# Some Tradeoffs of Competition in Grant Contests

Kyle R. Myers Harvard Business School<EMAIL_ADDRESS>This paper would not
have been possible without Kevin Gross sharing both code and thoughtful
comments. I am also grateful for feedback from Heidi Williams, Carl Bergstrom,
Charles Ayoubi, Manuel Hoffman, Pierre Azoulay, and Wei Yang Tham. All errors
are my own.

(March 1, 2024)

###### Abstract

When funding public goods, resources are often allocated via mechanisms that
resemble contests, especially in the case of research grants. A common
critique of these contests is that they induce “too much” effort from
participants. This need not be true if the effort in the contest is itself
directed towards the public good. This papers analyzes survey data on
scientists’ time use and finds that scientists allocate their time in a way
that is consistent with fundraising effort (e.g., grant writing) having
inherent scientific value—scientists who spend more time fundraising do not
spent significantly less time on research even after conditioning on
confounding factors. Theoretical models of contests are used to show that the
presence of such a positive effort externality, where scientists generate
social value when pursuing grants, changes the relationship between
competition and the aggregate productivity of a grant contest. Ensuring that
scientists exert socially valuable effort to obtain grants is increasingly
important as grant contests become more competitive.

_Keywords_ : contests; public goods; research grants; scientific funding;
competition

##  1 Introduction

There is no shortage of critiques claiming that competition for research
grants incentivizes scientists to spend “too much” time applying for funding.
Furthermore, some critics have suggested that funders should introduce
randomized lotteries or reduce application requirements.111For example, see:
Herbert et al., (2013); Fang and Casadevall, (2016); Gallup Jr. and Svare,
(2016); Vaesen and Katzav, (2017); Gross and Bergstrom, (2019); Piper, (2019);
Else, (2021); Santoro, (2021); Dresler et al., (2022); Ross, (2022); Thompson,
(2022); Smith, (2024). More generally, it has long been appreciated that
competitions structured as contests—where participants sink effort in exchange
for increasing the probability they win a prize—can induce over-investment
relative to the social optimum when participants’ efforts are unproductive
(Loury, 1979).

Obtaining a research grant is certainly a difficult and competitive endeavor.
Using success rates as a proxy for competition, Figure 1 shows that scientists
pursuing a grant from a range of major funders currently have a 10–30% chance
of success with significant variation across funders (Panel a) and within
funders over time (Panel b).222Data for funders shown in Figure 1 are as
follows: Wellcome Trust (applications: 3,584; success rate: 0.11) European
Research Council (applications: 9,304; success rate: 0.13) Canadian Institutes
of Health Research (applications: 4,488; success rate: 0.15) US National
Institutes of Health (applications: 55,038; success rate: 0.21) UK Research
Council (applications: 19,497; success rate: 0.21) US National Science
Foundation (applications: 42,726; success rate: 0.28) German Research
Foundation (applications: 14,700; success rate: 0.33) (Wellcome Trust, 2021;
European Research Council, 2024; Canadian Institutes of Health Reearch, 2021;
UK Research and Innovation, 2021; US National Institutes of Health, 2023; US
National Science Foundation, 2022; German Research Foundation, 2020). This
competition requires scientists to spend a significant amount of time on their
fundraising efforts. In the sample I study in this paper (described below),
scientists spend an average of roughly 7 hours per week (s.d. 4.8; 15% of
their time) developing, writing, and submitting grant applications. But how
should we judge this variation; are more competitive funding environments
inefficient; is fundraising effort a waste; or are there important tradeoffs
to consider?

Figure 1: Competition at science funding agencies

(a)

(b)

> Note: Panel (a) shows the success rates for major funders in 2020. Panel (b)
> shows the trend in the number of annual applications and success rates for
> “Research Project Grants” at the US National Institutes of Health.

Figure 2 provides a conceptual framework to organize (some of) the tradeoffs
here. It is drawn from the perspective of an individual scientist and
illustrates how competition they face for funding ($C$) can potentially affect
their time allocations ($F$ and $R$), the amount of grant funding they obtain
($G$), the quality of their ideas ($Q$), the value created by those ideas that
accrues to the scientist ($V^{p}$), and the total value to society ($V^{s}$).

A few points are worth emphasizing here. First, a key point of this framework
is that the quality of ideas scientists are working on will affect their time
allocations and the amount of resources they can obtain (e.g., a scientist
with a great idea may spend more time fundraising, obtain more funding, and
spend more time on research as well).333Furthermore, note that quality could
reflect notions of speed (e.g., the same project completed sooner is more
valuable to society). Second, it has long been appreciated that scientists
capture a tiny fracture of the social value they generate (Nordhaus, 2004;
Lakdawalla et al., 2010), so improvements in quality are much more valuable to
society than they are the scientist ($V^{s}>>V^{p}$). Third, in this
framework, and throughout this paper, I will use the terms “fundraising” and
“research” to delineate effort that is best classified by those labels;
however, as indicated by the path between $F$ and $Q$ in Figure 2 and
supported by evidence discussed below, “fundraising” may very well include
scientific efforts that are socially valuable.444This framework treats each
component as a single, scalar variable and abstracts away from potentially
important multi-dimensional issues where, for example, fundraising effort
improves quality only on dimensions related to the private value (to the
scientist) of the project. Furthermore, it abstracts away from potentially
important sources of heterogeneity as well as the possibility that competition
might influence the allocation process (e.g., the cost to a funder of
identifying the most promising ideas may be a function of competition for the
funder’s funding). I return to these and other limitations in the Discussion
section. Lastly, this framework abstracts away from the mechanisms of
competition completely. “Competition” could reflect more competitors competing
for the same grants, it could reflect the amount of preliminary results
required to receive a grant, etc.555For more on competition for grants in the
context of relative ranking mechanisms, see Adda and Ottaviani, (2023).

Figure 2: Conceptual framework

fundraising time ($F$)competition ($C$)research time ($R$)grant $ ($G$)project
quality ($Q$)social value ($V^{s}$)private value ($V^{p}$)

> Note: Shows a directed graph of the key elements that determine how the
> level of competition a scientist faces for grant funding can ultimately
> affect their scientific output.

It is useful to phrase the aforementioned critiques through the lens of this
framework. In short, some critics claim that the amount of fundraising
scientists undertake detracts from their research ($F\rightarrow R$ is
negative) and/or generates no value ($F\rightarrow Q$ is non-positive); it is
a waste. The specific mechanism underlying these claims varies, but often can
be traced to competitive pressures.666Obviously, any activity that does not
either (a) improve a funders’ ability to efficiently allocate their funding or
(b) improve the social value of a scientists’ idea is wasteful by definition.
This motivates proposals for mechanisms that dampen the returns to fundraising
effort (decrease $F\rightarrow G$) such as lotteries or applications that do
not require preliminary results.

