculty post ($M) 0.028 0.045 0.003 0.034 (0.115) (0.201) (0.019) (0.181) Yearly NSF funding from the start of the faculty post until the rotator's return from the NSF ($M) 0.099 0.108 0.068 0.042
(0.315) (0.238) (0.261) (0.134)
Total NSF funding in the 5 years ex post rotator return ($M) 0.831 0.543 0.418 0.409 (1.229) (0.913) (0.929) (0.584) Male 0.710 0.720 0.683 0.733 (0.455) (0.458) (0.468) (0.446) Years as a postdoc 2.181 2.320 2.308 2.650 (2.006) (1.6) (2.252) (1.83) H-index at the time of the first faculty post 2.345 3.898 1.821 3.429 (3.204) (4.26) (2.643) (3.43) Yearly non-NSF funding until first faculty post ($M) 0.006 0.002 0.004 0.002
(0.054) (0.01) (0.028) (0.013)
Years between PhD graduation and first faculty post 3.676 2.400 3.827 4.017
(2.045) (2.021) (2.545) (2.221)
First author publication before PhD graduation 0.719 0.000 0.654 0.783
(0.451) (0.000) (0.478) (0.415)

Figures reflect average values, with standard deviations in parentheses.

Table 2.
Departments with and without a Rotator Raise Similar Amounts from the NSF
Average Yearly Department NSF Funding the Five Years Preceding the Rotator's Return from the NSF
TotalPer Faculty Member
Treatment department $1,220,694$33,871
Control department $1,438,457$39,974
Average Yearly Department NSF Funding the Five Years Preceding the Rotator's Return from the NSF
TotalPer Faculty Member
Treatment department $1,220,694$33,871
Control department $1,438,457$39,974
Table 3.
Departments with and without a Rotator Are of Similar Status and Productivity
Treatment DepartmentControl Department
Member of the Association of American Universities  42% 40%
Department-specific Shanghai ranking the year the rotator returns First quartile 24% 22%
Second quartile 17% 14%
Treatment DepartmentControl Department
Member of the Association of American Universities  42% 40%
Department-specific Shanghai ranking the year the rotator returns First quartile 24% 22%
Second quartile 17% 14%

Difficult-to-quantify or -observe factors at the department level may induce changes in fund acquisition in the future. These can include visiting faculty transmitting knowledge on fund acquisition or shocks such as increased teaching load at time $t$ that can limit the capacity to submit research proposals at time $t+1$, 2, 3, among others. We control for such effects by adding the variables Rotator Department 1 up to Rotator Department 5 in the analysis. The variables take the value of 1 when the person-year observations refer to academics who joined a department from which a rotator originated from one to five years before the rotator's return from the NSF. To illustrate, if the person-year observations refer to academics who, for instance, joined the focal department two years before the return of the rotator, then Rotator Department 1 and Rotator Department 2 would assume positive values, while Rotator Departments 3, 4, and 5 would assume the value of 0. To account for potential learning effects during postgraduate studies, we include the variable PostDoc that measures the number of years during which the focal new hire was employed in a postdoctoral position before assuming a faculty post. The variables Assistant Professor and Associate Professor denote experience and take the value of 1 for person-years during which the focal academic held an assistant professor and associate professor position, respectively, and 0 otherwise (the base category is professor; this category is composed of nine scientists who became professors within our time window). We include the dummy variable Male for male academics to account for gender differences in grant acquisition. The time-varying variable H-index (lagged by one year) measures the H-5 citation index of the academic in question and controls for the influence of an academic's existing track record on grant acquisition. The availability of research funds in previous years or from different sources may condition one's NSF funding record in a given year. As such, we include the variable External Funding in the analysis that measures the funding amounts from sources other than the NSF; we also include the variable Previous NSF that measures the sum of NSF funding raised by the focal academic during the five years preceding the focal person-year observation.

Furthermore, we incorporate explanatory variables that reflect potential influences from the host institution. We include the following: (a) the time-varying variable (Ranking) that measures the ranking quartile of the focal university to account for potential status effects afforded to academics in higher-ranked universities and (b) the time-varying Faculty NSF variable that measures the sum of NSF funds raised by existing faculty members in the rotator's department before the rotator's return from the NSF; this variable accounts for potential learning on how to raise NSF funds from existing faculty members other than the rotator. Finally, we include the field of science and year-fixed effects to control for differences (a) across the scientific fields in the propensity and need to raise funds from the NSF and (b) in funding cycles at the agency. In models reported in online appendix table 2 we also include department and scientist fixed effects. The inclusion of these fixed effects consumes many degrees of freedom but the results are similar to the baseline estimates as presented in table 5.

### G. Descriptive Statistics

In this section, we provide evidence that our research design allows us to isolate the effect of the rotator; this isolation is possible because the academics who make up the treatment and control groups are similar before the return of the rotator and start their assistant professor positions in similar departments. We also provide a description of the rotators.

In table 1, we present selected statistics for the academics in the treatment and the three control groups. At the start of their faculty position, between 2003 and 2015 (2012 for those in the treatment group), academics in the four groups were similar in many respects: experience, gender distribution, publication records, and, importantly, previous funding from the NSF. For instance, 71% of the scientists in the treatment group were male, had an H-index of 2.34, and had raised, on average, $28,000 from the NSF as a principal investigator when they started their first faculty post. The weighted averages corresponding figures for the scientists in the three control groups were 70%, 2.60, and$18,000. Additionally, when the rotator was at the NSF, the funding records across scientists in the four groups were similar. Where we do observe a significant difference is on the total amount raised from the NSF in the five years following the return of the rotator (and the equivalent period for those in control groups). Academics in the treatment groups raise, on average, $831,000, while the weighted average of the total amount raised by academics in the three control groups is nearly half that amount:$432,000.

But what could explain the difference in funding records among academics in the treatment and control groups is heterogeneity in the universities and departments the sample scientists belong to. However, tables 2 and 3 exhibit contrary findings. The departments with a rotator raised $1.2 million annually from the NSF during the period preceding the rotator's return from the NSF (table 2). The departments without a rotator raised$1.4 million in the equivalent period. The status and research productivity indicators in table 3 paint a similar picture: 42% of the academics in the treatment group are employed at universities that are members of the prestigious Association of American Universities. The corresponding percentage for universities without a rotator is 40%. Along the same lines, 24% of the academics in the treatment group are employed at departments in the first quartile in the science-field-specific Shanghai ranking. The equivalent figure for academics in the control groups is 22%. Overall, we do not observe significant differences in terms of funding records and status or productivity indicators between the departments that are with and without a rotator.