How plausible are these claims about wasted efforts? All scientists face time
constraints. So, holding fixed the amount of funding a scientist could expect
to obtain (conditional on $G$), more fundraising could decrease time spent on
research. But that fundraising effort may serve two purposes. First, it may be
necessary to identify scientists with high-quality ideas and therefore is a
source of allocative efficiency (i.e., how well the contest can identify
scientists with higher quality ideas). Second, fundraising effort may itself
be inherently valuable if it improves the quality of the ideas submitted and
therefore is a source of aggregate productivity (i.e., the total benefits less
costs). Second, it may be inherently valuable as a determinant

This paper is focused on the latter possibility—the inherent value of
fundraising efforts. If fundraising effort is itself important, it could imply
two features: (1) the net effect of fundraising on research conditional on
grant funding (per $F\rightarrow R$ and $F\rightarrow Q\rightarrow R$) need
not be negative; and (2) the net effect of competition on social value
($C\rightarrow...\rightarrow V^{s}$) need not be negative.

To date, surprisingly little empirical work has investigated these
relationships. It is unclear how shifts in fundraising time affect shifts in
research time. But there is some evidence that we should not ignore the
possibility that fundraising effort may improve project quality and spark more
research time. First, applications almost always require some degree of
“science” to be performed. As evidence to this, scientists participating in
federal grant competitions report that approximately 38% of their time spent
on proposal preparation contributes directly to their scholarship (Schneider,
2018).777It seems reasonable to treat this self-reported estimate as a lower
bound since it would be in scientists’ self-interest to report a low estimate
on a survey focused on the (private) costs of grant applications. Furthermore,
studies of science funding agencies typically find that (1) scientists who
compete for these grants publish much more than those who do not apply, (2)
applicants tend to publish ideas related to their applications whether they
are funded or not, and (3) the estimated treatment effect of receiving these
grants based on comparisons of the publication output of funded and un-funded
applicants appears relatively small or even negative (Jacob and Lefgren, 2011;
Li, 2017; Wang et al., 2019; Ayoubi et al., 2019; Myers, 2020). These patterns
could be described by selection effects dominating the returns to the grant
funding, but they are also consistent with these competitions incentivizing
significant amount of productive scientific effort.

In this paper, I provide new evidence on scientists’ time allocations and the
relationship between fundraising and research efforts. First, I analyze survey
data from a sample of research-active professors at major US universities. In
the survey, professors report their expected time use and funding over the
coming five years, which I use to uncover how they view the relationship
between fundraising and research per their own stated time allocations and
funding expectations. In order to estimate the net effect of fundraising on
research conditional on grant funding (i.e., the net effect of $F\rightarrow
R$ and $F\rightarrow Q\rightarrow R$ conditional on the effect of
$F\rightarrow G\rightarrow R$), I use a large set of control variables as well
as an instrumental variable in an attempt to isolate variation in fundraising
that is driven by competition. Although the data and my empirical approach are
not without significant limitations, which I discuss throughout the paper,
they provide a novel, quantitative view of relationships that have largely
been debated only via anecdote and opinion. Overall, I cannot reject a null
effect—conditional on funding, scientists who plan to spend more time on
fundraising do not expect to spend any less (or more) time on research.
Notably, I do estimate that the effect of fundraising on research to be
significantly smaller (in absolute terms) than the effect of scientists’ other
duties (e.g., teaching, administration) on their research—if fundraising time
does reduce research time, it does so at a significantly lower rate than other
demands on professors’ time.

The opportunity cost of fundraising time appears to be significantly lower
than the opportunity cost of other duties. The results are consistent with the
following model: the negative effects of fundraising on research driven by
time constraints are offset by the positive effects driven by the improvement
in a project’s quality that spur more research effort. This is socially
efficient if the social value generated by this quality improvement is greater
than the cost to the scientist of this additional fundraising effort. The
positive externalities of science are thought to be very large (i.e.,
$\frac{V^{p}}{V^{s}}$ is very small); so, this seems plausible.

In order to better understand how the productivity of a grant contest depends
on the extent to which fundraising effort generating social value, the second
analyses in this paper uses theory to illustrate the importance of effort
externalities in contests. Using both an elementary and a more realistic model
(building closely off of Gross and Bergstrom, 2019), I show the (social)
benefit of inducing (privately) costly effort in contests for funding public
goods, so long as that work is directed towards the public good, here,
“science.” This echoes results in other work on how the presence of positive
externalities can lead contests to have desirable social properties (e.g.,
Morgan, 2000). The rest of the paper is as follows: Section 2 contains the
empirical analyses of the survey data; Section 3 contains the theoretical
analyses of effort externalities in contests; and Section 4 concludes with a
discussion of the limitations and implications of this work.

##  2 Empirics: Does fundraising spur or steal research?

###  2.1 Research design

Ideally, all of the components of Figure 2 would be observable and I could
trace an exogenous source of variation in competition through the model to see
how it affects each component. That is not currently possible. However, using
the survey data described below, I can make some progress on understanding a
portion of the relationships.

To organize my empirical approach, Figure 3 presents a reduced-form
representation of the conceptual framework that focuses on the variables I can
observe and the relationships I can estimate. Since “quality” is notoriously
unobservable, I cannot separately estimate the different paths through which
fundraising time could affect research time. Thus, I focus on estimating
$\beta_{F}$, which reflects the effect of fundraising time on research time,
conditional on the grant dollars generated by the fundraising. Referring back
to Figure 2, $\beta_{F}$ is the net effect of $F\rightarrow R$ and
$F\rightarrow Q\rightarrow R$ (e.g., the net effect of any substitution away
from research due to time constraints versus any complementarities driven by
an improvement in quality). This is a policy-relevant parameter that is
necessary for evaluating policies that shift competition in research grant
contets.888The indirect effect of fundraising time on grant funding and, in
turn, the effect of that funding on research time are also important, policy
relevant relationships to investigate. However, as will be clear below, I lack
a source of variation in fundraising time that is not also plausibly
correlated with grant funding itself. This prevents me from identifying
$F\rightarrow G$ and $G\rightarrow R$. The returns to research grant funding
($G\rightarrow R$) is a popular, but still very active topic for obvious
reasons (See: Jacob and Lefgren, 2011; Li, 2017; Wang et al., 2019; Ayoubi et
al., 2019; Myers, 2020).

Figure 3: Empirical model

fundraising time ($F$)research time ($R$)grant $ ($G$)$\omega$$Z$$\beta_{F}$

> Note: Shows a directed graph of the empirical analyses where variables in
> boxes are observable data, $\omega$ represents an unobservable shock that
> jointly affects scientists’ time allocations and grant funding (e.g., a
> promising new idea), and $Z$ represents either an unobservable source of
> variation or an instrumental variable.