Table 4 describes the rotators in the sample. They are typically midcareer academics who have been successful in raising funds from the NSF and have varied publications and citation records.

Table 4.
Descriptive Statistics of the 64 Sample Rotators
MeanSD
Years in rotation 1.625 0.951
Male 0.734 0.445
Career age at start of rotation 20.536 7.947
Publications (5 years ex ante) 16.300 18.887
Citations per paper (5 years ex ante) 67.556 133.203
NSF funding (5 years ex ante) $527,426$1,664,688
MeanSD
Years in rotation 1.625 0.951
Male 0.734 0.445
Career age at start of rotation 20.536 7.947
Publications (5 years ex ante) 16.300 18.887
Citations per paper (5 years ex ante) 67.556 133.203
NSF funding (5 years ex ante) $527,426$1,664,688

## IV. Main Results

Table 5 presents the baseline estimates. We cluster the standard errors at the department level. This choice is predicated on the finding that, as in our case, when the treatment is at the department level but the unit of analysis is at the individual level, the estimation needs to employ a White/Huber heteroskedasticity correction for the standard errors (Bertrand, Duflo, & Mullainathan, 2004). As we find in unreported results, the inference remains nearly identical when we cluster the errors at the scientist level to account for the fact that each scientist enters the analysis more than once.

Table 5.
OLS Baseline Estimates: Dependent Variable: Yearly NSF Funding (in millions)
Model 1: Treatment Group and First Control GroupModel 2: Treatment Group and Second Control GroupModel 3: Treatment Group and Third Control Group
RotatorDepartment t $-$ 5 −0.014 −0.010 −0.003
(0.015) (0.010) (0.012)
RotatorDepartment t $-$ 4 0.059 0.079 0.099
(0.040) (0.045) (0.055)
RotatorDepartment t $-$ 3 −0.010 0.002 0.019
(0.018) (0.018) (0.017)
RotatorDepartment t $-$ 2 0.007 0.005 0.029
(0.027) (0.028) (0.027)
RotatorDepartment t $-$ 1 0.007 −0.003 0.010
(0.023) (0.020) (0.021)
Treatment 0 0.034 0.037 0.040
(0.021) (0.019) (0.022)
Treatment 1 0.092*** 0.058** 0.070**
(0.032) (0.026) (0.027)
Treatment 2 0.113*** 0.061** 0.088***
(0.036) (0.026) (0.024)
Treatment 3 0.072** 0.034 0.042**
(0.035) (0.018) (0.019)
Treatment 4 0.030 0.007 0.005
(0.037) (0.020) (0.024)
Treatment 5 −0.000 −0.001 −0.004
(0.033) (0.025) (0.026)
PostDoc −0.003 −0.003 −0.003
(0.002) (0.002) (0.002)
Assistant Professor 0.017 0.025** 0.011
(0.016) (0.012) (0.013)
Associate Professor 0.009 0.008 −0.007
(0.015) (0.012) (0.013)
Male −0.001 0.013 0.010
(0.011) (0.009) (0.009)
H-index −0.000 0.001 0.000
(0.001) (0.001) (0.001)
External Funding ($M) 0.355 0.381** 0.341 (0.186) (0.181) (0.187) Previous NSF ($M) 0.113*** 0.098*** 0.122***
(0.017) (0.015) (0.017)
Ranking −0.007** −0.007** −0.007**
(0.003) (0.003) (0.003)
Faculty NSF ($M) 0.000 0.000 0.000 (0.000) (0.000) (0.000) Constant 0.039 0.035 −0.004 (0.022) (0.023) (0.019) Science field FE Yes Yes Yes Year FE Yes Yes Yes Observations 2,152 2,642 2,319 $R2$ 0.170 0.156 0.179 Adjusted $R2$ 0.155 0.144 0.166 Number of departments 65 158 80 Model 1: Treatment Group and First Control GroupModel 2: Treatment Group and Second Control GroupModel 3: Treatment Group and Third Control Group RotatorDepartment t $-$ 5 −0.014 −0.010 −0.003 (0.015) (0.010) (0.012) RotatorDepartment t $-$ 4 0.059 0.079 0.099 (0.040) (0.045) (0.055) RotatorDepartment t $-$ 3 −0.010 0.002 0.019 (0.018) (0.018) (0.017) RotatorDepartment t $-$ 2 0.007 0.005 0.029 (0.027) (0.028) (0.027) RotatorDepartment t $-$ 1 0.007 −0.003 0.010 (0.023) (0.020) (0.021) Treatment 0 0.034 0.037 0.040 (0.021) (0.019) (0.022) Treatment 1 0.092*** 0.058** 0.070** (0.032) (0.026) (0.027) Treatment 2 0.113*** 0.061** 0.088*** (0.036) (0.026) (0.024) Treatment 3 0.072** 0.034 0.042** (0.035) (0.018) (0.019) Treatment 4 0.030 0.007 0.005 (0.037) (0.020) (0.024) Treatment 5 −0.000 −0.001 −0.004 (0.033) (0.025) (0.026) PostDoc −0.003 −0.003 −0.003 (0.002) (0.002) (0.002) Assistant Professor 0.017 0.025** 0.011 (0.016) (0.012) (0.013) Associate Professor 0.009 0.008 −0.007 (0.015) (0.012) (0.013) Male −0.001 0.013 0.010 (0.011) (0.009) (0.009) H-index −0.000 0.001 0.000 (0.001) (0.001) (0.001) External Funding ($M) 0.355 0.381** 0.341
(0.186) (0.181) (0.187)
Previous NSF ($M) 0.113*** 0.098*** 0.122*** (0.017) (0.015) (0.017) Ranking −0.007** −0.007** −0.007** (0.003) (0.003) (0.003) Faculty NSF ($M) 0.000 0.000 0.000
(0.000) (0.000) (0.000)
Constant 0.039 0.035 −0.004
(0.022) (0.023) (0.019)
Science field FE Yes Yes Yes
Year FE Yes Yes Yes
Observations 2,152 2,642 2,319
$R2$ 0.170 0.156 0.179
Adjusted $R2$ 0.155 0.144 0.166
Number of departments 65 158 80

Robust standard errors in parentheses clustered at the department level. ***$p$$<$ 0.01 and **$p$$<$ 0.05. Coefficients in bold indicate the main findings.

In model 1, we use the sample that includes the academics in the treatment group and the academics in the first control group. The coefficients of the Treatment 1 and Treatment 2 variables (also plotted in figure 1) suggest that rotators induce positive and economically meaningful changes in the funding acquisition of their early career colleagues. The Treatment 3 coefficient is also statistically significant. However, we interpret such evidence as suggestive because the significance does not hold across specifications for the baseline estimates and selected robustness checks. Addressing our first research question, overlapping with the rotator one and two years after her return from the NSF leads to an increase in funding that exceeds $200,000. To put this in perspective, as shown in table 1, academics in the treatment groups raise$831,000 during the five years following the return of the rotator, while in the corresponding period, academics in the control groups raise $432,000. At the same time, the average first-time grant from the NSF across directorates is$439,000. As such, given the Treatment 1 and Treatment 2 estimates, it appears that the rotator treatment effect increases the fund acquisition record of early-career scientists by more than 50% and is responsible for close to half of an academic's first grant from the agency.

Figure 1.

Dynamics of the Rotator Effect

Years before and after the return of the rotator to the department (year 0 is the return from the NSF)

Figure 1.

Dynamics of the Rotator Effect

Years before and after the return of the rotator to the department (year 0 is the return from the NSF)

The estimates also imply that the treatment effect of rotators has an important magnitude relative to the overall NSF funding for research. Based on data from 2004 to 2017, the NSF allocates, on average, $4.5 billion every year for research grants. Forty-nine million of those (or more than 1%) can be attributed to the effect of rotators on their junior colleagues (using average figures: 80 (returning rotators in $t-2$) $×$$92,000 (Treatment 2 coefficient) $×$ 80 (returning rotators in $t-1$) $×$ $113,000 (Treatment 1 coefficient) $×$ 3 (junior colleagues who interact with the rotator and raise NSF funds) $=$$∼$$49 million). The 1% estimate is noteworthy when considering that it originates from a small number of academics when the NSF receives around 40,000 proposals yearly, and it is likely a lower bound of the true effect of rotators as it is not accounting for the potential impact that rotators have on collaborators, senior colleagues, colleagues in different institutions whose rotators deliver seminars, and the like.

Finally, the $200,000 figure allows us to compare the effect of rotators on early-career scientists with their effects on their established colleagues with limited fund acquisition in the past as measured by Kolympiris et al. (2019), who find that within a five-year window since interaction with a rotator, established colleagues raise$138,000 more than similar others. This gain is $62,000 less than what early-career colleagues gain due to a rotator or nearly half of the full gains realized by established colleagues. Finally, the fact that we find that rotators have an impact on their same-department peers implies that access to high human capital gained from experience within academia differs from access to high human capital gained from experience outside academia: Waldinger (2012) and Borjas and Doran (2012) found no or negative effects for same department peers, respectively. Addressing our second research question, the gains from the rotator are stronger in the first two years of overlapping (when, roughly, the tenure track clock is about to run out) and do not extend beyond that time period. As we demonstrate in section VII, two main reasons underpin this finding. First, within the five-year window, the increased workload following the award of a grant limits new grant application submissions in the subsequent years. Second, over a period, there is a decay in the value of the knowledge the rotator transmits to her colleagues as the agency evolves and changes priorities, among others. In model 2, we conduct the analysis using the academics on the treatment group and the academics in the second control group. Similar to the results in model 1, the Treatment 1 and Treatment 2 estimates indicate that overlap with a rotator is indeed beneficial to research funding, even after accounting for individual-specific heterogeneity. The reduced magnitude of the Treatment 1 and Treatment 2 coefficients in model 2 when compared to the model 1 coefficients implies the significance of individual-specific factors for fund acquisition. In model 3, we employ the sample composed of the treatment group and the third control group. The results are qualitatively similar to the results in models 1 and 2. The Treatment 1 and Treatment 2 estimates suggest that rotators induce an increase in the NSF funding records of their early career colleagues. Concerning control variables, we find that academics with previous NSF funding in higher-ranked universities, perhaps due to the availability of internal grant writing support or status effects, raise more funds from the NSF. We also document a suggestive positive relationship between non-NSF grants and NSF funding. Importantly, the Rotator Department minus 1 to 5 variables are not statistically significant, indicating that the estimates are driven by the overlap with the rotator after her NSF experience. To address our third research question, we build logit models using the same setup of person-year observations, the same set of right-hand-side variables, and the samples used for table 5. The models measure the change in probability of securing NSF grants of different sizes after interacting with a rotator (the dependent variable takes the value of 1 if in a given year, the focal scientist receives a grant of a given size, 0 otherwise). As shown in table 6, the probability of winning a grant is significantly higher for academics in the treatment group when compared to academics in the first control group (similar estimates for the other two control groups). The magnitude of the effects allows us to infer the sort of change that rotators bring about (research question 3). An increase in the probability of academics winning grants in the treatment group is significant for small to medium-sized grants (82% and 57% more likely for grants above$50,000 and $250,000, respectively); this probability diminishes for larger grants (18% for grants above$500,000) and becomes nonexistent for grants above $1 million. This finding is consistent with the$200,000 difference in fund acquisition between academics in the treatment and control groups, as reported in the baseline estimates. Importantly, it suggests that rotators, experienced individuals with informed priors as to how academic careers unfold, promote a go-safe approach as the most promising way forward for their early-career colleagues.

Table 6.
Change in Probability of Securing an NSF Grant after the Rotator Returns
Grant Larger Than $50,000Grant Larger Than$250,000Grant Larger Than $500,000Grant Larger Than$1,000,000
Treatment 0 0.160** 0.152** 0.036 −0.008
Treatment 1 0.209*** 0.193*** 0.091** 0.017
Treatment 2 0.231** 0.222*** 0.091** 0.010
Treatment 3 0.222** 0.143 0.002 −0.005
Treatment 4 0.095 0.034 0.013 −0.003
Treatment 5 0.062 0.038 0.002 −0.004
Grant Larger Than $50,000Grant Larger Than$250,000Grant Larger Than $500,000Grant Larger Than$1,000,000
Treatment 0 0.160** 0.152** 0.036 −0.008
Treatment 1 0.209*** 0.193*** 0.091** 0.017
Treatment 2 0.231** 0.222*** 0.091** 0.010
Treatment 3 0.222** 0.143 0.002 −0.005
Treatment 4 0.095 0.034 0.013 −0.003
Treatment 5 0.062 0.038 0.002 −0.004

The change in probability is calculated after holding all other variables at their means. ***$p<0.01$ and **$p<0.05$. Coefficients in bold indicate the main findings.