The key challenge when using non-experimental data to estimate $\beta_{F}$, as
I will attempt to do, is ensuring that there is no unobservable factor jointly
determining the outcomes. Figure 3 shows this possibility with $\omega$, which
is analogous to the quality factor ($Q$) in the framework of Figure 2. The
concern is, for example, that a scientist who has a high-quality idea they
want to pursue may (i) spend more time fundraising, (ii) receive more funding
per time spent fundraising, and (iii) spend more time on research.

I lack a silver bullet to handle this sort of endogeneity concern, but I take
two steps to address it as much as possible. First, I use Lasso to select from
a high-dimensional set of possible controls in an attempt to reduce the
possibility that an endogenous factor such as $\omega$ is influencing the
(residual) variation. If I can eliminate all variation driven by $\omega$ then
any variation left in fundraising time should be driven by some other force
($Z$) that affects just fundraising time (and possibly grant funding, $G$) but
not research time (e.g., the amount of competition a scientist expects when
fundraising). I can’t ever guarantee that the residual variation does not
affect $G$. But, since my focus is $\beta_{F}$, I’ll always be conditioning on
the mediator $G$.999Since this mediator $G$ is not as-good-as randomly
assigned, I do not report nor interpret the relationships between $G$ and $R$.

Instead of relying on residual variation (i.e., leaving $Z$ unobserved), my
second approach is to identify a proxy for competition in the data and use it
as an instrumental variable that satisfies the necessary
assumptions.101010Those assumptions are relevance ($Z\rightarrow F$),
independence ($Z\not\leftrightarrow\omega$), and exclusion
($Z\not\leftrightarrow R$). I will always be conditioning $Z$ on $G$ in order
to shut down that indirect causal path from $Z$ to $R$ I explore a number of
alternative proxies for competition, but my primary measure is based on field-
level variation in how much funding scientists expect to obtain per hour of
fundraising time: $G/F$. Intuitively, if all scientists in a field report that
they expect to obtain fewer grant dollars per fundraising hour, they are more
likely to be in a more competitive environment and less likely to spend time
fundraising on average. In order to generate this proxy in a way that is not
biased by each individuals’ data point I construct a jackknife or “leave-one-
out” average of $G/F$, where the average value assigned to each professor is
the average of $G/F$ in their field calculated without their own
value.111111Specifically, for scientist $i$ in field $d$ where $N_{d}$ is the
number of scientists in the field:
$Z_{id}\equiv\frac{1}{N_{d}-1}\sum_{i^{\prime}=1}^{N_{d}}\frac{G_{i^{\prime}}}{F_{i^{\prime}}}\,\forall
i^{\prime}\neq i$.

###  2.2 Data

All data here comes from Myers et al., (2023). It is a survey of professors at
major US institutions of higher education across all fields of science. See
Myers et al., (2023) for full description of the population definition,
sampling methodology, and survey instrument. In total, 131,672 professors at
roughly 150 universities were invited and 4,388 (3.33%) completed the survey.

Table 1: Summary statistics

| count | mean | sd
---|---|---|---
_Broad field_ {0,1} |  |  |
Engineering, math, & related | 2,640 | 0.20 | 0.40
Humanities & related | 2,640 | 0.16 | 0.37
Medical & health sciences | 2,640 | 0.27 | 0.44
Natural sciences | 2,640 | 0.20 | 0.40
Social sciences | 2,640 | 0.17 | 0.38
_Professor rank & tenure_ {0,1} |  |  |
Assistant | 2,640 | 0.29 | 0.45
Associate | 2,640 | 0.25 | 0.44
Full | 2,640 | 0.41 | 0.49
Other | 2,640 | 0.05 | 0.21
Tenure track | 2,640 | 0.27 | 0.44
Tenured | 2,640 | 0.59 | 0.49
Non-tenure track | 2,640 | 0.14 | 0.34
_Time use, hrs. per week_ (0,$\infty$) |  |  |
Research | 2,640 | 19.53 | 8.80
Fundraising | 2,640 | 6.95 | 4.84
Teaching | 2,640 | 12.45 | 7.45
Administration, clinical, etc. | 2,640 | 11.81 | 8.75
All non-research/fundraising | 2,640 | 24.15 | 10.75
_Funding, $-M per year_ [0,$\infty$) |  |  |
Fundraising expectations | 2,640 | 0.13 | 0.16
Guaranteed funding | 2,640 | 0.08 | 0.12

> Note: Reports the mean and standard deviation (sd) of key variables used in
> the analyses. {0,1} indicates the variable is a binary indicator and the
> other interval notation indicates the range of possible support.

Starting with this full sample, I first restrict the sample to professors
reporting non-zero research time (4,186; 95.40%). Then, I restrict the sample
to those reporting non-zero time on other work including teaching or
administration (4,135; 98.78%). Lastly, I restrict the sample to those
reporting non-zero fundraising time (2,640; 63.85%). The first restriction
ensures all professors are active scientists. The second is useful because I
use professors’ time on these other activities as a benchmark of time-
constraint driven substitution across tasks.121212It also ensures the sample
doesn’t include professors in particularly unique circumstances where all they
do is research. The last restriction significantly reduces the sample size;
however, it ensures that all professors in the analyses are at risk of
fundraising effort. Furthermore, it implies that the results are driven by
(and therefore relevant to) changes in fundraising effort on the intensive
margin.

The top of Table 1 reports the share of respondents from five broad field
groupings as well as some other descriptors related to the professors’ rank
and tenure status. In the Appendix, Table A1 provides the share of professors
in each of twenty narrower fields. Myers et al., (2023) provides a much more
detailed view of the sample. Including the high-dimensional set of potential
control variables I include in some regressions.

Figure 4: Distributions and correlations of time use

(a)

(b)

(c)

> Note: Panel (a) shows the average amount of time spent on each activity.
> Panel (b) shows the distribution of average weekly time use that scientists
> forecast over the coming five years, where “Other work” includes teaching,
> administration, clinical, and any other work not reported as being either
> “Research” or “Fundraising” efforts. Panel (c) shows binned scatterplots of
> the unconditional relationship between scientists’ forecasted fundraising
> expectations (i.e., how much grant funding they expect to obtain over the
> coming five years) and their time spent on research and fundraising; note
> the log scale of the $x$-axis.

Two components of the survey are relevant here. First, the survey asked
professors to report their expected time allocations over the coming five
years. The questions solicited professors’ expected time they will spend on
“fundraising (e.g., writing grants)” and “research” as well as other tasks
(e.g., teaching, administration). It is important to emphasize that these time
allocations are unverified forecasts. Thus measurement error is likely.
However, it is plausible that this measurement error is common to all
activities professors report (i.e., the error is not task-specific nor a
function of the amount of time spent on the task). The bottom of Table 1
reports the summary statistics for these time use measures, and Figure 4
Panels (a–b) show further information on these distributions.

Second, the survey asked professors how much grant funding they expect to
obtain given the amount of time they expect to spend fundraising. These
fundraising expectations (and professors pre-existing and/or guaranteed grant
funding levels) are summarized at the bottom of Table 1.

On average, professors in our sample expect to spend roughly 7 hours per week
(15% of total work hours) on fundraising, 20 hours per week (38% of total work
hours) on research, and 24 hours per week (47% of total work hours) on all
other tasks and duties. On average, professors expect that this 7 hours per
week of fundraising efforts will translate to a total of $130,000 in grant
funding per year (over five years). Figure 4 Panel (c) shows this clear
positive relationship along with a clear positive relationship between
research time and these funding expectations.

###  2.3 Regression models and results

Since the dependent variable, research time, is non-negative, I estimate a
series of poisson regression models of the following form:

$\mathbb{E}[\text{Research}_{i}\,|\,\mathbf{W}_{i};\bm{\uptheta}]=\exp\bigl{(}\alpha_{2}+\beta_{\text{F}}\log(\text{Fundraising}_{i})+\beta_{\text{O}}\log(\text{Other}_{i})+g(\text{Grant
\$}_{i},\mathbf{X}_{i})\bigr{)}\,,$ (1)

where $\beta_{\text{F}}$ is the focal parameter that identifies the elasticity
of research time with respect to fundraising time. $\mathbf{W}_{i}$ is the
vector of all observable variables (which contains $\mathbf{X}_{i}$, the
vector of potential covariates to be selected by Lasso) and $\bm{\uptheta}$ is
the vector of parameters. $g(\cdot)$ represents the control function. To
flexibly control for grant funding, I use restricted cubic splines with four
knots. When using Lasso, I include grant funding plus $\mathbf{X}_{i}$ and let
Lasso select which controls to include in $g(\cdot)$.131313All models are
estimated either using the poisson or ivpoisson gmm commands in Stata©
depending on whether an instrumental variable is used or not. To incorporate
Lasso, I first use the popoisson command to select a subset of the potential
controls ($\mathbf{X}_{i}$) and then include all selected controls in the
poisson regressions. I use all default settings for the Lasso-based popoisson
command, and, in tables, report the number selected out of the number of
potential controls. I use two sets of potential controls. The smaller set of
potential controls is 57 variables spanning the socio-demographics,
professional, and scientific features of each professor based on Myers et al.,
(2023). The larger set is those same controls interacted with the grant
funding controls less any perfectly collinear interactions.

To provide a benchmark, I also test the null hypothesis that
$\beta_{\text{F}}=\beta_{\text{O}}$. To the extent that other duties are as-
good-as-randomly assigned (conditional on the controls), this provides a way
of testing how large the effects of fundraising on research are relative to
other tasks that affect scientists time allocations.141414Though, as evidenced
in Table 1, other tasks are on a different scale than fundraising (mean is
almost three times higher). Thus, elasticities may be less relevant than
linear relationships. For this and other reasons, I also report results from
linear models in the Appendix.

Table 2 reports the main regression results. First, Column (1) shows that
research and fundraising time are unconditionally positively correlated. This
may of course be representative of a true causal effect, but as noted
previously, there is good reason to think that these two variable are
positively correlated due to other unobservable forces. Columns (2–4) are all
identified via conditional independence and include successively more control
variables. When professors’ other work time and grant funding expectations are
included as controls, the association between fundraising and research time
becomes smaller and statistically insignificant from zero (Col. 2). Including
more control variables selected via Lasso does not change this (Cols. 3–4). In
all of these initial cases I can reject the null that fundraising time affects
research time in the same way that other work does.

Table 2: Poisson regression results

| Research time
---|---
| Poisson |  | IV Poisson
| (1) | (2) | (3) | (4) |  | (5) | (6)
Fundraising time, log. |  0.090∗∗∗ | 0.020 | 0.015 | 0.019 |  | –0.077 | –0.015
| (0.012) | (0.013) | (0.012) | (0.012) |  | (0.081) | (0.081)
Other work time, log. |  |  –0.282∗∗∗ |  –0.281∗∗∗ |  –0.280∗∗∗ |  |  –0.275∗∗∗ |  –0.277∗∗∗
|  | (0.015) | (0.016) | (0.016) |  | (0.018) | (0.017)
$p$–value($\beta_{\text{F}}=\beta_{\text{O}}$) |  |  $<$0.01 |  $<$0.01 |  $<$0.01 |  | 0.02 |  $<$0.01
Incl. $g(\scriptsize{\text{Grant \$}})$ |  | Y | Y | Y |  | Y | Y
Lasso $g(\scriptsize{\text{Grant \$},X})$ |  |  | Y | Y |  | Y | Y
$X$ sel./poss. |  |  | 19/57 | 24/219 |  | 19/57 | 24/219
$F$–stat. |  |  |  |  |  | 33.1 | 33.4
$N$ obs. | 2,640 | 2,640 | 2,640 | 2,640 |  | 2,640 | 2,640

> Note: Reports the results from estimating variations of Equation 1 using
> either poisson regression (Col. 1–4) or poisson regression with an
> instrumental variable (Col. 5–7, where the competition proxy is the
> instrumental variable). $p$–value($\beta_{\text{F}}=\beta_{\text{O}}$) is
> based on a test of the null hypothesis that the coefficients on fundraising
> and other work time are equal. “Incl. $g$(Grant $)” indicates that the
> flexible controls for expected grant funding are included. “Lasso $g$(Grant
> $,$X$)” indicates that lasso was used to select from the flexible controls
> for expected grant funding as well as the additional set of covariates, and
> “$X$ sel./poss.” reports the number of selected and possible controls.
> Robust standard errors in parentheses;
> ${}^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.

It is possible that there are still unobservable confounders driving the null
effects identified in Columns (1–4) of Table 2, so Columns (5–6) report the
results using the competition proxy as an instrumental variable. The first
stages of these models (reported in the Appendix Table A2) indicate the
instrument is relevant and that scientists in fields where their fundraising
time is less productive (i.e., converts into less grant funding) spend less
time fundraising. But when using an instrumental variable, the results are
very similar. The point estimates are negative, but continue to be close to
zero and are not statistically significant. Furthermore, I can still reject
the null of equality between fundraising and other work time.

In the Appendix, I estimate linear versions of these same regressions and
obtain similar estimates (Table A4). I find some negative effects of
fundraising on research in the models with just controls, but when using the
instrumental variable I again no longer reject the null hypothesis.

###  2.4 Implications

The results indicate that, on the margin, an hour less of fundraising effort
does not change scientists’ research effort. Why would fundraising time not
detract from research time in the same way that other duties do? Let’s
consider the following representation of a scientists’ objective function:

$\max_{F,R}p\bigl{(}G(F),F,R\bigr{)}-c(F,R,O)\,,$ (2)

where $p(\cdot)$ and $c(\cdot)$ are the production and cost functions,
respectively, and all variables are the same as before. Scientists must choose
how to allocate their fundraising and research time given the positive returns
via $p$ and costs via $c$.