## V. Robustness of the Results

To measure the potential rotator effect, we include in the analysis, as a subgroup of the 210 academics in the treatment group, 55 new hires who joined a department with a rotator after the rotator returned from the NSF. This modeling choice may plague the estimates if these 55 new hires chose to join the focal department because of the presence of the rotator among the faculty and the expected knowledge transfer from this rotator. To test whether such potential endogeneity biases our estimates in test 1 in table 7, we omit these new hires from the analysis (showing only the results with the first control group for ease of presentation). The results are qualitatively similar to the baseline estimates, suggesting that this source of potential endogeneity does not influence our analysis.

Table 7.
Omit from the Treatment Group New Hires Who Join the Rotator Department after the Rotator Has Returned $+$ Relax Same Advisor and Graduation-Year Criteria
Test 1: Omit Hires Who Joined the Department after the Rotator ReturnedTest 2: Add Academics with the Same Advisor Who Graduated 3 to 10 Years before the focal Academic Who Joined a Department with a RotatorTest 3: Use Coarsened Exact Matching to Populate the Control Group
RotatorDepartment t $-$ 5 −0.010 0.008 −0.009
(0.015) (0.012) (0.069)
RotatorDepartment t $-$ 4 0.067 0.081** 0.046
(0.041) (0.038) (0.054)
RotatorDepartment t $-$ 3 −0.000 −0.005 0.023
(0.020) (0.019) (0.047)
RotatorDepartment t $-$ 2 0.007 0.003 0.036
(0.029) (0.023) (0.036)
RotatorDepartment t $-$ 1 0.007 −0.022 0.003
(0.025) (0.022) (0.027)
Treatment 0 0.032 0.025 0.054**
(0.024) (0.018) (0.023)
Treatment 1 0.098*** 0.055** 0.064***
(0.037) (0.026) (0.021)
Treatment 2 0.119** 0.072*** 0.060***
(0.045) (0.024) (0.020)
Treatment 3 0.084 0.039** 0.026
(0.042) (0.017) (0.020)
Treatment 4 0.033 0.006 0.003
(0.042) (0.020) (0.019)
Treatment 5 −0.010 0.004 0.001
(0.046) (0.024) (0.019)
PostDoc −0.003 −0.003 −0.004
(0.003) (0.002) (0.003)
Assistant Professor 0.010 0.030*** 0.013
(0.017) (0.010) (0.019)
Associate Professor 0.006 0.016 −0.008
(0.015) (0.011) (0.021)
Male 0.002 0.012 0.004
(0.014) (0.008) (0.010)
H-index −0.000 0.001 0.001
(0.001) (0.001) (0.001)
External Funding ($M) 0.395** 0.338 −0.038 (0.176) (0.186) (0.055) Previous NSF ($M) 0.111*** 0.096*** 0.104***
(0.018) (0.013) (0.009)
Ranking −0.006 −0.006** −0.005
(0.003) (0.002) (0.003)
Faculty NSF ($M) 0.000 0.000 0.000 (0.000) (0.000) (0.000) Constant 0.049 −0.032 −0.022 (0.030) (0.022) (0.045) Science field FE Yes Yes Yes Year FE Yes Yes Yes Observations 1,800 3,181 2,654 $R2$ 0.197 0.138 0.094 Adjusted $R2$ 0.179 0.127 0.0813 Number of departments 180 193 66 Test 1: Omit Hires Who Joined the Department after the Rotator ReturnedTest 2: Add Academics with the Same Advisor Who Graduated 3 to 10 Years before the focal Academic Who Joined a Department with a RotatorTest 3: Use Coarsened Exact Matching to Populate the Control Group RotatorDepartment t $-$ 5 −0.010 0.008 −0.009 (0.015) (0.012) (0.069) RotatorDepartment t $-$ 4 0.067 0.081** 0.046 (0.041) (0.038) (0.054) RotatorDepartment t $-$ 3 −0.000 −0.005 0.023 (0.020) (0.019) (0.047) RotatorDepartment t $-$ 2 0.007 0.003 0.036 (0.029) (0.023) (0.036) RotatorDepartment t $-$ 1 0.007 −0.022 0.003 (0.025) (0.022) (0.027) Treatment 0 0.032 0.025 0.054** (0.024) (0.018) (0.023) Treatment 1 0.098*** 0.055** 0.064*** (0.037) (0.026) (0.021) Treatment 2 0.119** 0.072*** 0.060*** (0.045) (0.024) (0.020) Treatment 3 0.084 0.039** 0.026 (0.042) (0.017) (0.020) Treatment 4 0.033 0.006 0.003 (0.042) (0.020) (0.019) Treatment 5 −0.010 0.004 0.001 (0.046) (0.024) (0.019) PostDoc −0.003 −0.003 −0.004 (0.003) (0.002) (0.003) Assistant Professor 0.010 0.030*** 0.013 (0.017) (0.010) (0.019) Associate Professor 0.006 0.016 −0.008 (0.015) (0.011) (0.021) Male 0.002 0.012 0.004 (0.014) (0.008) (0.010) H-index −0.000 0.001 0.001 (0.001) (0.001) (0.001) External Funding ($M) 0.395** 0.338 −0.038
(0.176) (0.186) (0.055)
Previous NSF ($M) 0.111*** 0.096*** 0.104*** (0.018) (0.013) (0.009) Ranking −0.006 −0.006** −0.005 (0.003) (0.002) (0.003) Faculty NSF ($M) 0.000 0.000 0.000
(0.000) (0.000) (0.000)
Constant 0.049 −0.032 −0.022
(0.030) (0.022) (0.045)
Science field FE Yes Yes Yes
Year FE Yes Yes Yes
Observations 1,800 3,181 2,654
$R2$ 0.197 0.138 0.094
Adjusted $R2$ 0.179 0.127 0.0813
Number of departments 180 193 66

Robust standard errors in parentheses clustered at the department level. ***$p$$<$ 0.01 and **$p$$<$ 0.05. Coefficients in bold indicate the main findings.