First, it seems very reasonable to assume that tasks are complements in the
cost function (i.e., $\frac{\partial^{2}c}{\partial F\partial R}>0$, etc.).
Scientists all face the same constraint of 24 hours in a day, and as time is
spent on one activity, the cost of spending additional time on other
activities increases. Assuming this is true, then more time spent on a task
that only enters the cost function should decrease time spent on other tasks.
This is what I find in the relationship between research ($R$) and other tasks
($O$). However, if a task enters both the cost and production function, this
need not be the case. If two tasks are complements in both the cost and
production functions, then it is possible for a null relationship between the
two to exist—more time on one task both increases the costs _and_ benefits of
time on the other task, leading to no change. This is what I find in the
relationship between research $R$ and fundraising $F$. And that this null
result persists after conditioning on $G$ (which accounts for $\frac{\partial
p}{\partial G(F)}>0$) suggests $F$ itself directly enters the production
function.

This is consistent with the survey results of Schneider, (2018), where
scientists report that 38% of fundraising effort involves meaningful science.
If this magnitude is taken seriously, the null effect I estimate implies that
one hour less of fundraising time is 23 minutes less of scientific work at the
mean values of time allocations. Ignoring statistical significance, the most
negative elasticities identified are in the range of –0.07, which implies 23
minutes less of “fundraising” based scientific work would spark approximately
12 minutes more of “research” based scientific work. Is the 37(=60–23) less
minutes of non-scientific fundraising effort worth 11(=23–12) less minutes of
total scientific effort? The answer to this tradeoff depends on the private
and social costs and benefits of this effort and how it is influenced by
competition, which I explore in the next section.

##  3 Theory: Contest productivity and effort externalities

The prior section provides evidence that fundraising efforts do not affect
research efforts, which is consistent with fundraising involving some
inherently productive scientific tasks. How does the presence of this factor
moderate the relationship between a contests’ aggregate productivity (i.e.,
total benefits less total costs) and the level of competition (i.e., the share
of potential applicants that receive an award)? In the following section, I
answer this question using model of grant contests. In the model, there can be
value generated by fundraising effort as an externality from the perspective
of the scientist.151515This reflects two points: (i) the positive
externalities of all scientific activities are very large relative to their
private costs, and (ii) while this entire paper is agnostic about “when”
effort occurs (i.e., the models are static), it is reasonable to assume that
scientific effort exerted in a funding contest will occur before it would have
otherwise and society benefits from having the value of the scientists’ work
sooner (even if the same amount of value is generated). However, there may
also be negative externalities associated with application effort. Most
notably, the social opportunity costs of this effort may be non-trivial
because effort spent towards applications reduces the amount of effort that
could be spent directly on other scientific activities. There also may be
social costs of effort insofar as the delay in time necessary to accommodate
the effort induced by the contest leads the social value of the grant to be
reduced (e.g., in an emergency).

In Section 3.1 I outline an elementary model of contests with no effort
externalities and contrast a traditional competitive model to a non-
competitive lottery (where there is no competition). I evaluate which
mechanism maximizes the planners’ surplus, which I term the aggregate
productivity. The lottery is more productive. In Section 3.2, I introduce
positive effort externalities and show that the contest is more productive. In
Section 3.3, I build on the work of Gross and Bergstrom, (2019), who in turn
build on Moldovanu and Sela, (2001) and Hoppe et al., (2009), to show that
this role of effort externalities is not unique to the highly stylized model
in Sections 3.1–3.2, but is also present in more realistic models of
competitive grant contests.

###  3.1 Simple model—Baseline

There is a single funder who will award a grant valued $v$ to one of $n$
scientists. Once awarded, the grant generates social benefits of $mv$, where
$m>1$ determines the degree to which the grant generates positive
externalities.161616The private return to winning the grant is $v$ and the
size of the positive externalities is $mv-v$. Scientists are equal in all
regards (an assumption relaxed below) and can compete for the grant by
submitting an application. Let $x_{i}$ be the effort scientist $i$ invests in
their application with $cx_{i}$ denoting the disutility from this effort
($c>0$). I focus on the symmetric equilibrium where all scientists choose the
same effort, $x^{*}$.

The funder’s optimization problem is to choose a funding regime that maximizes
the difference between the value generated by the grant and the total
disutility of scientists’ effort, $mv-ncx^{*}$.

One option is to use a “contest” regime where the probability that a scientist
wins the grant is given by $\frac{x^{*}}{nx^{*}}$. It is straightforward to
show the symmetric equilibrium gives $x^{*}=v\frac{(n-1)}{cn^{2}}$, which
implies that the social value created is $(m-\frac{(n-1)}{n})v\equiv
V_{\text{contest}}$.

Alternatively, the social planner could use a “lottery” regime by randomly
allocating the grant to one scientist. Assuming this randomization is
costless, the social value created is simply $mv\equiv V_{\text{lottery}}$.
This will always generate more social value than in the first case
($V_{\text{lottery}}>V_{\text{contest}}$). This sort of argument either
explicitly or implicitly underlies many of the proposals for lottery-based
funding mechanisms: the introduction of randomness reduces the effort
scientists invest in the grant competition.

However, this argument ignores the reality that the effort put forward in
grant competitions generates spillovers – scientists can generate, refine, and
share their ideas, regardless of whether or not they ultimately receive the
funding. In other words, the effort exerted in these contest can involve
positive (or negative) externalities.

###  3.2 Simple model—With effort externalities

To see how effort externalities change the optimal regime choice, let $w$
determine the degree of these externalities so that $wx^{*}$ is the social
benefit (or cost if $w<0$) each scientist’s effort generates. This leads to a
new problem for the funder: maximize $mv-n(c-w)x^{*}$. Scientists’ strategies
remain unchanged since, by definition, they do not take externalities into
account when making their decisions.

The social value generated by the contest regime in this setting is
$(m-(c-w)\frac{(n-1)}{cn}))v\equiv V^{\prime}_{\text{contest}}$, while the
value of the lottery regime is unchanged. The contest is more efficient if the
social value of the effort externalities is greater than the private cost of
that effort ($V^{\prime}_{\text{contest}}>V_{\text{lottery}}$ if $w>c$).
Furthermore, the social return to increasing competition ($n$) is increasing
in the size of these externalities ($\partial
V^{\prime}_{\text{contest}}/\partial n\partial w>0$). Similarly, larger
competitions have more to gain from increasing the size of the effort
externalities.

###  3.3 Expanded model

The following closely matches Gross and Bergstrom,’s (2019) model. Some minor
changes are also made to more closely align the model with traditional
economic definitions of private versus social costs and benefits.