Along the same lines, if unobserved factors in raising funds were not captured by our research design to compare new hires from the same university, advisor, and graduation year—if, for instance, the inherent ability of raising funds was not distributed normally among the population—then it would have been difficult to interpret our estimates as causal. Indeed, in test 4, presented in online appendix table 3, we employ a difference-in-differences specification under which early-career scientists from different universities, advisor, and graduation year enter the analysis in either the treatment or the control group. Academics who joined a department with a returning rotator before her return from the NSF belong to the treatment group, and those who joined departments without a rotator belong to the control group. The dependent variable is the average NSF funds raised by the focal individual during the three years before the return of the rotator (ex ante period) or during the three years after the return of the rotator to the department (ex post period). The allocation of scientists to treatment and control groups should be quasi-random as we do not expect most academics to select a department based on the presence of the rotator. Indeed, we include a variable that measures the number of years in the focal department to account for potential selection effects. The statistically significant positive interaction of the ex post and treatment group variables is in line with the argument that we are unraveling causal effects.

## VI. The Mechanism Driving the Results

In this section, we explore whether the findings we reveal are driven by mentoring from the rotator or by other means. We present only the estimates using the first control group for brevity, whenever applicable, as we expect this control group to approximate the counterfactual as closely as possible.

In the first two tests, we scrutinize the mentoring and knowledge transfer mechanism. The first test starts with the premise that if the mechanism underpinning the results is mentoring advice from the rotator, including direction on how to frame a proposal and to which program to submit, then we would expect more helpful rotators to induce more pronounced changes in the funding acquisitions of their emerging colleagues. Similar to Laband and Tollison (2003) and Oettl (2012) and based on the intensity of the thank-you notes in acknowledgments in PhD dissertations supervised by each rotator, we construct a helpfulness index using the sentiment analysis algorithm of Rinker (2013) and the weighted sentiment dictionary of Hu and Liu (2004). Higher values of the index correspond to more helpful rotators (we provide details in online appendix table 1). Indeed, early-career scientists in departments with rotators in the top tenth percentile of the helpfulness score raise, on average, $1,135,346 in the five years following the return of the rotator. The corresponding figure for early-career scientists in the remaining departments is$683,721.

The second test on knowledge transfer relies on the expectation that if rotators are indeed mentoring their early-career colleagues, we would expect them to influence the topics these emerging scientists pursue. Specifically, prompted by work on cognitive mobility (Borjas & Doran, 2015b), we form two groups of rotator colleagues, each with different exposure to a returning rotator, and check how similar the grants won by members of each group are to topics that the rotator's NSF directorate has funded during her tenure. The first group is composed of academics we expect to be subject to the rotator's influence: those who won a first-time grant from the NSF within three years of the rotator's return. The second group is composed of academics whom we expect to be less influenced by the rotator; those whose first-time grant from the NSF was awarded before the rotator's return to the department or those who won a first-time NSF grant after three years had elapsed from the rotator's return. If mentoring is the mechanism underpinning the results, the first group should be affected the most by the rotator. Indeed, we find preliminary evidence that this is the case.8 Specifically, first we develop a text similarity algorithm (details in online appendix table 1), which yields a score ranging from 0 (no similarity) to 1 (high similarity), where scores above 0.30 indicate meaningful levels of similarity. Then we compare the abstract of every grant awarded by the rotator's directorate when the rotator was at the NSF with the abstract of every first-time grant awarded to rotator colleagues belonging to the two groups above. 0.13% of first-time grants awarded to rotator colleagues in the first group had an average similarity score against the focal directorate's grants above 0.30; the equivalent figure for first-time grants awarded to junior scientists in the second group was 0.11. More important, while for 0.08% of the grants in the first group the similarity score was 0.40 and above, the corresponding percentage for the grants of the second group was half, 0.04. Consistent with mentoring driving the estimates, rotators appear to be pushing their colleagues toward areas with recent funding from the directorates they served.9

While the tests above indicate mentoring from the rotator as the mechanism, the estimates could also be driven by knowledge transfer from co-authors or co-investigators who had success in raising funds from the NSF. To test for such potential mechanisms, we conduct three tests that are presented in online appendix table 4. In the first test in online appendix table 4, we omit from the analysis scientists whose more recent and frequent co-authors experienced improvement in their ex post NSF funding record. Specifically, we omit from the analysis academics whose at least one of the three most frequent coauthors gained more NSF funding in the previous three years than the sample average. In the second test, we omit from the analysis scientists whose co-investigator in the focal grant had recent success with the NSF. In other words, after a focal academic's co-investigator is awarded an NSF grant as a principal investigator, all subsequent person-year observations of this focal academic are omitted. In the third test, we limit the analysis to grants without co-investigators (69% of the grants had no co-investigators). The results from all three tests suggest that neither the coauthors nor the co-investigator account for the findings we reveal.

Besides knowledge transfer from the rotator, the results could also be driven by scientists in the treatment departments working on hot topics that typically attract more funds. To test for such possibility, we conducted the following exercise. First, we counted the number of articles in the SCOPUS bibliographic database that include, in their list of keywords, the 3 most occurring keywords for articles published in 2010 by all academics in the sample. Subsequently, we counted the number of articles in SCOPUS that five years later, in 2014, included the same keywords. The number of articles that include in their list of keywords the 284 unique keywords of the articles published by the 110 scientists in departments without a rotator who published in 2010 increased by 27.7%. The corresponding increase for the 470 unique keywords from articles of the 168 scientists in departments with a rotator who published in 2010 was 23.7%. We observe similar trends when we use articles published in 2008 and 2009 as our template. Therefore, academics in departments with and without a rotator appear to work on topics that increase in popularity in parallel.