There is a single funding contest run by the social planner, whose budget is
such that they can fund a proportion of scientists given by $p$. Each
scientist $i$ has a single idea they need funding to pursue and the quality of
that idea is given by the scalar $v_{i}\geq 0$, which is private information
known only to $i$, but it is drawn from a publicly known distribution $F$.

The sequence of events and nature of the contest is as follows:

  1. 1.

Scientists draw $v_{i}$ from $F$.

  2. 2.

Scientists choose how much effort to exert to develop an application of
quality $x_{i}$, where the private costs of applying are given by
$c(v_{i},x_{i})$.

  3. 3.

Applications are reviewed in a “noisy” process that imperfectly ranks
applications per their quality ($x_{i}$) and applications are funded subject
to the budget constraint given by $p$.

  4. 4.

Scientists with funded applications receive a payoff of $v_{i}$. All
scientists (funded or not) recoup some share of the private costs of applying,
given by the parameter $k\in[0,1]$. The planner receives a payoff of $mv_{i}$
if $v_{i}$ is funded.171717Gross and Bergstrom, (2019) also include a private
payoff for funded applications (the $v_{0}$ parameter in their model) that
does not enter into the planner’s objective function. Since I am adopting the
traditional economic definition of a social planner which incorporates the
utility of all parties (scientists included), this term should also enter the
planners’ payoff. Instead, I am using the $m$ parameter to clearly generate a
wedge between the private and social payoffs of the grant. This effectively
sets $v_{0}$ to zero in terms of Gross and Bergstrom,’s (2019) model. Whether
or not $v_{0}$ is included in my model turns out to be irrelevant since it is
an additive term and unrelated to the degree of effort-based externalities,
and the addition of the $m$ parameter only shifts the levels of the costs and
benefits in the model which is not the focus.

Each scientists’ optimal choice of application quality ($x^{*}_{i}$) is given
by the bid function

$b(v_{i})=\operatorname*{arg\,max}_{x_{i}}\;v_{i}\eta(x_{i})-c(v_{i},x_{i})(1-k)\equiv
x^{*}_{i}\;,$ (3)

where $\eta$ is the contest success function and describes the equilibrium
funding probability for an application of quality $x_{i}$. This function
depends on the payline ($p$), the distribution of realized applications, and
the amount of noise in the review process.

The expected value of the contest for each applicant (if participating) is

$v_{i}\eta\bigl{(}b(v_{i})\bigr{)}-c\bigl{(}v_{i},b(v_{i})\bigr{)}(1-k)$ (4)

and zero otherwise. By assumption, only applicants with positive expected
values will enter the contest. Also, unfunded applications generate no value
beyond the private returns accrued to those applicants per the parameter $k$.

In the case without any positive externalities from application effort, the
expected value per award (the measure of the contests’ aggregate productivity)
for the social planner is

$\frac{1}{p}\Biggl{(}\underbrace{\int
mv\eta\bigl{(}b(v)\bigr{)}dF(v)}_{\text{benefit}}-\underbrace{\int
c\bigl{(}v,b(v)\bigr{)}(1-k)dF(v)}_{\text{cost}}\Biggr{)}\;.$ (5)

Gross and Bergstrom, (2019) show that the aggregate productivity of the
contest is decreasing in the payline, $p$ (where the top $p$ applications are
funded) as well as the value of instituting a lottery. is the same as the
efficiency of a contest with a lottery line of $p$, even if the share that can
be funded is less than $p$.

Formally, let $f$ be the share of applications that can be funded given the
budget. In a standard contest, a payline $p$ is set to equal $f$ such that the
top $p=f$ applications are funded. In the lottery mechanism, a lottery line
$l$ is set greater than or equal to $f$ such that the top $l$ applications are
entered into a randomized lottery where $f$ are funded. Gross and Bergstrom,
(2019) show that the aggregate productivity of a payline of $p=f$ is the same
as the productivity of a lottery line of $l\geq f$. For example, the
productivity of a contest with a lottery line of 30% is the same as the
productivity of a non-lottery contest with a payline of 30%, even if less than
30% of the applications can be funded. Loosely speaking, the presence of a
lottery lowers the optimal choice of effort for each scientist by reducing the
effective level of competition they will face.

I incorporate effort externalities into this model by assuming that the
planner’s benefit now includes a “bid-effort externality” function $w(v,x)$,
which can be thought of as the opposite of the private cost function,
$c(v,x)$.181818Very similar results (reported below) are obtained if one
incorporates this externality by assuming that a portion of the idea’s quality
is realized and value by the social planner regardless of whether or not the
idea is funded, with that portion realized being determined by the scientists’
bid. Now, the per-award benefit to the planner (omitting the cost component,
which remains unchanged) is

$\frac{1}{p}\int w(v,b(v)\bigr{)}+mv\eta\bigl{(}b(v)\bigr{)}dF(v)\;.$ (6)

The scientist’s problem has not changed, so their bid function remains the
same as in Equation 3.

Participants who work harder on their bid likely generate more externalities,
but it is reasonable to assume there are decreasing returns (i.e., the initial
conception of an idea may lead to many future ideas, but the 100th hour of
work on a proposal is assumed to be spent on more wasteful activities). Thus,
I choose a concave function for $w$ defined below.

The distributions and functional forms used are exactly as in Gross and
Bergstrom, (2019).191919The distribution of idea quality is:
$F(v)=1-(16/9)(1-v)^{2})$, $v\in[0.25,1]$. The cost function and recovered
costs are given by: $c(v,x)=x^{2}/v$ and $k=1/3$. The joint distribution of
actual and evaluated quality are based on a Clayton copula with $\theta=10$.
In the baseline case, I set $m=1$, which eliminates the positive externalities
generated by science in my model, but allows me to match Gross and
Bergstrom,’s (2019) results exactly.

To parameterize the bid effort externalities, I choose a function form for $w$
that mirrors $c$ as a sort of inverse cost function:

$w(v,x)=kv(x)^{1/r}\;,$ (7)

where $r$ influences the shape of the function. $w$ also includes the $k$
parameter that governs how much of their disutility from effort scientists
recoup because that effort is spent on valuable research activities (per
$kc(v,x)$).

Figure 5: Competition, externalities, and aggregate contest productivity

(a)

(b)

> Note: Shows the productivity of a contest (total value per award) as a
> function of the contest payline (i.e., the percent of applications that are
> supported when ranked by quality). Panel (a) compares the baseline results
> of Gross and Bergstrom, (2019) (the “No effort externality” line) to
> scenarios where there are positive effort externalities (governed by the
> size of $r$). Panel (b) shows an alternative way of formulating the effort
> externality (as partial project completion) compared to the formulation
> shown in Panel (a) (as an inverse cost function).

Figure 5 Panel (a) illustrates the contest’s productivity under the baseline
case of no effort externalities (exactly replicating Gross and Bergstrom,
(2019); see their Figure 3) as well as with externalities under a range of
values for $r$. Because the support of the bid values lies below one, values
of $r<1$, which dramatically reduce the size of the effort externalities, are
necessary to eliminate the pattern whereby more competition increases the
productivity of the contest. At $r=1/2$, the private costs and externalities
perfectly offset, leading the productivity of the contest to be equal under
all levels of competition.

Another way one could incorporate bid effort externalities into this model
would be to assume that a fraction of the idea’s quality is produced as a
function of each applicant’s bid, regardless of funding status, with the
remainder only being realized if the grant is awarded. For simplicity, let’s
also assume that the scientists’ utility function is unchanged, which implies
that they receive the full private value of the idea ($v_{i}$) only if funded
whereas the social planner receives some portion of this value in the
application process and (for those funded) the remainder.

Formally, the the per-award benefit to the planner (omitting the cost
component, which remains unchanged) is now

$\frac{1}{p}\int w(b(v))v+\Bigl{(}1-w(b(v)\bigr{)}\Bigr{)}v\eta(b(v))dF(v)\;,$
(8)

where $w(b(v))v$ is the partial realization of all ideas due to application
effort, and $\left(1-w\left(b\left(v\right)\right)\right)v$ is the realization
of the remainder of each idea’s value for the subset funded. Assuming the
functional form of $w$ is again similar in nature to the other parts of the
model, $w(b(v))=b(v_{i})^{(1/2)}/3$, yields very similar results to the
original formulation of externalities—see Figure 5 Panel (b).

Overall, the theories illustrate that the aggregate productivity of a contest
can vary dramatically depending on the nature of effort externalities. The
more competitive the contest, the more there is to be gained from increasing
the size of positive externalities. In other words, ensuring that scientists
exert socially valuable effort to obtain grants is increasingly important as
grant contests become more competitive.

##  4 Discussion

It is a waste when allocation mechanisms induce participants to exert effort
that neither improves the allocative efficiency (i.e., the identification of
scientists with higher quality ideas) nor the aggregate productivity of the
mechanism (i.e., the total benefits less costs); this is a tautology. The
question is _to what degree_ might competitive pressures of a contest improve
efficiency or productivity. In the case of research grant contests, this paper
is focused with the latter possibility—fundraising effort may be inherently
valuable. If this is the case, then debating policies that influence
competition in grant contests (e.g., the use of lotteries, the amount of
preliminary results required) will involve debates about the tradeoffs of
different kinds of efforts.

Using survey data on research-active professors who pursue grants, I find that
the way they report their time use is consistent with fundraising generating
value _besides being a means to grant funding_. After accounting for many
confounding factors, I find that more fundraising time neither spurs nor
steals research time; I cannot reject the null hypothesis of no effect. But,
the estimates are precise enough for me to reject the null hypothesis that
fundraising time steals as much research time as professors’ other duties
(e.g., teaching and admin); the opportunity costs of fundraising (conditional
on grant funding) appear much smaller than the opportunity costs of
professors’ other activities. An important caveat is that these time
allocations are self-reported forecasts of averages over the next five years.
On one hand, this introduces the possibility of significant measurement error
and bias that may be correlated with professors’ actual time allocations. On
the other hand, analyzing these more aggregated patterns is informative of the
longer-run equilibrium and is, in a sense, asking scientists how they plan to
“vote with their feet.” While I can introduce a large number of potential
control variables and also identify a plausibly exogenous source of
fundraising time driven by competition across fields, there is still much room
for improvement on both the measurement and identification of these variables
and relationships.

Motivated by this result, I then show in theory how the presence of effort
externalities (i.e., fundraising effort generates value the scientist does not
capture) relates to the aggregate productivity of a grant contest. I build on
Gross and Bergstrom, (2019) to show that when positive effort externalities
exist, the aggregate productivity of the contest can be increasing in the
level competition. Broadly speaking, this result is not new—it is a well-known
result in economic theory that the social value of competition depends on
whether competitive efforts generate positive or negative externalities. But
this is one of the first times these externalities have been studied in a
contest model designed to reflect the research grant environment.

This paper does not take a stance on whether the application processes of
current funding environments are socially optimal. Unnecessary requirements or
overly burdensome standards may be pervasive. Rather, this paper emphasizes
that there can be large returns to designing grant applications that
incentivize scientists to conduct science before the funding is awarded. The
specifics of how to best do this is an open question and involves some
tradeoffs not studied in this paper. Intuitively, application-centric work
should probably not require substantial funding since this could handicap
scientists in resource-intensive fields and those yet to acquire much funding.
This suggests the type of effort that applications should incentivize should
be towards theoretical and conceptual tasks: formalizing research questions,
describing research designs and plans of work, etc.

Still, continued theoretical and empirical research is necessary to better
understand the parameters highlighted here, as well as many of the complicated
and dynamic factors not addressed, especially those related to allocative
efficiency. For example, the theoretical models in this paper effectively
assume a perfect correlation between scientists’ research productivity and
their ability to compete in the grant contests—the best researcher is also the
best grant-writer. The pervasiveness of discussions surrounding
“grantsmanship” amongst scientists suggests this is very likely not the case
(e.g., Sauer and Gabbi, 2018; Botham et al., 2020). Furthermore, it is not
always clear that faster science is higher quality science (Hill and Stein,
2021), so the “quality-adjusted” level of scientific effort within grant
competitions may not be comparable.

More generally, the results imply that program evaluations comparing the
outcomes of marginally funded and non-funded scientists (e.g., Jacob and
Lefgren, 2011; Myers, 2020) may be limited in their policy relevance. While
these research designs can provide strong internal validity with respect to
scientist-level effects, they cannot identify the possibly large effects a
contest has on all who participate. Given recent evidence on the declining
productivity of the scientific sector (Bloom et al., 2020), the growing
knowledge burden at the frontier of science (Jones, 2009), and the increasing
division of labor between academia and corporate science (Arora et al., 2020),
improving our ability to identify and incentivize the “best” scientists,
whatever that may mean, continues to be an important issue.

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##  Appendix A Appendix

Table A1: Distribution of narrow fields

| count | mean | sd
---|---|---|---
Agriculture | 2,640 | 0.03 | 0.17
Biology | 2,640 | 0.06 | 0.24
Business | 2,640 | 0.03 | 0.16
Chemistry | 2,640 | 0.03 | 0.17
Communication | 2,640 | 0.03 | 0.16
Computer science | 2,640 | 0.02 | 0.15
Economics | 2,640 | 0.02 | 0.15
Education | 2,640 | 0.04 | 0.19
Engineering | 2,640 | 0.08 | 0.28
Geography | 2,640 | 0.06 | 0.24
Humanities | 2,640 | 0.08 | 0.28
Law | 2,640 | 0.01 | 0.11
Mathematics | 2,640 | 0.04 | 0.18
Medical school | 2,640 | 0.20 | 0.40
Medicine and health | 2,640 | 0.07 | 0.25
Other social sciences | 2,640 | 0.04 | 0.18
Physics | 2,640 | 0.05 | 0.21
Political science | 2,640 | 0.04 | 0.18
Psychology | 2,640 | 0.04 | 0.21
Sociology | 2,640 | 0.03 | 0.18

> Note: Reports the share of the sample in each of the twenty narrower fields.