Similarly, the fact that the NSF picks a given scientist to be a rotator may indicate that the scientist's research area is gaining traction and her department is more active in that area when compared to the other departments. The following factors lead us to discount this as a likely driver of the findings: (a) as shown above, the control and treatment departments are similar to each other and their research topics grow in a similar fashion in popularity, (b) the analysis includes fixed effects for science field, and (c) rotators are not headhunted by the NSF very often; they are typically self-nominated and decide to apply for a rotator position mostly because they want to learn more about the NSF and contribute to the field of science.10

## VII. Supplementary Analysis

In this section, we further elucidate the driver of our findings by exploring whether the estimates are driven by an increase in the applications submitted by the rotator's colleagues on her return, whether the applications submitted are of higher quality, or whether they are better targeted and hence are more likely to be successful. Because the NSF does not release rejected applications on an individual basis, we cannot address the question directly. However, the empirical exercises we describe below suggest that for the largest part, the estimates are not driven by an increased number of applications but an improvement in the quality of the submitted applications.

First, in unreported results, we econometrically find that rotators do not have an effect on the number of awarded grants. If more applications correlated with an increase in awarded grants, then this finding would imply that the rotator effect stems from direction and feedback, among others, for better and more carefully targeted proposals. Second, as shown in table 6 and discussed in section IV, the probability of winning a grant is significantly higher for academics in the treatment group when compared to academics in the first control group. This is supportive of our expectation because better and more carefully targeted proposals (and not necessarily more) are more likely to be funded.

In the last set of supplementary analyses, we inform the mechanism that drives the results by shedding light on why we observe an effect in Treatment 1 and Treatment 2 but not in the later treatment years. We consider two main potential explanations. First, in line with the discussion that an increase in the number of applications to the NSF does not drive the results, it is possible that once the focal academic raises a grant in, for instance, treatment year 2, then that person would devote time toward conducting the research of that grant instead of submitting additional grant applications. To test this proposition, we start with the premise that more grants correlate with more applications. Subsequently, in online appendix table 7, we limit the analysis to the top three directorates in terms of the number of grants awarded from 2006 to 2016 (engineering, computer science, and math and physics) and, hence, the need for a continuous flow of grants is larger. If the lack of applications following the award of a grant would drive the results, then among fields of this kind, we would expect an effect in the later treatment years. However, this is contrary to our observation. Second, it is possible that the rotator's effect wanes over time in that the insights and knowledge gained by a rotator are not updated as the NSF progresses, and likely change focus and priorities, among others. The figures in table 8 do not dismiss such possibility. The longer the rotator stays away from the NSF, the lesser the gain of the new hires in their first year of overlap with the rotator. To illustrate, if the rotator returns at year $t$, hires who join the department at $t-1$ and at $t$ raise, on average, $123,855 and$130,252 at $t$and $t+1$, respectively. On the other hand, those who joined the department during $t+1$ raise $70,144 in $t+2$. Table 8. The Longer the Rotator Has Been Away from the NSF, the Less New Hires in Their First Year of Overlap with the Rotator Gain Average NSF Funding Acquired during First Three Years of Overlap with Rotator After Return from NSF VariableTr0Tr1Tr2Tr3Tr4 Joined 1 year before the rotator returned$123,855 $239,955$198,553
Joined the same year the rotator returned $10,654$130,252 $130,834 Joined 1 year after the rotator returned$26,840 $70,144$61,849
Joined 2 years after the rotator returned   $76,057$24,383 $78,931 Average NSF Funding Acquired during First Three Years of Overlap with Rotator After Return from NSF VariableTr0Tr1Tr2Tr3Tr4 Joined 1 year before the rotator returned$123,855 $239,955$198,553
Joined the same year the rotator returned $10,654$130,252 $130,834 Joined 1 year after the rotator returned$26,840 $70,144$61,849
Joined 2 years after the rotator returned   $76,057$24,383 $78,931 Overall, the tests devised to understand the reason behind the absence of an effect past Treatment 2 imply that the following two forces are at play: increased workload after the award of a grant that limits the number of new applications and diminishing applicability of the insights that the rotator conveys as the NSF changes over time. Empirically, we cannot separate the two forces mainly because the NSF does not provide access to rejected applications, and it is prohibitively difficult to measure with accuracy whether the relevance of the rotator's insights indeed diminishes over time. ## VIII. Conclusion We study knowledge spillovers from academics with a temporary experience in government jobs and reveal evidence consistent with a causal link between an increase in the NSF funding record of newly hired assistant professors and their exposure to academics in their department who return after their tenure at the NSF as PDs (rotators). We document an economically meaningful increase (approximately$200,000 more, which is nearly half of the average of the first-time grant from the NSF), which arises from mentoring as rotators advise their colleagues on what to write in and how to write a proposal and where to send a proposal. Importantly, the gains from having access to a rotator diminish sharply with time, which implies that recent insights (and not general knoweldge) gained via short tenure at continuously evolving funding organizations such as the NSF are required to induce gains in resource acquisition among early-career academics. Rotators' colleagues are more likely to secure medium-sized (but not large) grants, and this finding implies that informal mentoring encourages a go-safe, not a go-big, approach at the formative stages of one's career.

Overall, our research highlights that insiders, individuals with insights of an organization type that is different from the one in which they are permanently employed, can generate positive spillovers for their colleagues. These findings contribute to the literature analyzing the effects of access to high human capital in academia (Azoulay et al., 2010; Waldinger, 2012, 2010, 2016; Borjas & Doran, 2012; Borjas & Doran, 2015a; Colussi, 2018) by adding novel evidence on gains from high human capital with insights from experience outside academia. As well, the work speaks directly to the literature on success in science (Kelchtermans & Veugelers, 2013; Kahn & MacGarvie 2016), academic mentoring (Blau et al., 2010; Heggeness et al., 2018; Jacob & Lefgren, 2011), and resource acquisition (Feinberg & Price, 2004; Arora & Gambardella, 2005; Li, 2017). Broadly, the results are informative for the academic labor market too. Apparently rotators with recent experience at the NSF are equipped to contribute positively to the careers of their colleagues by inducing significant changes in early fund acquisition. Essentially, the presence of a rotator in a given department may be a decisive factor when selecting a job offer.