Table A2: First stage, log. transformation

| Fundraising time, log.
---|---
| (1) | (2) | (3) | (4) | (5)
Funding intensity, std. |  0.202∗∗∗ |  0.188∗∗∗ |  0.060∗∗∗ |  0.101∗∗∗ |  0.100∗∗∗
| (0.015) | (0.016) | (0.016) | (0.017) | (0.017)
Other work time, log. |  |  –0.110∗∗∗ | –0.021 | 0.044 | 0.044
|  | (0.032) | (0.027) | (0.029) | (0.029)
Incl. $g(\scriptsize{\text{Grant \$}})$ |  |  | Y | Y | Y
Lasso $g(\scriptsize{\text{Grant \$},X})$ |  |  |  | Y | Y
$X$ sel./poss. |  |  |  | / | /
$R^{2}$ | 0.06 | 0.07 | 0.25 | 0.25 | 0.25
$N$ obs. | 2,640 | 2,640 | 2,640 | 2,640 | 2,640

> Note: Reports the results from the first stage regressions of logged
> fundraising time on the focal instrumental variable, the proxy for grant
> funding competition (jackknife field-level average of grant funding expected
> per fundraising hour). $p$–value($\beta_{\text{F}}=\beta_{\text{O}}$) is
> based on a test of the null hypothesis that the coefficients on fundraising
> and other work time are equal. “Incl. $g$(Grant $)” indicates that the
> flexible controls for expected grant funding are included. “Lasso $g$(Grant
> $,$X$)” indicates that lasso was used to select from the flexible controls
> for expected grant funding as well as the additional set of covariates, and
> “$X$ sel./poss.” reports the number of selected and possible controls.
> Robust standard errors in parentheses;
> ${}^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.

Table A3: IV poisson regressions—Alternative instrumental variable
formulations

| Research time
---|---
| (1) | (2) | (3) | (4)
Fundraising time, log. | –0.015 | –0.011 | –0.033 | 0.027
| (0.081) | (0.081) | (0.047) | (0.096)
Other work time, log. |  –0.277∗∗∗ |  –0.277∗∗∗ |  –0.276∗∗∗ |  –0.280∗∗∗
| (0.017) | (0.017) | (0.017) | (0.018)
$p$–value($\beta_{\text{F}}=\beta_{\text{O}}$) |  $<$0.01 |  $<$0.01 |  $<$0.01 |  $<$0.01
IV version | 1 | 2 | 3 | 4
Incl. $g(\scriptsize{\text{Grant \$}})$ | Y | Y | Y | Y
Lasso $g(\scriptsize{\text{Grant \$},X})$ | Y | Y | Y | Y
$X$ sel./poss. | 24/219 | 24/219 | 24/219 | 24/219
$F$–stat. | 33.4 | 34.2 | 112.5 | 23.2
$N$ obs. | 2,640 | 2,640 | 2,640 | 2,640

> Note: Reports the results from using alternative instrumental variables for
> fundraising time. Column (1) uses the preferred instrument, jackknife field-
> level average of grant funding expected per fundraising hour and replicates
> Column (6) of Table 2. The instrument for Column (2) is the jackknife field-
> level average of grant funding expected per share of time spent fundraising.
> The instrument for Column (3) is the jackknife field-level average of total
> funding (grant funding expected plus prior and guaranteed funding). The
> instrument for Column (4) is the jackknife field-level average of the share
> of total funding that is expected grant funding. All other elements are the
> same as in Table 2. $p$–value($\beta_{\text{F}}=\beta_{\text{O}}$) is based
> on a test of the null hypothesis that the coefficients on fundraising and
> other work time are equal. “Incl. $g$(Grant $)” indicates that the flexible
> controls for expected grant funding are included. “Lasso $g$(Grant $,$X$)”
> indicates that lasso was used to select from the flexible controls for
> expected grant funding as well as the additional set of covariates, and “$X$
> sel./poss.” reports the number of selected and possible controls. Robust
> standard errors in parentheses; ${}^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.

Table A4: Linear regression results

| Research time
---|---
| OLS |  | 2SLS
| (1) | (2) | (3) | (4) |  | (5) | (6)
Fundraising time |  0.233∗∗∗ |  –0.084∗∗ |  –0.109∗∗∗ |  –0.097∗∗ |  | 0.009 | 0.070
| (0.035) | (0.038) | (0.039) | (0.039) |  | (0.291) | (0.296)
Other work time |  |  –0.374∗∗∗ |  –0.342∗∗∗ |  –0.341∗∗∗ |  |  –0.340∗∗∗ |  –0.337∗∗∗
|  | (0.016) | (0.017) | (0.017) |  | (0.017) | (0.017)
$p$–value($\beta_{\text{F}}=\beta_{\text{O}}$) |  |  $<$0.01 |  $<$0.01 |  $<$0.01 |  | 0.22 | 0.16
Incl. $g(\scriptsize{\text{Grant \$}})$ |  | Y | Y | Y |  | Y | Y
Lasso $g(\scriptsize{\text{Grant \$},X})$ |  |  | Y | Y |  | Y | Y
$X$ sel./poss. |  |  | 18/57 | 22/219 |  | 18/57 | 22/219
$F$–stat. |  |  |  |  |  | 42.6 | 41.1
$N$ obs. | 2,640 | 2,640 | 2,640 | 2,640 |  | 2,640 | 2,640

> Note: Reports the results from estimating
> $\text{Research}_{i}=\alpha+\beta_{\text{F}}\text{Fundraising}_{i}+\beta_{\text{O}}\text{Other}_{i}+g(\text{Grant
> \$}_{i},\mathbf{X}_{i})+\epsilon_{i}$ using either OLS (Col. 1–4) or 2SLS
> (Col. 5–7, where Funding intensity is the instrumental variable).
> $p$–value($\beta_{\text{F}}=\beta_{\text{O}}$) is based on a test of the
> null hypothesis that the coefficients on fundraising and other work time are
> equal. “Incl. $g$(Grant $)” indicates that the flexible controls for
> expected grant funding are included. “Lasso $g$(Grant $,$X$)” indicates that
> lasso was used to select from the flexible controls for expected grant
> funding as well as the additional set of covariates, and “$X$ sel./poss.”
> reports the number of selected and possible controls. Robust standard errors
> in parentheses; ${}^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.