The work also breaks new ground in the emerging literature on the effects of experience outside academia using the rotation program as its template (Kolympiris et al., 2019). We bring to light three new findings: (a) rotators benefit their early-career colleagues considerably more than they benefit other colleagues, (b) their effects decay with time, and (c) rotators have no effect on the acquisition of larger grants. Still, we have only started to scratch the surface before we understand what experience outside academia entails, the sorts of knowledge spillovers it can generate, and the conditions that shape the magnitude of those spillovers. Rotators are main actors in the knowledge economy (Li & Marrongelle, 2013), but have received considerably less attention in the literature when compared to inventors, entrepreneurs, patent examiners, and others (Lampe, 2012; Lemley & Sampat, 2012; Moser, Voena, & Waldinger, 2014). As such, the research program on knowledge transfer from insights gained outside academia can be extended in a number of ways, and we see at least two as immediate additions to this work. First, what is the full extent of knowledge transmission from rotators? For instance, we do not know whether the recipients of the rotator's knowledge share this knowledge with others, likely outside their institution; whether the seminars that rotators often give outside their university also generate gains in NSF funding; and whether the collaborators of rotators also accumulate new knowledge or whether they are left behind. This is an important line of inquiry to investigate because it has implications for the organization of the distribution of research funding, among others. Second, besides mentoring their early-career colleagues to win grants, do rotators have any influence in how these grants are best utilized? Addressing this question is relevant because it can inform the literature about the long-term effects that rotators may have for academic careers and for scientific progress at large.

Our research is timely and has policy implications. Because scientific advancements are built on the progress of early-career scientists, it is imperative to explore ways in which these early-career scientists can gain access to relevant resources that can contribute toward scientific advancements. Indeed, the difficulties this cohort of academics faces in securing resources is a cause for concern (Poirazi 2017), and it may impede scientific progress and harm the overall social welfare (Alberts et al., 2014; Nature, 2016). Policymakers have started to take initiatives mostly by altering the institutional environment to ensure that it improves the chances of early-career scientists in raising research funds (Kaiser, 2017). Here, we demonstrate that informal mentoring, tapping into existing knowledge held by colleagues' human capital, might also be a complementary and less resource-intensive strategy with immediate results that would address one of the main obstacles early-career academics face: lack of experience and insights. This obstacle puts them at a disadvantage as they often compete for the same grants with high-status scientists who have established funding and publication records.

This study speaks directly to the design of the rotation program. Under the premise that home universities gain from the rotation program, a recent policy mandates that they cover part of the rotation program bill (Mervis, 2016). Here, while we do not fully measure the benefits and the costs of the program, we do find that home institutions realize gains from returning rotators.

Our analysis, albeit careful, has caveats that render it incomplete; hence, our study is subject to improvements. First, we follow previous contributions (e.g., Kahn & MacGarvie, 2016) to construct one of our control groups by matching on observable characteristics such as having the same PhD advisor. Success in raising funds may be driven by unobservable factors that we cannot account for in this study. Our expectation, however, is that the unobserved factors correlate, at least to a certain extent, with the observable factors. The difference-in-differences analysis that we conducted as a robustness check supports this expectation. Second, we focus on early-career scientists who land their first faculty position in the United Sates. However, not all PhD holders follow such a career trajectory. Accordingly, our analysis is conditional on early-career scientists having secured a faculty position in a U.S. university. We do not see this as a major concern because our focus is not on who lands a U.S. faculty post in the first place as we compare only similar emerging scientists who follow an academic career in similar institutional environments. Third, the analysis focuses on the United States; hence, the results may not generalize directly to other countries as the rotation setting is unique to the NSF. This uniqueness of the rotation program at the NSF, together with our estimates, gives rise to the question of whether other funding agencies in the United States and elsewhere would benefit from a similar setting. This is because the diffusion of knowledge that we document is likely predicated on the design of the NSF that requires the inclusion of external academics in its grant review process not only as reviewers but also, and perhaps more important, in more central roles as decision makers.

## Notes

1

The blog entry of Dan Cosley, associate professor at the Cornell University, about his rotation experience serves as a good example of why academics choose to work at the NSF and the types of insights they gain (http://blogs.cornell.edu/danco/2016/09/09/why-im-rotating-at-nsf/)

2

We track grant acquisition five years before the departure of the rotator and five years after the rotator's return. As such, we focus on academics who returned from the NSF between 2009 and 2011 mainly because the start of the ex ante period (2004) is recent enough to source comprehensive data from online sources and the end of the ex post period (2016) allows us to observe the ex post period in its entirety.

3

The 64 sample rotators are similar to remaining rotators in terms of gender distribution, years of professional experience, success in fundraising and publication, and citation records.

4

A threat to identification would be when rotation improves the selection criteria and allows rotators to give informal advice on the selection of candidates during their tenure at the NSF or during their short visits to their institutions. If this holds true, then the new hires around the time of rotation and rotator's return from the NSF would be different from other candidates. However, this is contrary to our observations.

5

The small size of the first control group is consistent with the tenure track system in the United States where (in) voluntary departures from a given department are uncommon before the end of the tenure clock. Fifteen of the 25 academics in the first control group did not overlap with the rotator because they left the department, and 10 did not overlap with the rotator because once the rotator's tenure at the NSF was over, she moved to a different university. If bad fit with the department prompted these 15 academics or the rotator to change institution, the control group could be less comparable to the treatment group, and this could plague our estimates. We do not find evidence of such possibility: When we omit from the analysis, sequentially, academics who did not overlap with the rotator because they changed university or because the rotator changed university, we find qualitatively similar results to the baseline estimates.

6

As already discussed, we pose different research questions and focus on different cohorts of scientists when compared to the only other paper on rotators (Kolympiris et al., 2019). This dictated separate research designs, different sets of methods, and entirely new samples and data (e.g., no scientist is present in both data sets). For example, the research design of the our work allocates junior scientists in one of the control groups if they have had the same advisor with scientists who overlapped with a rotator. On the other side, the research design of Kolympiris et al. (2019) looks for faculty in similar departments in different universities of similar ranking.

7

We used the following matching criteria: PhD-granting university ranking, H-Index at the time of joining the focal department, and having at least one first authored publication before the PhD graduation (following Kahn & MacGarvie, 2016, our measure of innate ability). In a separate test, presented in the online appendix, we created a random sample of academics who did not match the academics in the treatment group ex ante to determine that our conclusions are not tied to the way we construct the three control groups.

8

We interpret these findings as preliminary because we cannot rule out the case that the sets of abstracts we compare are the outcomes of a selection process. For instance, we analyze only junior scientists who interacted with a rotator. Then, within this cohort, by design, we focus only on those that won a grant. Largely based on such factors, which could introduce selection bias in the analysis, we opt to not draw statistical inferences by conducting the focal exercises using regressions.

9

We also checked whether rotators push their junior colleagues (a) toward areas they research themselves and (b) away from their doctoral work. Regarding (a), we do not find such evidence, as only a handful of grants and publications authored by rotators are meaningfully similar to the grants won by rotator colleagues (i.e., similarity score above 0.30). Regarding (b), when we compare dissertation abstracts to first-time grant abstracts, we find that rotators steer their junior colleagues away from their doctoral work (i.e., the similarity score between dissertation and grant abstract is lower for those who interact with a rotator). But even for junior colleagues who are not influenced by the rotator, the similarity between dissertation and grants is, for the most part, below the threshold score of 0.30.

10

The online appendix includes tests that dismiss favoritism toward a rotator's colleagues as the mechanism and shows, via a placebo test, that the effects we observe are tied to the actual timing of the return of the rotator, and not any other point in time.

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## Author notes

The paper is dedicated to Silva and Pascal Hoenen who survive the first author, Sebastian Hoenen, who passed away far too young, He is deeply missed. NSF grant SMA-1548028 supported part of the research. We are thankful to the editor and three anonymous reviewers. We are grateful to Sandra Evans for processing the FOI request. Maryann Feldman and Jeffrey Mervis sparked our interest in developing the research stream on NSF rotators. Virgilio Failla, Christian Fons-Rosen, Patrick Gaule, Martin Goossen, Nicholas Kalaitzandonakes, Stijn Kelchtermans, Peter G. Klein, Keld Laursen, Cornelia Lawson, Alexandre Magnier, Solon Moreira, Nicos Nicolaou, Joshua Rosenbloom, Ammon Salter, Eunhee Sohn, Spiros Stefanou, and Martin Watzinger provided valuable comments.

A supplemental appendix is available online at http://www.mitpressjournals.org/doi/suppl/10.1162/rest_a_00859.

format: plain


text:
# Question b98fe

May 16, 2017

1. $1 m o l {K}^{+} , 1 m o l C {l}^{-}$
2. $1 m o l M {g}^{2 +} , 2 m o l N {O}_{3}^{-}$

#### Explanation:

In one liter of a one molar solution, the number of moles of the solute is

$\left(M\right) \left(V\right) = \left(1 \frac{m o l}{L}\right) \left(1 L\right) = 1 m o l$

For $K C l$, there are one atom of each per formula unit, so there are one mole of each ${K}^{+}$ and $C {l}^{-}$ in one liter of a $1 M$ solution of potassium chloride.

For $M g {\left(N {O}_{3}\right)}_{2}$, there are two moles of $N {O}_{3}^{-}$ per one mole of $M {g}^{2 +}$, so there is one mole of $M {g}^{2 +}$ and two moles of $N {O}_{3}^{-}$ in one liter of a $1 M$ solution of magnesium nitrate.

May 16, 2017

$K C l$: $2 m o l$
$M g {\left(N {O}_{3}\right)}_{2}$: (Approximately) $3 m o l$.

#### Explanation:

Both $K C l$ and $M g \left(N {O}_{3}\right) 2$ are salts. Thus they completely ionize when dissolved in water (to yield ${K}^{+}$, $C {l}^{-}$, $M {g}^{+ 2}$ and NO_(3)^(2-), respectively.)
The number of moles of ions produced from $K C l$ dissolving:
$1 m o l {K}^{+} + 1 m o l C {l}^{-} = 2 m o l \left(i o n s\right)$
The number of moles of ions generated from $M g \left(N {O}_{3}\right) 2$ dissolving:
$1 m o l M {g}^{2 +} + 2 m o l \left(N {O}_{3}^{-}\right) = 3 m o l \left(i o n s\right)$

However, if you take the reversible reaction into account: $M {g}^{2 +} + 2 \left(O {H}^{-}\right) r i g h t \le f t h a r p \infty n s M g \left(O H\right) 2$
K_(sp)=5.61×10−12 for $M g \left(O H\right) 2$.
Let the number of $M {g}^{2 +}$ converted in this reaction equals to $x$, using the RICE table,
(1-x)*(10^(-7)-2x)=5.61×10^(−12)#, $x = 4.99972 \cdot {10}^{-} 8$.
This value is too small to be considered.
Therefore the moles of ions in $1 L$ of $1 M$ $M g {\left(N {O}_{3}\right)}_{2}$ solution is $3 m o l$.

(reference: https://en.wikipedia.org/wiki/Magnesium_hydroxide )
[What's the meaning of the ICE table.. as seen in this equilibrium solution?],(https://socratic.org/questions/what-s-the-meaning-if-ice-table-as-seen-in-this-equilibrium-solution).


text:
# zbMATH — the first resource for mathematics

A generalization of Reifenberg’s theorem in $${\mathbb{R}}^3$$. (English) Zbl 1169.49040
E. R. Reifenberg [Acta Math. 104, 1–92 (1960; Zbl 0099.08503)] formulated the Plateau problem for $$m$$-dimensional surfaces of varying topological type in $$\mathbb R^ k$$ and proved that a given set $$\Gamma\subset\mathbb R^ k$$ homeomorphic to $$\mathbb S^{m-1}$$ bounds a set $$\Sigma_ 0$$ which minimizes the $$\mathcal H^ m$$ Hausdorff measure among all sets in the appropriate class and he showed that for almost every $$x\in\Sigma_ 0$$ there exists a neighborhood of $$x$$ which is a topological disk of dimension $$m$$. Finally, it was shown that if a set is close to an $$m$$-plane in the Hausdorff distance sense at all points and at all scales, then it is locally bi-Hölder equivalent to a ball of $$\mathbb R^ m$$.
In this paper, the authors prove that a subset of $$\mathbb R^ 3$$ which is well approximated in the Hausdorff distance sense by one of the three standard area-minimizing cones at each point and at each scale is locally a bi-Hölder deformation of a minimal cone. Also, they prove an analogous result for more general cones in $$\mathbb R^ n$$.

##### MSC:
 49Q05 Minimal surfaces and optimization 49Q20 Variational problems in a geometric measure-theoretic setting 28A75 Length, area, volume, other geometric measure theory
##### Keywords:
minimal cones; bi-Hölder parameterizations
Full Text: